Download Ab-initio Modeling of Cold Gases November 11, 2009

Ab-initio Modeling of Cold Gases
November 11, 2009 - November 13, 2009
CECAM-ETHZ, Zurich, Switzerland
Lode Pollet
LMU Munich, Germany
Tilman Esslinger
Swiss Federal Institute of Technology Zurich (ETHZ), Switzerland
Antoine Georges
College de France and Ecole Polytechnique, France, France
Alejandro Muramatsu
University of Stuttgart, Germany
1 Description
We will first outline the state of the art of experiments on cold atoms in an optical
lattice. We will then show how numerics are useful for these systems, and finally
discuss how successful numerical studies have been, which is the keystone of this
proposal.
Since the seminal paper by Greiner et al. [1], showing the transition from the superfluid
to the Mott-insulating phase in the Bose-Hubbard model, physicists have realized that
modeling strongly-interacting systems in the atomic physics lab is feasible.
The field had started with the theoretical prediction by Jaksch et al., showing
theoretically that this model could indeed be analyzed realistically in experiments [2].
The key observation was that the atom-photon interactions could be used and
controlled in such a way that the Bose-Hubbard model can be realized for a sufficiently
long time and at sufficiently low temperature.
Systems consisting of atoms in an optical lattice have the advantage over
strongly-interacting systems of (1) being ultra-clean, (2) the interaction couplings are
controllable, and (3) the type, mass and density of the atoms are controllable. Having
the possibility to change the parameters of the Hamiltonian at will makes these
systems prime candidates for building a quantum analog computer. On the negative
side, the detection of (neutral) atoms is more difficult than detection in condensed
matter physics, the temperature is relatively high (e.g., in units of the Fermi
temperature for fermionic systems present experiments operate on the scale of 0.1 ),
there are no phonons since the lattice is built by laser light, and there is an external
harmonic trapping potential.
Experimental progress has been rapid. The most recent advances include the
observation of the Mott-instulating phase in the Fermi-Hubbard model [2] and the
observation of the superexchange mechanism in a two-well system [3].
These experiments have mostly been explained qualitatively so far. Further progress is
only possible when lower temperatures are reached and better detection schemes
developed, but also when current experiments are better understood quantitatively, and
this is where numerics become useful.
In particular for the bosons, the theory is well understood and the numerical algorithms
(Quantum Monte Carlo) very powerful. The so-called 'worm algorithm' is at present
able to address the Bose-Hubbard model from first principles and for realistic system
sizes [4]. Previous studies addressed individual aspects of the experiments, such as
the role of the trapping potential, the role of entropy in fixing the temperature and the
influence of the time-of-flight duration [5]. Fully ab-initio studies took off approximately a
year ago and are still going on, with promising first results. The overall agreement is
close to excellent, but it turns out that there are deviations which are not completely
negligible though controllable. They hint at experimental imperfections, such as density
variations, lattice laser calibration uncertainties, heating, and losses of atoms.
Estimating the importance of such effects accurately has now become available thanks
to the large-scale simulations.
For the fermions, such numerical methods as DMFT [6] and high-temperature series
expansions [7] addressed the recent observation of the Mott-insulating state. Fermions
are intrinsically harder to handle experimentally than bosons. The Mott-insulating state
has only been observed experimentally over the last few months [2]. Numerical studies
using Dynamical Mean Field Theory (DMFT) and high-temperature series expansions
have already appeared [8, 2], but finding a quantity that clearly indicated the transition
is hard to find. Temperature and out-of-equilibrium effects are more serious concerns
here than for the bosons. It is clear that much more numerical and experimental work is
needed before consensus can be reached in the community. Numerical studies have
also looked at lower temperatures, trying to see where anti-ferromagnetism sets in [8].
At these temperatures the numerical methods are no longer exact, but the
approximations need further assessment.
Experimental studies have also been undertaken to measure critical exponents. The
critical exponent of the correlation length of the U(1) transition between a normal and a
condensed
three-dimensional
Bose
gas
was
measured
[9].
The
Berezinskii-Kosterlitz-Thouless for a two-dimensional Bose gas was also successfully
studied experimentally [10]. A full numerical study taking the trapping potential,
temperature, heating, and detection schemes into account is numerically challenging
and largely open.Key references
[1] M. Greiner, O. Mandel, T. Esslinger, T. W. Haensch, and I. Bloch, Nature 415, 39 (2002).
[2] D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, Phys. Rev. Lett. 81, 3108 (1998).
[3] R. Joerdens, N. Strohmaier, K. Guenter, H. Moritz, and T. Esslinger, Nature 455, 204 (2008) ; U.
Schneider et al, cond-mat/0809.1464 (2008).
[4] S. Foelling et al, Nature 448, 1029 (2007), S. Trotzky et al., Science 319, no. 5861, 295 (2008).
[5] N. V. Prokofev,B. V. Svistunov, and I. S. Tupitsyn, Sov. Phys. JETP 87, 310 (1998); Phys. Lett. A 238,
253 (1998).
[6] L. Pollet, K. Collath, K. Van Houcke, and M. Troyer, New Journal of Physics 10, 065001 (2008); F.
Gerbier et al., accepted for publication in Phys. Rev. Lett., cond-mat/0808.2212 (2008).
[7] A. Georges, G. Kotliar, W. Krauth, and M. J. Rozenberg, Rev. Mod. Phys. 68, 13 (1996).
[8] J. Oitmaa et al., Series Expansion Methods for Strongly Interacting Lattice Models, Cambridge
University Press, Cambridge, 2006.
[9] L. De Leo, C. Kollath, A. Georges, M. Ferrero, and O. Parcollet, cond-mat/0807.0790 (2008); V. W.
Scarola, L. Pollet, J. Oitmaa, and M. Troyer, cond-mat/0809.3239 (2008).
[10] T. Donner, S. Ritter, T. Bourdel, A. Oettl, M. Koehl, and T. Esslinger, Science 315, 1556 (2007)
[11] Z. Hadzibabic, P. Krueger, M. Cheneau, B. Battelier, and J. B. Dalibard, Nature 441, 1118 (2006);
New Journal of Physics 10, 045006 (200).
2 Program
Day 1 - Wednesday November 11, 2009
Session 1 chair : tilman esslinger
• 8:30 to 8:40 - Welcome
• 8:40 to 9:15 - Presentation - Cheng Chin
Emergence of mott insulating phase of ultracold atoms in an optical lattice
• 9:15 to 9:40 - Presentation - Nandini Trivedi
Single atom addressability and mapping the finite temperature phase diagram of
the bose hubbard model
• 9:40 to 10:05 - Presentation - Matthias Troyer
Validating a quantum simulator
• 10:05 to 10:30 - Presentation - Sebastian Huber
The inverted kagome lattice: frustrated bosons without superexchange
Session 2 chair : lode pollet
• 11:05 to 11:30 - Presentation - Andrew Daley
An atomic colour superfluid via three-body loss
• 11:30 to 11:55 - Presentation - Nikolay Prokofev
Diagrammatic monte carlo: what happens to the sign-problem?
• 11:55 to 12:20 - Presentation - Stefan Wessel
Spin liquid phase in the hubbard model on the honeycomb lattice
Session 3 chair lode pollet
• 14:20 to 14:55 - Presentation - Henning Moritz
Studying the fermi-hubbard model with cold atoms
• 14:55 to 15:20 - Presentation - Lorenzo De Leo
Trapping and cooling fermionic atoms into mott and neel states
• 15:20 to 15:45 - Presentation - Vito Scarola
Discerning incompressible and compressible phases of cold atoms in optical
lattices
• 15:45 to 16:10 - Presentation - Andreas Ruegg
From fermi's golden rule to rabi oscillations: dynamical unbinding transition in a
periodically driven mott insulator
Colloquium by randy hulet 16.45 - 18.00
Free evening
Day 2 - Thursday November 12, 2009
Session 4 chair alejandro muramatsu
• 8:45 to 9:20 - Presentation - Frederic Chevy
Weighing a particle immersed in a fermi sea
• 9:20 to 9:45 - Presentation - George Batrouni
Pairing in mass and/or population imbalanced fermion systems
• 9:45 to 10:10 - Presentation - Andreas Läuchli
Pairing properties of population imbalanced fermions with two and three flavors
Session 5 chair alejandro muramatsu
• 11:00 to 11:35 - Presentation - Robert Loew
Long-range interacting rydberg atoms
• 11:35 to 12:00 - Presentation - Vincent Liu
Cold atoms and molecules in elongated wannier orbitals
• 12:00 to 12:25 - Presentation - Hans Peter Büchler
Feshbach resonance in an optical lattice
Session 6 chair fabian hassler
• 15:00 to 15:35 - Presentation - Fabrice Gerbier
Implementing artificially engineered gauge potentials in a lattice
• 15:35 to 16:00 - Presentation - Iacopo Carusotto
Non-equilibrium many-body physics in quantum gases of interacting photons
• 16:00 to 16:25 - Presentation - Ignacio Cirac
Projected entangled-pair and plaquette states
Session 7 chair fabian hassler
• 16:55 to 17:30 - Presentation - Simon Foelling
Fully resolved optical imaging of a 2d quantum gas
• 17:30 to 17:55 - Presentation - Tommaso Roscilde
"escaping from the trap" : extracting bulk properties of strongly correlated
systems from measurements on trapped ultracold gases
• 17:55 to 18:20 - Presentation - Eugene Demler
Probing many-body physics with ultracold atoms
Poster session starting at 18:30
Day 3 - Friday November 13, 2009
Session 8 chair boris svistunov
• 8:45 to 9:20 - Presentation - Ulrich Schneider
Ultracold fermionic atoms in optical lattices:
out-of-equilibrium
experiments
in-
and
• 9:20 to 9:45 - Presentation - Sebastian Schmidt
Strongly correlated polaritons on a lattice
• 9:45 to 10:10 - Presentation - Fabian Heidrich-Meisner
The sudden expansion of interacting fermions in one dimensional optical lattices
• 10:10 to 10:35 - Presentation - Kristian Baumann
Observation of a non-equilibrium dicke-type quantum-phase transition
Session 9 chair antoine georges
• 11:05 to 11:40 - Presentation - Randy Hulet
Phase diagram of a spin-imbalanced fermi gas in 1d
• 11:40 to 12:05 - Presentation - Marcos Rigol
breakdown of thermalization in finite one-dimensional systems
• 12:05 to 12:30 - Presentation - Vladimir Gritsev
Relaxation of antiferromagnetic order in spin-1/2 chains following a quantum
quench
Session 10 chair lode pollet
• 14:15 to 14:40 - Presentation - Sankar Das Sarma
Localization in one-dimensional cold atomic gases
• 14:40 to 15:05 - Presentation - Ehud Altman
Bosons in disordered 1d traps: a new paradigm for the superfluid-insulator
transition?
• 15:10 to 15:35 - Presentation - Boris Svistunov
Disordered commensurate bosons: 20-year-old conjectures are now theorems
End of conference
3 Abstracts
Emergence of Mott insulating phase of ultracold atoms in an optical lattice
Cheng Chin
Unviversity of Chicago, USA
We present direct measurement of atomic density profiles in an optical lattice across the
superfluid-Mott insulator quantum phase transition.High resolution absorption imaging is used to
probe the “ wedding-cake” structure of a trapped gas as it crosses the phase boundary at finite
temperature. Detailed analysis of images yields measurements of temperature and local
compressibility; for the latter we observe a strong suppression deep in the Mott-insulating
phase, which is recovered for the superfluid and normal phases. Furthermore, we measure
spatially resolved fluctuations and correlations. Results in the superfluid, insulator and quantum
critical regime will be discussed.
Single atom addressability and mapping the finite temperature phase
diagram of the Bose Hubbard Model
Nandini Trivedi
Ohio State University, USA
I will discuss recent results of large scale QMC simulations of the bose Hubbard model with
~10^6 particles in a trap using the worm algorithm. I will focus on mapping the finite temperature
phase diagram using kinks in the local compressibility.I will also discuss thermodynamic and
frequency-dependent properties for the fermion Hubbard model with attractive and repulsive
interactions, using determinantal or auxiliary field QMC plus analytic continuation methods. I will
end with open questions related to the physics and computational techniques for these
problems.
Validating a quantum simulator
Matthias Troyer
Swiss Federal Institute of Technology Zurich (ETHZ), Switzerland
The inverted kagome lattice: frustrated bosons without superexchange
Sebastian Huber, Ehud Altman
Weizmann Institute, Israel
The route to quantum magnetism in ultracold atom systems is obstructed by the difficulties of
reaching low enough temperatures of the order of the superexchange coupling J. The prospect
of simulating the square lattice antiferromagnet, and its expected descendant, the d-wave
superconductor arouse a lot of current interest. Here we want to show how a frustrated
"quantum magnet" can be obtained with bosons in an inverted kagome lattice without the need
for temperatures that are much smaller than the hopping t. We discuss a possible
experimental setup and the rich zoo of phases which can be expected in this system: ranging
from glassy arrangements of localized states over a coexisting density-wave--superfluid phase
to the exp(3 i phi) condensate.
An atomic colour superfluid via three-body loss
Andrew Daley
University of Innsbruck, Austria
We discuss how three-body loss, which is ubiquitous and typically undesirable in cold gases
experiments can be used to generate an effective three-body hard-core constraint, preventing
three atoms from occupying the same lattice site. This mechanism not only serves to suppress
the occurance of actual three-body losses, but generates interesting many-body physics due to
the effective three-body interactions.We first consider this mechanism in the context of bosonic
atoms, where suppression of three-body occupation can stabilise the system with attractive
two-body interactions, and gives rise to a superfluid phase of dimers. We then discuss the case
of three-body loss in a three-component Fermi gas, where suppression of three-body
occupation of lattice sites can stabilise phases with BCS pairing by suppressing the formation of
trimers. Via a master equation treatment, we study the full dynamics including loss, both to test
how well real three-body losses are suppressed, and to determine schemes to produce
interesting many-body states in the presence of loss. We treat the master equation essentially
exactly for 1D systems by combining time-dependent DMRG techniques with quantum
trajectories methods from quantum optics.
Diagrammatic Monte Carlo: what happens to the sign-problem?
Nikolay Prokofev
University of Massachusetts at Amherst, USA
Feynman diagrams are the most celebrated and powerful tool of theoretical physics usually
associated with the analytic approach. I will argue that diagrammatic expansions are also an
ideal numerical tool with enormous and yet to be explored potential for solving interacting
many-body systems by direct simulation of Feynman diagrams for the proper self-energies and
polarization operators up to high order. Though the original series based on bare
propagatorsare sign-alternating and often divergent one can determine the answer behind them
by using proper series re-summation techniques and working with skeleton diagrams, i.e. by
making the entire scheme self-consistent. The first results for the resonant Fermi gas and the
Fermi-Hubbard model at U/t=4 away from half-filling prove that this approach is promising.
Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice
Stefan Wessel
University of Stuttgart, Germany
Employing projective quantum Monte Carlo simulations, we study the ground state phase
diagram of the fermionic Hubbard model on the honeycomb lattice at half-filling. We provide
evidence for a intervening phase separating the weak-coupling semi-metal and the
antiferromagnetically ordered phase at strong coupling. In this intermediate interaction region,
the system exhibits finite quasi-particle and spin excitation gaps, without long-range magnetic or
bond-order nor superconductivity being developed. Several proposals on novel phases in
related models have been put forward, whereas our simulations exhibit a spin liquid - even in
the absence of magnetic frustration.
Studying the Fermi-Hubbard model with cold atoms
Henning Moritz
ETH Zurich,
In a solid material strong interactions between the electrons can lead to surprising properties. A
prime example is the Mott insulator, where the strong repulsive interaction make it energetically
very unfavorable to place two fermions of opposite spin on the same lattice site. Hence, a Mott
insulator is characterized by insulating behavior, incompressibility and a strong reduction of
double occupancy. The physics of this paradigm of strong correlations is well captured by the
celebrated Hubbard model, which is widely used to describe strongly interacting electrons in a
solid. In my talk I will present experiments in which we have realized theFermi-Hubbard model
with ultracold atoms and investigated equilibrium and non-equilibrium properties. Due to the
intrinsic purity of the experimental system we can directly compare the experimental results with
theory. I will focus on precision measurements of the double occupancy, which - whencompared
with DMFT or high-temperature series expansion - can serve as a thermometer. The far-from
equilibrium dynamics of such strongly correlated systems is mostly unchartered territory and I
will present experimental and theoretical results revealing the importance of higher order
processes for thermalization.
Trapping and Cooling Fermionic Atoms into Mott and Neel States
Lorenzo De Leo
Ecole polytechnique Paris, France
We perform a theoretical study of a fermionic gas with two hyperfine states confined to an
optical lattice. We derive a generic state diagram as a function of interaction strength, particle
number, and confining potential. We discuss the central density, the double occupancy, and
their derivatives as probes for the Mott state, connecting our findings to recent
experiments.Using entropic arguments we compare two different strategies to reach the
antiferromagnetic state in the presence of a trapping potential and propose an experimental
procedure to cool fermionic atoms to the required temperatures.
Discerning Incompressible and Compressible Phases of Cold Atoms in
Optical Lattices
Vito Scarola
Virginia Polytechnic Institute and State University, USA
Experiments with cold atoms trapped in optical lattices offer thepotential to realize a variety of
novel phases but suffer fromsevere spatial inhomogeneity that can obscure signatures of
newphases of matter and phase boundaries. Optical lattice realizationsof the Fermi-Hubbard
model are of particular interest because oftheir connection to models of high temperature
superconductors. Iuse a high temperature series expansion to show that compressibilityin the
core of a trapped Fermi-Hubbard system is related tomeasurements of changes in double
occupancy.
This corecompressibility filters out edge effects, offering a direct probe
ofcompressibility independent of inhomogeneity. A comparison withrecent experiments is
made.
From Fermi's Golden rule to Rabi oscillations: Dynamical Unbinding
Transition in a Periodically Driven Mott Insulator
Andreas Ruegg
The University of Texas at Austin, USA
Modulation spectroscopy has been used in several experiments to study cold atomic gases in
optical lattices. We present analytical work on the dynamical generation of double occupancy in
Fermi systems described by a single-band Hubbard model. Thereby, the amplitude of the
periodic modulation (as compared to the single-particle band-width) allows us to distinguish two
different regimes: For weak modulation, the rate of change in the number of doubly occupied
sites is explained by a "Fermi's golden rule"-like analysis. For strong modulation, coherent Rabi
oscillations between a doublon-holon pair and a singlet are expected. In this talk we show that
reducing the modulation strength reveals a dynamical unbinding transition where doublon and
holon are free to separate. This transition marks the boundary to the intermediate regime where
both coherent and incoherent features are present.
Weighing a particle immersed in a Fermi sea
Frederic Chevy
LKB - ENS Paris, France
Recent experiments on Fermi gases with imbalanced spinpopulations have attracted
considerable attention to the problem of an impurity immersed in a Fermi sea, an extension of
the so-calledpolaron problem of condensed matter physics, where an electron isimmersed in a
bath of (bosonic) phonons. Theoretical investigationshave demonstrated that, even in the
regime of strong interactions,this "Fermi-polaron" was actually behaving like a free particle,
butwith renormalized physical properties (like its chemical potentialand mass). In this talk, we
will show how the latest experiments onultra-cold Fermi gases have confirmed this picture. In
particular, wewill discuss how recent measurements made at ENS on the breathing mode of a
spin polarized Fermi gas gave us access to the effective mass of the Fermi-polaron.
Pairing in mass and/or population imbalanced Fermion systems
George Batrouni
,
I will discuss pairing in fermionic systems on optical lattices with mass and/or population
imbalance. This will be done in the context of the attractive fermionic Hubbard model using
Quantum Monte Carlo methods. I will argue that, in the ground state, the dominant pairing
mechanism is at nonzero center of mass momentum, i.e. FFLO. If the mass imbalance is large
enough, spatial collapse of the system results. Finite temperature effects will also be discussed.
Pairing properties of population imbalanced fermions with two and three
flavors
Andreas Läuchli
Max Planck Institute for Physics of Complex Systems, Dresden,
We discuss the superfluid pairing properties of attractively interacting fermions on a
one-dimensional optical lattice. For the case of two flavors, we employ Bethe-Ansatz results and
DMRG simulations to reveal an extended region of FFLO type pairing, where the superfluid is
formed by Cooper pairs carrying finite momentum and discuss the effect of FFLO pairing on
noise correlation spectra. In the case of three flavors there is competition between three
different FFLO modes, which exhibits an interesting interaction and imbalance dependence.
Furthermore the system is unstable towards collapse and phase separation at strong attraction,
essentially due to a dynamical mass imbalance effect.
Long-range interacting Rydberg atoms
Robert Loew
University of Stuttgart, Germany
We report on a strongly interacting frozen Rydberg gas excited from a ultracold trapped
ensemble of Rubidium atoms. This system can be described by a spin Hamiltonian where the
long-range strong repulsive van der Waals interaction is responsible for novel manybody
physics. Universal scaling behaviour due to an underlying quantum phase transition based on
the socalled Rydberg blockade is observed [1,2].
[1] R. Heidemann, U. Raitzsch, V. Bendkowsky, B. Butscher, R. Löw, L. Santos, T. Pfau "Evidence for
coherent collective Rydberg excitation in the strong blockade regime" Phys. Rev. Lett.. 99, 163601 (2007).
[2] R. Löw, H. Weimer, U. Raitzsch, R. Heidemann, V. Bendkowsky, B. Butscher, H. P. Büchler, and T.
Pfau "Universal scaling in a strongly interacting Rydberg gas" arXiv:0902.4523 (2009).
Cold atoms and molecules in elongated Wannier orbitals
Vincent Liu, K. Sun and E. Zhao
University of Pittsburgh, USA
We show that topological phases with fractional excitations can risein two-dimensional ultracold
dipolar gases on a particular class ofoptical lattices. Due to the dipolar interaction and lattice
confinement, a quantum dimer model emerges naturally as the effective theory describing the
low energy behaviors of these systems under well-controlled approximations. Using a
nonstandard optical lattice consisting of periodically arranged double-well potentials, we identify
the elongated wavefunction at each site with an ``orbital dimer'', and map the problem to dimer
covering of the dual lattice. The hard core constraint of the quantum dimer model is enforced by
the dipolar interactions, and the desired hierarchy of interaction energy scales is achieved by
controlling the anisotropy of the orbital dimers. Experimental realization and detection of various
phases are discussed. Work done in collaboration with K. Sun and E. Zhao, with support from
U.S. DOE and U.S. ARO.
Feshbach resonance in an optical lattice
Hans Peter Büchler
University of Stuttgart, Germany
Cold atomic gases in optical lattices represent a perfect laboratory system for the quantum
simulation of strongly correlated many-body systems described by Hubbard models. Recently,
experimental and theoretical efforts focus on the observation of a Fermionic Mott insulator, and
the ultimate goal towards the realization of magnetic and superconducting phases. The
quantitative understanding of these experimental results and the comparison with the theoretical
predictions require a precise knowledge of the parameters in the Hubbard model for cold atomic
gases interacting with a Feshbach resonance. We present the solution to the two-particle
problem in an optical lattice interacting via a Feshbach resonance, and provide a microscopic
derivation of the parameters in the Hubbard model and the two-particle bound state energies.
Implementing artificially engineered gauge potentials in a lattice
Fabrice Gerbier
Laboratoire Kastler Brossel, ENS, Paris, France
TBA
Non-equilibrium many-body physics in quantum gases of interacting
photons
Iacopo Carusotto
Universita'' de Trento, Italy
Experiments have recently started providing evidence for a variety of non-equilibrium
many-body effects in gases of interacting photons in nonlinear optical cavities. In this talk, I will
review the present status of the experiments as well as of their theoretical understanding.
Analogies and differences with standard systems such as liquid Helium and ultracold atoms will
be illustrated. New developments in the direction of exploring the peculiar phases that originate
from the interplay of strong correlations with the non-equilibrium condition will be discussed.
Projected Entangled-Pair and Plaquette States
Ignacio Cirac, F. Mezzacapo, N. Schuch, A. Sfondrini, M. Sanz, V. Murg, M.C. Banuls,
F. Verstraete
Max-Plank Institute for Quantum Optics, Garching, Germany
We will report on the latest numerical results using differenttechniques which combine PEPS
and Monte Carlo Methods. We haveapplied those techniques to frustrated spin systems and
cold atomicgases.
Fully resolved optical imaging of a 2D quantum gas
Simon Foelling
Harvard University, USA
With ultracold quantum gases, very idealized implementations of complex many-body systems
can be realized in order to closely model fundamental hamiltonians. In addition, these systems
can enable the realization of tools for manipulating and probing the gaswhich are not available
for classical condensed matter systems. I will present our experiment that enables the
preparation of a cold quantum gas in a single, strongly two-dimensional trapping potential. This
potential is located a few micrometers from a glass surface, allowing for optical access with an
extremely high numerical aperture. This enables us to image and manipulate the quantum gas
with a resolution on the scale of 500,nm. We cangenerate optical lattices by direct projection
through the lens and detect the atoms with fluorescence imaging inside the trap. In this way, we
can detect individual atoms in each lattice site with high fidelity, allowing for complete
site-resolved readout of the quantum state, with all degrees of freedom known for the detected
atoms.
"Escaping from the trap" : extracting bulk properties of strongly
correlated systems from measurements on trapped ultracold gases
Tommaso Roscilde
ENS Lyon, France
Ultracold gases trapped in optical potential enable to literally implement fundamental models of
strongly correlated systems, realizing Feynman's visionary proposal of a "quantum analog
simulator". Despite the high tunability of the Hamiltonians realized e.g. by ultracold bosons in
optical lattices, a major drawback is represented by the high inhomogeneity of the system, due
to the presence of an overall trapping potential. Here I will describe a proposal to "get rid of the
trap" by performing realistic local measurements in the trap center, and by using in turn the
trapping potential to achieve a fine control on the chemical potential of the system. This
measurement scheme, together with conventional time-of-flight measurements, enables to
characterize the phasediagram of the Hamiltonian implemented in the system without the trap
and in the grand-canonical ensemble. In particular I will present the application of this method to
the measurement of the detailed phase diagram of the Bose-Hubbard model on a simple lattice,
as well as in an external (periodic or random) potential.
Probing many-body physics with ultracold atoms
Eugene Demler
Harvard, USA
TBA
Ultracold Fermionic Atoms in optical lattices: Experiments in- and
out-of-equilibrium
Ulrich Schneider
LMU Munich, Germany
Ultracold fermionic atoms in an optical lattice represent a versatilequantum simulator for
correlated electrons in a solid, as they allow for a clean and defect-free implementation of the
Fermi Hubbard model with tunable perameters. In this talk, I present experimental and
theoretical data concerning in- and out-of-equilibrium properties of interacting fermionic atoms in
a blue detuned optical lattice, which allows for an independent control of lattice depth and
additional harmonic confinement. For repulsive interactions, we studied the crossover from a
metallic into a Mott insulating regime and compared our results with a DMFT calculation. In
addition, I present measurements in the attractive Hubbard model, where we observed an
anomalous expansion of the atomic cloud in the pseudogap regime of the BEC-BCS
crossover. These measurements represent a new possible way to investigate the properties of
low entropy phases using a high entropy sample. Furthermore, ultracold atoms offer the
possibility to control all relevant parameters in real time during the experiment. By suddenly
changing the harmonic confinement at constant lattice depth we could create a particular
out-of-equilibrium situation which allows us to study transport properties of the Hubbard model.
Strongly correlated polaritons on a lattice
Sebastian Schmidt
ETH Zurich, Switzerland
Motivated by the recent success of engineering light-matter interaction in cavity QED and
trapped ion systems, we investigate the superfluid-insulator transition of polaritons (i.e.
quasiparticles which form through the interaction of a single bosonic mode with a quantum
two-level system) as described by the Jaynes-Cummings-Hubbard model. Using a
diagrammatic linked-cluster expansion in the Mott regime and a slave-boson approach in the
superfluid regime we calculate quantum phase diagram,critical exponents and excitation spectra
of both phases.The presence of additional conversion modes in the Mott phase and an anomaly
of the sound velocity as a function of detuning in the superfluid phase signal clear deviations
from Bose-Hubbard like behaviour and can be attributed to the composite nature of polaritons.
The sudden expansion of interacting fermions in one dimensional optical
lattices
Fabian Heidrich-Meisner
RWTH Aachen, Germany
Time-dependent phenomena in ultracold atomic gases are currently attracting a lot of attention,
as such phenomena give insights into nonequilibrium properties of interacting particles. We
analyze the example of the sudden expansion of fermions in an optical lattice. Our main focus is
on the case in which the initial state has a strong admixture of double occupancies. We promote
the notion of quantum distillation: during the expansion, and in the presence of strongly
repulsive interactions, doublons group together, forming a nearly ideal band insulator, which is
metastable with a low entropy. Our analysis employs the density matrix renormalization method,
and we present results for experimentally observable quantities such as the radius of the
particle cloud. We suggest that the quantum distillation effect could be used for cooling
purposes in experiments with two-component Fermi gases.
Heidrich-Meisner, Manmana, Rigol, Muramatsu, Feiguin, Dagotto: arXiv:0903.2017
Heidrich-Meisner, Rigol, Muramatsu, Feiguin, Dagotto: Phys. Rev. A 78, 013620 (2008)
Observation of a Non-Equilibrium Dicke-Type Quantum-Phase Transition
Kristian Baumann
ETH Zurich, Switzerland
The Dicke Model describes the interaction between N two level atoms and a single
electromagnetic field mode which remains a fundamental problem in quantum optics. In the
thermodynamic limit the system was predicted to undergo a quantum phase transition from a
normal to a superradiant phase. Here we present a non-equilibrium realization of the Dicke
model in a Bose-Einstein condensate coupled to a high-finesse optical cavity. The superfluid
atoms collectively coupled a far-detuned transverse pump field to an empty cavity mode. The
atoms self-organize into an emergent checkerboard pattern above a critical pump power. When
entering this self organized phase, the gas initially maintains phase coherence and can thus be
regarded as a supersolid. Over a wide range of parameters, the boundary of this novel quantum
phase is mapped out and compared to a theoretical model. This work opens up new aspects of
quantum many-body physics with global interactions mediated by the cavity field.
Phase Diagram of a Spin-Imbalanced Fermi Gas in 1D
Randy Hulet, Yean-an Liao, Ann Sophie Rittner, Tobias Paprotta, Wenhui Li, Stefan
Bauer and Erich Mueller
Rice University, USA
We have obtained the phase diagram of a spin-imbalanced Fermi gas and compared it with
theory. Approximately 105 6Li atoms are trapped in a two-dimensional array of 1D tubes
formed from a 2D optical lattice. A weak axial harmonic potential confines ~100 atoms per
tube. The entire tube bundle is optically imaged, and analyzed to determine the phase
boundaries. We find that the gas phase separates axially into a central partially polarized
region, and outer regions that are either fully paired, for small population imbalance, or fully
polarized for larger imbalance. The locations of these boundaries are in good quantitative
agreement with theory. Phase separation in 1D is inverted in comparison with 3D, where the
fully paired region is in the center. We are exploring the crossover from 1D to 3D by lowering
the lattice depth. Finally, we also plan to investigate the nature of the partially polarized phase,
which is predicted to be a modulated FFLO superfluid.
Breakdown of thermalization in finite one-dimensional systems
Marcos Rigol
Georgetown University, USA
Little more than fifty years ago, Fermi, Pasta, and Ulam (FPU) set up a numerical experiment to
prove the ergodic hypothesis for a one-dimensional lattice of harmonic oscillators when
nonlinear couplings were added. Much to their surprise, the system exhibited long-time periodic
dynamics with no signals of ergodic behavior. Those results motivated intense research, which
ultimately gave rise to the modern chaos theory and to a better understanding of the basic
principles of classical statistical mechanics. More recently, experiments with ultracold gases in
one-dimensional geometries have challenged our understanding of the quantum domain. After
bringing a nearly isolated system out of equilibrium, no signals of relaxation to the expected
thermal equilibrium distribution were observed. Some of those results can be understood in the
framework of integrable quantum systems, but then it remains the question of why
thermalization did not occur even when the system was supposed to be far from integrability. In
the latter regime, thermalization is expected to occur and can be understood on the basis of the
eigenstate thermalization hypothesis. In this talk, we utilize quantum quenches to describe how
the transition between thermalization and its absence occurs in finite one-dimensional lattices.
We find the latter to be a smooth process in which the predictions of standard statistical
mechanics continuously worsen as one approaches the integrable point. We establish a direct
connection between the presence or absence of thermalization and the validity or failure of the
eigenstate thermalization hypothesis, respectively.
Relaxation of antiferromagnetic order in spin-1/2 chains following a
quantum quench
Vladimir Gritsev
Universite de Fribourg, Switzerland
We study the unitary time evolution of antiferromagnetic order in anisotropic Heisenberg chains
that are initially prepared in a pure quantum state far from equilibrium. Our analysis indicates
that the antiferromagnetic order imprinted in the initial state vanishes exponentially. Depending
on the anisotropy parameter, oscillatory or non-oscillatory relaxation dynamics is observed.
Furthermore, the corresponding relaxation time exhibits a at the critical point, in contrast to the
usual notion of critical slowing down, from which a maximum is expected.
P. Barmettler et al, Phys. Rev. Lett. 102, 130603 (2009)
Localization in one-dimensional cold atomic gases
Sankar Das Sarma
University of Maryland, USA
Bosons in disordered 1d traps: a new paradigm for the
superfluid-insulator transition?
Ehud Altman
Weizmann Institute of Science, Israel
Ultracold bosons in one dimensional traps are typically weakly interacting, whereas the disorder
potential generated e.g. by microfabricated "atomchips", is highly tunable. How is superfluidity
destroyed in such a system with increasing disorder strength? Giamarchi and Schulz famously
describe one possible transition [Europhys. Lett. 3, 1287 (1987)] . However their analysis is
perturbative and strictly valid only for weak disorder and tunable interactions, opposite of the
natural regime of cold atoms. Using a strong randomness RG approach we show that the
transition in a typical atomic system is very different than the weak disorder scenario. In marked
contrast to the latter, it occurs at a non universal value of the correlation exponent (Luttinger
parameter). Rather, the critical point is marked by universal mezoscopic fluctuations in physical
observables including the critical current and the correlation exponent. We show how signatures
of the transition may be detected with interference experiments.
Disordered Commensurate Bosons: 20-Year-Old Conjectures Are Now
Theorems
Boris Svistunov, V. Gurarie, L. Pollet, N.V. Prokof'ev, and M. Troyer
University of Massachusetts at Amherst, USA
We prove the theorem of inclusions stating that in the presence of generic bounded disorder
there exist rare, but arbitrarily large, regions of the competing phase across the generic
transition line. We argue that the only non-generic phase transitions are the Griffiths-type ones,
driven by rare regions in which disorder emulates some regular external perturbation. An
immediate implication of the theorem of inclusions is the absence of direct
superfluid-to-gapped-insulator quantum phase transitions. With an enhanced version of the
theorem of inclusions we prove finite compressibility (and thus relevance of disorder) on the
critical line of superfluid to Bose glass transition. The exceptional role of the Griffiths-type
transitions implies that the transition from Mott insulator to any gapless insulator should be
inevitably of this type.Quantum dynamics in ultracold atomic gases
Corinna Kollath
Ecole Polytechnique, Switzerland
Recent experimental developments increased the interest in quantum systems far from
equilibrium. In particular, the good tunability of ultracold quantum gases now allows for a rapid
change of the system parameters and the observation of the subsequent quantumevolution
decoupled from the environment. For example the non-adiabatic dynamics across
thesuperfluid-Mott-insulating phase transition has been realized inbosonic gases confined to
optical lattices. The theoretical description of these time-dependent phenomena is very
involved. We discuss the response of these strongly correlated quantum systems to
differentparameter changes as a change in their interaction strength.
DYNAMICS OF BOSONS IN OPTICAL LATTICES IN THE PRESENCE OF
MODULATED TRAPS
Rosario Fazio
Scuola Normale Superiore, Pisa, Italy
I will present our results on the behavior of bosons in optical lattices confined in time-dependent
traps. I first consider the case of dipole oscillations induced by displacing the trap center of a
few lattice sites [2]. Depending on the system parameters this motion can vary from
undamped to overdamped. The dipole oscillations as a function of the lattice displacement, the
particle density and the strength of interparticle interactions were studied by means of DMRG
calculations. I will then present the case in which the frequency of the trap is modulated
periodically in time [2] allowing to probe the dynamical compressibility of the system. Also in this
case the results of the DMRG calculation will be compared with experiments.
4 Posters
Diagrammatic Monte Carlo method for bosonic impurity problems
Peter Anders
Institute for Theoretical Physics, Switzerland
We present a continuous-time Monte Carlo method for bosonic impurity models which allows
the study of bosonic lattice models within the recently developed bosonic dynamical mean field
(B- DMFT) framework. The method is based on a Monte Carlo sampling of a perturbation
expansion in the hybridization functions as well as the condensate wave function. It allows us to
solve the B-DMFT equations and to calculate the Green’ s function for various temperatures
and coupling parameters. As an application we present the finite temperature B-DMFT phase
diagram for the bosonic Hubbard model on the Bethe lattice.
Dynamical simulations of infinite chains using Matrix Product States
Mari-Carmen Banuls, M. B. Hastings, F. Verstraete and J. I. Cirac
Max Planck Insitute of Quantum Optics, Garching, Germany
Techniques based on Matrix Product States, as DMRG, have provenextremely successful for
the numerical simulation of ground states inthe case of one dimensional systems. When the
quantities of interestare not static, but one wants to simulate out-of-equilibrium dynamics,the
applicability of such methods is limited to very short times, ingeneral.We propose a new
method, based on a transverse contraction ofthe tensor network, which allows the calculation of
time dependentexpectation values and dynamical correlation functions for infinitetranslationally
invariant chains to much longer times than any otherexisting method. The technique is
applicable to a broad range ofproblems, including finite systems, and also periodic infinite
chainsand impurity models, among others.
M.C. Banuls, M. B. Hastings, F. Verstraete and J. I. Cirac, Phys. Rev. Lett. 102, 240603 (2009).
Observation of a Self-Organized Quantum Phase
Kristian Baumann, C. Guerlin, F. Brennecke, T. Esslinger
ETH Zurich, Switzerland
We experimentally investigate a non-equilibrium quantum phase transition in an open system
formed by a Bose-Einstein condensate and an ultrahigh-finesse optical cavity. The superfluid
atoms collectively couple a transverse pump field, formed by a standing-wave laser beam, to an
empty cavity mode. Above a critical pump intensity the cavity field builds up in a Dicke-type
phase transition accompanied by self-organization of the atoms in an emergent checkerboard
pattern. The Bose-Einstein condensate acquires a density modulation reflecting a reduced
symmetry compared to the underlying mode structure of the cavity and pump field. When
entering the self-organized phase the gas initially maintains its first-order spatial coherence, and
can thus be regarded as a supersolid, similar to those proposed for two-component systems.
Thereafter dephasing sets in, yet it is possible to retrieve a Bose-Einstein condensate when
lowering the pump intensity again. For a wide range of parameters the boundary of this novel
self-organizedquantum phase is mapped out and compared to a theoretical model. This work
opens up new aspects of quantum many-body physics with global interactions, and provides the
first experimental realization of an effective Dicke Hamiltonian including counter-rotating
coupling terms.
Variational wave functions for Mott insulators
Federico Becca
International School for Advanced Studies (SISSA) and CNR-DEMOCRITOS IOM, Italy
We give a review of recent developments on the possibility to have a faithful representation of
strongly correlated systems by using improved variational wave functions. In particular, we
focus the attention on the bosonic Hubbard model, where the numerically exact solution is
known by Monte Carlo simulations, which allow us to assess the variational accuracy. We show
how it is possible to describe the superfluid-insulator transition by using the Gutzwiller wave
function supplemented with a long-range Jastrow factor. An appealing interpretation in terms of
the binding-unbinding Kosterlitz-Thouless transition is obtained through the mapping onto a
classical model. Finally, the case with long-range interactions will be also briefly discussed.
Polar Molecules with Three-Body Interactions on the Honeycomb Lattice
Lars Bonnes
Institute for Theoretical Physics III, University of Stuttgart, Germany
Motivated by a recent proposal on using polar molecules in optical lattices driven by microwave
fields to induce strong three-body interactions (H. P. B"uchler et al., Nature Physics 3, 726
(2007)), we analyze the quantum phase diagram of the boson Hubbard model with nearest
neighbor three- and two-body repulsions using quantum Monte Carlo simulations. In particular,
we consider a honeycomb lattice, where three-body repulsions lead to degenerate classical
regions at various unconventional lattice fillings. Furthermore, we consider the interplay of twoand three-body repulsions for the experimentally relevant parameter regime, and find evidence
for an cascaded transition to the checkerboard solid for finite two-body repulsions.
Cavity Optomechanics with a Bose-Einstein Condensate
Ferdinand Brennecke, K. Baumann, C. Guerlin, S. Leinss, S. Ritter, T. Donner, T.
Esslinger
ETH Zurich,
In our experiment we couple a Bose-Einstein condensate with anultrahigh-finesse optical cavity.
The tremendous degree of control over atomic gases achieved in Bose-Einstein Condensates
combined with the rich field of cavity quantum electrodynamics opens access to a wealth of new
physics. In the dispersive regime, our system realizes a model of cavity optomechanics. This
research field typically studies the coupling of the mechanical motion of one of the cavity mirrors
to the light field. In our case, the mechanical oscillator is given by a coherent density modulation
of the atomic cloud. We have observed this density modulation and strong optical nonlinearities,
present at the single photon level. Furthermore our mechanical oscillator naturally starts inits
ground state, from which a single motional excitation can cause a shift of the cavity resonance
on the order of the cavity linewidth. Our system is promising to study the quantum regime of
cavity optomechanics.
Multi-particle composites in density-imbalanced quantum fluids
Evgeni Burovski, Giuliano Orso and Thierry Jolicoeur
LPTMS, Universite Paris-Sud, France
We consider two-component one-dimensional quantum gases with density imbalance. While
generically such fluids are two-component Luttinger liquids, we show that if the ratio of the
densities is a rational number, p/q, and mass asymmetry between components is sufficiently
strong, one of the two eigenmodes acquires a gap. The gapped phase corresponds to
(algebraic) ordering of (p+q)-particle composites. In particular, for attractive mixtures, this
implies that the superconducting (FFLO) correlations are destroyed. We illustrate our
predictions analytically for a dipolar gas and numerically for the fermionic Hubbard model with
hopping asymmetry.
arXiv:0904.0569
arXiv:0907.1533
Three Species Fermi Gas in 2D Optical Lattice with Dynamic Constraint
Soon-Yong Chang
University of Innsbruck, Austria
We present analysis of the attractively interacting three species Fermi gas in the 2D optical
lattice with the dynamically imposed three body constraint by using a variational many body
method. We discuss crossing of symmetries in the ground state and the pairing. We also
discuss experimental implications.
Single site addressability in optical lattices
Marc Cheneau
Max Planck Institute for Quantum Optics, Germany
xperiments with optical lattices have so far suffered from an important drawback: it has been
impossible to probe or to manipulate the atoms at the level of a single lattice site, while
maintaining a sufficiently tight spacing to allow for a nearest neighbour coupling through
tunnelling. For quantum processing, this means that only simple algorithms have been
implemented, in which the same operation was applied to all pairs of qubits. In condensed
matter-like experiments, this lack of a local probe also constitutes a severe limitation as dilute
gases are intrinsically inhomogeneous (trapped), meaning that any measurement performed on
a macroscopic scale inevitably leads to a blurred, incomplete characterisation of the system.
Our new experimental setup allows for single site addressability of bosonic atoms in a tight
optical lattice, thanks to a specially designed lens system with a resolution smaller than the
lattice spacing. Using this new tool, it is possible to observe and manipulate density, spin
structure, and correlations at the scale of a lattice site. This will allow us to investigate
steady-state and dynamical properties of low-dimensional systems, such as spin-charge
separation, which were out of reach of previous experiments. We also plan to engineer fast,
high-fidelity, quantum gates and to build massively entangled systems as a resource for
quantum computation.
Effects of Ground Hyperfine Energy Separation on Quantum
Computation and Frequency Standard
GOPAL DIXIT
TECHNICAL UNIVERSITY MUNICH, Germany
The quantum information processing (QIP) is one of the interesting areas in physics which is
gaining momentum both in theoretical and experimental fronts in the recent days. The single
valence ions, particularly the ones with 2S1/2 ground state are being chosen for QIP studies [1]
to encode qubits into the ground state hyperfine levels. These levels are chosen due to their
relatively long lifetimes against spontaneous decay rates and long phase coherence because of
their small energy separations. The hyperfine studies help us understanding the nuclear
structure of an atom and its influence on the short range wavefunctions.
Recently trapped
and laser cooled ions are excellent candidates for many high precision measurements [2, 3].
Due to the decoupling of the internal states caused by the collisions and Doppler shifts, trapped
and laser-cooled ions have been regarded as nearly isolated quantum systems [4]. Therefore,
precise measurements of hyperfine transition frequencies of several species of trapped ions
have been performed, which lead to develop the better frequency standard in microwave and
optical frequency regions [5-7].
Experiments on singly ionized trapped and laser-cooled
cadmium (Cd+1) ions and zinc (Zn +1) have raised their potential for applications in quantum
computing and information processing [8]. Besides, both the ions are promising candidate for
new frequency standard in microwave region [5]. It is, therefore, of great importance to have
precise study of the hyperfine energy separations of ground as well as few excited states of
those ions. However, rare accurate ab initio many-body estimations are available in literature of
these properties. Here I will present about the above applications and our recent studies [8, 9]
of these properties using highly correlated relativistic coupled cluster technique using single,
double and partial triple excitations. Contributions of different correlation effects, like core-core,
core-polarization and core-valence correlations, will be discussed in details.
1. R. Ozeri et al., Phys. Rev. A 75, 042329 (2007).
2. P. K. Ghosh, Ion Traps: Oxford Science Publications (Oxford: Clarendon) (1995).
3. D. J. Wineland and W. M. Itano, Phys. Today 40, 34 (1987).
4. U. Tanaka et al., Phys. Rev. A 53, 3982 (1996).
5. U. Tanaka et al., Appl. Phys. B 78, 43-47 (2004).
6. B. M. Jelenkovic et al., Phys. Rev. A 74, 022505 (2006).
7. K. Matsubara et al., Appl. Phys. B 76, 209 (2003).
8. B.B. Blinov, D.L. Moehring, L.M. Duan and C. Monroe, Nature (London) 428, 153 (2004)
8. Gopal Dixit et al., Phys. Rev. A 77, 012718 (2008).
9. Gopal Dixit et al., J. Phys. B 41, 025001 (2008).
DMFT simulations of ultracold fermions in optical lattices
Elena Gorelik
University of Mainz, Germany
Ternary flavor mixtures of ultracold fermionic atoms in an optical lattice are studied in the case
of equal, repulsive on-site interactions U>0. The corresponding SU(3) invariant Hubbard model
is solved numerically exactly within dynamical mean-field theory usingmultigrid Hirsch-Fye
quantum Monte Carlo simulations. We establish Mott transitions close to integer filling at low
temperatures and show that the associated signatures in the compressibility and pair occupancy
persist to high temperatures, i.e., should beaccessible to experiments. In addition, we present
spectral functions and discuss the properties of a novel "semi-compressible" state observed for
large U near half filling. We also present first results for two-flavor systems in a harmonic
potential using a QMC implementation of the real-space DMFT approach. In particular, we show
the gradual melting of a central antiferromagnetic phase with increasing temperature in 2
dimensions.
Equilibrium and out of equilibrium studies of ultracold fermions in an
optical lattice
Daniel Greif
ETH Zurich, Switzerland
In our experiment we use a two component Fermi gas in a 3D optical lattice to realize the
Fermi-Hubbard model. This clean approach offers the advantage of posing well defined
questions and accessing clean probes. Here we present recent measurements of equilibrium
and out of equilibrium properties of this model system. Tuning the interaction via a Feshbach
resonance over a broad range we investigate the crossover from a metallic to Mott insulating
state. This is signaled by a drastic reduction of double occupancy and the appearance of a
gapped mode in the doublon spectrum probed by lattice modulation. The resolution in double
occupancy of our most recent measurements allows for precise comparison with both DMFT
calculations and high-temperature series expansions. The remarkable agreement allows us to
determine the temperature, which reaches values on the order of the tunneling energy T~t. If
the lattice modulation is sufficiently weak, the increase of doublons with time is well captured by
linear response theory. In this regime the buildup rate of doublons is a measure for equilibrium
properties such as the temperature sensitive local spin ordering, which could in principle be
used to detect anti-ferromagnetic ordering. For long modulation times the system is driven into a
far from equilibrium state with many additional doublons. We show that the dominant decay
mechanism is a high-order scattering process and the doublon lifetime depends exponentially
on the ratio of onsite interaction to tunneling energy.
Creating and modifying Feshbach resonances with rf radiation
Thomas Hanna, Adam Kaufman, Russell Anderson, David Hall, Eite Tiesinga and
Paul S. Julienne
NIST, USA
We have developed a method for studying the modification of scattering properties of atoms in
the vicinity of a Feshbach resonance, including the effects of strong rf radiation for which
multiphoton effects are significant. Apart from known atomic properties, only three input
parameters are required to construct a complete model of Feshbach resonances: the singlet
and triplet scattering lengths, and the coefficient of the long range van der Waals potential. We
apply our technique to collisions of 87Rb, which has several resonances around 9 G and 18
G. As the rf frequency or amplitude change, the bound states causing the different resonances
can be coupled together, leading to rich variation of the scattering properties with magnetic
field, and rf frequency and amplitude. Our calculations quantitatively reproduce experimental
data for 87Rb. We also study the creation and manipulation of 6Li resonances with rf radiation,
and suggest regimes in which rf could be a useful tool for manipulating scattering properties.
The BCS-BEC crossover and the disappearance of FFLO-correlations in
a spin-imbalanced, one-dimensional Fermi gas
Fabian Heidrich-Meisner, A.E. Feiguin, U. Schollwoeck, W. Zwerger
RWTH Aachen, Germany
We present a numerical study of the one-dimensional BCS-BEC crossover of a spin-imbalanced
Fermi gas. The crossover is described by the Bose-Fermi resonance model in a real space
representation. Our main interest is in the behavior of the pair correlations, which, in the BCS
limit, are of the Fulde-Ferrell-Larkin-Ovchinnikov type, while in the BEC limit, a superfluid of
diatomic molecules forms that exhibits quasi-condensation at zero momentum. We use the
density matrix renormalization group method to compute the phase diagram as a function of the
detuning of the molecular level and the polarization. As a main result, we show that FFLO-like
correlations disappear well below full polarization close to the resonance. The critical
polarization depends on both the detuning and the filling.
Preprint
arXiv:0908.3074
Momentum distribution, renormalization factor, and effective mass of the
two-dimensional electron gas
Markus Holzmann
LPTL, Jussieu, Paris, France
We calculate the momentum distribution of the Fermi liquidphase of the homogeneous,
two-dimensional electron gas. We showthat, close to the Fermi surface, the momentum
distribution ofa finite system with $N$ electrons approaches itsthermodynamic limit slowly, with
leading order correctionsscaling as $N^-1/4$. These corrections dominate theextrapolation of
the renormalization factor, $Z$, and thesingle particle effective mass, $m^*$, to the infinite
systemsize. We show how convergence can be improved analytically. Inthe range $1 le r_s le
10$, we get a lower renormalizationfactor $Z$ and a higher effective mass, $m^*>m$,
compared tothe perturbative RPA values.
M. Holzmann, B. Bernu, V. Olevano, R.M. Martin, and D.M. Ceperley,
Phys. Rev. B 79, 041308(R) (2009).
Diagrammatic Monte Carlo for the Hubbard Model
Evgeny Kozik
ETH Zurich, United Kingdom
We show that Monte Carlo sampling of the Feynman diagrammatic series (DiagMC) can be
used for tackling hard fermionic quantum many-body problems in the thermodynamic limit by
presenting accurate results for the repulsive Hubbard model in the correlated Fermi liquid
regime. Using perturbative Feynman diagrams (rather than skeleton, or ``bold-line'', graphs) for
the single-particle self-energy we can study moderate values of the on-site repulsion ($U/t sim
4$) and temperatures down to $T/t=1/40$. We compare our results with high temperature series
expansion and with single-site and cluster dynamical mean-field theory. We find that going from
single site to large clusters is essential for obtaining the same level of accuracy as provided by
DiagMC.
Fermionic Projected Entangled Pair States
Christina Kraus
Max-Planck Institut für Quantenoptik, Garching, Germany
We introduce a family of states, the fPEPS, which describes fermionic systems on lattices in
arbitrary spatial dimensions. It constitutes the natural extension of another family of states, the
PEPS, whichefficiently approximate ground and thermal states of spin systems with short-range
interactions. We give an explicit mapping between those families, which allows us to extend
previous simulation methodsto fermionic systems. We also show that fPEPS naturally arise as
exact ground states of certain fermionic Hamiltonians. We give an example of such a
Hamiltonian, exhibiting criticality while obeyingan area law.
Luttinger liquid of trimers in Fermi gases with unequal masses
Giuliano Orso, Evgeni Burovksi, and Thierry Jolicoeur
LPTMS, University of Paris South, France
An experimentally hot topic in the field of ultra-cold atoms is the study of Fermi mixtures where
the standard BCS pairing mechanism is frustrated. Can a gas be superfluid if the number of up
and down fermions is different ? What is the nature of superfluidity when pairing occurs between
two different species, say Li-K ?In this respect, one dimensional (1D) systems are particularly
interesting. First they stabilize exotic phases that are extremely fragile in higher dimensions, like
the celebrated Fulde Ferrell Larkin Ovchinnikov (FFLO) state. Second, powerful numerical
methods allow to go beyond mean field theories and unveil new effects. Here I present some
recent theoretical work [1] on attractive fermions in a 1D optical lattice with unequal tunneling
rates, corresponding to different effective masses for the two components. In the presence of
mass asymmetry, the microscopic model is no longer integrable and multi-particle bound states
appear. Here I will focus on trimers, namely three-body bound state made of one light and two
heavy fermions. I will first present the solution of the three-body problem, yielding the binding
energy and the effective mass of a single trimer. I will then show that, undercertain conditions,
trimers can dramatically affect the properties of a many-body system, leading to a suppression
of FFLO correlations and topological changes in the grand-canonical phase diagram.
Experimental signatures of trimers in cold atoms experiments will be discussed.
[1] G. Orso, E. Burovski and T. Jolicoeur, arXiv:0907.1533
Superfluid Transition of an interacting Bose gas in a random potential: a
Path Integral Monte Carlo study
Sebastiano Pilati
The Abdus Salam International Centre for Theoretical Physics, Italy
We study the superfluid transition of an Interacting Bose gas in thepresence of correlated
disorder using Path Integral Monte Carlo techniques based on the Worm Algorithm. Disorder is
introduced into the system by a 3D speckle potential whose intensity and correlation length can
be varied at will. We determine the critical temperature, chemical potential and density as a
function of the disorder intensity. We observe that disorder causes a reduction of the critical
temperature. This effect diminishes for increasing inter-particle repulsion. In the regime of strong
disorder, we show the behavior of the density profiles, of the condensate and of the superfluid
fraction as a function of the temperature and of the interaction strength. We observe that in the
weakly interacting limit the gas localizes in the deepest wells on the external field and has no
long-range order. Strong inter-particle repulsion can delocalize the system and increase the
superfluid component. Finally, we study the equation of state of the exotic normal phase that we
observe at low temperatures in the presence of strong disorder.
Pfaffian state(s) simulation in Spin-1 Optical Lattices
Matteo Rizzi, L. Mazza, M. Rizzi, M. Lewenstein, J.I. Cirac
Max Planck Institut für Quantenoptik - Garching, Germany
We investigate the possibility of simulating bosons subject to an infinite three-body contact repulsion, and
to an external magnetic field, with experimentally feasible cold atoms setups. The need for three local
degrees of freedom drives the attention to spin-1 atomic Mott insulator with filling factor 1. A proper
perturbative treatment, and a coupling to auxiliary F=2 ancillas, allows to identify a regime where the
mapping holds.
Such a scheme can be used to investigate Pfaffian states, introduced in the context of Quantum Hall effect
by Moore and Read. They indeed arise if particles are constrained to be not more than two in a single
place. They are known to support non-abelian topological excitations; moreover, they are claimed to be the
underlying pairing mechanism in p+ip superconductors. Their bosonic version displays a QH filling factor
u=1, i.e. one particle for each quantum of magnetic flux. Up to now, the long quest for them has not yet
produced experimental fingerprints.
At dilute enough limit of our discretized system, topological properties are conserved. With the help of
Chern numbers and ground state degeneracy, we show that even increasing the magnetic field these
properties should not be abruptly washed out. The proposed scheme thus opens a route towards the study
of exotic states and non-abelian quasi-excitations with cold atomic quantum simulators.
Probing a Mott insulator of cold atoms by dynamically generating double
occupancy
Andreas Ruegg, S. D. Huber
The University of Texas at Austin, USA
Modulation spectroscopy has been used in several experiments to study cold atomic gases in
optical lattices. We present analytical work on the dynamical generation of double occupancy in
Fermi systems and propose a "Fermi's golden rule"-like expression to quantify the rate of
change in the number of doubly occupied sites due to a periodic modulation of the hopping
amplitude. Using different approximative methods we aim at a qualitative understanding of this
rate in a wide parameter regime. We find that conclusive evidence for a Mott phase can be
inferred from such a measurement.
Spectral functions of one-dimensional quantum liquids
Mikhail Zvonarev
LPTMS, France
I will report on a theoretical progress in understanding the spectral properties of
one-dimensional quantum liquids. While for small energy and momentum transferred the
spectral properties are explained (with notably exceptions) by the Luttinger model, their
description at arbitrary energy/momentum remained an open problem until very recently. The
situation changed in the last three years, and at present there exist several theories explaining
the spectral properties of 1D systems away from the Luttinger Liquid regime. I will discuss these
theories and some open questions.
5 Participant List
Organizers
Esslinger, Tilman
Swiss Federal Institute of Technology Zurich (ETHZ), Switzerland
Georges, Antoine
College de France and Ecole Polytechnique, France, France
Muramatsu, Alejandro
University of Stuttgart, Germany
Pollet, Lode
LMU Munich, Germany
Altman, Ehud - Weizmann Institute of Science, Israel
Anders, Peter - Institute for Theoretical Physics, Switzerland
Banuls, Mari-Carmen - Max Planck Insitute of Quantum Optics, Garching, Germany
Batrouni, George - ,
Baumann, Kristian - ETH Zurich, Switzerland
Becca, Federico - International School for Advanced Studies (SISSA) and
CNR-DEMOCRITOS IOM, Italy
Blatter, Gianni - Theoretische Physik, ETH Zurich,
Bonnes, Lars - Institute for Theoretical Physics III, University of Stuttgart, Germany
Brennecke, Ferdinand - ETH Zurich,
Büchler, Hans Peter - University of Stuttgart, Germany
Buhmann, Jonathan - Institute for Theoretical Physics, ETH Zürich, Switzerland
Burovski, Evgeni - LPTMS, Universite Paris-Sud, France
Carusotto, Iacopo - Universita'' de Trento, Italy
Chang, Soon-Yong - University of Innsbruck, Austria
Cheneau, Marc - Max Planck Institute for Quantum Optics, Germany
Chevy, Frederic - LKB - ENS Paris, France
Chin, Cheng - Unviversity of Chicago, USA
Cirac, Ignacio - Max-Plank Institute for Quantum Optics, Garching, Germany
Daley, Andrew - University of Innsbruck, Austria
Das Sarma, Sankar - University of Maryland, USA
De Leo, Lorenzo - Ecole polytechnique Paris, France
Demler, Eugene - Harvard, USA
DIXIT, GOPAL - TECHNICAL UNIVERSITY MUNICH, Germany
Fischer, Mark - ETH Zürich, Switzerland
Foelling, Simon - Harvard University, USA
Gerbier, Fabrice - Laboratoire Kastler Brossel, ENS, Paris, France
Gorelik, Elena - University of Mainz, Germany
Greif, Daniel - ETH Zurich, Switzerland
Gritsev, Vladimir - Universite de Fribourg, Switzerland
Gupta, Jyotsana - Max Planck Institute for Polymer Research Mainz, Germany
Hanna, Thomas - NIST, USA
Hassler, Fabian - ETH Zurich, Switzerland
Heidrich-Meisner, Fabian - RWTH Aachen, Germany
Holzmann, Markus - LPTL, Jussieu, Paris, France
Huber, Sebastian - Weizmann Institute, Israel
Hulet, Randy - Rice University, USA
Jordens, Robert - ETH Zurich, Switzerland
Kollath, Corinna - Ecole Polytechnique, Switzerland
Kozik, Evgeny - ETH Zurich, United Kingdom
Kraus, Christina - Max-Planck Institut für Quantenoptik, Garching, Germany
Läuchli , Andreas - Max Planck Institute for Physics of Complex Systems, Dresden,
Liu, Vincent - University of Pittsburgh, USA
Loew, Robert - University of Stuttgart, Germany
Ma, Ping Nang - ETH Zurich, Switzerland
McCulloch , Ian - University of Queensland, Australia
Moritz, Henning - ETH Zurich,
Orso, Giuliano - LPTMS, University of Paris South, France
Pilati, Sebastiano - The Abdus Salam International Centre for Theoretical Physics,
Italy
Prokofev, Nikolay - University of Massachusetts at Amherst, USA
Rigol, Marcos - Georgetown University, USA
Rizzi, Matteo - Max Planck Institut für Quantenoptik - Garching, Germany
Roscilde, Tommaso - ENS Lyon, France
Ruegg, Andreas - The University of Texas at Austin, USA
Scarola, Vito - Virginia Polytechnic Institute and State University, USA
Schmidt, Sebastian - ETH Zurich, Switzerland
Schneider, Ulrich - LMU Munich, Germany
Sigrist, Manfred - Swiss Federal Institute of Technology Zurich (ETHZ), Switzerland
Strohmaier, Niels - ETH Zurich, Switzerland
Svistunov , Boris - University of Massachusetts at Amherst, USA
Tarruell, Leticia - Swiss Federal Institute of Technology Zurich (ETHZ), Switzerland
Theiler, Barbara - ETH Zurich, Switzerland
Tiecke, Tobias - University of Amsterdam, The Netherlands
Trivedi, Nandini - Ohio State University, USA
Troyer, Matthias - Swiss Federal Institute of Technology Zurich (ETHZ), Switzerland
Werner, Philipp - ETH Zurich, Switzerland
Wessel, Stefan - University of Stuttgart, Germany
Zvonarev, Mikhail - LPTMS, France