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Quantum information with
cold atoms
Zheng-Wei Zhou(周正威）
Key Lab of Quantum Information ,
CAS, USTC
October, 2009
KITPC
Outline
• Backgrounds on Quantum Computation(QC)
• Quantum Computation(QC) and Quantum
Simulation(QS) with Cold atoms
Standard model for QC
One-Way QC
QS for highly-correlated many body models
• Quantum Communication
• Summary and Outlook
Backgrounds on Quantum Computation(QC)
Father of QC（1981－1985）
R. Feynman
D. Deutsch
Elementary Gates for QC （1995）
A. Barenco (Oxford), C. H. Bennett (IBM), R. Cleve
(Calgary), D. P. DiVincenzo (IBM), N. Margolus (MIT),
P. Shor (AT&T), T. Sleator (NYU), J. Smolin (UCLA),
H. Weinfurter (Innsbruck)
C. H. Bennett
Quantum Algorithms
1994
1997
Some Methods to Overcome Decoherence
（1）Quantum Error Correcting Codes
（Shor，Steane，Calderbank，Laflamme，Preskill，etc.）（1995－2000）
（2）Decoherence-Free Subspaces
（Duan, Guo, Zanardi, Whaley，Bacon, Lidar, etc.）（1997－2000）
（3）Dynamical Decoupling method
（Lolyd，Viola，Duan，Guo, Zanardi，etc.） （1998－1999）
Standard Model for QC
Beyond Standard model (I)
• Topological Quantum Computing
A. Kitaev (1997)
Beyond Standard model (II)
• One Way Quantum Computing
R. Raussendorf
H. Briegel (2000)
Beyond Standard model (III)
• Adiabatic Quantum Computation
Dorit Aharonov et.
al (2004)
J. Goldstone et. al
(2000)
......
E
Standard QC
t
Adiabatic QC
Intermediate targets of QC——Simulating
highly-correlated many body systems
D. Jaksch
P. Zoller
D. Jaksch, C. Bruder, C.W. Gardiner, J.I. Cirac and P. Zoller (1998)
model
Adiabatic
QC
Beyond Classical Computer
Topological
QC
Decoherence, Scalability, Energy gap, etc
Standard QC
Quantum Computer
Quantum Simulation
Once Fault-Tolerant
QC can be realized…
Quantum Computation(QC) and Quantum
Simulation(QS) with Cold atoms
Standard model for QC
One-Way QC
QS for highly-correlated many body models
Standard Model for QC
1. Register of 2-level systems (qubits)
The physical origin of the confinement of cold
atoms with laser light is the dipole force:
Olaf Mandel, et al., Phys. Rev. Lett. 91, 010407 (2003)
2. Initialization of the qubit register
However, nonideal conditions will always result in defects in that
phase (i.e., missing atoms and overloaded sites). How to suppress
these defects in the lattice?
A possible approach is: the coherent filtering scheme.
P. Rabl, et al., Phys. Rev. Lett. 91,110403, (2003)
3、4. Tools for manipulation: 1- and 2-qubit gates and readout 1-qubit
As far as ultracold atoms trapped in an optical lattice is concerned, global
operations on atoms are available. However, addressing individual atom
becomes very difficult. So, to implement universal quantum computation,
we should answer the following questions:
1: Whether global operations are enough to
implement universal quantum computation?
OR
2: How to addressing single qubit in this system?
Some proposals for QC via global operations
Cellular-automata Machine
(S. Lloyd, Science 261, 1569 (1993); S. C. Benjamin, PRA 61,
020301R, 2000, PRL 88, 017904, 2002)
QC via translation-invariant operations
R. Raussendorf, Phys. Rev. A 72, 052301 (2005). K. G. H. Vollbrecht et al., Phys.
Rev. A 73, 012324 (2006). G. Ivanyos, et al., Phys. Rev. A 72, 022339 (2005).
Z. W. Zhou, et al., Phys. Rev. A 74, 052334 (2006).
In the above proposals, only translationally invariant global
operations are required!
Shortcomings:
Redundant qubits (space and time overhead)
Initialization
Physical implementation
Bose Hubbard model
Ising Model
PRL 81, 3108 (1998); 90, 100401(2003); 91,090402 (2003)
Type I
Type II
PRL 91,090402 (2003)
(Effective periodic magnetic field induced by left and right circularly polarized light)
Z. W. Zhou, et al., Phys. Rev. A 74, 052334 (2006).
1D
Two-qubit
operation
Addressing
single qubit
2D
Z. W. Zhou, et al., Phys. Rev. A 74, 052334 (2006).
Some proposals for QC via addressing single atom
Marked Qubit as Data-bus
(Phys. Rev. A 70, 012306 (2004); Phys. Rev. Lett. 93, 220502 (2004))
Phys. Rev. A 70, 012306 (2004)
single-qubit rotation via multiqubit addressing
J. Joo, et al., PHYSICAL REVIEW A 74, 042344 (2006)
single-qubit rotation via Position-dependent hyperfine splittings
C. Zhang, et al., PHYSICAL REVIEW A 74, 042316 (2006)
the progress of experiments
Imaging of single atoms in an optical lattice
Nelson, K. D., Li, X. & Weiss, D. S. Nature Phys. 3, 556–560 (2007).
effective magnetic
field results from
the atom‘s vector
light shift：
Novel quantum gates via exchange interactions
Anderlini, M. et al.
Controlled exchange
interaction between pairs
of neutral atoms in an
optical lattice. Nature 448,
452–456 (2007).
Science 319, 295–299 (2008).
Trotzky, S. et al. Time-resolved observation and control of superexchange
interactions with ultracold atoms in optical lattices. Science 319, 295–299 (2008).
5. Long decoherence times
How many gate operations could be carried out within a fixed
decoherence time?
“ For the atoms of ultracold gases in optical lattices, Feshbach
resonances can be used to increase the collisional interactions
and thereby speed up gate operations. However, the ‘unitarity
limit’ in scattering theory does not allow the collisional interaction
energy to be increased beyond the on-site vibrational oscillation
frequency, so the lower timescale for a gate operation is typically
a few tens of microseconds.”
“ Much larger interaction energies, and hence faster gate times,
could be achieved by using the electric dipole–dipole interactions
between polar molecules, for example, or Rydberg atoms; in the
latter case, gate times well below the microsecond range are
possible.”
I. Bloch, NATURE|Vol 453|19 June 2008|doi:10.1038.
Quantum Computation(QC) and Quantum
Simulation(QS) with Cold atoms
Standard model for QC
One-Way QC
QS for highly-correlated many body models
R. Raussendorf
H. Briegel
R. Raussendorf and H. J. Briegel, Phys. Rev. Lett. 86, 5188, (2001)
Graph states
Graph States
Given a graph
, the corresponding graph state is
Given a graph
, the corresponding graph state is
Stabilizer code
For Example:
1
X 1Z 2
Z1 X 2 Z3
X 2 Z3
2
3
 L  ( 000  001  010  011  100  101  110  111 )
A Controlled Phase Gate
D. Jaksch, et. al., Entanglement of atoms via cold controlled collisions, Phys.
Rev. Lett. 82, 1975 (1999).
Nature 425, 937 (2003)
Nature 425, 937 (2003)
New Journal of Physics 10 (2008) 023005
New Journal of Physics 10 (2008) 023005
Preparation of decoherence-free cluster states with optical superlattices
V  Vx ( x )  V y ( y )
Vx ( x)  V1x cos 2 (kx)  V2 x cos 2 (2kx)
Vy ( x)  V1 y cos 2 (ky)  V2 y cos 2 (2ky)
Liang Jiang, et. Al., Phys. Rev. A 79, 022309 (2009)
Logical qubit in decoherence-free subspace
Here,
Logical
qubit:
H  S
1,2
V  S
2,3
S
i, j


1

2
i
 S
 S
3,4
4,1
 
j
i

j

0  V
1 
2 1




V
H 

32

Implementing a C-Phase Gate
Quantum Computation(QC) and Quantum
Simulation(QS) with Cold atoms
Standard model for QC
One-Way QC
QS for highly-correlated many body models
Cold Atoms Trapped in Optical Lattices to Simulate
condensed matter physics
D. Jaksch, C. Bruder, C.W.
Gardiner, J.I. Cirac and P.
Zoller (1998)
Advantages as one of promising candidates of quantum simulations
Neutral atoms couple only weakly to the environment, allowing long
storage and coherence times.
So far, cold atoms trapped in optical lattices is the only system in
which a large number of particles can be initialized simultaneously.
Highly controllability
Control of interaction strength with magnetic field (Feshbach
Resonance)
Various geometry of optical lattices
Controllable tunneling rates
Bosons, Fermions, or mixture
Effective highly-correlated many body models
Bose-Hubbard Model
Two-component Bose-Hubbard Model
Fermions in an Optical Lattice
Feshbach resonance -- magnitude
Optical lattice
-- diversity
Experiments: Ketterle, Esslinger etc.
• Weakly interacting fermions in an optical lattice
-- single-band Hubbard model (Hofstetter et al, PRL 2003)
H weak  t  ai a j  u  ai ai ai ai
i, j
i
• Strongly (resonantly) interacting fermions in optical lattice
-- Boson-fermion Hubbard model ??
H strong  H weak  g on  bi ai ai   bibi
i
Stoof, Holland, Zhou, etc., 2005
i
Inadequate!
Strong interaction effects
Why is it inadequate?
H strong  H weak  g on  bi ai ai   bibi
i
i
• Multi-band populations (T.-L. Ho, cond-mat/0507253; 0507255, PRL 2006)
g on  Ebg ~ 
On-site
coupling rate
Band gap

g
b
 pqr ipaiq air
i ; pqr
Different bands
• Off-site collision couplings (L.-M. Duan, PRL 95, 243202,2005)
g off  t
Off-site
coupling rate
Tunneling
rate
g off
Off-site coupling
t
• Starting point: the field Hamiltonian
•Keep all the bands
•Keep the off-site couplings
L.-M. Duan, PRL 95, 243202,2005
• Limiting case 1: atom limit
• Limiting case2: molecule limit
Quantum simulation with polar molecules
A. Micheli, G. K. Brennen and P. Zoller, A toolbox for lattice-spinmodels
with polar molecules, Nature Physics, 2, 341 (2006)
Detection of ultracold atoms
• Time-of-flight imaging
expansion
condensate
  rt  rt 
  k  k 
density
rt  r0  kt / m
Diagonal correlation in momentum space
One can also utilize density-density correlations in the image of an expanding
gas cloud to probe complex many-body states.
Nature Physics, 4, 50 (2008)
Nature Physics, 4, 50 (2008)
Quantum
Computer
Quantum
Simulation
Limits from classical
world
Starting
point
Quantum Communication
 Why long-distance quantum communication is so difficult?

Transmission loss/fidelity of entanglement—decreasing exponentially with
the length of the connecting channel
 Solution: Quantum repeater combining entanglement
swapping and purification [H. Briegel et al., Phys. Rev. Lett. 81, 5932
(1998)]
Atomic-ensemble-based quantum memory
Atomic-ensemble-based quantum memory is used to
transfer the photonic states to the excitation in atomic
internal states so that it can be stored, and after the
storage of a programmable time, it should be possible to
read out the excitation to photons without change of its
quantum state.
M.D. Lukin et al., Phys. Rev. Lett. 84, 4232 (2000); M. Fleischhauer
and M.D. Lukin, Phys. Rev. Lett. 84, 5094 (2000).
Physical implementation of Quantum Repeater:
A Scheme based on atomic ensembles, the DLCZ scheme
[L.-M. Duan et al., Nature 414, 413 (2001)]
The phase stability problem in the DLCZ scheme

In the DLCZ protocol, two entangled pairs are generated in parallel. The
relative phase between the two entangled states has to be stabilized
during the entanglement generation process.
As entanglement generation process is probabilistic. The experiment has to
be repeated many times to ensure that there is a click at the detectors. The two
phases achieved at different runs of the experiments are usually different due to
the path length fluctuations in this time interval.
A robust, fault-tolerant quantum repeater
•a) Local preparation of entanglement (at adjacent nodes) by a linear-optical polarization entangler and then
entanglement swapping
•(b) Entanglement connection
•(c) Linear-optical entanglement purification
B. Zhao, Z.-B.Chen. et al., Phys. Rev. Lett, 98, 240502 (2007); Z.-B.Chen. et al.,
Phys. Rev. A 76, 022329 (2007).
Summary and Outlook
Quantum Computation(QC) and Quantum
Simulation(QS) with Cold atoms
Standard model for QC
One-Way QC
Lowering the temperature
Achieving single-site addressing
QS for highly-correlated many body models
Quantum Communication