Download Atom Interferometry and Precision Tests in Gravitational Physics

Atom Interferometry and
Precision Tests in Gravitational Physics
Lecture II
Calculation of the phase difference between the two arms of an atom
interferometer
• Examples
• Experiments
•
Main references
- A. D. Cronin, J. Schmiedmayer, D. E. Pritchard, Optics and interferometry with atoms and molecules, Rev. Mod. Phys. 81, 1051
(2009).
- C. Cohen-Tannoudji, D. Guery-Odelin, Advances in Atomic Physics: An Overview, World Scientific (2011)
- J. Schmiedmayer, Interferometry with atoms, Lectures at the E. Fermi School on Atom Interferometry, Varenna (2013).
- G. M. Tino, M. A. Kasevich (eds). Atom Interferometry. Proc. International School of Physics ‘Enrico Fermi’, Course
CLXXXVIII, Varenna 2013, SIF and IOS (2014).
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014
In two-slit interference is it possible to
determine which slit the atom passes through?
Discussion between Bohr and Einstein,
Fifth Solvay International Conference on Electrons and Photons, 1927
Einstein: The recoil of the slits’ support B is δp if the particle passes in the upper slit and -δp if the
particle passes in the lower slit.
The path of the particle can be determined by measuring the momentum of the slits’ support.
Bohr: The slits’ support momentum should be known with an uncertainty much smaller than δp.
Because of the uncertainty principle, the spread δx in the position of the support would then be larger
than the separation between the slits so that the interference pattern is washed out.
(Question called “which-path information” or “welcher weg”. See also discussion in terms of
entanglement of particle and apparatus)
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014
Recoiling Beam Splitter
how to build a “light“ beam splitter
Emitting one Photon
one Photon and a mirror
Bragg scattering from a
standing light wave
two classical fields
mirror
The emitted photon has full
information about the path
Information about the path is
erased by the mirror
Diffraction at a standing light wave
= diffraction at a grating (λ/2)
The photon is the ultimate light weight
beam splitter, the path of the atom can
be inferred from the recoil
The photon acts as a beamsplitter
The recoil is taken up by the mirror
The scattered photon is hidden in the
classical light field and has
no information about the path.
from J. Schmiedmayer, E. Fermi School on “Atom Interferometry”, Varenna 2013
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014
Emission of a single photon:
The ultimate light weight beam splitter
Single spontaneous photon generates coherence between matterwaves
J. Tomkovic, et al., Single spontaneous photon as a coherent beamsplitter for
an atomic matter-wave, Nature Physics, 7, 379–382 (2011)
from J. Schmiedmayer, E. Fermi School on “Atom Interferometry”, Varenna 2013
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014
Calculation of the phase difference between
the two arms of an atom interferometer (1)
Reference: Pippa Storey and Claude Cohen-Tannoudji,
The Feynman path integral approach to atomic interferometry.
A tutorial, J. Phys. II France 4, 1999-2027 (1994)
REVIEW OF CLASSICAL LAGRANGIAN DYNAMICS
Lagrangian for a particle
of mass M in a potential V(z)
Canonical momentum
Hamiltonian
Action
Principle of least action. The actual path Γcl taken by a classical particle
is the one for which the action is extremal.
Alternative expression for the classical action
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014
Calculation of the phase difference between
the two arms of an atom interferometer (2)
THE QUANTUM PROPAGATOR
Evolution operator U
Quantum propagator
Amplitude for the particle to arrive
at point zbtb starting from point zata.
Feynman's expression for the quantum propagator
Feynman (1948)
Pippa Storey and Claude Cohen-Tannoudji, The Feynman path integral approach
to atomic interferometry. A tutorial, J. Phys. II France 4, 1999-2027 (1994)
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014
Calculation of the phase difference between
the two arms of an atom interferometer (3)
THE QUANTUM PROPAGATOR FOR QUADRATIC LAGRANGIANS
Quadratic Lagrangian
Free particle
Examples:
Particle in a gravitational field
Particle in a rotating reference frame
Simplified expression for the propagator
=>
In the case of a plane wave incident
=>
∝
To calculate the final wavefunction at a particular position we consider the trajectory of a classical particle whose initial
momentum is po and which passes through that final point. The phase of the final wavefunction is determined by the action
along this classical path and the phase of the wavefunction at the trajectory's initial point.
P. Storey and C. Cohen-Tannoudji, J. Phys. II France 4, 1999 (1994)
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014
Calculation of the phase difference between
the two arms of an atom interferometer (4)
EFFECT OF A PERTURBATION ON THE LAGRANGIAN
Perturbation on the Lagrangian
=>
To first order in ϵ, the phase shift δφ introduced into the final wavefunction by the perturbation
is determined simply by the integral of the perturbation along the unperturbed path.
APPLICATION TO INTERFEROMETRY
Total phase shift between the two arms
=>
introduced by the perturbation
The phase shift introduced by a perturbation on the Lagrangian is determined simply by the integral
of the perturbation around the closed unperturbed path comprising the two arms of the interferometer.
Pippa Storey and Claude Cohen-Tannoudji, The Feynman path integral approach
to atomic interferometry. A tutorial, J. Phys. II France 4, 1999-2027 (1994)
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014
Calculation of the phase difference between
the two arms of an atom interferometer (5)
EXAMPLES IN INTERFEROMETRY (I): FREE PARTICLE
Lagrangian
Classical action
Quantum propagator
Wavefunction at the initial point
(
)
=> Wavefunction at the final point
Pippa Storey and Claude Cohen-Tannoudji, The Feynman path integral approach
to atomic interferometry. A tutorial, J. Phys. II France 4, 1999-2027 (1994)
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014
Calculation of the phase difference between
the two arms of an atom interferometer (6)
EXAMPLES IN INTERFEROMETRY (II): 2-LEVEL ATOM CROSSING A TRAVELLING LASER WAVE
The effect of the laser interaction is to change the atomic
wavefunction by one of the four multiplying factors:
Uij is defined as the transition amplitude from the jth to
the ith internal atomic state, calculated by taking the
coordinate origin to be z1 t1 and the phase φ to be zero.
Ch. J. Bordé, Atomic Interferometry and Laser Spectroscopy,
in Laser Spectroscopy X, World Scientific (1991)
Pippa Storey and Claude Cohen-Tannoudji, The Feynman path integral approach
to atomic interferometry. A tutorial, J. Phys. II France 4, 1999-2027 (1994)
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014
Calculation of the phase difference between
the two arms of an atom interferometer (7)
EXAMPLES IN INTERFEROMETRY (III): PARTICLE IN A GRAVITATIONAL FIELD
Lagrangian
From Lagrange equations =>
=>
=>
Classical action
Momentum
Hamiltonian
Pippa Storey and Claude Cohen-Tannoudji, The Feynman path integral approach
to atomic interferometry. A tutorial, J. Phys. II France 4, 1999-2027 (1994)
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014
Calculation of the phase difference between
the two arms of an atom interferometer (8)
EXAMPLES IN INTERFEROMETRY (IV): ATOM INTERFEROMETRY GRAVIMETER
=0
Raman pulse interferometer
M. Kasevich, S. Chu (1991)
=0
:
Path ACB
Path ADB
=>
=>
P. Storey and C. Cohen-Tannoudji, J. Phys. II France 4, 1999 (1994)
ω is swept continuously to
compensate for Doppler effect.
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014
Stanford atom gravimeter
Resolution: 3x10-9 g after 1 minute
Absolute accuracy: Δg/g<3x10-9
A. Peters, K.Y. Chung and S. Chu, Nature 400, 849 (1999)
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014
Calculation of the phase difference between
the two arms of an atom interferometer (8)
EXAMPLES IN INTERFEROMETRY (V): PARTICLE IN A ROTATING FRAME
Lagrangian for a free particle, in
terms of the coordinates of the
Galilean frame R'
=>
=>
Rotation considered as a perturbation
=>
=>
=>
Pippa Storey and Claude Cohen-Tannoudji, The Feynman path integral approach
to atomic interferometry. A tutorial, J. Phys. II France 4, 1999-2027 (1994)
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014
Comparison with Sagnac effect
in an optical interferometer
=>
Sagnac phase shift
(considering the same area A)
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014
Gyroscope
F. Riehle, Th. Kisters, A. Witte, J. Helmcke, Ch. J. Bordé, Phys. Rev. Lett. 67, 177 (1991)
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014
Stanford/Yale gyroscope
T.L. Gustavson, A. Landragin and M.A. Kasevich, Class. Quantum Grav. 17, 2385 (2000)
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014
SYRTE cold atom gyroscope
50 cm
30 cm
One pair of Raman
lasers switched on 3
times
Detections
Ω
Launching velocity: 2.4 m.s-1
Maximum interaction time : 90 ms
3 rotation axes
2 acceleration axes
Cycling frequency 2Hz
Expected sensitivity (106 at):
• gyroscope : 4 10-8 rad.s-1.Hz-1/2
• accelerometer : 3 10-8 m.s-2.Hz-1/2
Magneto-Optical Traps
B. Canuel et al., Six-Axis Inertial Sensor Using Cold-Atom Interferometry, PRL 97, 010402 (2006)
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014
compact
From M. Kasevich, Stanford University
Talk at the International Workshop on Advances in Precision Tests
and Experimental Gravitation in Space, Firenze, September 2006
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014
Calculation of the phase difference between
the two arms of an atom interferometer (9)
EXAMPLES IN INTERFEROMETRY (VI): AHARONOV-BOHM EFFECTS
Lagrangian for a charged particle
in an electromagnetic field
=>
The scalar Aharonov-Bohm effect
Phase shift introduced between
the two wavepackets by an
electric potential U applied for
a time T
The vector Aharonov-Bohm effect
Phase shift introduced between
the two wavepackets by the
vector potential A
The important features of both the scalar and vector Aharonov-Bohm
effects are: the absence of force on the particle, the topological nature of
the effect, and the fact that the phase shift is global and non-dispersive.
Pippa Storey and Claude Cohen-Tannoudji, The Feynman path integral approach
to atomic interferometry. A tutorial, J. Phys. II France 4, 1999-2027 (1994)
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014
Experiments on topological phases
with neutral atom interferometers
EXAMPLES IN INTERFEROMETRY (VII): TOPOLOGICAL PHASES
topological phase in a matter wave
interferometer operated with a
particle carrying a magnetic dipole if
the interferometer arms encircle a line
of electric charges producing a field E.
Aharonov-Casher topological phase
He-McKellar-Wilkens topological phase
topological phase when a particle
with an electric dipole d propagates in a
magnetic field B
S. Lepoutre, A. Gauguet, G. Trénec, M. Buchner, and J. Vigué,
He-McKellar-Wilkens Topological Phase in Atom Interferometry,
PRL 109, 120404 (2012)
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014
Beam splitters
Alexander D. Cronin, Jörg Schmiedmayer, David E. Pritchard, Optics and
interferometry with atoms and molecules, Rev. Mod. Phys. 81, 1051 (2009).
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014
Multi-photon Bragg diffraction
In multiphoton Bragg diffraction, the atom coherently scatters 2n photons from a pair of antiparallel
laser beams with frequencies ω1 and ω2.
The atom emerges in its original internal quantum state moving with a momentum 2nℏk.
Atom kinetic energy
Match with the energy nℏk(ω1-ω2) lost by the laser field, determines the resonance condition for the
Bragg diffraction order n.
Holger Mueller, Sheng-wey Chiow, Quan Long, Sven Herrmann, Steven Chu,
Atom Interferometry with up to 24-Photon-Momentum-Transfer Beam Splitters,
PRL 100, 180405 (2008)
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014
Precision gravity measurement at µm scale with Bloch
oscillations of Sr atoms in an optical lattice
ν = m g λ /2 h
G. Ferrari, N. Poli, F. Sorrentino, G. M. Tino, Long-Lived Bloch Oscillations with Bosonic Sr Atoms and Application
to Gravity Measurement at the Micrometer Scale, Phys. Rev. Lett. 97, 060402 (2006)
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014
Particle in a periodic potential:Bloch oscillations
periodic potential
Bloch’s theorem
λ/2
with a constant external force F
quasimomentum q [2π/λ]
Bloch oscillations
Quantum theory for electrons in crystal lattices: F. Bloch, Z. Phys. 52, 555 (1929)
Never observed in natural crystals (evidence in artificial superlattices)
Direct observation with Cs atoms: M.Ben Dahan, E.Peik, J.Reichel, Y.Castin, C.Salomon, PRL 76, 4508 (1996)
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014
Bloch oscillations in a vertical optical lattice
Gravity force makes the momentum oscillate
!"#
!$#
−kL
0
+kL
G. Ferrari, N. Poli, F. Sorrentino, G. M. Tino, Long-Lived Bloch Oscillations with Bosonic Sr Atoms and Application
to Gravity Measurement at the Micrometer Scale, Phys. Rev. Lett. 97, 060402 (2006)
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014
N. Poli, F.Y. Wang, M.G. Tarallo, A. Alberti, M. Prevedelli, G.M. Tino,
Phys. Rev. Lett. 106, 038501 (2011)
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014
Large momentum beam-splitters
G.M. Tino, School on Ultracold
Atoms
Precision
Les Houches,
September
2014
G.M. Tino,
“E. and
Fermi”
SchoolMeasurements,
on Atom Interferometry,
Varenna,
July 2013
Lecture by Pierre Cladé
G.M. Tino, School on Ultracold
Atoms
Precision
Les Houches,
September
2014
G.M. Tino,
“E. and
Fermi”
SchoolMeasurements,
on Atom Interferometry,
Varenna,
July 2013
Precision measurement of h/M and α
Stanford: X ≡ Cs σα/α ~ 7 ppb
A.Wicht, J. M. Hensley, E. Sarajlic, S. Chu,
Phys. Scr. 102, 82 (2002).
Berkeley: X ≡ Cs σα/α ~ 2 ppb
S.-Y. Lan, P.-C. Kuan, B. Estey, D. English, J. M. Brown, M. A. Hohensee, H. Muller,
Science 339, 554 (2013).
Paris: X ≡ Rb σα/α ~ 0.6 ppb
R. Bouchendira, P. Cladé, S. Guellati-Khelifa, F. Nez, F. Biraben,
Phys. Rev. Lett. 106, 080801 (2011).
σα/α < 0.1 ppb ?
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014
Search for physics beyond the SM
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014
Atom IFM Experiments
Atomic and Molecular Physics
Electric Polarizability
Ekstrom et al. PRA 51, 3883 (1995)
Insert an interaction region in the interferometer
which allows to ally a constant electric field to one
arm of the interferometer
Applying an electric field E to one arm creates a
phase shift
from J. Schmiedmayer, E. Fermi School on “Atom Interferometry”, Varenna 2013
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014
Coherence Length
Experiment
Ekstrom et al. PRA 51, 3883 (1995)
Coherence length
Na:
λdB = 17 pm
lcoh = 160 pm
Experiment:
• shift the matter wave in one arm of
the interferometer by a potential
• Observe the contrast of the
interference pattern
In the experiment with Na2 molecules or in the experiment with C-60 the coherence length is
smaller than the object !
from J. Schmiedmayer, E. Fermi School on “Atom Interferometry”, Varenna 2013
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014
Refractive Index
In Analogy to Light
Refractive index for matter waves
Refractive index for a Potential V(r):
Refractive index from
(forward-) scattering :
Refractive index: light in matter
matter waves in light
matter waves in matter
Example:
Neutrons in a solid:
Na (v=1000 m/s) in 1 mtorr Ne:
atoms in light
from J. Schmiedmayer, E. Fermi School on “Atom Interferometry”, Varenna 2013
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014
Atom IFM Experiments
Atomic and Molecular Physics
Schmiedmayer et al. PRL 74, 1043 (1995)
Refractive index for
Na matter waves
What can we measure best
from J. Schmiedmayer, E. Fermi School on “Atom Interferometry”, Varenna 2013
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014
Search for electron-proton charge inequality
• Electrostatic, ferromagnetic, diamagnetic levitation
Millikan (1935), Morpurgo (1966-1984), Braginsky (1970), Stover (1967), Rank (1968), LaRue (1979)
• Gas flow
Piccard and Kessler (1925), Hillas & Cranshaw (1960), King (1960)
• Acoustic cavity
Dylla and King (1973)
• Atomic and molecular beams
Hughes (1957), Chamberlain & Hughes (1963), Fraser (1965), Shapiro (1957), Shull (1967)
Present limit
δep< 1x10-21 e
(From G. Carugno and G. Ruoso, 2005)
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014
Proposals to Test Atom Neutrality with Atom Interferometry
δep ~ 10-21 e
C. Champenois, M. Büchner, R. Delhuille, R. Mathevet, C.
Robilliard, C. Rizzo, J. Vigué, Matter Neutrality Test Using a
Mach-Zehnder Interferometer, in The Hydrogen Atom,
Lecture Notes in Physics Vol. 570, Springer (2001)
+/- V
δep ~ 10-25 e
G. Ferrari, G. M. Tino, Measuring the electric charge of
neutral atoms by atom interferometry, INFN Internal Report
(2006)
δep ~ 10-28-10-30 e
A. Arvanitaki, S. Dimopoulos, A. A. Geraci, J. Hogan, M.
Kasevich, How to Test Atom and Neutron Neutrality with
Atom Interferometry, Phys. Rev. Lett. 100, 120407 (2008)
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014
Interferometry
with trapped
atoms
from J. Schmiedmayer, E. Fermi School
on “Atom Interferometry”, Varenna 2013
Atom Chip Review:
R.
FolmanSchool
et al.
Adv.At.Mol.Opt.Phys.
2002
Varenna-Summer
July 2013
J. Schmiedmayer: Lecture 2:
Atom IFM @ Chips
ATOM CHIP
components for atom manipulation
Magnetic interaction
U mag
! !
= "µ ! B
current carrying wires: very versatile, tight confining
micro magnets: strong quiet fields, tighte confinement
+
=
Electric interaction
additional degree of freedom to manipulate atom potentials
together with magnetic traps: state dependent optical elements
Adiabatic Potentials
Couple internal states by RF, MW, optical fields
additional degree of freedom to structure potentials
state dependent guides and traps,
Integration with other techniques
optical lattices (addressable 2-d lattice)
cavity QED
nano-optics, nano electronics
many more ...
from J. Schmiedmayer, E. Fermi School on “Atom Interferometry”, Varenna 2013
I. Bloch
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014
neutral-atom manipulation using integrated
micro-devices
combining the best of two worlds:
•cold neutral atoms - a well
controllable quantum system
• technologies of nano-fabrication,
micro-electronics, micro-optics
ATOM CHIP
Take the tools of quantum optics and
atomic physics and make them robust
and applicable by miniaturizing and
integrating them using the techniques
of nano-fabrication, micro-electronics
and micro-optics.
• create a tool box for building
quantum devices
from J. Schmiedmayer, E. Fermi School on “Atom Interferometry”, Varenna 2013
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014
Beam splitter
splitting the trapped wave function
in a double well
Generic double well potential:
U(x,t) = a(t) x2 + b x4
from J. Schmiedmayer, E. Fermi School on “Atom Interferometry”, Varenna 2013
U. Hohenester et al. PRA 75, 023602 (2007)
J. Ground et al. PRA 79, 021603(R) (2009)
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014
RF and MW induced adiabatic
potentials
create adiabatic dressed state potentials by coupling
electronic ground states of an atom
– coupling between stable states allows to create conservative
potentials even with on resonant radiation
– shaping the potential:
• detuning the states with an external magnetic field
• spatial dependent coupling strength (RF field)
-> allows strong field seeker traps
– coupling is magnetic:
the amplitude and the relative orientation of the RF field and
the detuning field are important
–
–
–
–
first experiment: dressed neutrons:!
E. Muskat et al., PRL 58, 2047 (1987).
first proposal of a MW trap (detuned)!
C. Agosta, et al. PRL. 62, 2361 (1989).
MW experiment (Cs, detuned)!
R. Spreeuw, et al. PRL 72, 3162 (1994).
RF dressed state traps !
!
O. Zobay, B. M. Garraway, PRL 86, 1195 (2001).
(with magnetic field detuning but neglecting polarization)
– RF potentials for thermal Rb atoms:!
Y. Colombe, et al. Europhys. Lett. 67, 593 (2004).
– Full implementation !
!
T. Schumm et al Nature Physics 1, 57 (2005)
from J. Schmiedmayer, E. Fermi School on “Atom Interferometry”, Varenna 2013
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014
Mach-Zehnder
Interferometer for
trapped BEC
T. Berrada, et al., Nat. Comm. 4, 2077 (2013)
from J. Schmiedmayer, E. Fermi School on “Atom Interferometry”, Varenna 2013
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014
Interferometer signal
trapped MZ interferometer
T. Berrada, et al., Nat. Comm. 4, 2077 (2013)
Interferometer signal stays with full contrast even though
thermal coherence length lth << system size!
Physics: the emerging pre-thermalized length scale >> system size
M. Gring, et al., Science 337, 1318 (2012)
-> 1d de-phasing is irrelevant
M. Kuhnert et al. PRL 110, 090405 (2013)
from J. Schmiedmayer, E. Fermi School on “Atom Interferometry”, Varenna 2013
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014
Phase diffusion
T. Berrada, et al., Nat. Comm. 4, 2077 (2013)
Phase diffusion
Uniform distributions
Peaked distributions
Number squeezing
reduces phase diffusion
Castin & Dalibard, PRA 55, 4330 (1997)
Javanainen & Wilkens, PRL 78, 4675 (1997)
from J. Schmiedmayer, E. Fermi School on “Atom Interferometry”, Varenna 2013
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014
Cavity-assisted spin squeezing
Coherent spin state
Spin squeezed state
Exploit QND cavity/probe interactions
to create spin-squeezed input state for
atom interferometry.
Possible >100x gain in sensor
sensitivity.
Squeezing via QND
optical probe
from M. Kasevich - ICAP 2014
Implementation
Homogeneous atom/cavity
coupling allows for free
space read-out.
Lee, et al. Opt. Lett. 2014
from M. Kasevich - ICAP 2014
Squeezed state atom detection noise
π/2 – cavity homodyne readout/squeezing – cavity homodyne readout
17 dB
reduction in
variance
from M. Kasevich - ICAP 2014
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014
G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014