Lecture #1
Light-Pulse Atom Optics and
Interferometry
Prof. Mark Kasevich
Dept. of Physics and Applied Physics
Stanford University, Stanford CA
Young’s double slit interferometer with atoms
Mlynek, PRL, 1991
Young’s double slit interference fringes
Mlynek, PRL, 1991
1991 Light-pulse atom interferometer
See Borde, 1989
6 mm at 2% contrast
Light-pulse atom interferometry
Pulses of light are used to coherently manipulate atom de
Broglie waves:
Kasevich and Chu, PRL, 1991
Semi-classical approximation
Three contributions to interferometer phase shift:
Propagation
shift:
Laser fields
(Raman
interaction):
Wavepacket
separation at
detection:
For example, Bongs, App. Phys. B, 2006;
with Gen. Rel., Dimopoulos, PRD, 2008.
Graham lectures
Lagrangian
Action evaluation includes rotations (Coriolis,
centrifugal), gravity, and gravity gradient terms:
Trajectory evaluation contains gravity and rotations;
Integrate above expression over trajectories determined by:
See Storey and CCT, 1994 for
perturbative treatment.
Accelerometer phase shifts in long T fountain
Gravity
Coriolis
Timing asymmetry
Curvature, quantum
Gravity gradient
Wavefront
(Tij, gravity gradient; vi, velocity; xi, initial position; α, wavefront
curvature; g, acceleration; T, interrogation time; keff, effective
propagation vector)
T = 1.15 s in 10 m fountain.
Quantum corrections: Dubetsky, PRA (2006)
Reference frames and paths for uniform acceleration
In reference frame co-falling with atoms:
Phase shift due to relative motion of atom with respect to
optical phase fronts
In reference frame anchored to optical fields:
Phase shift due to relative motion of atom with respect to
optical phase fronts*
* Path kinetic term cancels optical shift; has been
as redshift measurement (Mueller)
interpreted
In reference frame anchored to optical fields, integration over
unperturbed trajectories (Storey and CCT, 1994):
Phase shift from path phase
Questions
Can sensitivity be improved with new classes of
atom optics?
Can precision atom interferometric methods be
extended to massive particles?
Can quantum metrology approaches be used to
improve interferometer sensitivity?
How can improved sensitivity be exploited for
technology and fundamental science?
Physical sensitivity limits (10 m apparatus)
Quantum limited accelerometer resolution: ~
7x10-20 g
Assumptions:
1)
Wavepackets (Rb) separated by z = 10
m, for T = 1 sec. For 1 g acceleration:
∆φ ~ mgzT/h ~ 1.3x1011 rad
2)
Signal-to-noise for read-out: SNR ~
105:1 per second.
3)
Resolution to changes in g per shot:
4)
δg ~ 1/(∆φ SNR) ~ 7x10-17 g
106 seconds data collection
Applications?
Gravity wave detection, tests of General Relativity, new
atom charge neutrality tests, tests of QED (photon
recoil measurements), searches for anomalous forces,
geodesy …
Large momentum transfer (LMT) at long T
6 photon recoil
beamsplitter
(sequential Raman)
2T = 2.3 s
Wavepacket
separation ~4 cm
Inferred acceleration
sensitivity
δg
~ 4e-12 g/shot
Dickerson, Hogan, Kovachy, Sugarbaker, unpublished
LMT atom optics
102 photon recoil atom optics
Chiow, Kovachy, PRL, 2011
Sequential Bragg LMT atom optics
Employ sequences of multi-photon Bragg pulses to obtain large
momentum recoil
Sample
interferometer
pulse sequence
(LMT sequences of Raman pulses, McGuirk, PRL, 2000)
Multi-photon Bragg transitions
The frequencies of two fardetuned counter-propagating
beams are tuned to drive multiphoton transitions between two
momentum eigenstates.
We have driven transitions
ranging from 6 and 30 photon
recoils
Initially demonstrated by S.A.
Lee in 90’s.
Where does overall sequence efficiency optimize as function of number of
recoils in each Bragg pulse?
Experiment: 6 photon recoils (!)
Sequential Bragg beamsplitter and mirror
30 photon recoil
momenta (20 cm/s)
beam splitter and
mirror pulses.
5 sequential 6 photon
recoil Bragg pulses
Wavepackets in
coherent
superposition state
Wavepacket separation
of
~1 mm
Beamsplitter
Mirror
High contrast LMT atom interferometers
30 photon
recoil
102 photon
recoil
70% contrast
18% contrast
Interferometer output phase distributions
Interferometer phase
flucutates due to
phase noise on the
Bragg lasers.
(λ/100 fluctuations
lead to 1 rad phase
shifts)
Distribution of
observed shifts has
expected behavior.
18% contrast for 102 hk
Comments
•
Ultra-cold source required for high diffraction efficiency.
–
–
•
Effective optical phase grating periodicity is λ/102
~ 8 nm.
–
–
•
4 nK temperatures used in this work
>99%/hk achieved
effective x-ray photon
stringent demands placed on optical wavefronts
With improved laser source/optics, 1000 hk appears
feasible.
Differential accelerometer
Simultaneous, vertically displaced interferometers
Despite fluctuations in the phase shift of each individual
interferometer, differential phase shift between two interferometers is
constant
False color
images of
interferometer
outputs, 30
photon recoil
Such cancellation is crucial to advanced sensors ( e.g., gravity
gradiometers)
Dual interferometer correlated phase outputs
The two
interferometers
display the
expected (anti-)
correlated phase
shifts.
10 hk Adiabatic Rapid Passage Bragg pulses
Black: ARP
Red: Standard
Use frequency chirped/amplitude shaped pulses to overcome
the limited velocity acceptance of multi-photon Bragg pulses.
Appropriately designed pulses can have 2 photon recoil velocity
acceptance (max. allowed).
Kovachy, et al., PRA 2012
Interferometer pulse efficiency
BEC
Thermal
π pulse
π/2 pulse
Pulse efficiency
Left:
+30 hk
(12 msec
drift time)
Right:
+50 hk
followed by
-50 hk
99.7% transfer efficiency per photon recoil
Interferometer contrast and phase
2T = 10 msec
interferometer contrast:
Interferometer phase as a
function of pulse detuning:
Optical lattice interferometry
Optical lattice manipulations are thought to enable
very large area atom interferometry
Schematic illustration of
lattice atom beam splitter
Analysis: T. Kovachy, J. M. Hogan, D. M. S. Johnson, and M. A.
Kasevich, 0910.3435 (2009), PRA (2009). Lattice interferometry proof-of-concept
Kovachy, Chiow, 2010 unpublished. Poor contrast for
longer hold times.
2296 photon recoil lattice manipulation
Image of atom
cloud after 8.5 m
launch.
99.995% / hk pulse efficiency.
No observable heating.
Enables meter-scale wavepacket
separation which combined with a
beamsplitter pulse?
Coherent
lattice
launch.
Momentum
transfer
quantized
in 2hk
increments.
105 atoms
3 nK (evaporatively cooled)
2.64 sec drift time
m=0 state prep
2296 photon recoil launch
(150 g accel. on launch)
Atomic solitons as massive quasi-particles for AI
Atomic soliton
produced in
hybrid
magnetic/optical
trap with 7Li
Forced
evaporation
produces
stable, ~100
atom, single
solitons
(Medley, submitted)
Soliton center-of-mass wavefunction dynamics (1)
Sequence of images of solitons
(100 atoms in each)
adiabatically (a) or suddenly (b)
released from a tight optical
trap.
Histogram of observed
soliton positions at a 60
msec time of flight
following sudden release
from the trap.
Soliton center-of-mass wavefunction dynamics (2)
Center-mass-wavefunction spreading for single solitons
released from tight traps.
Dashed: Expected
behavior from
Heisenberg uncertainty
principle.
Control: soliton
adiabatically released
from trap.
…. Precursor to soliton
interferometry experiments
Soliton collisions
Sequence of
images
illustrating a
collision between
two solitons.
The initial soliton
phase is not
controlled
between shots.
Multiple collisions
Images after 7
collisions.
~50% of
experimental
trials result in
single (merged)
solitons.
Possibly
illustrates phase
depended
collision
dynamics.