precision atom interferometry in a 10 meter tower

Jason Hogan Stanford University

July 20, 2013

Varenna 2013

Precision atom interferometry

in a 10 meter tower

Gravitational wave detection

Technology development for GW detectors

1) Long interrogation time atom interferometry

2) Large wavepacket separation (meter scale)

3) Ultra-cold atom temperatures (picoK)

4) Spatial wavefront noise characterization

5) Laser frequency noise mitigation strategies

Light Pulse Atom Interferometry

• Lasers pulses are atom beamsplitters & mirrors (Raman or Bragg atom optics)

• pulse sequence

• 1D (vertical) atomic fountain

• Atom is freely falling

Apparatus

Ultracold atom source >106 atoms at 50 nK

3e5 at 3 nK

Optical Lattice Launch 13.1 m/s with 2372 photon recoils to 9 m

Atom Interferometry 2 cm 1/e2 radial waist

500 mW total power

Dynamic nrad control of laser angle with precision piezo-actuated stage

Detection Spatially-resolved fluorescence imaging

Two CCD cameras on perpendicular lines of sight

Current demonstrated statistical resolution, ~5 ×10-13 g in 1 hr (87Rb)

Ultra-cold atom source

< 3 nK

Atom cloud imaged after 2.6 seconds free-fall

No apparent heating from lattice launch

BEC source in TOP trap, then diabatic steps in strength of trap to further reduce velocity spread:

Interference at long interrogation time

2T = 2.3 sec Near full contrast 6.7×10-12 g/shot (inferred)

Interference (3 nK cloud)

Wavepacket separation at apex (this data 50 nK)

Dickerson, et al., arXiv:1305.1700 (2013)

Equivalence Principle Test

Co-falling 85Rb and 87Rb ensembles

Evaporatively cool to enforce tight

control over kinematic degrees of

freedom

Statistical sensitivity

dg ~ 10-15 g with 1 month data collection (2 hk atom optics)

Systematic uncertainty

dg/g ~ 10-16 limited by magnetic

field inhomogeneities and gravity

anomalies.

Phase shifts

Observe velocity dependent shifts with spatial imaging

(useful when atoms expand from a point source)

(Tij, gravity gradient; vi, velocity; xi, initial position; a, wavefront curvature; g, acceleration; T, interrogation time; keff, effective

propagation vector)

Gravity

Coriolis

Timing asymmetry

Curvature, quantum

Gravity gradient

Wavefront

Rotation Compensation System

nanopositioner (x3) mirror

< 1 nrad measured precision ~ 1 nrad repeatability Piezoresistive position sensors Rigidly anchored to quiet floor

In-vacuum nanopositioning stage & mirror

Anchor plate

Coarse alignment

Observing velocity-dependent phase

Point Source Interferometry (PSI)

• Long time of flight position-velocity correlation

• Velocity-dependent phase spatial phase gradient

• Spatially resolved detection

“point source” Final size much larger than initial size

Coriolis phase shift


Side view

Expansion from point source:

Coriolis phase shift:

Phase gradient No gradient

F=2

F=1

F=2

F=1

Coriolis phase shift


Side view

Coriolis phase shift:

Phase gradient No gradient

F=2

F=1

F=2

F=1

Expansion from point source:

Spatial fringes versus rotation rate

Interference patterns for rotating platform:


• Spatial frequency increases with increased rotation

• Imaging the fringe pattern improves contrast

Integrated contrast

Fringe contrast

Dual-axis gyroscope

Rotation phase shift:

CC

D2

CCD1

y

x z

CCD1:

CCD2:

Measurement of rotation rate near null rotation operating point.

Ellipse Fits CCD 1 CCD 2

F = 2 (pushed)

F = 1

Dual-axis gyroscope

Rotation phase shift:

CC

D2

CCD1

y

x z

CCD1:

CCD2:

Precision:

Noise Floor:

CCD1

CCD2

Measurement of rotation rate near null rotation operating point.

Phase shear readout (PSR)

g

Tilt angle of final pulse to introduce a phase shear:

Fluorescence image y

Phase shear readout

Tilt angle of final pulse to introduce a phase shear:

Sugarbaker, et al., arXiv:1305.3298 (2013).

Enables simultaneous readout of contrast and phase

-80 µrad 0 µrad 80 µrad -40 µrad 40 µrad

Phase shear readout

g

1 cm

F = 2 (pushed)

F = 1

≈ 4 mm/s

g

1 cm

F = 2 (pushed)

F = 1

Phase Shear Readout (PSR)

Mitigates noise sources:

Pointing jitter and residual rotation readout

Laser wavefront aberration in situ characterization

Single-shot interferometer phase measurement

Phase shear readout

g

1 cm

F = 2 (pushed)

F = 1

≈ 4 mm/s

g

1 cm

F = 2 (pushed)

F = 1

Phase Shear Readout (PSR)

Single-shot interferometer phase measurement

Mitigates noise sources:

Pointing jitter and residual rotation readout

Laser wavefront aberration in situ characterization

Deterministic Phase Extraction

T = 25 ms, 60 μrad misalignment at final pulse

Demonstrate single shot phase using short T interferometer

(less sensitive to seismic noise)

Residual Coriolis

Applied shear Use PSR:

Measuring small phase shears with PSR

Alternate sign of tilt

Trial 1 Trial 2

• Applied shear adds or subtracts from residual Coriolis.

• Analogous to a heterodyne measurement in the time domain.

Can be difficult to measure small phase gradients

Gyrocompass demonstration using phase shear

Use phase shear to determine true North

Vary rotation compensation direction, measure phase shear

0.01 deg resolution in 1 hr.

g

PSR with timing asymmetry

δT fringes discussed earlier in lectures by E. Rasel.

(see H. Müntinga et al., PRL 2013)

-240 µs -160 µs 240 µs 160 µs 0 µs

-160 µs -80 µs 160 µs 80µs 0 µs

Beam tilt + timing asymmetry:

Vertical shear due to asymmetric pulse spacing:

Large momentum transfer atom optics

Chiow, PRL, 2011 102 photon recoil atom optics 0.6 m/sec recoil

LMT power requirements

• Higher Rabi frequency

• Spontaneous emission

• Larger beam diameter

Impacts temperature requirement

(Doppler broadening)

Faster transitions

More pulses/bigger LMT

Intensity uniformity impacts temperature requirement

Wavefront uniformity

Rayleigh range

Need high power lasers:

High power laser at 780 nm

Frequency double 1560 nm fiber amplifiers in PPLN

Coherently combine two 30 W beams @ 1560 nm

S.-w. Chiow et al., Optics Letters 37, 3861 (2012)

High power laser system for LMT in tower

• Dual output, fiber coupled

• Each output fiber gives up to 7 W at 780 nm

• Frequency control provided by phase modulation of seed light before fiber amplifiers

• Amplitude control provided by acousto-optic modulators after doubling crystals

Wavepacket

separation at the top:

4 cm

LMT with long interrogation time

6 ħk sequential Raman in 10 meter tower

2T = 2.3 seconds

Delta kick cooling in a harmonic trap

Harmonic Lens:

At the end of evaporation BEC:

Atom number: ~106 atoms

Cloud diameter: 10 -- 50 μm

Temperature: ~1 μK (from chemical potential)

t = 0 t < tLens t = tLens t = tLens + ε

vx

C. Monroe et al., PRL 65, 1990.

Ammann & Christensen, PRL 78, 1997

Magnetic lens in a harmonic trap

Trap turned off

Magnetic lens in a harmonic trap

Residual velocity is x0ω

Trap turned off

x0

Oscillations in a TOP trap

Absorptive images of atoms released into weak TOP potential (3.7 G & 25 G/cm)

Cloud width oscillations (breathing modes) Radial Vertical

anisotropy

Isotropic turning points in a TOP trap

Radial Vertical

TOP turn-off time

Absorptive images of atoms released into weak TOP potential (3.7 G & 22.9 G/cm)

Cloud width oscillations (breathing modes)

Tune radial and vertical trap frequencies of gravity + TOP trap using field gradient.

Lattice Solution to Anisotropy

Lattice locks atoms vertically

z

x

Another solution: optical lattice confinement


Radial (two-dimensional) expansion

z

x x



Lattice turns off -- Expansion in three dimensions

z

x x x



Turn off trap

z

x x x x


Lattice-Aided Lens Cooling

Lattice turn-off time

Cloud launched to 9 meters

20x colder (50 nK)

5 mm

TOP turn-off time

Radial

Vertical

Extending to colder temperatures

• Delta kick in micro gravity weaker potential, more expansion

• Multiple lens sequences

• Apply additional kick at the fountain turning point?

• Apply optical potential for radial delta kick? (high power AI laser)

Collaborators

NASA GSFC

Babak Saif

Bernard D. Seery

Lee Feinberg

Ritva Keski-Kuha

Stanford Mark Kasevich (PI)

Susannah Dickerson

Alex Sugarbaker

Sheng-wey Chiow

Tim Kovachy

Theory:

Peter Graham

Savas Dimopoulos

Surjeet Rajendran

Former members:

David Johnson Visitors:

Philippe Bouyer (CNRS) Jan Rudolph (Hannover)

Launch using optical lattice

Far-detuned optical standing wave potential

Velocity set by frequency difference

Coherent acceleration (negligible spontaneous emission)

PSR phase reference

• Absolute phase depends on the path of the laser

• Atoms “illuminate” the phase prescribed by the laser sequence

Laser phase:

• Large momentum transfer (LMT) beamsplitters – multiple laser interactions

• Each laser interaction adds a momentum recoil and imprints the laser’s phase

Example LMT interferometer LMT energy level diagram

Phase amplification factor N

LMT Beamsplitters: Coherent Phase Amplification

AI Geometry with Large Rotation Bias

t k

0 1

T 9/4

3T 5/2

5T 9/4

6T 2

Five pulse sequence:

• Beamsplitter momenta chosen to give symmetry and closure

• Insensitive to acceleration + gravity gradients

x

z

precision atom interferometry in a 10 meter tower

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