Jason Hogan Stanford University

January 28, 2014

Leibniz Universität Hannover

RTG 1729, Lecture 2

Optical lattice launching and delta

kick cooling for atom interferometry

Testing fundamental physics with AI

Some physics motivation for increasing sensitivity

Testing general relativity

• Equivalence principle

• Short range gravity/fifth forces

• Post-Newtonian effects

Gravitational wave astronomy

• Terrestrial and space detectors

Tests of QED

• Photon recoil (alpha measurements)

Tests of quantum mechanics

• Macroscopic superposition states

• Decay of coherence

Large wavepacket separation

4 cm

• Long interferometer time (>2 seconds)

• Large momentum transfer beam splitters (>10 hk)

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)

LMT and Optical Lattice Acceleration

Large momentum transfer

Diabatic

• Sequential Raman/Bragg

• Multi-photon Bragg

General requirements

• Efficient

• Coherent

• Fast

• Minimal phase errors (for interferometry)

Need to transfer momentum to atoms

• Large momentum transfer (LMT) beamsplitters enhance sensitivity:

• Launching atoms in fountains

• Generally moving atoms from one place to another

Adiabatic

• Optical lattice (Bloch oscillations)

• ARP Raman

• Sequential Raman

• N-Photon Bragg

• Sequential 2-Photon Bragg

…

Diabatic LMT processes

…

…

(flip)

Nearby levels limit the Rabi frequency for sequential Bragg

Optical lattice circumvents this speed limit by overlapping several

Bragg transitions in time.

Breakdown of the two-level Bragg picture

“Standing wave” potential moving with velocity

Lattice Depth

Effective Bragg Hamiltonian (with time dependent optical frequencies):

Optical lattice

Optical lattice acceleration:

• Adiabatic evolution of the ground state of the Bragg Hamiltonian

• Atom in a superposition of free space momentum eigenstates

• Fast, efficient momentum transfer

(e.g., frequency chirp)

“Solid State” picture

translation phase

(quasimomentum)

• Energy eigenvalues form band structure

• Adiabatic acceleration: atom stays in ground state as quasimomentum grows

ħΩ = 1.5 ER

See Piek, PRA 55, 2989–3001 (1997).

Lattice acceleration simulation

Lattice Ramp Up Acceleration Lattice Ramp Down

Optical lattice acceleration losses

1) Landau-Zener tunneling

2) Spontaneous emission

Loss probability:

Scattering rate:

Avoided crossing.

Band gap • Diabatic transition to higher band

• Atom tunnels out of lattice

frequency chirp

Combined Loss

• Absorption followed by incoherent scattering

(both beams) 88 g, 13.2 m/s

Can be mitigated using blue detuning

Red vs blue detuning

Ground state lattice eigenstate overlap with laser intensity depends on sign of detuning:

Red detuning

Blue detuning Wavefunction overlap with light decreases with increasing lattice depth

Atoms confined at intensity maxima

Light intensity

Optical lattice launch in the 10 m fountain

Small 1/e2 waist for high intensity:

Lattice launch beams: 1.5 mm

Atom optics beams: 2 cm

Off-axis beam delivery advantages:

• Higher lattice intensity

• No reflection lattice parasite

• Spontaneous emission suppression

(for blue detuning)

Measured launch performance

See also blue vs. red heating (theory): H. Pichler, PRA 82, 063605 (2010).

Lattice launch efficiency preliminary parametric study:

Fraction lost (theory)

• Qualitative correspondence with loss theory (LZ tunneling, spontaneous emission)

• Blue detuning enhances performance

Delta Kick Cooling

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

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

Lattice Solution to Anisotropy

Radial (two-dimensional) expansion

z

x x

Another solution: optical lattice confinement

Lattice Solution to Anisotropy

Lattice turns off -- Expansion in three dimensions

z

x x x

Another solution: optical lattice confinement

Lattice Solution to Anisotropy

Turn off trap

z

x x x x

Another solution: optical lattice confinement

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)

AC Stark Lens

Apply transient optical potential (“Lens beam”) to collimate atom cloud in 2D

Lens beam parameters:

3 mm radial waist, ~3 Watts, 1 THz red detuned, ~30 ms duration (typical)

Lens

beam

Le

ns

2D AC Stark Lens

North

View

West

View

No Lens With Lens

Demonstrated refocusing in 2D

Atom cloud radius <200 microns (resolution limited) after 2.6 seconds drift!

Focusing atom cloud with AC Stark lens

Refocusing lens:

Time

Time

Collimating lens:

Vary effective focal length of AC Stark lens by changing lens pulse duration

• Apply lens near top of fountain (~ 1 s TOF)

• With collimating lens, delta kick theory suggests temperature < 100 pK (!)

Challenge: Measure pK temperature when TOF expansion is small compared to size.

Work ongoing!

Initial application: Relaunch sequence

Lens

beam

Le

ns

Launch Lens Relaunch Detect

• Launched to 9.375 meters

• Relaunched to 6 meters

• 5 seconds total free fall time

• Not possible without lens

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)