Supported by NIST, the Packard Foundation, the NSF, ARO. Penn State

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1 Measuring the electron edm using Cs and Rb atoms in optical lattices (and other experiments) Fang Fang Osama Kassis Xiao Li Dr. Karl Nelson Trevor Wenger Josh Albert Dr. Toshiya Kinoshita DSW Penn State Supported by NIST, the Packard Foundation, the NSF, ARO

2 Optical Lattices Calculable, versatile atom traps Far from resonance, no light scattering 1D: I. electron electric dipole moment search precision measurement U AC Intensity 2D: II. 1D systems model manybody system D: λ λ.5 III. Neutral atom quantum computing device

3 I. Features of this atomic electron EDM experiment Cold Cs and Rb atoms in 1D optical lattice traps large trap volume; uniform polarization; long measurement times, >2 s; negligible vxe systematic error no magnetic bias field needed Cs (and Rb) edm enhancement accurately known 114±3, ultimately a precision measurement Cs and Rb similar trap dynamics, but the edm enhancement factor differs by 4.2 We project a 4x1-3 e-cm sensitivity (4x more precise)

4 The EDM Measurement z E E y x ψ = 1 evolve in E 4 4 i t i t h h 3pE exp 3pE exp optically pump, turn on E 1 1 Coherent rf transfer ( ) ( ) ( ) + h A NA cos θ ψ sin θ ψ 3 θ = pe+μb t 4 Final m F = pop. Coherent transfer back 1 -π π B

5 Processing the Atoms 1 cm capture and cool atoms in Yag lattices Oven latticeguided launch 1 1 atoms/s Zeeman slower MOT collect and precool Launch ~2x to fill up the lattices

6 EDM Chamber 8.28 ŷ ˆx ẑ Magnetic Shields 8.28

7 Electric Field Plates: Side View ŷ ˆx ẑ 1 cm Linear CCD Array Linear CCD Array Yag lattice

8 Electric Field Plates: Top View ˆx ŷ ẑ Fiber coupled Optical Molasses Beams AR ITO AR Fiber coupled Linear CCD Array Linear CCD Array ITO + dielectric mirror The trap laser polarization can be made parallel to E minimal trap systematic errors

9 Cancelling B-field Gradients db z /dz measure it directly db z /dx = db x /dz ŷ ˆx ẑ top view 1 cm We can map out the B-field in detail, and cancel it. B-field gradient stability is critical State College has no BART, no Blue Line, no IRT 8 mm side view

10 The Shot Noise Limit Electric Field: 5 V E~1.5 1 cm Coherence time: Atom number (density-limited): Integration time: T~2 s N ~2x1 Cs N ~8x1 Rb τ ~24 hr 8 9 4h δp e = = 6R E NTτ Cs 4x1-3 e -cm For Cs, F=3 Rb h -3 δp e = = 4x1 e -cm R E NTτ For Rb, F=1

11 EDM Measurement We continue to build an experiment to measure the edm of Cs and Rb. We could be taking edm data in 2 years (funding and manpower allowing). Sensitivity at shot noise limit: 4x1-3 e-cm of electron edm (4 times improvement in sensitivity) There are many handles on systematic errors, including: two sets of spatially resolved atoms two alkali species No apparent miracles required If an alkali EDM can be measured, the atomic theory allows for precision determination of the electron EDM

12 II. 1D Bose gases with variable Solutions parameterized by γ>>1 Tonks-Girardeau gas point-like interactions Elliot Lieb and Werner Liniger, 1963: Exact solutions for 1D Bose gases with arbitrary δ(z) interactions m g γ = 2 2 h n 1D 1D h 2 2 H 1D =- + 2 g1dδ z 2m z all all atoms pairs kinetic energy dominates ( ) γ<<1 mean field theory (Thomas-Fermi gas) mean field energy dominates

13 1D Bose atomic gases Maxim Olshanii, 1998: Adaptation to real atoms γ 2 a a 2 3D n 1D a 3D = 3D scattering length 1D waveguide a For 1D: all energies << ħω ; negligible tunneling γ when a 3D, n 1D or a

14 Expansion in the 1D tubes ms TOF in 1D tubes 7 ms 5-25 atoms/tube 17 ms 1-5 tubes up

15 1D energy parameterized by γ Exact theory: Lieb & Liniger, PR 13, 165 (1963); Dunjko, Lorent, Olshanii, PRL 86, 5413 (21) Expt: Kinoshita, Wenger, Weiss, Science 35, 1125 (24) no free parameters Tonks- Girardeau gas.5 1D quasi- BEC weak coupling γ strong coupling

16 Normalized Local Pair Correlations Theory: Gangardt & Shlyapnikov, PRL 9 (141),23 Expt: Kinoshita, Wenger, Weiss, PRL 95 (1946),25 g (2) of the 3D BEC is 1. ( 2) g By photo-association Energy ~2 Pauli exclusion for Bosons R (nm).3 1 γ 3 1 eff

17 Collisions in 1D For identical particles, reflection looks just like transmission! Two-body collisions among distinct bosons cannot change their momentum distribution. But the momentum distribution of an expanding 1D Bose gas does change, in both the TF and TG limits Do 1D Bose gases thermalize? Do 3 or more body collisions matter? Do longitudinal potentials matter?

18 Creating Non-Equilibrium Distributions Long after release of bundles of equilibrium 1D Bose gases, we measure Gaussian distributions Optical thickness -2ħk +2ħk 1 standing wave pulse Position (μm) 2 standing wave pulses Wang, et al., PRL 94, 945 (25) Optical thickness Position (μm)

19 Harmonic Trap Motion x A classical Newton s cradle v We make thousands of parallel quantum Newton s cradles, each with 5-25 oscillating atoms.

20 1D Evolution in a Harmonic Trap ms Position (μm) μm Kinoshita, Wenger, Weiss Nature 44, 9 (26) 1 st cycle average 5 15τ 195 ms 1 3τ 39 ms

21 Negligible Thermalization Projected curves and actual curves at 3 τ or 4 τ Optical thickness (normalized) Optical Thickness A B C Position (μm) Spatial Distribution (μm) γ=18 τ th >39τ >71 refl. γ=3.2 τ th >191τ >96 refl. γ= 1.4 τ th >2τ >23 refl. After dephasing, the 1D gases reach a steady state that is not thermal equilibrium Each atom continues to oscillate with its original amplitude

22 What happens in 3D? Thermalization occurs in ~3 collisions. τ 2 τ 4 τ 9 τ

23 Making 1D gases thermalize: controlled non-integrability Allow tunneling among tubes 1D 2D and 3D behavior Thermalization Rate (per collision) Negligible Thermalization Top view Tunneling Amplitude (pk) We can also add a lattice potential in 1D to compromise integrability

24 Weakly coupled 1D Bose gases do thermalize. We can learn about the transition to chaos in many-body systems. 1D Bose gas experiments Experiments with equilibrium 1D Bose gases across coupling regimes: total energy; cloud lengths, momentum distributions, local pair correlations Experiments agree with the exact 1D Bose gas theory, from Thomas-Fermi to Tonks-Girardeau. We know exactly what s in these experimental systems. They can be used to solve interacting systems with unknown solutions Non-equilibrium 1D Bose gases: the quantum Newton s cradle Independent 1D Bose gases do not thermalize!

25 III. Large Scale Optical Lattice for quantum computing 4-5 μm site spacing ~4 sites Sites can be individually addressed for quantum gates and measurement 5

26 1D Bose gases: Toshiya Kinoshita, Trevor Wenger, Josh Albert Scientists Electron EDM: Fang Fang, Osama Kassis Quantum computing Xiao Li, Karl Nelson

27 Summary Multiple ways to use an optical lattice: Electron EDM measurement Experiments with 1D Bose gases across coupling regimes, in and out of equilibrium A neutral atom quantum computer