Niels Bohr Institute Copenhagen University. Eugene Polzik

Transcription

1 Niels Bohr Institute Copenhagen University Eugene Polzik

2 Ensemble approach Cavity QED Our alternative program (997 - ): Propagating light pulses + atomic ensembles Energy levels with rf or microwave separation - no need for λ 3 confinement e i δk r = e i δω r > Collective = ensemble quantum variables δω Ground state Hf or Zeeman sublevels Strong coupling to a single atom - qubit Caltech optical λ Paris microwave MPQ optical MPQ, Innsruck ions Stanford - solid state

3 Spin Squeezed Atoms Very inefficient lives only nseconds, but a nice first try

4 Light pulse consisting of two modes and feedback applied Strong driving Weak quantum Passes through one or more atomic samples Dipole off-resonant interaction entangles light and atoms J. Sherson, B. Julsgaard, and E.S. P. to appear in Advances of Atomic Molecular and Optical Physics, 006. available on quant-ph Projection measurement on light can be made

5 Thermal cloud Examples of interfaces discussed in this talk Cold Cs sample BEC F=4 m=3 Cs m=4-0 Rb Atomic entanglement Quantum memory Quasi-spin squeezing Clock applications Atomic cat state generation Least invasive quantum state, quantum correlations measurement

6 0. Quantum variables for light: Coherent state [ X ˆ, Pˆ ] = i Var ( ) ( ) X ˆ = Var Pˆ = Pˆ Xˆ Eˆ Xˆ cos( ω t) + Pˆ sin( ωt) t Pulse: + Xˆ L = ( aˆ ( t) + aˆ( t)) dt T T

7 + Sˆ = [( A + aˆ) ( A + aˆ) 4 ( A aˆ) + ( A aˆ )] = + A( a + a) = AXˆ Sˆ 3 = APˆ x Strong field A(t) λ/4 Polarizing cube Polarizing Beamsplitter 45 0 /-45 0 Quantum field a -> X,P

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9 Complimentary quantum variables for an atomic ensemble: y z x [ ] x z y x y z J J J ij J J ˆ, ˆ = δ δ [ ] x y A x z A A A J J P J J X i P X ˆ, ˆ ˆ ˆ, ˆ = = = x z y Coherent Spin state

10 Object gas of spin polarized atoms at room temperature Optical pumping with circular polarized light Decoherence from stray magnetic fields Magnetic Shields Special coating 0 4 collisions without spin flips

11 Dipole off-resonant interaction entangles light and atoms Hˆ = asˆ ˆ 3J z Pˆ L Xˆ A

12 Physics behind the Hamiltonian:. Polarization rotation of light Polarizing Beamsplitter 45 0 /-45 0 x Polarizing cube Quantum field

13 Physics behind the Hamiltonian:. Dynamic Stark shift of atoms ( A + iaˆ ) ( A iaˆ ) x Strong field A(t) Atoms Quantum field - a iϕ e EOM y Polarizing cube

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15 Einstein-Podolsky-Rosen paradox entanglement; 935 particles entangled in position/momentum L Xˆ, Pˆ X ˆ Xˆ = X ˆ, Pˆ = L Pˆ mv + Pˆ = 0 Simon (000); Duan, Giedke, Cirac, Zoller (000) Necessary and sufficient condition for entanglement δ ( X X ) + δ ( P + P ) <

16 B. Julsgaard, A. Kozhekin and EP, Nature, 43, 400 (00) Experimental long-lived entanglement of two macroscopic objects. x 0 spins in each ensemble y z pins which are more parallel than that are entangled ~ N y x z

17 Stern-Gerlach projection on any axis to x: + J J J Along y,z: ideally no misbalance between heads and tails of the two ensembles, or, at least, less than random misbalance N

18 Material objects deterministically entangled at 0.5 m distance Atom/shot(comp) / PN,00 0,95 0,90 0,85 0,80 0,75 0, Mean Faraday angle [deg] 003/noise.opj Quantum uncertainty J x Niels Bohr Institute December 003 J + J or J + J z z y y

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20 What do we want to achieve? Ψ Ψ Atoms Classical approach - measure and write Problem: Cannot measure an unknown state Example: single polarized photon

21 x Strong field A(t) Polarizing cube Preparation of the input state of light Quantum field - X,P EOM S Vacuum P Coherent Squeezed Pˆ Input quantum field Polarization state X Xˆ

22 Implementation: light-to-matter state transfer No prior entanglement necessary Hˆ = asˆ Jˆ Pˆ Xˆ 3 z L A Pˆ = Pˆ + mem A in A Pˆ in L Xˆ = Xˆ + out L in L Xˆ in A = C Xˆ = mem A Xˆ in A -C = Xˆ squeeze atoms first in L F 00% F 80% B. Julsgaard, J. Sherson, J. Fiurášek, I. Cirac, and E. S. Polzik Nature, 43, 48 (004); quant-ph/04007.

23 (a) (b) J x RF-feedback EOM Detectors Pulse shape Sy/ Sz- modulation J x Local oscillator Lockin amplifier ti:sapph Verdi V8 Pulse sequence Optical pump ms Feedback τ ms π/-rotation Integrator PC Nature, Nov. 5 (004) quant-ph/ Input pulse Magnetic feedback Readout pulse

24 Quantum tomography of the collective atomic state (a) (b) X L P L read-out L / X k 0 4 X k read-out L / -6-4 X A - -P A

25 X plane Y plane read Stored state versus Input state: mean amplitudes output Magnetic feedback π / - rotation write input t Atomic mean value [xp-units] Gain plot for S y and S z modulation. g F = g BA = S y modulated S z modulated y = 0.797*x y = 0.836*x Mean(S y or S z ) [xp-units] P in ~ S Yin X in ~ S Zin

26 Stored state: variances 3.0 Absolute quantum/classical border <P mem >,4 +g =.3 (classically best for n <= 8) <X mem> Atomic noise [PN units],,0,8,6,4,,0 0,8 0,6 PN level σ BA =.88(75)*PN σ F =.643(67)*PN Perfect mapping <P in >=/ 0,4 0, 0,0 <X in> =/ Mean value S y or S z [xp-units]

27 F Fidelity of quantum storage ( Ψ ) in Ψin out Ψin d Ψin = P ρˆ - State overlap averaged over the set of input states F Coherent states with 0 < n <8 Experiment Experiment Coherent states with 0 < n < Best classical mapping Gain Best classical mapping

28 Quantum memory lifetime 65 Fidelity versus delay. Calculated for <n> <= Fidelity [%] Classical limit 45 Quiet data Extrapolated /mapping.opj Pulse delay [ms]

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30 ω ω 0 ω + OPO T=0.03 filter APD Squeezed cavity mode ω 0 delay line Squeezed state: ψ = (tanhς ) coshς n= 0 n n 0 + ς + O( ς ) pulse shaper Atoms homodyning After photon subtraction

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32 CESIUM LEVEL SCHEME 6P /.7 GHz F=4 F=3 6P 3/ 5 MHz 0 MHz 5 MHz F=5 F=4 F=3 F= 85nm J x = N L a L 0 ( σ + σ + ) dz 6S / 9.9 GHz F=4 F=3 J J y z = = N L N L a a L 0 L 0 ( σ ( σ σ σ + ) dz ) dz

33 Spin squeezing with cold atoms (clock transition in Cs) z y x CESIUM LEVEL SCHEME 6P 3/ 5 MHz 0 MHz 5 MHz F=5 F=4 F=3 F= 6P /.7 GHz F=4 F=3 85nm F=4 6S / 9.9 GHz F=3

34 Interferometry on a pencil-shaped atomic sample (dipole trap)

35 Quantum noise limited sensitivity to number of atoms MOT QND MOT QND t Spin noise, ( δφ) [Rad 0-4 ] Dc-Phase shift, φ N at [Rad]

36 Non-destructive measurement of Clock oscillation