Niels Bohr Institute Copenhagen University Eugene Polzik
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
Spin Squeezed Atoms Very inefficient lives only nseconds, but a nice first try
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
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
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 5.5 0 -.5-5 0. 0. Pulse: + Xˆ L = ( aˆ ( t) + aˆ( t)) dt T T 0 -.5 0.5 5 7.5 0
+ Sˆ = [( A + aˆ) ( A + aˆ) 4 ( A aˆ) + ( A aˆ )] = + A( a + a) = AXˆ -45 0 45 0 Sˆ 3 = APˆ x Strong field A(t) λ/4 Polarizing cube Polarizing Beamsplitter 45 0 /-45 0 Quantum field a -> X,P
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
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
Dipole off-resonant interaction entangles light and atoms Hˆ = asˆ ˆ 3J z Pˆ L Xˆ A
Physics behind the Hamiltonian:. Polarization rotation of light -45 0 45 0 Polarizing Beamsplitter 45 0 /-45 0 x Polarizing cube Quantum field
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
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 ) <
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
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
Material objects deterministically entangled at 0.5 m distance Atom/shot(comp) / PN,00 0,95 0,90 0,85 0,80 0,75 0,70 0 4 6 8 0 4 6 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
What do we want to achieve? Ψ Ψ Atoms Classical approach - measure and write Problem: Cannot measure an unknown state Example: single polarized photon
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
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.
(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/04007. Input pulse Magnetic feedback Readout pulse
Quantum tomography of the collective atomic state (a) (b) - - 0 0.4 0.3 X L 0. -6-4 P L - - - 0 0 0. 0 0.4 0.3 read-out L / -8-6 -4 - X k 0 4 X k read-out L / -6-4 X A - -P A 0 0. 0. 0
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] 8 6 4 0 - -4-6 -8 Gain plot for S y and S z modulation. g F = 0.797 g BA = 0.836 S y modulated S z modulated y = 0.797*x y = 0.836*x -0-8 -6-4 - 0 4 6 8 0 Mean(S y or S z ) [xp-units] P in ~ S Yin X in ~ S Zin
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> =/ -0-8 -6-4 - 0 4 6 8 0 Mean value S y or S z [xp-units]
F Fidelity of quantum storage ( Ψ ) in Ψin out Ψin d Ψin = P ρˆ - State overlap averaged over the set of input states F 0.64 0.6 Coherent states with 0 < n <8 Experiment Experiment 0.68 0.66 0.64 Coherent states with 0 < n <4 0.6 0.58 0.56 0.54 Best classical mapping 0.80.840.860.88 0.9 Gain 0.58 0.56 Best classical mapping 0.650.70.750.80.850.9
Quantum memory lifetime 65 Fidelity versus delay. Calculated for <n> <= 0. 60 Fidelity [%] 55 50 Classical limit 45 Quiet data Extrapolated 40 0 4 6 8 0 6-06-004/mapping.opj Pulse delay [ms]
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
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
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
Interferometry on a pencil-shaped atomic sample - 005 (dipole trap)
Quantum noise limited sensitivity to number of atoms MOT QND MOT QND t Spin noise, ( δφ) [Rad 0-4 ] 5.0 4.0 3.0.0.0 0.0 0.00 0.05 0.0 0.5 0.0 Dc-Phase shift, φ N at [Rad]
Non-destructive measurement of Clock oscillation