Light-Matter Quantum Interface Danish Quantum Optics Center University of Aarhus QuanTOp Niels Bohr Institute Copenhagen University Light-Matter Quantum Interface Eugene Polzik LECTURE 4 IHP Quantum Information Trimester

Quantum memory for light: criteria Memory must be able to store independently prepared states of light The state of light must be mapped onto the memory with the fidelity higher than the fidelity of the best classical recording The memory must be readable B. Julsgaard, J. Sherson, J. Fiurášek , I. Cirac, and E. S. Polzik Nature, 432, 482 (2004); quant-ph/0410072.

Mapping a Quantum State of Light onto Atomic Ensemble Spin Squeezed Atoms The beginning. Complete absorption 1 > 2 > Squeezed Light pulse Proposal: Kuzmich, Mølmer, EP PRL 79, 4782 (1997) 0 > Experiment: Hald, Sørensen, Schori, EP PRL 83, 1319 (1999) Atoms Very inefficient lives only nseconds, but a nice first try…

interaction entangles Our light-atoms interface - the basics …and feedback applied Light pulse – consisting of two modes Strong driving Weak quantum Projection measurement on light can be made… Dipole off-resonant interaction entangles light and atoms or more atomic samples Passes through one…

vertical horizontal Polarization quantum variables – Light x y 45 -45 Polarization – Stokes parameters vertical Propagation direction Linear polarizations Circular polarizations horizontal

Canonical quantum variables for an atomic ensemble: y z x Quantum state (Wigner function)

Decoherence from stray Special coating – 104 collisions Object – gas of spin polarized atoms at room temperature Optical pumping with circular polarized light Decoherence from stray magnetic fields Magnetic Shields Special coating – 104 collisions without spin flips

t Pulse: Canonical quantum variables for light Complementarity : amplitude and phase of light cannot be measured together t Pulse: Various states

Polarization homodyning - measure X (or P) -450 450 l/4 Polarizing Beamsplitter 450/-450 Strong field A(t) x EOM Polarizing cube Quantum field a -> X,P S1

Teleportation in the X,P representation Bell measurement

another idea for (remote) state transfer Today: another idea for (remote) state transfer and its experimental implementation for quantum memory for light Projection measurement X See also work on quantum cloning: J. Fiurasek, N. Cerf, and E.S. Polzik, Phys.Rev.Lett. 93, 180501 (2004)

Implementation: light-to-matter state transfer No prior entanglement necessary squeeze atoms first = C - C F≈80% F→100% B. Julsgaard, J. Sherson, J. Fiurášek , I. Cirac, and E. S. Polzik Nature, 432, 482 (2004); quant-ph/0410072.

These criteria should be met for memory in: Quantum computing with linear operations Quantum buffer for light Quantum Key storage in quantum cryptography More efficient repeaters

Classical benchmark fidelity for transfer of coherent states e.-m. vacuum Atoms Best classical fidelity 50% K. Hammerer, M.M. Wolf, E.S. Polzik, J.I. Cirac, Phys. Rev. Lett. 94,150503 (2005),

Preparation of the input state of light Strong field A(t) Quantum field - X,P x EOM Polarizing cube S1 Vacuum Input quantum field Coherent P Squeezed Polarization state X

Physics behind the Hamiltonian: 1. Polarization rotation of light -450 450 Polarizing Beamsplitter 450/-450 x Polarizing cube Quantum field

Physics behind the Hamiltonian: 2. Dynamic Stark shift of atoms Strong field A(t) Quantum field - a x EOM Polarizing cube y

atoms Entanglement XL Quantum memory – Step 1 - interaction Light rotates atomic spin – Stark shift XL atoms Atomic spin rotates polarization of light – Faraday effect Output light PL Input light Entanglement

light out atoms c XL Quantum memory – Step 2 - measurement + feedback Polarization measurement c light out PL Feedback to spin rotation atoms Compare to the best classical recording Fidelity – > 100% (82% without SS atoms)

Experimental realization of quantum memory for light

B B Memory in rotating spin states y z Atomic Quantum Noise 2,4 2,2 2,0 1,8 1,6 1,4 1,2 Atomic noise power [arb. units] 1,0 0,8 0,6 0,4 0,2 0,0 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0 Atomic density [arb. units]

B B x Memory in rotating spin states - continued z y Atomic Quantum Noise 2,4 2,2 2,0 1,8 1,6 1,4 1,2 Atomic noise power [arb. units] 1,0 0,8 0,6 0,4 0,2 0,0 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0 Atomic density [arb. units]

Encoding the quantum states in frequency sidebands

Memory in atomic Zeeman coherences Cesium Rotating frame spin 4 3 2

x B B z y

Readout Input pulse pulse Magnetic feedback Nature, Nov. 25 (2004) quant-ph/0410072.

Light t Stored state versus Input state: mean amplitudes p X plane read write t output input Y plane Magnetic feedback p / 2 - rotation Xin ~ SZin Pin ~ SYin Light

Atoms Light Stored state: variances Absolute quantum/classical border 3.0 Absolute quantum/classical border Perfect mapping Atoms <P2mem > <X2mem> <X2in> =1/2 <P2in >=1/2 Light

Fidelity of quantum storage State overlap averaged over the set of input states 0.65 0.7 0.75 0.8 0.85 0.9 0.56 0.58 0.62 0.64 0.66 0.68 Coherent states with 0 < n <4 Experiment Best classical mapping F 0.82 0.84 0.86 0.88 0.9 0.54 0.56 0.58 0.62 0.64 Gain Experiment Best classical mapping Coherent states with 0 < n <8

Quantum memory lifetime

Decoherence Limitations Typical estimate of linewidth: G[Hz] = 5 + 0.1*q[deg] + 1.0*P[mW] + 0.5*P[mW]*q[deg] 1-2Hz 3-6Hz 25-40Hz Dominating Working values: Important for entanglement: Atomic/shot ratio (T is time, typical 2ms) Decoherence (retaining the dominating term) up to around 0.5 Theoretical entanglement with no decoherence: Need k2 large and h low, impossible.

Realized by an extra QND Deterministic quantum memory for a light Qubit Initial state of atoms Initial state of atoms coherent squeezed State overlap Input state 63% Fidelity 100% for a qubit input state 78% 90% Realized by an extra QND measurement pulse Qubit fidelity A. Sørensen, NBI

Quantum Memory for Light demonstrated Deterministic Atomic Quantum Memory proposed and demonstrated for coherent states with <n> in the range 0 to 10; lifetime=4msec Fidelity up to 70%, markedly higher than best classical mapping

Spatial array of memory cells Detector array Scalability – an array of dipole traps or solid state implementation – quantum holograms Detector array Spatial array of memory cells I. Sokolov and EP, to be submitted

Future: Inverse Mapping Atoms Light Detector Proposals: Kuzmich, EP. 2001; Kraus, Giedke, Cirac 2001 Y l/4 wave plate Recent advanced proposals: K. Hammerer, K. Mølmer, EP, J.I. Cirac. Phys.Rev. A., 70, 044304 (2004). J. Sherson, K. Mølmer, A.Sørensen, J. Fiurasek, and EP quant-ph/0505170 Atoms Y Light pulse

z x y z y Quantum memory read-out: single pulse in squeezed state Step 1 Exchange y and z components: pass light through l/4 plate and probe along spin-y axis y z Step 2

Light-Atoms Q-interface with cold atoms 6P Cesium clock levels F=4 F=3 D. Oblak C. Alzar, P. Petrov

Memory Summary New state transfer protocol → quantum memory for light Experimental demonstration for coherent states Nature, 432, 482 (2004) Prediction for a qubit state – bridging dicrete and continuous variables State retrieval protocols

Criteria for light-ensemble interface 2-level stable state with long coherence time Initialization: collective coherent spin state (CSS) Coupling of the CSS to light corresponding to high optical density Figure of merit Probe depumping parameter:

Entangled atoms + Entangled light Light/atoms QI exchange Atomic teleportation 3-party entanglement/ Secret sharing Scaling/ solid state implementation Entangled atoms + Entangled light Light/atoms QI exchange Quantum memory for light Color code hard “easy” Distillation by local operations Multi-atom Cat states Continuous variable logic Discrete variable logic

cavity enhanced interaction enhanced phase shift power build-up inside cavity compensate with smaller photon number cold atomic cloud T: mirror transmission a: absorption

Coupling strength of the interface x y z Initial coherent spin state: results in distribution Measurement on light Spin squeezed state Z degree of squeezing in Jz Figure of merit for the quantum interface Duan, Cirac, Zoller, EP PRL (2000)

Figure of merit for the quantum interface Probe scattering parameter:

+ h Spontaneous emission – the fundamental limit 0.3 10 30 50 Single pass interaction degree of entanglement Figure of merit for the quantum interface + h Spontaneous emission probability K. Hamerrer, K. Mølmer, E. S. Polzik, J. I. Cirac. PRA 2004, quant-ph/0312156