Quantum teleportation between light and matter Eugene Polzik

Quantum teleportation between light and matter Eugene Polzik Niels Bohr Institute Copenhagen University

Quantum mechanical wonders (second wave) Quantum Information Science • Quantum memory • Communications with absolute security • Computing with unprecedented speed • Teleportation of objects (or at least of their quantum states)

Teleportation a la Star Trek, what’s the problem? Problem: Matter cannot be reversibly converted into light! Question: If matter if not teleported, then what is being transmitted? Answer: information - is what should be transmitted

Problem: electrons, atoms and humans cannot be described as a set of classical bits 00111010111000010101

The more precisely the position is determined, the less precisely the momentum is known in this instant, and vice versa. --Heisenberg 1927 Blegdamsvej 17, Copenhagen Heisenberg in 1927. Minimal symmetric Uncertainty: Bohr’s complementarity principle Perfect measurement of both position and momentum is impossible Noncommuting operators:

Challenge of Quantum Teleportation: transfer two non-commuting operators from one system onto another (Heisenberg picture) equivalent to: Transfer an unknown quantum state from one system onto another (Schördinger picture) Teleportation experiments so far: Light onto light: Innsbruck(97), Rome(97), Caltech(98), Geneva, Tokyo, Canberra… Single ion onto single ion: Boulder (04), Innsbruck (04)

Teleportation cartoon Classical communication Bell measurement Ensemble of 1012 atoms <n> = 0 – 500 photons

Interaction↔entanglement=conservation of energy momentum angular momentum σ+ + σ0 + -1 Single atom/ion Ann Arbor Singlet or e-bit – maximally entangled pair 1 Ensembles of atoms -1 1 Harvard, Caltech, Georgia. Tech -1 0 Copenhagen, Caltech

Einstein-Podolsky-Rosen (EPR) entanglement Canonical operators: position/momentum or real/imaginary parts of the e. -m. field amplitude, etc EPR paradox 1935 • 2 particles entangled in position/momentum • EPR state of light Caltech 1992 • EPR state of atoms Aarhus 2001

Teleportation principle (canonical operators) L. Vaidman Einstein-Podolsky-Rosen entangled state

Canonical operators for light Coherent state: t Pulse:

-450 (t) A d iel l/4 450 Polarizing Beamsplitter 450/-450 f g n o x r t S Polarizing cube Quantum field a -> Y, Q

Quantum tomography – with many copies of a state Coherent state Wigner function Squeezed single photon state QUANTOP 2006

Canonical quantum variables for an atomic ensemble: x y z Quantum state (Wigner function) 3 4

Light modes and atomic levels Orthogonally polarized Teleported operators – of quantum mode Strong field 3 4 Extra benefit: homodyne measurements on quantum mode carried at beatnote frequency Ω

Atoms: ground state Caesium Zeeman sublevels Rotating frame spin Atomic operators 3 4

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

Quantum Noise of Atomic Spin –

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

October 5, 2006 J. Sherson, H. Krauter, R. Olsson, B. Julsgaard, K. Hammerer, I. Cirac, and E. Polzik, Nature 443, 557 (2006).

Teleportation of light onto a macroscopic atomic sample Atoms – target object of teleportation Pulse to be teleported <n>=0– 200 photons

Off-resonant interaction entangles light and atoms 6 P 3/2 D = 800 MHz Upper sideband is teleported 6 S 1/2 W = 0. 3 MHz + magnetic field

Entanglement via forward scattering of light 4 Atoms

Addition of a magnetic field couples light to rotating spin states y z Atomic Quantum Noise 2, 4 2, 2 2, 0 Atomic noise power [arb. units] 1, 8 1, 6 1, 4 1, 2 1, 0 0, 8 0, 6 0, 4 0, 2 0, 0 0, 2 0, 4 0, 6 0, 8 Atomic density [arb. units] 1, 0 1, 2 1, 4 1, 6 1, 8 2, 0

-450 l/4 450 Polarizing Beamsplitter 450/-450

q y

322 k. Hz RF field Magnetic shields

Teleportation experiment Teleported operators: pulse sequence pump 4 ms feedback 2 ms entangling+ verifying Bell measurement

XA=Jz Mean values of operators are transferred PA=Jy Atomic variances are below a critical value

Teleportation of coherent state n ≈ 500

Teleportation of a vacuum state of light Teleported state readout determines atomic variance Input state readout

Teleportation of a coherent state, n ≈ 5

Raw data: atomic state for <n>=5 input photonic state Reconstructed teleported state, F=0. 58± 0. 02

Experimental quantum fidelity versus best classical case Upper bound on <n> ≈ 1000 – due to gain instability F quantum F classical = Anticipated qubit fidelity: Optimal gain Fqubit =72% (with feasible imperfections)

• Teleportation between two mesoscopic objects of different nature – a photonic pulse and an atomic ensemble demonstrated • Distance 0. 5 meter, can be increased (limited mainly by propagation losses) • Extention to qubit teleportation possible • Fidelity can approach 100% with more sophisticated measurement procedure plus using squeezed light as a probe J. Sherson, H. Krauter, R. K. Olsson, B. Julsgaard, K. Hammerer, I. Cirac, and ESP; quant-ph/0605095 , Nature, October 5, 2006

Outlook June 2001 Scientists teleport two different objects POSTED: 1113 GMT (1913 HKT), October 5, 2006 First Teleportation Between Light and Matter J. Sherson, H. Krauter, R. K. Olsson, B. Julsgaard, K. Hammerer, I. Cirac, and ESP; quant-ph/0605095 , Nature, October 5, 2006 Wed Oct 4, 1: 06 PM ET LONDON (Reuters) Quantum information teleported from light to matter

NBI - QUANTOP 2006