Cavity QED: Quantum Control with Single Atoms and Single Photons. Scott Parkins 17 April 2008

Transcription

1 Cavity QED: Quantum Control with Single Atoms and Single Photons Scott Parkins 17 April 2008

2 Outline Quantum networks Cavity QED - Strong coupling cavity QED - Network operations enabled by cavity QED Microtoroidal resonators and cold atoms - Cavity QED with microtoroids - Observation of strong coupling - The bad cavity regime - A photon turnstile dynamically regulated by one atom - Future possibilities

3 Quantum Networks Quantum node: generation, processing, & storage of quantum information (states) Quantum channel: transfer & distribution of quantum entanglement Matter, e.g., atoms (quantum information stored in internal, electronic states) Matter-light interface Light, e.g., single photons (quantum information stored in photon number or polarisation states) Require deterministic, reversible quantum state transfer between material system and light field C. Monroe, Quantum information processing with atoms and photons, Nature 424, 839 (2003)

4 Cavity Quantum Electrodynamics (Cavity QED) Atom-cavity interaction Hamiltonian H = ω cav a + a + ω atom σ + σ ( ) + g a + σ + σ + a 1> σ + σ 2-level atom 0> 1,1> 2,0> 2g g ~ µ 01 E µ 01 - atomic transition dipole moment E - electric field per photon E ~ hω cav V mode cavity photon number 0,1> 1,0> 0,0> atomic state g

5 Strong Coupling Cavity QED Strong dipole transition in optical cavity of small mode volume, high finesse g >> κ,γ γ - atomic spontaneous emission rate κ- cavity field decay rate Coherent dynamics dominant over dissipative processes Nonlinear optics with single photons Strong single-atom effects on cavity response Controllable manipulation of quantum states

6 Network Operations Enabled by Cavity QED (i) Quantum State Transfer: Atom Field (ii) Quantum State Transfer: Node Node (iii) Conditional Quantum Dynamics

7 (i) Quantum State Transfer: Atom Field SP, P. Marte, P. Zoller, & H.J. Kimble, Synthesis of arbitrary quantum states via adiabatic transfer of Zeeman coherence, Phys. Rev. Lett. 71, 3095 (1993) Theory ( α 0 + β 1 ) atom 0 field ( ) field 0 atom α 0 + β 1 Recent experiments T. Wilk, S.C. Webster, A. Kuhn, & G. Rempe, Single-atom single-photon quantum interface, Science 317, 488 (2007) A.D. Boozer, A. Boca, R. Miller, T.E. Northup, & H.J. Kimble, Reversible state transfer between light and a single trapped atom, Phys. Rev. Lett. 98, (2007)

8 (ii) Quantum State Transfer: Node Node J.I. Cirac, P. Zoller, H.J. Kimble, & H. Mabuchi, Quantum state transfer and entanglement distribution among distant nodes in a quantum network, Phys. Rev. Lett. 78, 3221 (1997) ( α 0 + β 1 ) atom 1 0 atom 2 0 atom 1 ( α 0 + β 1 ) atom 2

9 (iii) Conditional Quantum Dynamics L.-M. Duan & H.J. Kimble, Scalable photonic quantum computation through cavity-assisted interactions, Phys. Rev. Lett. 92, (2004) 0 atom 1 atom Atomic-state-dependent phase shift of h-polarisation ( α v + β h ) photon 0 atom 1 atom α v β h α v + β h ( ) photon 0 atom ( ) photon 1 atom

10 Experimental Cavity QED With Cold Atoms Cavity QED with cold neutral atoms (Fabry-Perot resonators) H.J. Kimble (Caltech) G. Rempe (MPQ, Garching) M. Chapman (Georgia Tech) D. Stamper-Kurn (Berkeley) D. Meschede (Bonn) L. Orozco (Maryland) g 2π ~ few 10 MHz Typically κ 2π ~ few MHz ( Q ~ 10 5 ) Cavity QED with trapped ions R. Blatt (Innsbruck) W. Lange (Sussex) C. Monroe (Maryland) M. Chapman (Georgia Tech)

11 New Architectures: Optical Microcavities K.J. Vahala, Optical microcavities, Nature 424, 839 (2003) Lithographically fabricated Integrable with atom chips, scalable networks

12 Microtoroidal Resonators Outline: Microtoroidal resonators and fiber tapers - critical coupling Microtoroidal resonators and cold atoms - physical setup, basic parameters - strong coupling cavity QED Experimental observation of strong coupling The bad cavity regime A photon turnstile dynamically regulated by one atom Further possibilities - single photon transistor

13 Microtoroidal Resonators + Fiber Tapers S.M. Spillane, T.J. Kippenberg, O.J. Painter, & K.J. Vahala, Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics, Phys. Rev. Lett. 91, (2003) Coupling through evanescent fields 99.97% fiber-taper to microtoroid coupling efficiency! Readily integrated into quantum networks Ultrahigh Q-factors and small mode volumes

14 Projected Cavity QED Parameters S.M. Spillane, T.J. Kippenberg, K.J. Vahala, W. Goh, E. Wilcut, & H.J. Kimble, Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics, Phys. Rev. A 71, (2005) Microtoroid of major diameter microns: g 2π ~ few 100 MHz κ i 2π <1MHz Q ~ ( ) near surface of toroid

15 Microtoroidal Resonator - Critical Coupling Output fields a out = a in + 2κ ex a b out = b in + 2κ ex b Critical coupling condition cr κ ex = κ ex = κ i 2 + h 2 T F ( Δ C = 0) = 0 (destructive interference in forward direction) T F = a + outa out a + in a in

16 Microtoroidal Resonators + Cold Atoms Atoms couple to evanescent field of whispering gallery modes, disrupt critical coupling condition

17 Microtoroid Cavity QED - Basic Parameters Mode-mode coupling h ( ) ( ) + ( E * p a + E p a + ) ( ) + ( g tw b + σ + g tw σ + b) H = Δ A σ + σ + Δ C a + a + b + b + h a + b + b + a + g tw a + σ + g tw σ + a ( Δ A = ω A ω p, Δ C = ω C ω p ) Atom-field coupling g tw ( r,x) = g tw 0 ( r)e ikx g tw 0 ( r) ~ e -kr Probe field driving, frequency ω p

18 Normal Mode Picture Define normal mode operators: A = 1 ( 2 a + b ), B = 1 ( 2 a b ) H = Δ A σ + σ + ( Δ C + h)a + A + ( Δ C h)b + B [ ( ) + E p ( A + + B + )] E * p A + B + g A ( A + σ + σ + A) ig B ( B + σ σ + B) g A = g 0 cos kx ( ) g B = g 0 sin( kx) g 0 = 2g 0 tw Normal modes standing waves around circumference of toroid

19 Microtoroid Cavity QED Level structure (vacuum Rabi splitting) Forward transmission T F = a + outa out a + in a in kx = 0 kx = π 4 Atom-cavity detuning Δ AC kx = π 2 no atom Probe field detuning Δ AC = 0 ( )

20 Microtoroid Cavity QED T F = a out + a out a in + a in Atom-cavity detuning Δ AC Can use dependence of T F on Δ AC to determine g 0

21 Observation of Strong Coupling g max 0 2π 50 MHz > κ tot 2π 18 MHz γ = 2π 2.6 MHz T. Aoki, B. Dayan, E. Wilcut, W.P. Bowen, SP, T.J. Kippenberg, K.J. Vahala & H.J. Kimble, Nature 443, 671 (2006)

22 Effect of Increasing Cavity Loss cr κ tot = κ i + κ ext = κ i + κ i 2 + h 2 κ tot < g 0 Vacuum Rabi splitting κ tot g 0 κ tot >> g 0 Cavity-enhanced atomic spontaneous emission

23 Bad Cavity Regime κ tot 2π 165 MHz >> g max 0 2π 70 MHz γ = 2π 2.6 MHz (Caltech 07) Theory: Adiabatic elimination of cavity modes Effective master equation for atomic density matrix: ρ A = i[ H A,ρ A ] + Γ ( 2 2σ ρ A σ + σ + σ ρ A ρ A σ + σ ) H A = Δ A σ + σ + ( Ω 0 σ + + Ω 0 σ ) Cavity-enhanced atomic spontaneous emission rate Γ ~ γ + 2g 2 0 κ tot = γ( 1+ 2C), C = g 2 0 κ tot γ single-atom cooperativity parameter

24 Output Fields: Bad Cavity Regime a out = a in + 2κ ex a α 0 + α σ b out = b in + 2κ ex b β 0 + β σ α 0 β 0 = coherent amplitudes without atom

25 Forward/Backward Spectra Forward Backward g tw 0 2π = 50 MHz κ i,κ ext h 2π = 50 MHz ( ) 2π = ( 75,90) MHz Central atomic resonance, width Γ Different azimuthal positions x

26 A Photon Turnstile Bad cavity regime a out α 0 + α σ b out β 0 + β σ Critical coupling: α 0 (Δ C 0) 0, β 0 (Δ C 0) 0 `1st photon transmitted into a out can only originate from atom Emission projects atom into ground state `2nd photon cannot be transmitted until atomic state regresses to steady-state, time scale 1/Γ excess photons `rerouted to b out Microtoroid-atom system only transmits photons in the forward direction one-at-a-time

27 Note: Other photon turnstile devices e.g., J. Kim, O. Benson, H. Kan, & Y. Yamamoto, A single-photon turnstile device, Nature 397, 500 (1999) (semiconductor) K.M. Birnbaum, A. Boca, R. Miller, A.D. Boozer, T.E. Northup, & H.J. Kimble, Photon blockade in an optical cavity with one trapped atom, Nature 436, 87 (2005) Blockade a structural effect due to anharmonicity of energy spectrum for multiple excitations Microtoroid-atom system: blockade regulated dynamically by conditional state of one atom efficient mechanism, insensitive to many experimental imperfections

28 Intensity Correlation Functions ( 2 g ) F = + ( a out ) 2 2 a out 2 a + 2, g B out a out ( ) = + ( b out ) 2 2 b out b + 2 out b out (probabilities of simultaneous photon detections) antibunching at Δ 0 bunching at Δ 0 + ( a out ) 2 2 a out ~ σ +2 σ 2 = 0

29 Experiment (Caltech 07) Cross correlation ξ 12 (τ) ξ 12 (τ) > ξ 12 (0) a prima facie observation of nonclassical light

30 Observation of Antibunching/Turnstile Effect Analysis of single and joint detections at D 1,2 conditioned on single atom transit ( ) g F 2 ( ) 2, 1 Γ 2.8 ns C ~ 5 ( τ) 1 e Γt 2 ( ) Blockade effect robust, e.g., requires only 2g( r ) 2 κ tot γ >1 Dayan, Parkins, Aoki, Kimble, Ostby & Vahala, A Photon Turnstile Dynamically Regulated by One Atom, Science 319, 1062 (2008)

31 In the Future Minimise intrinsic losses κ i << κ ex Large mode-mode coupling h Near-ideal input/output

32 Single Photon Transistor D.E.Chang, A.S. Sorensen, E.A. Demler, & M.D. Lukin, A single-photon transistor using nanoscale surface plasmons, Nature Physics 3, 807 (2007) transmission reflection

33 Single Photon Transistor D.E.Chang, A.S. Sorensen, E.A. Demler, & M.D. Lukin, A single-photon transistor using nanoscale surface plasmons, Nature Physics 3, 807 (2007)

34 Microtoroid + Atom: Over-Coupled Regime Bad cavity regime a out α 0 + α σ b out β 0 + β σ Strong over-coupling: κ ex >> h, κ i (κ tot κ ex ) No atom (α = β = 0): strong transmission, small reflection (β 0 0) With atom: destructive interference between α 0 and α σ strong reflection, small transmission

35 Spectra and Correlations: Over-Coupled Regime Transmission Reflection ( ) κ ex T B Δ C = 0 κ tot 2 2C 1+ 2C 2 κ tot κ ex C ~ g 2 0 κ tot γ >>1 Single atom cooperativity antibunching in reflected field

36 and beyond Controlled interactions of photons Trapping of atoms close to toroid Multi-toroid/atom systems Scalable quantum processing on atom chips

37 Microdisk-Quantum Dot Systems K. Srinivasan & O. Painter, Linear and nonlinear optical spectroscopy of a strongly coupled microdisk-quantum dot system, Nature 450, 862 (2007)

38 Cast SP Barak Dayan, Takao Aoki, Warwick Bowen (Otago), Elizabeth Wilcut, Scott Kelber, Daniel Alton, Jeff Kimble, Eric Ostby, Tobias Kippenberg (Garching), Kerry Vahala