Cavity QED: Quantum Control with Single Atoms and Single ... · Quantum channel: transfer & distribution of quantum entanglement Matter, e.g., atoms (quantum information stored in

Cavity QED: Quantum Control with Single Atomsand Single Photons

Scott Parkins17 April 2008

• 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

Outline

Quantum Networks

Quantum node:generation,processing, & storageof quantuminformation (states)

Quantum channel:transfer &distribution ofquantumentanglement

Matter, e.g., atoms (quantuminformation stored in internal,electronic states)

Light, e.g., single photons(quantum information stored in photon number or polarisation states)

Require deterministic, reversible quantum state transfer betweenmaterial system and light field

Matter-light interface

C. Monroe, “Quantum information processing with atoms and photons,” Nature 424, 839 (2003)

Cavity Quantum Electrodynamics (Cavity QED)

€

σ +

€

σ−2-level atom €

H =ωcava+a +ωatomσ

+σ−

+ g a+σ− +σ +a( )

€

E ~ hωcav Vmode€

g€

2g

|0,0>

|0,1>|1,0>

|1,1>|2,0>

cavity photonnumber

atomic state

|0>

|1>

€

g ~ µ01Eµ01 - atomic transition dipole momentE - electric field per photon

Atom-cavityinteractionHamiltonian

Strong Coupling Cavity QED

Coherent dynamics dominant over dissipative processesγ - atomic spontaneous

emission rateκ- cavity field decay rate

€

g >> κ,γ

Strong dipole transition in opticalcavity of small mode volume, high finesse

• Nonlinear optics with single photons• Strong single-atom effects on cavity response• Controllable manipulation of quantum states

Network Operations Enabled by Cavity QED

(i) Quantum State Transfer: Atom ↔ Field

(ii) Quantum State Transfer: Node ↔ Node

(iii) Conditional Quantum Dynamics

(i) Quantum State Transfer: Atom ↔ Field

€

α 0 + β 1( )atom ⊗ 0 field

→ 0 atom ⊗ α 0 + β 1( )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)

• 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, 193601 (2007)

Recent experiments

Theory

(ii) Quantum State Transfer: Node ↔ Node

€

α 0 + β 1( )atom 1⊗ 0 atom 2 → 0 atom 1 ⊗ α 0 + β 1( )atom 2

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)

(iii) Conditional Quantum Dynamics

€

α v + β h( )photon ⊗0 atom

1 atom

→

α v −β h( )photon ⊗ 0 atom

α v + β h( )photon ⊗ 1 atom

L.-M. Duan & H.J. Kimble, “Scalable photonic quantum computation throughcavity-assisted interactions,” Phys. Rev. Lett. 92, 127902 (2004)

€

0 atom

€

1 atom

Atomic-state-dependent phase shift of h-polarisation

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)• …

Cavity QED with trapped ions• R. Blatt (Innsbruck)• W. Lange (Sussex)• C. Monroe (Maryland)• M. Chapman (Georgia Tech)• …

€

g 2π ~ few ×10 MHz κ 2π ~ few MHz Q ~ 105( )

Typically

New Architectures: Optical Microcavities

K.J. Vahala, “Optical microcavities,” Nature 424, 839 (2003)

• Lithographically fabricated• Integrable with atom chips, scalable networks

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

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 quantumelectrodynamics,” Phys. Rev. Lett. 91, 043902 (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

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, 013817 (2005)

€

g 2π ~ few ×100 MHz κ i 2π <1MHz Q ~ 108−9( )

Microtoroid of major diameter 10-20 microns: near surfaceof toroid

Microtoroidal Resonator - Critical Coupling

€

κex =κexcr = κ i

2 + h2

⇒ TF ΔC = 0( ) = 0

€

aout = ain + 2κex a

bout = bin + 2κex b

€

TF =aout+ aoutain+ ain

Output fields

Critical coupling condition

(destructive interference in forward direction)

Microtoroidal Resonators + Cold Atoms

• Atoms couple to evanescent field of whispering gallery modes, “disrupt” critical coupling condition

Microtoroid Cavity QED - Basic Parameters

€

H = ΔAσ+σ− + ΔC a

+a + b+b( )+ h a+b + b+a( ) + Ep

*a + Epa+( )

+ gtw∗ a+σ− + gtwσ

+a( ) + gtwb+σ− + gtw

∗ σ +b( )

€

ΔA =ωA −ωp , ΔC =ωC −ωp( )

• Atom-field coupling

€

gtw r,x( ) = g0tw r( )eikx

g0tw r( ) ~ e-kr

• Mode-mode coupling h

Probe field driving,frequency ωp

Normal Mode Picture

€

H = ΔAσ+σ− + ΔC + h( )A+A + ΔC − h( )B+B

+12Ep* A + B( ) + Ep A

+ + B+( )[ ]+ gA A+σ− +σ +A( ) − igB B+σ− −σ +B( )

€

A =12a + b( ), B =

12a − b( )

€

gA = g0 cos kx( )

€

gB = g0 sin kx( )

€

g0 = 2g0tw

Define normal mode operators:

Normal modes ↔ standing waves around circumference of toroid

Microtoroid Cavity QED

€

TF =aout+ aoutain+ ain

Level structure (vacuum Rabi splitting) Forwardtransmission

Probe field detuning

€

kx = 0

€

kx = π 4

€

kx = π 2

€

ΔAC = 0( )

Atom-cavity detuning ΔAC

no atom

Microtoroid Cavity QED

Atom-cavity detuning ΔAC

Can use dependence ofTF on ΔAC to determine g0

€

TF =aout+ aoutain+ ain

Observation of Strong Coupling

T. Aoki, B. Dayan, E. Wilcut, W.P. Bowen, SP, T.J. Kippenberg, K.J.Vahala & H.J. Kimble, Nature 443, 671 (2006)€

g0max ≈ 2π ⋅ 50MHz >

κ tot ≈ 2π ⋅18MHzγ⊥ = 2π ⋅ 2.6 MHz

Effect of Increasing Cavity Loss

€

κ tot =κ i +κextcr =κ i + κ i

2 + h2

€

κ tot < g0

€

κ tot ≈ g0

€

κ tot >> g0

Vacuum Rabi splitting

Cavity-enhancedatomic spontaneousemission

“Bad Cavity” Regime

€

κ tot ≈ 2π ⋅165MHz >>g0max ≈ 2π ⋅ 70MHzγ⊥ = 2π ⋅ 2.6 MHz

• Theory: Adiabatic elimination of cavity modes• Effective master equation for atomic density matrix:

€

˙ ρ A = −i HA,ρA[ ] +Γ2

2σ−ρAσ+ −σ +σ−ρA − ρAσ

+σ−( )HA = ′ Δ Aσ

+σ− + Ω0σ+ +Ω0

∗σ−( )

• Cavity-enhanced atomic spontaneous emission rate

€

Γ ~ γ +2g0

2

κ tot= γ 1+ 2C( ), C =

g02

κ totγ

(Caltech ‘07)

single-atom“cooperativity” parameter

Output Fields: Bad Cavity Regime

€

aout = ain + 2κex a → α0 +α−σ−

bout = bin + 2κex b → β0 + β−σ−

€

α0

β0

= coherent amplitudes without atom

Forward/Backward Spectra

Differentazimuthalpositions x

Forward Backward

Centralatomicresonance,width ≈ Γ

€

g0tw 2π = 50 MHz κ i,κext( ) 2π = 75,90( ) MHzh 2π = 50 MHz

A Photon “Turnstile”

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aout →α0 +α−σ−

bout →β0 + β−σ−

• Critical coupling: α0(ΔC ≈ 0) ≈ 0, β0(ΔC ≈ 0) ≠ 0• `1st’ photon transmitted into aout 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 bout

Bad cavity regime

Microtoroid-atom system only transmits photons in theforward direction one-at-a-time

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

Intensity Correlation Functions

€

gF2( ) =

aout+( )2aout2

aout+ aout

2 , gB2( ) =

bout+( )2bout2

bout+ bout

2

antibunching at Δ ≈ 0

bunching at Δ ≈ 0

(probabilities of “simultaneous” photon detections)

€

aout+( )

2aout2 ~ σ +2σ−2 = 0

Experiment (Caltech ‘07)

• Cross correlation ξ12(τ)• ξ12(τ) > ξ12(0) a prima facie observation of nonclassical light

Observation of Antibunching/Turnstile Effect

Dayan, Parkins, Aoki, Kimble, Ostby & Vahala, “A Photon Turnstile DynamicallyRegulated by One Atom,” Science 319, 1062 (2008)

• Analysis of single and joint detections at D1,2 conditioned on single atom transit

€

gF2( ) τ( ) ≈ 1− e−Γt 2( )

2, 1 Γ ≈ 2.8 ns C ~ 5( )

€

2g r r ( )2

κ totγ>1

“Blockade” effect robust, e.g., requires only

In the Future …

• Minimise intrinsic losses κi << κex • Large mode-mode coupling h

⇒ Near-ideal input/output

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

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)

Microtoroid + Atom: Over-Coupled Regime

• Strong over-coupling: κex >> h, κi (κtot ≈ κex)• No atom (α–= β–= 0): strong transmission, small reflection (β0 ≈ 0)• With atom: destructive interference between α0 and α–σ –

⇒ strong reflection, small transmission

€

aout →α0 +α−σ−

bout →β0 + β−σ−

Bad cavity regime

Spectra and Correlations: Over-Coupled Regime

Transmission Reflection

€

TB ΔC = 0( ) ≈ κexκ tot

22C1+ 2C

2

€

κ tot ≈κex

€

C ~ g02

κ totγ>>1

Single atomcooperativity

antibunching in reflected field

… and beyond

• Controlled interactions of photons• Trapping of atoms close to toroid

• Multi-toroid/atom systems

→ Scalable quantum processing on atom chips

Microdisk-Quantum Dot Systems

K. Srinivasan & O. Painter, “Linear and nonlinear optical spectroscopy of astrongly coupled microdisk-quantum dot system,” Nature 450, 862 (2007)

Cast

SP

Barak Dayan, Takao Aoki,

Warwick Bowen (Otago), Elizabeth Wilcut,

Scott Kelber, Daniel Alton, Jeff Kimble,

Eric Ostby, Tobias Kippenberg (Garching),

Kerry Vahala