February 2007

Cavity QED in the Regime of Strong Coupling with Chip-Based Toroidal Microresonators

Barak Dayan, Takao Aoki, E. Wilcut, A. S. Parkins, W. P. Bowen, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble

California Institute of Technology

February 2007

Cavity QED: Engineering coherent interactionsbetween single atoms and single photons

ω

dVE∫VolumeMode

2||~ω

MHzg 402 ×≈ π

μ40~

The coherent coupling rate

gEdHdipole =⋅=

February 2007

Strong Coupling

VdEdg

00 2ε

ω⋅=⋅=The coherent coupling rate:

1/T

The dissipation rates:

Strong Coupling ：g >> γ, κ, 1/Τ

MicrocavityHigh Finesse

Cold Atoms

February 2007

Cavity QED with Fabry-Perot Resonators

Mirrorsubstrates

MOT

3 mm

February 2007

Cavity QED with Fabry-Perot Resonators

Single Photon Generation On DemandJ. McKeever, A. Boca, D. Boozer, R. Miller, J. Buck, A. Kuzmich, & HJK, Science 303, 1992 (2004)

3 , 4Ω

Cavity QED “by the Numbers”J. McKeever, J. R. Buck, A. D. Boozer & HJK,Phys. Rev. Lett. 93, 143601 (2004)

0.4

0.3

0.2

0.1

0.0

Prob

e Tr

ansm

issi

on

1.00.80.60.40.20.0Time [sec]

0 atoms

1 atom

2 atoms

3 atoms4+ atoms

Photon BlockadeK. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T. E. Northup & HJK, Nature 436, 87 (2005)

2.0

1.5

1.0

0.5

0.0

g yz(2

) (τ)

-1.0 -0.5 0.0 0.5 1.0

τ (μs)

i1(t)

i2(t)APD2

APD1

February 2007

Scalability ?

February 2007

Possible Alternatives

A global perspective –Single atoms coupled to diverse resonators

Spillane et al., PRA 71, 013817 (2005)

Ultra-high-Q toroid microcavity, K. Vahala, Nature 424, 839 (2003)

February 2007

Toroidal Microresonators

Major diameter D = 44 μmMinor diameter d = 6 μm

D

d

February 2007

Toroidal Microresonators for Cavity QED

Cesiumatom

February 2007

Toroidal Microresonators for Cavity QED

D. W. Vernooy, V. S. Ilchenko, H. Mabuchi, E. W. Streed & HJK, Opt. Lett. 23, 247 (1998)

9 108 10 10measured projectedQ Q≈ × → ≥

Coupling to Micro-Toroidal Resonators with Tapered Optical Fibers

S. M. Spillane, T. J. Kippenberg, O. J. Painter, & K. J. Vahala, PRL 91, 043902 (2003)

Ideality ~ 99.97%

Monolithic,

Mass-produced

February 2007

Toroidal Microresonators for Cavity QED

• Quantum channel -transport and distributequantum entanglement

• Quantum node -generate, process, store quantum information

Provide a realistic pathway to quantum networkswith strong coupling and

high intrinsic efficiency for input/output operations

Caltech Quantum Optics Group

H. Jeff Kimble Visitor:A. Scott Parkins

February 2007

Welcome to the Toroids cQED Lab

Micro-toroids -• Professor K. VahalaTobias Kippenberg

Barak Dayan

Liz Wilcut Takao Aoki

A. Scott ParkinsWarwick Bowen

February 2007

The Experiment

Tapered fiber

Probe beam

February 2007

The Experiment

Tapered fiber

Probe beam

February 2007

The Experiment

Probe beam

50/50 splitter SPCM2

SPCM1

February 2007

The Experimental Setup

MOT

Atom Counting

PGC

ProbeScan

(High&LowPower)

Repump

MEMS

February 2007

The Experimental Setup

February 2007

The Experiment

Probe beam

50/50 splitter SPCM2

SPCM1

?

February 2007

Theoretical model for toroidal microcavityPin

κex

κiωωC

Pout

February 2007

Theoretical model for toroidal microcavityPin

κex

κiωωC

Pout

M. Cai et al., PRL 85, 74 (2000)

P out

κex

κex = κi

Critical coupling condition

Pout(ω = ωc) = 0

February 2007

ab

bbaaH CC++ += ωω/

ωωC

X2

Theoretical model for toroidal microcavity

February 2007

ab

( )abbahbbaaH CC++++ +++= ωω/

ωωC

Theoretical model for toroidal microcavity

X2h

February 2007

( ) ( ) BBhAAhH CC++ −++= ωω/

( )2baA +

=

ωωC

2h

Theoretical model for toroidal microcavity

( )2baB −

=B A

February 2007

σσωωω +++ ++= ACC bbaaH /ωωC= ωΑ

X3

ab

Theoretical model for toroidal microcavity

σ

February 2007

( )σσσσ

σσωωω++++

+++++

++++

++++=

bgbgagag

abbahbbaaH

TWTWTWTW

ACC**

/

( ) ikrTWTW ezfgg ,0 ρ=

ab

ωωC

Theoretical model for toroidal microcavity

0TWgh X3

December 2006

( ) ( )( ) ( )BBigAAg

BBhAAhH

BA

ACC++++

+++

+−++

+−++=

σσσσ

σσωωω/

( )( ) )sin(,2

)cos(,20

0

krzfgg

krzfgg

TWB

TWA

ρ

ρ

=

=

ωωC

Theoretical model for toroidal microcavity

02 TWg

B

A

X3

December 2006

( ) ( )( ) ( )BBigAAg

BBhAAhH

BA

ACC++++

+++

+−++

+−++=

σσσσ

σσωωω/

( )( ) )sin(,2

)cos(,20

0

krzfgg

krzfgg

TWB

TWA

ρ

ρ

=

=

ωωC

Theoretical model for toroidal microcavityπmkr ±= 0

B

A

X3

February 2007

2

2σ

σ

−=

+=

AY

AX

ωωC

A

Theoretical model for toroidal microcavity

( )( )( ) BBh

YYgh

XXghH

C

TWC

TWC

+

+

+

−+

−++

++=

ω

ω

ω0

0

2

2/

B XY

02 TWgπmkr ±= 0

B

2h

February 2007

2

2σ

σ

−=

+=

BY

BX

ωωC

B

A

Theoretical model for toroidal microcavity

( )( )( ) YYgh

XXgh

AAhH

TWC

TWC

C

+

+

+

−−+

+−+

+=

0

0

2

2

/

ω

ω

ω

ππ mkr ±= 21

2h

02 TWg

A XY

February 2007

2

2σ

σ

−=

+=

CY

CX

ωωC

A

Theoretical model for toroidal microcavity

( )( )( ) YYg

XXg

DDH

TWC

TWC

C

+

+

+

−+

++

=

0

0

2

2

/

ω

ω

ω

D XY

02 TWgππ mkr ±= 4

1

B

February 2007

Single atom transit

ωωC

Pout

t

Pout (ω = ωC)

Pout

February 2007

Single atom transit

ωωC

Pout

t

Pout (ω = ωC)

Pout

February 2007

Experimental Results: Single Atom Transits

• Critical Coupling

Extinction > 99.5%

without atoms

with atoms

PinPout = 0

Takao Aoki, Barak Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala & H. J. Kimble, Nature 443, 671 (2006)

(24,000 data points)

February 2007

Experimental Results: Single Atom Transits

Histograms of photon counts per 2μs time bin

February 2007

Experimental Results: Single Atom Transits

10 mm

3 mm

Average # of events (C 6) in 1ms

February 2007

Temporal profile of single atom transit

Cross correlation of two SPCMs

February 2007

Observation of single atoms coupled to the cavity

Strong coupling regime?

February 2007

ωωC

Pout

Detuning Dependence of Transit Events

February 2007

Measuring the coherent coupling rate

mg0

February 2007

Measuring the coherent coupling rate

eg0

February 2007

Detuning Dependence of Transit EventsTakao Aoki, Barak Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg,

K. J. Vahala & H. J. Kimble, Nature 443, 671 (2006)

February 2007

Detuning Dependence of Transit EventsTakao Aoki, Barak Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg,

K. J. Vahala & H. J. Kimble, Nature 443, 671 (2006)

February 2007

Detuning Dependence of Transit Events

g0m / 2π = (50 + 12) MHz >> (γ, κ) / 2π = (2.6, 18) MHz

Takao Aoki, Barak Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala & H. J. Kimble, Nature 443, 671 (2006)

February 2007

Detuning Dependence of Transit Events

g0e / 2π = (40 + 10) MHz >> (γ, κ) / 2π = (2.6, 18) MHz

Takao Aoki, Barak Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala & H. J. Kimble, Nature 443, 671 (2006)

February 2007

Summary

• We have observed transits of single atoms through the evanescent field of the microtoroidal cavity.

• From the dependence of single atom transit events on the atom-cavity detunings, we have determined g0

m / 2π = 50 MHz.

• Future plans: Probing the sidebands, Trapping single atoms in the cavity mode

Strong coupling regime