Post on 31-Jul-2020
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