cavity qed in the regime of strong coupling with chip-based … · micro-toroids - • professor k....
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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
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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 =⋅=
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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
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February 2007
Cavity QED with Fabry-Perot Resonators
Mirrorsubstrates
MOT
3 mm
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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
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February 2007
Scalability ?
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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)
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February 2007
Toroidal Microresonators
Major diameter D = 44 μmMinor diameter d = 6 μm
D
d
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February 2007
Toroidal Microresonators for Cavity QED
Cesiumatom
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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
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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
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Caltech Quantum Optics Group
H. Jeff Kimble Visitor:A. Scott Parkins
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February 2007
Welcome to the Toroids cQED Lab
Micro-toroids -• Professor K. VahalaTobias Kippenberg
Barak Dayan
Liz Wilcut Takao Aoki
A. Scott ParkinsWarwick Bowen
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February 2007
The Experiment
Tapered fiber
Probe beam
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February 2007
The Experiment
Tapered fiber
Probe beam
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February 2007
The Experiment
Probe beam
50/50 splitter SPCM2
SPCM1
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February 2007
The Experimental Setup
MOT
Atom Counting
PGC
ProbeScan
(High&LowPower)
Repump
MEMS
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February 2007
The Experimental Setup
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February 2007
The Experiment
Probe beam
50/50 splitter SPCM2
SPCM1
?
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February 2007
Theoretical model for toroidal microcavityPin
κex
κiωωC
Pout
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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
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February 2007
ab
bbaaH CC++ += ωω/
ωωC
X2
Theoretical model for toroidal microcavity
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February 2007
ab
( )abbahbbaaH CC++++ +++= ωω/
ωωC
Theoretical model for toroidal microcavity
X2h
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February 2007
( ) ( ) BBhAAhH CC++ −++= ωω/
( )2baA +
=
ωωC
2h
Theoretical model for toroidal microcavity
( )2baB −
=B A
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February 2007
σσωωω +++ ++= ACC bbaaH /ωωC= ωΑ
X3
ab
Theoretical model for toroidal microcavity
σ
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February 2007
( )σσσσ
σσωωω++++
+++++
++++
++++=
bgbgagag
abbahbbaaH
TWTWTWTW
ACC**
/
( ) ikrTWTW ezfgg ,0 ρ=
ab
ωωC
Theoretical model for toroidal microcavity
0TWgh X3
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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
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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
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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
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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
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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
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February 2007
Single atom transit
ωωC
Pout
t
Pout (ω = ωC)
Pout
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February 2007
Single atom transit
ωωC
Pout
t
Pout (ω = ωC)
Pout
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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)
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February 2007
Experimental Results: Single Atom Transits
Histograms of photon counts per 2μs time bin
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February 2007
Experimental Results: Single Atom Transits
10 mm
3 mm
Average # of events (C 6) in 1ms
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February 2007
Temporal profile of single atom transit
Cross correlation of two SPCMs
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February 2007
Observation of single atoms coupled to the cavity
Strong coupling regime?
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February 2007
ωωC
Pout
Detuning Dependence of Transit Events
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February 2007
Measuring the coherent coupling rate
mg0
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February 2007
Measuring the coherent coupling rate
eg0
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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)
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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)
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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)
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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)
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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