Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi1.pdf · Quantum Optics with...
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Quantum Optics with Propagating Microwaves in Superconducting Circuits I
2015 AMO Summer School
Io-Chun, Hoi
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Outline
1. Introduction to quantum electrical circuits
2. Introduction to superconducting artificial atom
3. Quantum optics with superconducting circuits
4. Single atom scattering
Io-Chun Hoi
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Introduction to quantum electrical circuits
Io-Chun Hoi
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Io-Chun Hoi
Quantum electrical circuits
Coherent superposition states:
Q
Φ
ChargeFlux
Charge on a capacitor: Current or magnetic flux in an inductor:
+1
2( )
+1
2( )
Probabilistic character.
The superposition states collapse when measure.
Properties:
Macrosopic system
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Io-Chun Hoi
Conventional electrical circuits First transistor 1947
Introduced 2007Clock speed >3GHzNumber of transistors820millionManufacturing technology 45nm
Dual-core Intel processor
Basic elements:
Fig. from Intel
Fig. from Intel
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Introduction to superconducting artificial atom
Io-Chun Hoi
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Io-Chun Hoi
Superconducting circuits are like LEGOS
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Basic Elements of Superconducting Circuits
Capacitance Inductance
Io-Chun Hoi
Josephson Junction:Non-disspative nonlinear inductance
LJ L C
Tunnel barrier between two superconductors
Al
Al
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Io-Chun Hoi
Fabrication of Josephson Junction
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Φ
+Q
−Q
U
Io-Chun Hoi
Constructing linear quantum electrical circuits
H = ω(a†a +1
2)
H =Q2
2C+Φ2
2L
H =Q̂2
2C+Φ̂2
2L
ω =1
LC
Classical physics:Quantum mechanics:
ω
Φ̂,Q̂⎡⎣ ⎤⎦ = i
Analogy with a moving particle in a harmonic potential H =
p2
2m+1
2kx2
M. H. Devoret, A. Wallraff, and J. M. Martinis. Superconducting qubits: A short review. http://arxiv.org/abs/cond-mat/0411174v1, 2004.
Quantization
∼ GHz
LCΦ
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-1.0
-0.5
0.0
0.5
1.0
Ener
gy(E
J)
-4 -2 0 2 4Phi (rad)
0
1
2
3U
Io-Chun Hoi
Constructing nonlinear Quantum circuit: Artificial atom
U = −EJ cosφ
φ
LJ =
4eIc cos πΦext
Φ0
⎛
⎝⎜⎞
⎠⎟
Replace linear inductance by Josephson junction(Nonlinear inductance)
Transition become addressable!
Emission spectrum
Frequencyω01ω12
α =ω01 −ω12
Anharmonicity:
C LJ
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kBT << ω << Δ s
How to operate electrical circuits quantum mechanically?
Avoid dissipation
Work at low temperaturesProvide reset of the circuit(Ground state)
Avoid broaden energy levels
Io-Chun Hoi
Superconducting gap energy
T@mKω / 2π ∼ 4 − 8GHz
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Family of superconducting artificial atom
Focus on Cooper Pair Box and Transmon! G. Wendin and V. S. ShumeikoLow Temp. Phys., 33(9):724-744, 2007.
J. Clarke and F. K. Wilhelm. Nature, 453:1031–1042, 2008.
Fig. fromMichel Devoret. Linneaus summer school in quantum engineering. 2010.
Io-Chun Hoi
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4
3
2
1
0
Energy
(Ec)
1.00.80.60.40.20.0ng
EJ/Ec=0.5
|0>
|0>|1>
|1>
1/√2(|0>-|1>)
1/√2(|0>+|1>)
Io-Chun Hoi
Artificial atom I: The Single-Cooper Pair Box
EQ = 4EC =(2e)2
2CΣ
ng = CgVg / (2e)
CΣ = Cg +CJ
But the coherence time is short (few ns)due to charge noise! Y. Nakamura et al. Nature, 398:786–788, 1999.
H = −1
2Echσ z −
1
2EJσ x
Ech = EQ (1− 2ng )
Map to a spin 1/2 particle inmagnetic field.
Depends on external flux
σ z ,σ x :Pauli matrix
EJ / Ec < 1
Coherent oscillations between ground state and excited state in time domain, demonstrated by
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Decoherence of artificial atom
Relaxation rate Pure dephasing rate
Random switching
Enviroment Enviroment
Phase randomization ω01→ω01 + δω01(t)
e− iω01t1 → 0
Γ01 Γϕ
(Effect from the environment)
ω01
Io-Chun Hoi
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CS
Io-Chun Hoi
Artificial atom II: The transmon
25
20
15
10
5
0
Energy
(Ec)
1.00.80.60.40.20.0ng
EJ/Ec=30
Jens Koch et al.
Insensitive to the charge noise
Long coherence time.Physical Review A, 76(4):042319, 2007.
20 < EJ / Ec < 100
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8
6
4
2
0
Energy
(Ec)
1.00.80.60.40.20.0ng
EJ/Ec=0.5
8
6
4
2
0
Energ
y(Ec
)
1.00.80.60.40.20.0ng
EJ/Ec=1
8
6
4
2
0
Energ
y(Ec
)
1.00.80.60.40.20.0ng
EJ/Ec=5
25
20
15
10
5
0
Energy
(Ec)
1.00.80.60.40.20.0ng
EJ/Ec=30
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-1.0
-0.5
0.0
0.5
1.0
Ener
gy(E
J)
-4 -2 0 2 4Phi (rad)
Natural atomOptical photons
Superconducting artificial atom Microwave photons
0
1
2
Io-Chun Hoi
Compare with optical photon, the frequency of microwave photon is 106 less.
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Io-Chun Hoi
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Superconducting circuitsQuantum optics
Microwave photonsOptical photons
Io-Chun Hoi
Comparison of the toolboxes
Detect I, Q
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Io-Chun Hoi
1. Photons and “atom” interaction can be engineered 2. The photons can be guided by waveguides; beam alignment is not needed.
3. Large vacuum field E0,rms 0.2V / m due to small mode volume 4. Standard on-chip fabrication technique 5. Tunable transition energy of the “atom” 6. Mechanical stable
Atom-light interaction on single photon level
Advantages of quantum circuit
dE0
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Quantum optics with superconducting circuits
Io-Chun Hoi
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Io-Chun Hoi
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Io-Chun Hoi
Fig: O. Astafiev, et al. 327, 840 Science (2010)
Resonant scattering
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Incoming light Atom/dipole emits light
Io-Chun Hoi
Resonant scattering in 3D space
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G. Wrigge et al. Nature Phys. 4, 60 (2008). M. Tey et al. Nature Phys. 4, 924 (2008).
The extinction signal is due to interference
Incoming light
Sum
Resonant scattering in 3D spaceAtom/dipole emits light
U. Håkanson
Fig. from
Io-Chun Hoi
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Fully coherent: no transmission, perfect reflection.
Io-Chun Hoi
D.E. Chang et al. Nature Physics 3, 807(2007)
Resonant scattering in 1D waveguide
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Fully coherent: no transmission, perfect reflection.
Io-Chun Hoi
Relaxation dominated by transmission line.O. Astafiev, et al. 327, 840 Science (2010) IoChun, Hoi et al. PRL 107, 073601 (2011)
λ >> d λ ∼ cm d ∼ μm Size of “atom”
Wavelength of EM field
Point like atom/dipole!
Al
Al
D.E. Chang et al. Nature Physics 3, 807(2007)
Resonant scattering in 1D waveguide
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Fully coherent: no transmission, perfect reflection.
Io-Chun Hoi
Relaxation dominated by transmission line.O. Astafiev, et al. 327, 840 Science (2010) IoChun, Hoi et al. PRL 107, 073601 (2011)
λ >> d λ ∼ cm d ∼ μm Size of “atom”
Wavelength of EM field
Point like atom/dipole!
Al
Al
2nm
Fig. from E. Olsson & S. M. Nik
JJ
D.E. Chang et al. Nature Physics 3, 807(2007)
Resonant scattering in 1D waveguide
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CC
CJS
φJ
φ0φ1Lφ2L φ2Rφ1R2LLL0 L0 L0 L0
C0 C0 C0 C0
Quantum circuit model
Io-Chun Hoi
Relaxation rate into 1D transmission line, indicates the strength of coupling!
Γ10ω012 Cc
2Z
4CΣ
CΣ = Cc + CJSZ =
L0C0
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Strong interaction limit:
Fully coherent.
Transmission and reflection
Io-Chun Hoi
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Saturation of transmission
Nonlinear nature of the atom!
Io-Chun Hoi
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Transmission comparing to theory
Io-Chun Hoi
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12
10
8
6
4
2
-140 -135 -130 -125 -120[dBm]
5 6 7 8 910
2 3 4 5 6 7 8
[MHz]
Total scattered BW=10MHz BW=100MHz
Elastic scattered Input field
Output Power(nW)
/ 2πΩ p
Pp
VR
2
VR
2
Ω p/2π
BW
30 MHz 83 MHz 250 MHz
δω p / 2π
ω10
Ω p
Coherent vs Incoherent scattering
I.-C. Hoi et al.
Io-Chun Hoi
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Tunable artificial atom
Φext /Φ0Φext /Φ0
f01
f12
( f12 + f01) / 2
Io-Chun Hoi
Two-Photon Transition
Low powerHigh power
Extract: EJ ,Max = 13GHzEc = 590MHzEJ / Ec = 23
Only two-photon transition occurs!Only 0-1 transition occurs!
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Fully coherent: perfect reflected by the atom.
measure the phase coherent signal.
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Io-Chun Hoi
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Two-Tone Spectroscopy
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Two-Tone Spectroscopy
Io-Chun Hoi
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ω p =ω12
T
1.0
0.8
0.6
0.4
0.2
0.07.47.27.06.86.66.46.2
GHz
Pump @ 7.1GHz Pump off-135dBm -131dBm -127dBm -123dBm -119dBm -115dBm
Io-Chun Hoi
ω p / 2π
Higher level effect
(Low Power)
Anharmonicity: ω12 / 2π = 6.38GHzω10 / 2π = 7.1GHz α =ω01 −ω12 720MHz
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5.2
5.0
4.8
4.6
-140 -130 -120 -110
1.0
0.9
0.8
ω10
Ω p
P01 [dBm]
[GHz]
ωp /2π
Tp,1
Mollow triplet
O. Astafiev, et al. 327, 840 Science (2010)
Io-Chun Hoi
B.R. Mollow, Phys.Rev. 188, 1969 (1969)
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Io-Chun Hoi
T
[dBm] Pc
ωp /2π[GHz]
A. A. Abdumalikov, Jr et al. PRL 104, 193601 (2010)
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Io-Chun Hoi
To be continued…