Quantum Optics with Propagating Microwaves in Superconducting Circuits I

2015 AMO Summer School

Io-Chun, Hoi

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

Introduction to quantum electrical circuits

Io-Chun Hoi

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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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

Introduction to superconducting artificial atom

Io-Chun Hoi

 

Io-Chun Hoi

Superconducting circuits are like LEGOS

Basic Elements of Superconducting Circuits

Capacitance Inductance

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Josephson Junction:Non-disspative nonlinear inductance

LJ L C

Tunnel barrier between two superconductors

Al

Al

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Fabrication of Josephson Junction

Φ

+Q

−Q

U

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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

-1.0

-0.5

0.0

0.5

1.0

Ener

gy(E

J)

-4 -2 0 2 4Phi (rad)

0

1

2

3U

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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

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

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Superconducting gap energy

T@mKω / 2π ∼ 4 − 8GHz

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.

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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>)

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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

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

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CS

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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

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

-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

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Compare with optical photon, the frequency of microwave photon is 106 less.

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Superconducting circuitsQuantum optics

Microwave photonsOptical photons

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Comparison of the toolboxes

Detect I, Q

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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

Quantum optics with superconducting circuits

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Io-Chun Hoi

Io-Chun Hoi

Fig: O. Astafiev, et al. 327, 840 Science (2010)

Resonant scattering

Incoming light Atom/dipole emits light

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Resonant scattering in 3D space

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

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Fully coherent: no transmission, perfect reflection.

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D.E. Chang et al. Nature Physics 3, 807(2007)

Resonant scattering in 1D waveguide

Fully coherent: no transmission, perfect reflection.

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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

Fully coherent: no transmission, perfect reflection.

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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

CC

CJS

φJ

φ0φ1Lφ2L φ2Rφ1R2LLL0 L0 L0 L0

C0 C0 C0 C0

Quantum circuit model

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Relaxation rate into 1D transmission line, indicates the strength of coupling!

Γ10ω012 Cc

2Z

4CΣ

CΣ = Cc + CJSZ =

L0C0

Strong interaction limit:

Fully coherent.

Transmission and reflection

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Saturation of transmission

Nonlinear nature of the atom!

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Transmission comparing to theory

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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.

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Tunable artificial atom

Φext /Φ0Φext /Φ0

f01

f12

( f12 + f01) / 2

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Two-Photon Transition

Low powerHigh power

Extract: EJ ,Max = 13GHzEc = 590MHzEJ / Ec = 23

Only two-photon transition occurs!Only 0-1 transition occurs!

Fully coherent: perfect reflected by the atom.

measure the phase coherent signal.

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Two-Tone Spectroscopy

Two-Tone Spectroscopy

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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

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ω p / 2π

Higher level effect

(Low Power)

Anharmonicity: ω12 / 2π = 6.38GHzω10 / 2π = 7.1GHz α =ω01 −ω12 720MHz

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)

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B.R. Mollow, Phys.Rev. 188, 1969 (1969)

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T

[dBm] Pc

ωp /2π[GHz]

A. A. Abdumalikov, Jr et al. PRL 104, 193601 (2010)

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To be continued…