Quantum Optics with Propagating Microwaves in Superconducting Circuits II

2015 AMO Summer School

Io-Chun, Hoi

Quantum applications

•  The single-photon router

•  The cross-Kerr phase shift

•  The photon-number filter

•  The quantum spectrum analyzer

•  Photon mediated interactions

Quantum network

Outline

Io-Chun Hoi

Resonant scattering in 1D waveguide

Io-Chun Hoi

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

Saturation of transmission

Nonlinear nature of the atom!

Io-Chun Hoi

Io-Chun Hoi

T

[dBm] Pc

ωp /2π[GHz]

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

Io-Chun Hoi

1(R) 2(T)

Probe input Control

1 2

I.-C. Hoi et al. PRL 107, 073601 (2011)

Io-Chun Hoi

By turning on or off the control tone, we can decide which port the input photons go to.

Off

On

Off

PP ,PC

time

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1.0

0.8

0.6

0.4

0.2

3.53.02.52.01.5μs

1.0

0.8

0.6

0.4

0.2

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T

1.0

0.8

0.6

0.4

0.2

3.53.02.52.01.5μs

1.0

0.8

0.6

0.4

0.2

Io-Chun Hoi

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Io-Chun Hoi

0

1

2

ωp

0

1

2

ωp

ωc

I

I

Q

Q

ΔϕP

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0

1

2

ωp

0

1

2

ωp

ωc

I

I

Q

Q

ΔϕP

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1.0

0.9

0.8

0.7

0.6

0.5

0.4

-30-20-10

01020

7.47.27.06.8

ϕ p

ωp /2π [GHz]

[Deg.]

t p

( on )

t p

( off )

Δϕ p

[GHz]ωp /2π

ωpωc

time

Device 1

Δϕ p

[Deg.]

NC � 0.3-4

-2

0

2

4

7.357.307.257.207.15

-140 dBm -127 dBm -117 dBm

Io-Chun Hoi

-30

-25

-20

-15

-10

-5

01.00.80.60.40.20.0

Δϕ p

Device 1Device 2

Nc

[Deg.]

I.-C. Hoi et al.

Io-Chun Hoi

-30

-25

-20

-15

-10

-5

01.00.80.60.40.20.0

Δϕ p

Device 1Device 2

Nc

[Deg.]

I.-C. Hoi et al.

N. Matsuda, et al. (

Io-Chun Hoi

V. Venkataraman, et al. (

Kerr medium

0

1

2

ωp

ωc

δω P

rP , 2

rC , 2

Nc

Device 2

r P,2

r C,2

,

1.0

0.8

0.6

0.4

0.2

0.01.00.80.60.40.20.0

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0

1

2NC

NP

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What is the photon statistics of the scattered field?

Io-Chun Hoi Io-Chun Hoi

Io-Chun Hoi

Intensity-Intensity Correlation

Single photon source Beam splitter

Source

Second-order

correlation function

HBT measurement

Hanbury Brown-TwissNature 177, 27 (1956)

Source

Coherent

state

ESONN 2010 lecture

Photon statistics from second order correlation function

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Photon number filter

Poisson probability distibution

Io-Chun Hoi Io-Chun Hoi

Photon number filter

Antibunching!Bunching!

Poisson probability distibution

Noise temperature of detection chain is about 7K

Noise of two amplifier is uncorrelated.

Covariance

Io-Chun Hoi

Hanbury Brown-Twiss measurement of output state

-30dB-30dB

-10dB

-20dB

-10dB

-20dB

DC Block

BPF

LPF

RT

4.2 K

1 K

50 mK

“Atom”Cc

Amplifier

ωp 1 2

∼

1

3 4

2

Commercial ”beam splitter”

Io-Chun Hoi

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2.42.22.01.81.61.41.21.0

-128 -124 -120

2.4

2.2

2.0

1.8

1.6

1.4

1.2

1.0

-150 -100 -50 0 50 100 150

P -129 dBm -128 dBm -127 dBm -125 dBm

g2 (0)

[dBm]

g2 (τ )

P

τ [ ]ns

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I.-C. Hoi et al.

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a)

Vr

Vin

320 um320 um

b)L

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Single ion: J. Eschner Nature, 413, 495 (2001)

Mirror shapes the modes of the vacuum that couple to atom.

Reflection coefficient:

p

50mK

6.0

5.8

5.6

5.4

5.2

5.0

4.8-0.2 -0.1 0.0 0.1 0.2

1.0

0.9

0.8

0.7

0.6

0.5

1.2

1.0

0.8

0.6

0.4

0.25.555.545.535.52

4.884.864.844.824.80

1.2 MHz 11.8 MHz

/Φ0Φ

[GHz]ωp /2π

p|r |

[GHz]ωp /2π

Γ1 /2π

p|r |

Changing the spontaneous emission rate

Experimental data Weak drive:

Io-Chun Hoi

6.0

5.8

5.6

5.4

5.2

5.0

4.8-0.2 -0.1 0.0 0.1 0.2

1.0

0.9

0.8

0.7

0.6

0.5

1.2

1.0

0.8

0.6

0.4

0.25.555.545.535.52

4.884.864.844.824.80

1.2 MHz 11.8 MHz

/Φ0Φ

[GHz]ωp /2π

p|r |

[GHz]ωp /2π

Γ1 /2π

p|r |

Changing the spontaneous emission rate

Experimental data Weak drive:

Io-Chun Hoi

Atom decoupled from vacuum fluctuations at node.

6.0

5.8

5.6

5.4

5.2

5.0

4.8-0.2 -0.1 0.0 0.1 0.2

1.0

0.9

0.8

0.7

0.6

0.5

1.2

1.0

0.8

0.6

0.4

0.25.555.545.535.52

4.884.864.844.824.80

1.2 MHz 11.8 MHz

/Φ0Φ

[GHz]ωp /2π

p|r |

[GHz]ωp /2π

Γ1 /2π

p|r |

Changing the spontaneous emission rate

Experimental data Weak drive:

Io-Chun Hoi

Atom decoupled from vacuum fluctuations at node.

Io-Chun Hoi

: relaxation rate of bare atom : phase difference between scattered field from the same atom

Spontaneous emission rate as a function of normalized distance

12

10

8

6

4

2

0

0.540.520.500.480.460.44

[MHz]

L /

Γ /2πΓ1 /2π

φ

Io-Chun Hoi

Probing quantum vacuum fluctuations from spontaneous emission rate

k: coupling constant

0.6

0.5

0.4

0.3

0.2

0.1

0.0

0.560.520.480.44

Theory Data

2.0

1.5

1.0

0.5

0.0

0.70.60.50.40.3

Theory Data

[ ]S Mirrorless

vacuumωah

Antinode vacuum

Node vacuum

L/L/

[ ]Sωah

Io-Chun Hoi

Fully coherent: no transmission, perfect reflection.

Io-Chun Hoi

Io-Chun Hoi

Io-Chun Hoi

Io-Chun Hoi

Double-peak split by 15MHz exchange interaction J, mediated by virtual photons.

The photon-number filter ( )

The cross-Kerr phase shift ( )

The single-photon router ( )

The quantum spectrum analyzer (Probing fluctuation)

Summary I

Io-Chun Hoi

Io-Chun Hoi

Io-Chun Hoi

Io-Chun Hoi

R.W. Andrews, et al. Nature Physics 10, 321 (2014) Y. Kubo et al. PRL 105, 140502 (2010)

Conclusion

Io-Chun Hoi

Acknowledgements

Io-Chun Hoi