Non classical radiation emitted by a Josephson junction

Olivier Parlavecchio, Max Hofheinz, Carles Altimiras, Patrice Roche, Philippe Joyez, Patrice Bertet, Denis Vion, Daniel Esteve & Fabien Portier

Nanoelectronics & Quantronics groups, SPEC, CEA-Saclay, France

Capri, May 1st, 2014

Discussions with: J. Leppäkangas, G. Johansson, J. Ankerhold, P. Millman, T. Coudreau, T. Douce, P. Simon, …

Context: quantum optics of quantum conductors

Atomic Physics: cavity QED

Quantum conductors

atom photons couplingH H H H reservoirs photons couplingH H H H

Excellent understanding (dressed atom formalism...)

Many open questions (properties of the emitted radiation, strong feedback of coupling to electromagnetic modes)

V

r’

t’ t

r

Dynamical Coulomb Blockade of current

(Too) Many degrees of freedom

Normal junction : many possibilities to create e-h pair

Standard environment : many possibilities to create excitation of a given energy

Can we reduce this combinatorial complexity ?

• Supress quasiparticle DOF: use Josephson junction

Simplifying the system

h0

2h0

3h0

4h0

… dc-current only if

02eV nh

2eV 2D

SIS Josephson Junction

"Clean situation"

Normal Junction

• Environment: single electromagnetic mode

V

SIS

†

2( 1/2) J Ji iJE

e eh a aH

The simplest system: model & rates

†( )

,

env r a

i

a

Q

†(/ )2J r aVt ae

2Ji

eT e

0 1 2 3 41E-6

1E-4

0.01

1

Exp

(-r)

rn/n

!

n

The simplest system: model & rates

( ) ( )2

exp( )

( )

2i

n

V e

r r

02J

2 0e

ehν 0 2

E2eVn nh

2eV

ν

n

n!nhν n

Perturbation in EJ gives the transition rates

D. Averin, Y. Nazarov, and A. Odintsov, Physica B 165-166, 945 (1990) H. Pothier, Quantronics, Ph. D. dissertation (1991)

2e

Cooper pair

V

e.g. ZLC=170 W r=0.08

At we get:

02eV hν

hν 2e

at T = 0K :

Josephson junction and resonator

500

0

Z (

W)

Holst et al, PRL 73, 3455 (1994)

Z2=28 Ω Z1=100 Ω

on res: 640 Ω 16 Ω 50 Ω

50 Ω

W 21 125 GHz, 5, 120 /4Q Z h e

1 3 5

Josephson junction and resonator

500

0

Z (

W) Z2=28 Ω Z1=100 Ω

on res: 640 Ω 16 Ω 50 Ω

50 Ω

1 25 GHz

1 3 5

Josephson junction and resonator

500

0

Z (

W) Z2=28 Ω Z1=100 Ω

on res: 640 Ω 16 Ω 50 Ω

50 Ω

ν1 = 25 GHz

Two photon processes weak

because

1 3 5

21 /4Z h e

Detecting both Cooper pairs and photons

~ 20 years later …

Setup

I V

15 mK

4 K

300 K 10M

100

1000

50

P

6 GHz

Φ

00( ) cos( / )J JE E

Quarter-wave resonator

0 160

10

LZ

C

Q

W

25W 135W

50W

1 3 5

0 6 12 18 24 30 360,0

0,5

1,0

1,5

Designed

Lorentzian

Fit

Re

(Z)

[kW

]

f(GHz)

Calibration of the detection impedance

5,0 5,5 6,0 6,5 7,00,0

0,5

1,0

1,5

2,0

Measured

Designed

Re

(Ze

nv)

[kW

]

frequency [GHz]

eV>> 2D, kT, h white shot-noise:

eV

DoS(E)

e-

0 2IIS eI

0IIS TR envZ

RT=18 kΩ

Cooper pair and photon rate match

Cooper pairs

Photons (5-7 GHz)

Second order processes

Photons in mode 0 (5 – 7 GHz)

Cooper pairs

1 3 5 7

1 3 5 7

1

1 3

12

1 5 1 7

1

Engineering the emitted field

V

Za Zb

h

Re Z

ha+hb=2eV

Emission of photons pairs

hb ha

4 5 6 7 80

2

4

ReZ

[k

W]

GHz

Engineering the emitted field

V b=7 GHz a=5 GHz

25 W 66 W 134 W 25 W 80 W 134 W

Basic measurement set-up

Pa

Pb

15 mK 4 K 300 K

5 MW

( )JE

100 W

a

b

50 W

V

50 W

50 W 50 W

Digitizer

τ~1ns

4 5 6 7 8

0

1

2

3

4

5

Measured

Re

Z [k

W]

(GHz)

Designed

Characterization of the environment

data eV>> 2D, kT, h white shot-noise:

eV

DoS(E)

e-

0 2IIS eI

0IIS TR envZ

Spectral density of the emitted radiation

First order peaks

1 CP 1 photon

2eV=h(a+b)

Second order peaks

1 CP 2 photons

Analysing the emitted radiation

What are the properties of the emitted radiation?

a

a

a

P

h

Expectations for Poissonian source of pairs

b

b

b

P

h

2

a a

a a

P P

h h

1a ab b

a b a b

P P

h h

P P

h h

2

b b

b b

P P

h h

a

ba

bh

P

h

P

b

a

Basic measurement set-up

Pa

Pb

15 mK 4 K 300 K

5 MW

( )JE

100 W

a

b

50 W

V

50 W

50 W 50 W

Measuring fluctuations

15 mK 4 K 300 K

5 MW

P1

P2

( )JE

100 W

a

b

V

-3 dB

coupler

Measuring fluctuations

15 mK 4 K 300 K

5 MW

P1

P2

( )JE

100 W

a

b

V

Measuring fluctuations

15 mK 4 K 300 K

5 MW

( )JE

100 W

a

b

V

Pa1

Pa2

1 2

0a a

a a

P P

h h

HBT correlations for Poissonian source

Measuring fluctuations

15 mK 4 K 300 K

5 MW

( )JE

100 W

a

b

V

Pb1

Pb2

HBT correlations for Poissonian source

1 2

0b b

b b

P P

h h

Measuring fluctuations

15 mK 4 K 300 K

5 MW

( )JE

100 W

a

b

V

Pb2

Pa1

2 1 21 1

2 2b b

b b

a a

a a

P

hh

P

h h

P P

Independant partitioning of photons

2

2 2,

11 1,

1

22

a

aa i a

a

bN

ib i b

b b

PP P

hCross

h N

PP

hP

h

Notations

Experimental results

1 2

2 a b

a b

P

h

P

h

Thermal source

0 20 40 60 80 100 120 1400

40

80

120

160

200

Cro

ss [

MH

z]

[MHz]

Cross 5-5 GHz

Cross 5-7 GHz

Cross 7-7 GHz

g(2) functions : non classical radiation

Cauchy-Schwartz inequality

For a classical field:

VIOLATED

g(2) functions: non classical radiation

Leppakangas et al.

Phys. Rev. Lett. 110, 267004

(2013)

(2), ,

) (2(,

)2 (( )( ) 00)0a b b ba a gg g

0 20 40 60 80 1000

4

8

12

16

20

g(2

)

[MHz]

Io-Chun Hoi et al.

Phys. Rev. Lett. 108, 263601

(2012)

g(2) time dependence

-10 -5 0 5 100

2

4

6

8

10

12

g(2

)

[ns]

(2)12 ( )g decays over time scale

of the order of 3 ns, consistent

with the 150 MHz width of the

emitted radiation.

Average photon number in the

resonator 0.06

at Γ=20 MHz

Increasing the resonator’s population

(2)12 ( )gCharacteristic decay time of

increased by 30.

Average photon number in the

resonator 6, if not taking into

account emission bandwidth

narrowing

-200 -150 -100 -50 0 50 100 150 2000

1

2

3

4

5

Cro

ss [

GH

z]

[ns]

g(2) time dependence

-150 -100 -50 0 50 100 1501.00

1.02

1.04

1.06

1.08

1.10

g(2

)

[ns]

Due to the very high emitted

power

(2) 1 2 1 2

12

1 2 1 2

( )( ) 1

h h P Pg

P P h h

(2)12 ( ) 1 1g

Conclusions

• Photon side of Coulomb blockade:

– single and multi photon processes

– spectral properties

– statistical correlations of photons and non classical radiation

– High photon population large increase of coherence time

• Simple, bright photon pair source

• Can work at 100s of GHz -10 -5 0 5 10

0

2

4

6

8

10

12

g(2

)

[ns]

Perspectives

• better characterization of radiation (phase correlations)

• High-population regime: stimulated emission and coherent tunneling?

• Non linear resonators

• Strong coupling regime (Zmode~ few kΩ)

• Possibility to create entangled photon pairs

• Characterize other mesoscopic conductors (QPC, QPC+QHE…)

+

b

a

a

b

ZRe

b

a b

aeV2

Thanks for your attention !

Related work

Arxiv 1403.5578

Forgues, Lupien & Reulet

Correlations Quasiparticles Shot Noise

20 40 60 80 100

0

20

40

60

SP

1P

2/(

h

1h

2)

[MH

z]

[MHz]

Correlations 5-5

Correlations 7-7

eV

DoS(E)

e-

g(2) functions DCB, quasiparticles shot noise

0 20 40 60 80 1000

2

4

6

8

[MHz]

DCB

QP Shot Noise

Naive predictions for HBT correlations

•P(E) therory Poissonian source of photon pairs ( , )ab

1 2 12 0a S

2 21 / /a Ph hP

1 2 12 0b S

21

1

12

2

/ (

)

a

bP a

b

PS S h h

21P PS Spectral density of power fluctuations

The simplest system: cartoon

Cooper pair tunneling only possible if photon emission

Biased under the gap: inelastic tunneling only

DE = 2eV

Only accomodates quantized energy

« photons »

Cooper pair tunneling

h = 2eV 2h = 2eV

3h = 2eV 4h = 2eV

…

V

DoS(E)

V 2e

Cooper pair

Dynamical Coulomb blockade

hole electron photoneV E E E

Energy balance

probability to emit Ephoton into

2

2

photon

Re[ ( )] /

2[ ]( ) Re[ ( )]

Z h e

eP Z E h Z

h h

V V

Delsing et al., PRL 63, 1180 (1989)

( )Z

photon( ):P E ( )Z

NIN

Tunnel

Junction

Ingold & Nazarov,arxiv:0508728 (1992)

e

Geerligs et al., EuroPhys. Lett. 10, 79 (1989)

Celand et al., PRL 64, 1565 (1990)

Measuring phase correlation: Very naïve and classical idea

cos[ ]

cos[ ]

( ) ( )

( ) ( )

( [( ) (

( ) ( )

( ) ( )

( )]

) (

c [(

) (0

os

s 0)

)

co )

b a b

b b

b b

a a a

a a

a a b

b

t

a

a

V t t

V t

V t t

V t V t

t

V t

t

( ) (0)( ]) 0)( )(b ba a

integrate finite BW constraint a+b=2eV/h , but possibility to exchange energy with low frequency modes → width of the first order peak

Dynamical Coulomb blockade

Dynamical Coulomb blockade:

• Effect due to photons

• DC side well established

• But no one has seen the photons

Ingold & Nazarov, arxiv:0508728 (1992)

Measuring photon correlations

V

15 mK

4 K

300 K 100 kW

10 W

50 W

Pa

6 GHz

Φ

Pb

ADC 2 2 , ,ba baPP PP

00( ) cos( / )J JE E

•Poissonian source of photon pairs ( , )ab

/( ) 2b Pba ba P aS S h h

0.00 0.05 0.10 0.150.0

0.1

0.2

0.3

0.4

0.5

Data: 2photon emission regime (2eVDS

~ha +h

b)

Theory: fully correlated

Poissonian emission

of photon pairs (a,

b)

S ab (

GH

z)

(a

b)

0.5 (GHz)

2

Statistical correlation of photon pairs

At large rates: stimulated emission ? Cooper-pair co-tunneling ?

JE

Superpoissonian correlations at large rates

Spectral density of emitted radiation

2eV h 12 ( )eV h

D120 MHz

D600 MHz

Finite spectral width 1st & 2nd peaks widths are different !

Hofheinz et al., PRL 106, 217005 (2011)

Coulomb blockade: multimode analysis Hofheinz et al., PRL 106, 217005 (2011)

2J

24 R(

e2

( ))2

2P e

hVE h

e Z

probability of emitting 1 photon at

probability to emit/absorb the remaining energy 2eV– h in the other modes

Spectral properties multimode dynamics