josephson-based parametric amplifiers … parametric amplifiers for quantum measurements applied...

JOSEPHSON-BASED PARAMETRICAMPLIFIERS

FOR QUANTUM MEASUREMENTS

Applied Physics and Physics, Yale University

N. BERGEAL (ESPCI Paris)F. SCHACKERT*A. KAMAL B. HUARD (ENS Paris)A. MARBLESTONE

R. VIJAY (U.C.Berkeley)I. SIDDIQI (U.C.Berkeley)C. RIGETTIM. METCALFEV. MANUCHARIAN*

N. MASLUKM. BRINKK. GEERLINGSL. FRUNZIOM. D.

Heraeus445Nov 09

Acknowledgments: R. Schoelkopf, S. Girvin, D. Prober

W.M. KECK

LABQUAN RONICSUM – MECHANICAL

ELEC

* see poster

OUTLINE

1. Introduction and motivation

2. Basic concepts of quantum signal description

3. Degenerate vs non-degenerate parametric amplifiers

4. Amplifier based on Josephson ring modulator

5. Squeezing

6. Link with microwave SQUID, conclusions and perspectives

RADIO-FREQUENCYPHENOMENON (MHz-GHz)

Deterministic signal

Noise signal from source(thermal and/or quantumfluctuations)

AMPLIFIER

DATA PROCESS STAGE

++

+

DETERtic

SIGNAL

NOISESIGNAL

ADDEDNOISE

PROBLEM: AMPLIFICATION IS NEEDED TOINCREASE ENERGY OF MEASURED SIGNAL, BUT

IT ALWAYS DEGRADES INFORMATION

Applications: • Readout of qubits• THz photon detection• Electrical metrology

EFFICIENCY = =INPUT NOISE

INPUT NOISE + ADDED NOISE

(S/N)out

(S/N)in

energysource

QUANTUM REGIME:ENERGY OF EACH MODE OF

SIGNAL AND THERMAL NOISEIS OF ORDER 1 PHOTON

INPUT AT T=0: EFFICIENCY =

12

12

+A

Caves' added photon number

AN IMPROVEMENT BYA FACTOR OF N IN EFFICIENCY

TRANSLATES IN AN IMPROVEMENT BYA FACTOR OF N2 IN MEASUREMENT TIME!

Sadi Carnot

THE PROBLEM OF HEAT ENGINES EFFICIENCYGAVE BIRTH TO THERMODYNAMICS

.HOT COLD

THEORHOT

T TT

η η −< = "Réflexions sur

la puissancemotrice du feu"

(1824)

THE PROBLEM OF AMPLIFIER EFFICIENCYOPENS A NEW AREA OF NON-EQUILIBRIUM

QUANTUM STATISTICAL PHYSICS

narrow band-pass filter

narrow band-pass filter

QUBITCIRCUIT

1

0

or

rf signal in rf signal out

A) SHELTER QUBIT FROM ALL RADIATION EXCEPT READOUT RF @ ωrB) AMPLIFY OUTGOING SIGNAL WITH LOWEST ADDED NOISEC) SEND ENOUGH PHOTONS TO BEAT ADDED NOISE

DISPERSIVE QUBIT READOUT STRATEGY

01rω ω≠

QUBIT STATEENCODED IN PHASE

OF OUTGOING SIGNAL,NO ENERGY

DISSIPATED ON-CHIP

Blais et al. PRA 2004, Walraff et al., Nature 2004

filte

r filter

its phaseis pointervariable

ADC

IN/OUT

CHIP

~

DISPERSIVE READOUT OF SUPERCONDUCTINGQUBITS

microwave generatorfor readout

amplifiers

mixer

circulator

λ/2 filter

Josephson qubit

ADC

IN/OUT

CHIP

~

EXCITATION OF QUBIT IS OFF-RESONANT

microwave generatorfor qubit excitation

amplifiers

mixer

circulator

~

Josephson qubit

ADC

IN/OUT

CHIP

~

amplifiers

mixer

circulator

Josephson qubit

~10 or

READOUT PROTOCOL: EXCITATION OF QUBIT

ADC

IN/OUT

CHIP

~microwave generator

for readoutfrequency f

amplifiers

mixer

circulator

phase shift (deg)

f

0

-360fr

1

0

width determined by resonator Q

PRINCIPLE OF DISPERSIVE READOUT

QND!

Josephson qubit

TOWARDS OBSERVATION OF BLOCH OSCILLATIONS

2Ife

Δ =

I

~

/ 4λf

Effective single JJ

linear microwave readout

Zorin, Averin and Likharev (1985)

sidebands of readout frequency @

very large inductance JJ array

TOWARDS OBSERVATION OF BLOCH OSCILLATIONS

2Ife

Δ =

I

~

/ 4λf

Effective single JJ

linear microwave readout

Zorin, Averin and Likharev (1985)

sidebands of readout frequency @

very large inductance JJ array

NOW EXISTS!See poster

2. Basics of quantum signal description

INCOMING AND OUTGOING SIGNAL AMPLITUDES

( )0 pA x v t→ −

2 WATTSA⎡ ⎤ =⎣ ⎦

( ) ( )0, pA x t A x v t= ∓solution:1

c

c

c

Z

Z

Z

A A

A

V V

I I I

I I

A

V

V V

→ ←

→ ←

→ ←

→ ←

→ ←

→ ←

⎡ ⎤= + = +⎣ ⎦

⎡ ⎤= − = −⎣ ⎦

= =

x

( )0 pA x v t← +

1

px vA

tA∂ ∂

=∂ ∂

∓@ location xand time t

[ ] [ ]/e px x

vd

idA Aωω ω+= ∓

in frequency domain:

x

V(x)I(x),c pZ v

portport 1

port 2 port ℓ

.....

.....

.....

..... .....

SIGNAL MODE DESCRIPTION INVOLVES(i) A SPATIAL PART....

.... AND (ii) A TEMPORAL PART

center time , center frequencypτ mb

2bτ π=

example:local cosine basisCoifman & Meyer '91

time

angularfrequency

τ

bm

Tiling of t-ω planewith basis of

orthonormal functions:

t

ω

0ω =p

"MODE AMPLITUDE"IS CONTENT OF THE TILE:

[ ] [ ]mpmpd Awa ω ω ω

ω∗+∞

−∞= ∫

τ

wavelet basis

( ) ( )' ' '' dpm m m p pp mw t w t t δ δ+∞

− −−∞=∫

GEOMETRIC REPRESENTATION OF SIGNAL MODE

θ

N noise fuzzdisc

(diam.= 2σΝ)

FRESNEL VECTOR

N = signal mode energy in photon number= signal mode phaseθ

FRESNEL "LOLLYPOP"

in-phase amplitude compnent

out-phase amplitude compnent

Im mpa aμ⊥⎡ ⎤ =⎣ ⎦

Re mpa aμ⎡ ⎤ =⎣ ⎦

Classical → Quantum: ˆa aμ μ→ N1 coth2 2 Bk T

μωσ =

12

G ⎛ ⎞+⎜ ⎟⎝ ⎠A

θ

N

θ

GN

OUTIN

'aμ

'aμ⊥

aμ

aμ⊥

QUANTUM LIMITED AMPLIFICATION WITH ALINEAR, PHASE-PRESERVING AMPLIFIER

STANDARD QUANTUM LIMIT:AMPLIFIER ADDS ONLY

ANOTHER ½ PHOTON OF NOISE !MINIMUM REQUIRED BY Q.M. FOR

A MEASUREMENT OF BOTH QUADRATURES

Shimoda, Takahasi and Townes, J. Phys. Soc. Jpn. 12, 686 (1957); Haus and Mullen, Phys. Rev. 128, 2407 (1962); Caves, Phys. Rev. D 26, 1817 (1982)

12

μ = mode index (ℓ,m,p)

min12

=A

θ

N

OUTIN

'aμ

'aμ⊥

aμ

aμ⊥

AMPLIFICATION AT THE QUANTUM LIMIT WITH ALINEAR, PHASE-SENSITIVE AMPLIFIER

(Caves, 1982)

12

de-amplification

amplification

QUANTUM LIMIT : NO ADDED NOISE (!)+ SQUEEZING OF QUANTUM FLUCTUATIONS

'N N

μ = mode index (ℓ,m,p)

TRANSM. LINES, WIRES

COUPLERS

CAPACITORS

GENERATORS

AMPLIFIERS

JOSEPHSON JUNCTIONS

FIBERS, BEAMS

BEAM-SPLITTERS

MIRRORS

LASERS

PHOTODETECTORS

ATOMS

QUANTUM OPTICS QUANTUM RF CIRCUITS

~

COULD WE BUILD AN IDEAL RF PHOTOMULTIPLIER WITH A QUANTUMLIMITED AMPLIFIER

FOLLOWED BY AN IDEAL SQUARE LAW DETECTOR?

RELATIONSHIP BETWEEN PHASE-PRESERVINGAND PHASE-SENSITIVE AMPLIFICATION

ϕ

ϕ + π/2

3. Degenerate versus non-degenerateparametric amplification

MICROWAVE AMPLIFIER CHARACTERISTICS

TbackactionTadded

noiselessamplifier1-port

Pin

REPRESENTATION OF MATCHED 2-PORT AMPLIFIER

ideal circulatorideal coupler

hot loads

• Power gain ( G = Pout /Pin )• Signal bandwidth B• Noise temperature TN=Tadded• Backaction Tbackaction• Dynamic range• Tuning bandwidth• Directionality

Pout

POWER

G

ideal circulator

(DC or RF)

MICROWAVE AMPLIFIER CHARACTERISTICS

TbackactionTadded

noiselessamplifier1-port

Pin

REPRESENTATION OF MATCHED 2-PORT AMPLIFIER

ideal circulatorideal coupler

hot loads

• Power gain ( G = Pout /Pin )• Signal bandwidth B• Noise temperature TN=Tadded• Backaction Tbackaction• Dynamic range• Tuning bandwidth• Directionality

Pout

POWER

G

ideal circulator

(DC or RF)

OUR MAIN GOAL: UNDERSTANDAND OPTIMIZE TRADE-OFFS• STABILITY vs GAIN & BANDWIDTH• BANDWIDTH vs GAIN• DYNAMIC RANGE vs GAIN• ETC....

difficultvery small~0dB1QPC

OKconcern10-20 dB1-2RF-SET

OKconcern20-30dB1-2μW

SQUID

commer-cialsmall25-35dB40-80

HEMT-FET

easeof

implemtion

out-of-bandback-action

noise

powergain

kTN/(ω/2)type

CRYOELECTRONIC PHASE PRESVING AMPLIFIERSPOWERED BY DC

HEMT: High Electron Mobility Transistor, SET: Single Electron Transistor, QPC: Quantum Point Contact

2A

CAN WE REACH QUANTUM LIMIT WITH SUFFICIENT GAINAND BANDWIDTH, WHILE PRODUCING

MINIMAL BACKACTION?

PARAMETRIC AMPLIFICATION WITHJOSEPHSON CIRCUITS

Yurke et al, Phys. Rev. A 39, 2519 (1989)Tholen et al., Appl. Phys. Lett. 90, 253509, (2007)Castellanos-Beltran and Lehnert, Appl. Phys. Lett. 91, 083509 (2007)Yamamoto et al. Appl. Phys. Lett 93, 042510 (2008) Bergeal et al. arXiv:0805.3452v1 (2008) to appear in Nature PhysicsSpietz, Irwin and Aumentado, APL 93, 082506 (2008)Clerk et al., to appear in Review of Modern Physics (2008)Abdo et al., arXiv:0811:2571; Eur. Phys. Lett. 85, 68001 (2009)Sandberg et al., arXiv:0811.4449v1, Appl. Phys. Lett. 92, 203501 (2008)

PARAMETRIC AMPLIFICATION PRINCIPLEIN THE SCATTERING LANGUAGE

ωpump

ωsignal

ωpump

ωsignal

ωidlerωidler(no signal)

Purely

Dispersive

Non-linear

Medium

PARAMETRIC AMPLIFICATION PRINCIPLEIN THE SCATTERING LANGUAGE

Purely

Dispersive

Non-linear

Medium

ωpump

ωsignal

ωpump

ωsignal

ωidler

idlersigna p pl umωω ω+ =

ωidler(no signal)

2idlersignal pumpω ω ω+ ="3-wave process"

"4-wave process"

HAVEN'T WE SAID WE WEREDEALING WITH A LINEAR AMPLIFIER?

FOR LARGE PUMP AMPLITUDESAND LOW PUMP DEPLETION,

THE BASIC NON-LINEAR WAVE-MIXING PROCESSESAPPEAR AS LINEAR SCATTERING PROCESSES

FROM THE POINT OFVIEW OF SIGNAL AND IDLER MODES

JOSEPHSON TUNNEL JUNCTIONPROVIDES A NON-LINEAR INDUCTOR

WITH NO DISSIPATION

1nm SI

S

superconductor-insulator-

superconductortunnel junction

φ

ΙΙ = φ / LJ

( )0 0sin /I I φ φ=

CJLJ

Ι

( )' 't

V t dtφ−∞

= ∫

0 2eφ =

0

0JL

Iφ

=

0I

JEJL

( )

2

20

2

020

22

( )6

JJ

JJ

LeIe E

L IL I II

δ

= =

=

( )JL IδIφ

BASIC PROCESS: 4-WAVE MIXING

Kerr

JEJL

( )

2

20

2

020

22

( )6

JJ

JJ

LeIe E

L IL I II

δ

= =

=

( )JL IδIφ

1 2 3 4ω ω ω ω+ = +

1ω

2ω

3ω

4ω


JEJL

( )

2

20

2

020

22

( )6

JJ

JJ

LeIe E

L IL I II

δ

= =

=

( )JL IδIφ

1 2 3 4ω ω ω ω+ = +

1ω

2ω

3ω

4ω

1ω

2ω

3ω

4ω

1 2 3 4ω ω ω ω= + +



JEJL

( )

2

20

2

020

22

( )6

JJ

JJ

LeIe E

L IL I II

δ

= =

=

( )JL IδIφ

1 2 3 4ω ω ω ω+ = +

1ω

2ω

3ω

4ω

1ω

2ω

3ω

4ω

1 2 3 4ω ω ω ω= + +

one wave can be at ω=0 (DC bias) 3-wave mixing


JEJL

( )

2

20

2

020

22

( )6

JJ

JJ

LeIe E

L IL I II

δ

= =

=

( )JL IδIφ

1 2 3 4ω ω ω ω+ = +

1ω

2ω

3ω

4ω

1ω

2ω

3ω

4ω

1 2 3 4ω ω ω ω= + +

If current I too large, more exotic, less controllable processes !

TWO TYPES OF PARAMETRIC AMPLIFIERS

phase-preserving(2-mode squeezing)

phase-sensitive(1-mode squeezing)

non-degenerate paramp.

degenerate paramp.

signalmode

idlermode

signalmode=idlermode

DEGENERATE PARAMP AS SIMPLEST EXAMPLE OFACTIVE LINEAR, DISPERSIVE 1-PORT

( ) ( )0[1 cos 2 ]L t L tε ω= +

C cZ

( )inA t

( )outA t

Just take a L and a C (pure dispersive elements, no internal dissipation)

C cZ

( )outA t

( )inA tPASSIVE ACTIVE

L

01

LCω =

PARAMETRICALLY PUMPED OSCILLATORS

MECHANICAL SYSTEM

0ω

2ω0

PUMP: WORK AGAINST CENTRIFUGAL

FORCE

( ) ( )0sin 2B B PI t I I tω= +

ELECTRICAL SYSTEM

RF FLUX BIASED DC SQUID (3W)


(NEC, Chalmers)

( ) ( )0sin 2B B PI t I I tω= +

ELECTRICAL SYSTEM

INDIRECT PARAMETRICPUMPING @ 2ω0

RF FLUX BIASED DC SQUID (3W)

EFFECTIVE PARAMETRIC DRIVE

(Yale, NISTKTH, Berkeley)

RF BIASED JUNCTION (4W)

( ) ( ) ( )0cosin inS

inPA A tt A t ω= +


(NEC, Chalmers)

= resonant frequency

DEGENERATE PARAMETRIC PUMPING

Iωω

INIω−

0

Sω− Sω

OUT 0

02p ωΩ =Pump frequency

Iω−Sω−Iω Sω

ω

0ω1 INTERNAL MODE

MINIMAL IMPLEMENTATION OF PHASE-PRESVING PARAMETRIC AMPLIFIER

aω bω

2 COUPLED OSCILLATORSWITH ACCESS PORTS.... M


( )1ina t

( )1outa t ( )2

outa t

( )2 0ina t =

TIME-DEPENDENTCOUPLING BETWEENTHE 2 OSCILLATORS ( )0 1 cos PM M tε= + Ω⎡ ⎤⎣ ⎦

21p ωωΩ = +

PUMP

aω bω

SIGNAL PORT IMAGE (OR "IDLER") PORT

( )1ina t

( )1outa t ( )2

outa t

( )2ina t

TIME-DEPENDENTCOUPLING BETWEEN

2 OSCILLATORS ( )0 1 cos PM M tε= + Ω⎡ ⎤⎣ ⎦

MECHANICAL ANALOG

PUMP


aω bω

aω bω

21p ωωΩ = +

WHY IS THE IMAGE PORT NEEDED?

PUMP

Manley-Rowerelations

S IP NN NΔΔ = = Δ

21p ωωΩ = +

NON-DEGENERATE PARAMETRIC PUMPING

Sωω

IN Sω−

0

Iω− Iω

OUT 0

21p ωωΩ = +Pump frequency

ω

resonant frequencies: and 1ω 2ω

SωSω−Iω− Iω

2 INTERNAL MODES

NON-DEGENERATE PARAMETRIC PUMPING

Sωω

IN Sω−

0

Iω− Iω

OUT 0

21p ωωΩ = −Pump frequency

ω

resonant frequencies: and 1ω 2ω

SωSω−Iω− Iω

2 INTERNAL MODES

NOISELESS,UNITY PHOTON GAIN

FREQUENCY CONVERSION!

1

1

Sω ωκ−

GAIN-BANDWIDTH COMPROMISE

-2 -1 0 1 2

0

10

20

30

40

( )1010 Log SG ω41

when

a b

a b

BG

G

κ κκ κ

⎛ ⎞= ⎜ ⎟+⎝ ⎠

→ ∞

( )22

1 2

11SG G ρω ω

ρ⎛ ⎞+

= = = ⎜ ⎟−⎝ ⎠ 1 2

S I

Z Zω ωρ ε=

4. Implementation of non-degenerateparamp with Josephson ring modulator

TOWARDS THE PUREST NON-LINEARITY: THE

JOSEPHSONRING MODULATOR

4 modes:

4 junctions in a ring threaded by flux

The Z mode can be understoodas providing an invertible mutual

inductance between the X and Y mode

(Bergeal et al., 2008, arXiv:0805.3452,to appear in Nature Physics )

Z

X Y

~ YXH Zcoupling

YX

Z W

pumpdetuning

0 ( ) /P rω ω− Γ

pump power

1c

PP

3−

chaos domain(high noise)

maximum gainpoint

for parametricamplification

pumpdetuning

0 ( ) /P rω ω− Γ

pump power

1c

PP

bistability (self-oscillation with 2 possible phases)

PURE

IMPURE

gain

Signal Idler

Φ= 1.6 GHz = 7GHz

Ip cosΩt

(Z)

(Y) (X)1ina

1outa

2ina

2outa

Ω = ωa+ ωb

Pump

ωb2π

ωa2π

IMPLEMENTATIONWITH JOSEPHSONRING MODULATOR

Bergeal et al. arXiv:0805.3452v1to appear in Nature Physics

0

2Φ

Φ

Signal Idler

Φ= 1.6 GHz = 7GHz

Ip cosΩt

(Z)

(Y) (X)1ina

1outa

2ina

2outa

GG

G −1

G −1

Ω = ωa+ ωb

Pump

0

14

pa b a b

Iρ Q Q p p

I=

22

0 2

11

G ρρ

⎛ ⎞+= ⎜ ⎟−⎝ ⎠

ωb2π

ωa2π

1ina

1outa

2outa2ina

IMPLEMENTATIONWITH JOSEPHSONRING MODULATOR

( )

( )

02

21/ 2

GG

B

ωω

=+

1/ 2

02 a b

a b

Q QB Gω ω

−

−⎛ ⎞= +⎜ ⎟

⎝ ⎠

Φωa=1.6 GHz ωb=7 GHz

Ip cosΩpt (Z)

(Y)(X)ina1

outa1

ina2

outa2

/P cI Iρ =

Amplification

21/ 2

2

1 11

G ρρ

+= >

−1ina1outa 2

ina

2outa

• 1-port: amplification • 2-port: up/down conversion• power gain (amp. & conv )• photon gain • minimal added noise : 1

2 ω

OPERATION OF JOSEPHSON PARAMETRIC CONVERTER

r =1− ρ2

1+ ρ2 <1

1-port: cooling • 2-port: up/down conversion• power gain in conv. if ωout> ωin• no photon gain • no added noise

Pure conversion

1ina1outa 2

ina

2outa

Ωp = ωa+ ωb Ωp = |ωa- ωb|

• Junctions: Io = 3μA

• Input capacitances: SiOx

• Resonators:Frequencies:

1.6 GHz and 7.2 GHz

Q's: 450 and 120

Bandwidths: 3.5 MHz and 60 MHz

CIRCUIT AT CHIP LEVEL

testJJ

Φ/ Φ00 1 2-2 -1

CHOSING WORKING POINT OF RING MODULATOR

upward flux sweep

downwardflux sweep

color:phase

of reflectedsignal

(HF port)

EXPERIMENTAL SETUP

CHIP

AMPLIFICATION CHARACTERISTICS: GAIN vs FREQUENCY

GG

G−1

G−1

GG

G −1

G −1

( ) 11/ 2 1 12

6.9 MHza bB G

−− −⋅ = Γ + Γ

EXCELLENTAGREEMENT

WITH PARAMPTHEORY

by extrapolationshould get10MHz with

gain of 20dBfor Q=100 @ 10GHz:

OK for S-qubits

up conversion down conversion

GG

G−1

G−1

GG

G−1

G−1

FREQUENCY CONVERSION

DYNAMIC RANGE

V output

pumpJPC

T

• Self-calibrated measurement:

T

Noise power

-TN

MEASUREMENT OF SYSTEM NOISE WITH HOT NANOWIRE

V output

pumpJPC

T

• Self-calibrated measurement:

T

Noise power

-TN

• Nanowire as noise source:

L= 4 μm, t = 20 nm, w = 80 nm

V

Cu⎟⎟⎠

⎞⎜⎜⎝

⎛=

),(2coth

2 VxTkN

B

ωω hh

(hot electron regime:2nd self-calibration)

(J. Teufel’s thesis, R. Schoelkopf, and D. Prober)

MEASUREMENT OF SYSTEM NOISE WITH HOT NANOWIRE

( )eVTkB <<<<ωh

DIFFERENT REGIMES OF NOISE FOR NANOWIRE

HOT ELECTRONREGIME

• Steinbach, Martinis, Devoret, PRL 76, 3806 (1996)• Pothier, Gueron, Birge, Esteve, Devoret, PRL 79, 3490 (1997)• Spietz , Schoelkopf and Pari, APL 89, 183123 (2006)• John Teufel's thesis, Yale 2008

• Steinbach, Martinis, Devoret, PRL 76, 3806 (1996)• Pothier, Gueron, Birge, Esteve, Devoret, PRL 79, 3490 (1997)• Spietz , Schoelkopf and Pari, APL 89, 183123 (2006)• John Teufel's thesis, Yale 2008

( )eVTkB <<<<ωh

80 Ω at 300K50 Ω at 4K

L=4 μm, t = 20 nm, w = 80 nm

Le-e<L< Le-ph

DIFFERENT REGIMES OF NOISE FOR NANOWIRE

HOT ELECTRONREGIME

10x10-6

8

6

4

2

0

Noi

se p

ower

(unc

alib

rate

d)

-80 -60 -40 -20 0 20 40 60 80Voltage (μV)

NOISE POWER vs BIAS VOLTAGE

10x10-6

8

6

4

2

0

Noi

se p

ower

(unc

alib

rate

d)

-80 -60 -40 -20 0 20 40 60 80Voltage (μV)

• Hot electron regime theory fits well:


10x10-6

8

6

4

2

0

Noi

se p

ower

(unc

alib

rate

d)

-80 -60 -40 -20 0 20 40 60 80Voltage (μV)

• Other theories like shot noise regime expression do not fit:


CAN CONVERT VOLTAGE INTO EFFECTIVE TEMPERATURE:eff

38

kT eV=

10x10-6

8

6

4

2

0

Noi

se P

ower

(Unc

alib

rate

d, in

Wat

ts)

200150100500-50-100-150Teff (mK)

NOISE POWER vs EFFECTIVE TEMPERATURE

10x10-6

8

6

4

2

0

Noi

se P

ower

(Unc

alib

rate

d, in

Wat

ts)

200150100500-50-100-150Teff (mK)


Quantum noise of load( )/ 2sω

10x10-6

8

6

4

2

0

Noi

se P

ower

(Unc

alib

rate

d, in

Wat

ts)

200150100500-50-100-150Teff (mK)


Quantum noise of load

Noise added by system

( )/ 2sω

10x10-6

8

6

4

2

0

Noi

se P

ower

(Unc

alib

rate

d, in

Wat

ts)

200150100500-50-100-150Teff (mK)



Noise added by system

system noise TN: 130mK

10x10-6

8

6

4

2

0

Noi

se P

ower

(Unc

alib

rate

d, in

Wat

ts)

200150100500-50-100-150Teff (mK)



IDEALCASE

( )/ 2sωQuantum noise of load

Quantum noise of idler load

10x10-6

8

6

4

2

0

Noi

se P

ower

(Unc

alib

rate

d, in

Wat

ts)

200150100500-50-100-150Teff (mK)



IDEALCASE


Quantum noise of idler load

quantum limited TN : 40mK

( )/ 2sω

5. Squeezing

SIGNAL AND IDLER CO-AMPLIFICATIONFOR NON-DEGENERATE PARAMETRIC

AMPLIFIER

ina

ina⊥

outa⊥

outa

signal

idler

sum of signal and idler is amplified


AMPLIFIER

ina

ina⊥

outa⊥

outa

signal

sum of signal and idler is amplified (G1/2)difference of signal and idler is de-amplified (G-1/2)

total volume in 4-d phase space is conserved

idler


AMPLIFIER

ina⊥

outa⊥

outa

signal

signal

ina

idler

idler

SQUEEZING OF QUANTUM FLUCTUATIONS FORFOR NON-DEGENERATE PARAMETRIC AMPLIFIER

ina

ina⊥signalport

idlerport

inb

inb⊥

outa

outa⊥

signalport

idlerport

outb

outb⊥

amplification

ofquantum

noise

vacuum state

vacuum state

see "Quantum Squeezing", Drummond and Ficek eds (Springer 2004)

2-MODE SQUEEZING


ina

ina⊥signalport

idlerport

inb

inb⊥

outa

outa⊥

signalport

idlerport

outb

outb⊥

amplification

ofquantum

noise

vacuum state

vacuum state



ina

ina⊥signalport

idlerport

inb

inb⊥

outa

outa⊥

signalport

idlerport

outb

outb⊥

amplification

ofquantum

noise

vacuum state

vacuum state

sub-ZPMcorrelations



ina

ina⊥signalport

idlerport

inb

inb⊥

outa

outa⊥

signalport

idlerport

outb

outb⊥

amplification

ofquantum

noise

vacuum state

vacuum state

thermal state

thermal state

sub-ZPMcorrelations



ina

ina⊥signalport

idlerport

inb

inb⊥

outa

outa⊥

signalport

idlerport

outb

outb⊥

amplification

ofquantum

noise

vacuum state

vacuum state

thermal state

thermal state

sub-ZPMcorrelations


B effk TG

ω=large gain limit:

GG

G−1

G−1

(no input)

(no input)

signal noise

idler noise

TWO-MODE SQUEEZING OF QUANTUM FLUCTUATIONS

2|| IeS iϕ+

idler

aω

aωbω

GG

G−1

G−1

(no input)

(no input)

signal noise

idler noiseϕ

baω ω+

S.A.

signal


2|| IeS iϕ+

idler

aω

aωbω

GG

G−1

G−1

(no input)

(no input)

signal noise

idler noiseϕ

baω ω+

S.A.

signal

1.0

0.8

0.6

0.4

0.2M

agni

tude

(nor

mal

ized

)

121086420-2

D ata S in


ϕ (in radians)

2|| IeS iϕ+

idler

aω

aωbω

GG

G−1

G−1

(no input)

(no input)

signal noise

idler noiseϕ

baω ω+

S.A.

signal

(in dB)

1.0

0.8

0.6

0.4

0.2M

agni

tude

(nor

mal

ized

)

121086420-2

D ata S in

-35

-30

-25

-20

-15

-10

-5

0

Pow

er (d

B, n

orm

aliz

ed)

121 086420-2

2|| IeS iϕ+

From noise measurement

( )2 20.25 | | | | 22

S I G ω⋅ + = ×

h

20 dB ≤ squeezing ≤ 26 dB

2 2| | | | 2 B NS I G k T+ = ×


G = 30dB

6. Link between Josephson paramps andμW-SQUIDs (with Archana Kamal and John Clarke)

PARAMP APPROACH TO SQUIDSSω

ωIN Sω− 0Jω− Jω

OUT

2 2p JωΩ =

ω

4 INTERNAL MODES

ω

ω

1 Jp ωΩ =

• Josephson paramps are predictible: experimental characte-ristics data agree very well with theoretical model, even forlarge gain. Their noise performance can be controlled.

• System noise performance ~ 20 times better than with HEMT amplifier only

• Evidence for 2-mode squeezing of quantum fluctuations,frequency conversion and dynamic cooling

• Next:

- Increase bandwidth, tailor resonant frequency and produce devices for qubit readout in cQED experiments

- Increase two-mode squeezing for multi-photon interference

- SQUID-paramp hybrid?

CONCLUSIONS AND PERPECTIVES

josephson-based parametric amplifiers … parametric amplifiers for quantum measurements applied...

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