Amplifying Quantum Signals with the Josephson Bifurcation Amplifier (JBA)

IRFAN SIDDIQIR. Vijay, E. Boaknin, M. Metcalfe, F. Pierre, C.M.

Wilson, C. Rigetti, L. Frunzio, and M. H. Devoret

Department of Applied PhysicsYale University

Acknowledgements: D. Prober, M. Dykman, D. Vion, D. Esteve, R.J. Schoelkopf, & S. Girvin

THE READOUT PROBLEM FOR SQUBITSDevoret & Schoelkopf (2000)

QUBITREADOUT

OFF0 1

10α β+ ON

0

1 1quantum information classical information

0

WANT:• Readout ON: T1 / τmeas >> 1• Readout OFF: T1, Tϕ not reduced• Short duty cycle• No energy dissipated on chip

(sensitivity, low backaction)

(good switch, low backaction)

(speed to fight drifts)

(no noise to junction)

ARTIFICIAL ATOM : SPLIT COOPER PAIR BOX

( )02ˆ 1( ) cos 1 12 2/

C jn

gH E n n n E nN n n n⎡ ⎤⎛ ⎞= − − + − +⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

Φ Φ∑

2

1 2

(2 )2( )C

g j j

eEC C C

=+ + 0 0 02jE i i

eϕ= =

BOX ENERGY SPECTRUM

Optimum Working Pointcharge capacitance

E1

Ng

Φ/Φ0

E0

hν01

kk

EQU

∂=

∂

2

2k

kEC

U∂

=∂

Ener

gy

(kBK

)current inductance

kk

EI ∂=

∂Φ

12

2k

kEL

−⎛ ⎞∂

= ⎜ ⎟∂Φ⎝ ⎠

CAN’T READ CHARGE OR CURRENT!

1 0

1 0

00

Q QC C

− ≠

−

1 0

1 0

00

Q QC C

− =− ≠

Ng

1 0

1 0

00

I IL L

− ≠

−

1 0

1 0

00

I IL L

− =− ≠

Φ

|0>

|1>

E

chargenoise

fluxnoise

QUANTRONIUM (a.k.a. Charge-Phase Qubit)

• IDC=0 Readout off

• 1/f charge & flux noise immunity

• T1 = 1.8 µsTφ= 500 ns

(D. Vion et al., Science 2002)

• Quasiparticles-slow reset (>10µs)

• Reduced Visibility

~103 ops!charge qubit

A > I0eff

DissipativeVDC=2∆/e

(DC Readout 1)

A < I0eff

SuperconductingVDC=0

(DC Readout 0)

DC DRIVE

2dV

e dtδ

=Josephson

0 sin( )I I δ=

0

0 cos( )2 2 DCU I Ie e

ϕ

δ δ= − −

0

0

1cos( )JL

Iϕ

δ= |qubit=0> (IDC < I0) zero-voltage state

|qubit=1> (IDC > I0) voltage state

READOUT: WHY NOT USE PHOTONS?

AC Drive: iRF sin(ωt)

0

0p

IC

ωϕ

=

iRF < iB (I0,∆ω) low-amp. & phase lagging (RF readout 0)

iRF > iB (I0,∆ω) high-amp. & phase leading (RF readout 1)

BIFURCATION AMPLIFICATION

• Bifurcation amplifier: sensitive to any input variable coupled to I0minimal back-action

- no on-chip dissipation- efficiently thermalize load- back-action narrow band

SCHEMATIC RF SETUP T = 300K

Ch1 AWG iRF(t)

πΨ

LO1.58 GHz CW

IF

IF

Ch2 AWG -iRF(t)

RF

1.48 GHz CW

IF

LO

RF

Digital Demodulation

2GS/sec

SCHEMATIC CRYOGENIC SETUP

4.2 K

0.3 K

NEW ERA OF FILTERS !

-3dB @ 1 MHz

-3dB @ 2 GHz

JUNCTION + MICROWAVE CAPACITOR

Al

Si3N4

27.3 pF

Cu

1000 nm Cu

20 nm Cr

35 nm Cr15 nm Ti

Silicon Substrate

Al

1 mm

200 nm Si3N4

=Cu

Alεr=7.5

Al/Al203/AlJunction (1.17 µA)

METALLICUNDERLAYER

MINIMAL STRAY INDUCTANCE

Lbond = 2.8 nH

LJ = ϕ0 / I0 = 0.28 nH

C

Lstray

20

1 12 stray

p

C C Le Iω

= +

Lstray = 0.003 nH

C = 27.3 pF

RF-DRIVEN JUNCTION: PHASE DIAGRAM

kT/EJ

1/Q

Q=ωpRC

See Delft

(0.1fW)

(1.5

4 G

Hz)

PHASE DIAGRAM:EXP & THYIN GOOD

AGEEMENT

• Dark region corresponds towell-jumping

• All parameters in predictionmeasured experimentally!

I.S. et al, cond-mat/0312553

DYNAMICS OF DYNAMICAL SWITCHING

• N = 600,000

• ∆φ = 74 deg

• HysteresisIB and IB’ correct ! ( )3/ 23/ 2

016 1

3 3BI Iα α⎡ ⎤= −⎢ ⎥⎣ ⎦1 0.122

p

ωαω

⎛ ⎞= − =⎜ ⎟⎜ ⎟

⎝ ⎠

I(t) 2 µs20 ns

0

time

RF vs. DC

I0IB (I0,∆ω)

0

1

0

1

I(t) IDC2 µs

iRF ↔ IDCφ ↔ VDC∆ω ↔ Rs

20 ns

00

~ 10 µs

timetime

SWITCHING HISTOGRAMS

• No latching• 40 ns rise + 20 ns settle• τm = 20 ns• N = 1.6 x 106

• Overlap = 10-2

Set by SNR

• Latching• 40 ns rise + 20 ns settle• τm = 300 ns• N = 1.5 x 105

• Overlap = 6 x 10-5

SWITCHING PROBABILITY

T = 340 mK

T = 540 mK• ∆I0/I0 = 1%

• d = 80% @ 250mKd = 57% @ 340mKd = 49% @ 540mK

• Predict d > 95% @ 60mK

• ∆IB/IB = 6%

0 0

/ 3 1 5.6/ 4 2

B BI II I α

∆= − =

∆ Single Shot, Latching Qubit Readout>95% Fidelity10-20 MHz Rep. Rate !

I.S. et al, cond-mat/0312623

1D METAPOTENTIAL

• Expand system near bifurcation

• Reduce to cubic metapotential

0 1exp

2

dyndyn a U

kTωπ→

⎛ ⎞∆Γ = −⎜ ⎟

⎝ ⎠

( ) ( )3/ 22

30 0

0

64, , 1 118 3

10K

dyn RFRF

B

dyn

iU I i IIe

u

α α α⎛ ⎞⎛ ⎞⎡ ⎤ ⎜ ⎟∆ = − − ⎜ ⎟⎢ ⎥ ⎜ ⎟⎣ ⎦ ⎝ ⎠⎝ ⎠

≈

met

a po

tent

ial

escape coordinate

( )0

1/ 222

(2 ) 35

4

0MHz

13 3

a

RFa p

B

iRCI

ω αω

ω π

⎛ ⎞⎛ ⎞⎡ ⎤ ⎜ ⎟= − ⎜ ⎟⎢ ⎥ ⎜ ⎟⎦ ⎝ ⎠ ⎠≈

⎣ ⎝i (M. Dykman)

ESCAPE RATES FOR DYN. SWITCHING

0 0

0 0

9.1K for 1.12 , 340mK( 10.0K)

10.7 K for 1.17 , 340mK( 11.0K)

dyn escst

dyn escst

u I A TTHY

u I A TTHY

µ

µ

= = ==

= = ==

YALE QUANTRONIUM

• Observe I0 modulation with gate volage

• Spectroscopy in progress

• T=400mK!

Φ Readout

IslandGate

-2

-1

0

1

2

dIef

f 0 / d

Ug (

mV

lock

in)

-6 -4 -2 0 2 4 6Gate Voltage Ug (mV)

Φ=0

Φ=Φ0/2

CRITICAL CURRENT FLUCTUATIONS

• Apply fixed iRF and observe variation in switching probability P(t)caused by I0(t)

• S1/2δI0/I0

(1Hz, 0.3K) = 3.5x10-6

SUMMARY & PERSPECTIVES

• BIFURCATION AMPLIFICATION OBSERVED AS PREDICTED

- GAIN- SPEED- ESCAPE RATES- ABSENCE OF EXCESS DISSIPATION

• QUBIT MEASUREMENTS: Bell Inequalities, Error Correction

• QUANTUM LIMIT: Quantum Diffusion vs MQT, Ultimate TN

• NOISE: Temperature dependence of 1/f

• APPLICATIONS: Current Standard, Single Photon Detectors