ULTRA-LOW-NOISE AMPLIFICATION FOR THE READOUT …kosborn/index_files/DISQ/Disq_Devor… ·...

ULTRA-LOW-NOISE AMPLIFICATIONFOR THE READOUT OF

SUPERCONDUCTING CIRCUITS

LABQUAN RONICSUM

ELEC

APPLIED PHYSICS, YALE UNIVERSITY

N. BergealF. SchackertM. BrinkL. FrunzioM. D.

R. VijayC. RigettiM. MetcalfeV. Manucharian

I. Siddiqi (U.C. Berkeley)F. Pierre (CNRS Marcoussis)C. Wilson (Chalmers)E. Boaknin (Montreal)

Work done in direct collaboration with S. Girvin and R. Schoelkopf

Ackments: J. ClarkeOther collaborations: D. Prober (Yale), D. Esteve (Saclay)

W.M. KECK DiSQ

Dec. 2007

DECOHERENCE AND READOUT AREINTIMATELY RELATED IN S-QUBITS

QUBIT READOUTON

OFF0 1

active circuit0 1

QUBIT READOUTON

OFF0 1

QUBIT READOUTOFF

ON

0 1 QUBIT READOUTOFF

ON

0 1

10

DECOHERENCE AND READOUT AREINTIMATELY RELATED IN S-QUBITS

active circuit

WANT:1) FAITHFUL READOUT → QND → T1

on >> mst time2) NO DECOHERENCE → T2

on , T1

on >> gate time→ complete decoupling when off

DISPERSIVE READOUT STRATEGY

rf signal in

01ω ω≠

QUBITCIRCUIT

0 1or


rf signal in

or

rf signal out

QUBITCIRCUIT

QUBIT STATEENCODED IN PHASE

OF OUTGOING SIGNAL,NO ENERGY DISSIPATED

ON-CHIP0 1or


rf signal in rf signal out

or

QUBITCIRCUIT

Important factors1) noise in detection2) phase shift per photon

0 1or

DO WITH ENOUGH PHOTONS TO GET1 CLASSICAL BIT OF INFORMATION

TWO KINDS OF DISPERSIVE READOUTS

"cQED" CIRCUIT:CAPACITIVE READOUTOFF-CHIP AMPLIFIER

in out

RESONATOR

"CBA" CIRCUIT:INDUCTIVE READOUT

IN-SITU AMPLIFICATION

outin

Exploit frequency shift of resonator coupled to qubit:readout off when resonator not driven

COMBINING SENSITIVITY & SPEED

NON-LINEAR OSCILLATORLINEAR OSCILLATOR

I. Siddiqi

COMBINING SENSITIVITY & SPEED01

01

NON-LINEAR OSCILLATORLINEAR OSCILLATOR(→ JBA-CBA)

not latching latching


01


Q and preamp noisesets sensitivity

continuous, not latching projective, latching


01


Q and preamp noisesets sensitivity

kT sets sensitivity !

continuous, not latching projective, latching

SOME REMARKS ONBIFURCATION READOUT

|0>

|1>

QUANTRONIUM IN MICROWAVE CAVITY

~ ADCIN OUT

AWG

40ns40ns200ns

t t

Metcalfe et al.Phys. Rev. B6174516 (2007)

QUANTRONIUM COMBINED WITHCAVITY BIFURCATION AMPLIFIER

Optical image3m

m

Output1

0

Input

Linear resonance frequency f0=9.64GHz, Quality factor: Q=160

10mm

readoutjunction

CPBSEM image

IMPLEMENTATIONS

Lumped-element parallel LC oscillator

(JBA)

Distributed element oscillator (CBA)

Coplanar waveguide

Coupled stripline

Parallel LC

(Limits Q-value)

Multiplexed readout and gate lines

Each resonator has different frequencyset by itslength

VARIATION: COUPLED STRIPLINE NON-LINEAR RESONATOR

Optical image of device

200µm

Gate

Slotline

SEM image of qubit

4µm

1. Completely fabricated using e-beam lithography2. Gate and readout lines separated3. Use differential mode in stripline for readout, common mode for gate

Advantages

Drawback: Purcell effect more difficult to control due to presence of common mode

CAVITY BIFURCATION : ANALOG OF OPTICALBISTABILITY

increasing the power in the cavity increases the readout coupling


20 cav Jc

J P

L EnQ L ω

≈h

~100

Mapping Transition Frequency(with one readout tone only)

Monitor phase atfixed frequency in linear regime

Frequency (GHz)

Pha

se (D

eg)180

-180

9.649.59 9.69

0


0 → 1Transitions:

0 → 2

ECP=17GHzEJ=15GHz


Bistable regime more gain

Gat

e ch

arge

(Coo

per p

airs

)

-1/2 Flux (flux quantum units)

1/2


-1/2 Flux (flux quantum units)

1/2

Bistable regime more gain

Gat

e ch

arge

(Coo

per p

airs

)

0 → 1, 2Transitions, # photons

0 → 2, 30 → 2, 4

π pulse UrfMEASUREMENT OFREADOUT FIDELITY

Urf

Relaxationinduced byreadout

Unlike JBA,slope3 timestoo smallcomparedwith thy

TOO MANY READOUT PHOTONS?

Variability ofRamsey fringes

T2 = 500ns ± 300ns

Example fit of 5averaged traces~2sec acquisition time(resolution: 0.5MHz onf01 and 20ns on T2)

MHz repetition rateLarge SNR

NOISE SOURCE?

DISTRIBUTION OF RAMSEY DATAmethod A of van Harlingen et al. 2004

Lopsided frequency fluctuations

Charge noise amplitude1/f2

3( ) , 1.9 10gNS eαω α

ω−= :

value OK

(Karlsruhe)

EJ/EC = 3.6

DISTRIBUTION OF RAMSEY DATAvan Harlingen et al. 2004

Lopsided frequency fluctuations

Charge noise amplitude1/f2

3( ) , 1.9 10gNS eαω α

ω−=

value OK

(Karlsruhe)

Need larger EJ/EC

CONCLUSIONS OF THIS SECTIONON BIFURCATION READOUT

Speed and resolution of CBA has allowedus to measure charge fluctuations at

sweet spot of Cooper pair box in real timefor time scales of 1 second and up.

Our results confirm 1/f noise model of dephasing of Cooper pair box.

For EJ/EC~4 , sweet spot T2 limited bysecond order effects of charge noise

Must increase EJ/EC! TRANSMON

THE JOSEPHSON PARAMETRIC "CONVERTER":A QUANTUM-LIMITED

PRE-AMPLIFIER FOR QUBITDISPERSIVE READOUT

goal: provide high-gain, low noise amplifier for c-QED readoutrelationship with CBA: uses also non-linear on-chip Josephson element for gain, but no latching

outline: 1) Principle2) Implementation3) Preliminary data

CRYOELECTRONIC AMPLIFIERSAPPROACHING THE QUANTUM LIMIT

type EN/( ω/2) powergain

out-of-bandback-action

noise

easeof

use

HEMT 40-80 25-35dB small easy

SQUID 1-2 20-30dB concern OK

SET 1-2 15-20 dB concern OK

QPC 1 ~0dB very small difficult

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

ARE THERE GENERAL GUIDING PRINCIPLESFOR CONSTRUCTING AN OPTIMAL AMPLIFIER?

CAN WE ACTUALLY BUILD ONE?

CAN WE DO A MEASUREMENT BEING ONLYLIMITED BY QUANTUM NOISE?

PIONEERING WORK BY Yurke et al. , 1986

RECENT THEORETICAL RESULTS BY Clerk, Girvin and Stone, 2004

principle of no wasted information

PARAMETRIC AMPLIFICATION PRINCIPLEIN THE SCATTERING LANGUAGE

Dispersive

Non-linear

Medium

ωpumpωpump

ωsignal ωsignal

ωidler ωidler(no signal)

FUNDAMENTAL EQUATION :

0 mod idlersig pnal umpω ωω + =

MASER/LASER

pumpωsignalω

pumpωsignalω

pumpωsignalω

idlerω

signal inMANY SYSTEMS

WITH FEW LEVELS:ATOMS,

MOLECULES, ETC

idlerω

pumpωsignalω SIGNAL OUT

DIFFICULT TO IMPLEMENTAT RF FREQUENCIES however see recent NEC results on single atom circuit maser

PREFER TO USE 1 NON-LINEAR DEGREE OF FREEDOM WITH MANY ENERGY LEVELS

CONTROLIS EASIERPotential energy

Position coordinate

Cj

2

20

11 ...4J

IL

I

⎛ ⎞⎜ ⎟+ +⎜ ⎟⎝ ⎠

in practice,of order 102-3

levels

TOWARDS THE PUREST NON-LINEARITY: THE

JOSEPHSONRING MODULATOR

4 modes:

SCHEMATICS OF JOSEPHSON AMPLIFIERBASED ON RING MODULATOR

SIGNAL (ω1)

IDLER (ω2)

Φ=Φ0/2

PUMP (Ω)

WHY THIS SYMMETRY?

-1

0

1

E/4E

J

0Φ

a

b

Φ0

4 states 4Φ0-periodic states

φa + φb + φc + φd =2πΦΦ0

sinφa = sinφb = sinφc = sinφd

satisfy

At Φ=Φ0/2 and for small X,Y,Z

Ering = α XYZ −X 2

4−

Y 2

4−

Z 2

2⎡

⎣ ⎢

⎤

⎦ ⎥

Mix 3 orthogonal

modes X, Y and ZSpurious terms renormalize

the mode frequencies(Steve Girvin)

Isolates useful non-linearity with minimal number of spurious terms

ACTUALIMPLEMEN-TATION OFJOSEPHSON

PARAMETRICAMPLIFIER

SIGNAL

IDLER

180ºhybridcoupler

Design goals:TN < hf/kBGain > 20 dBBandwidth > 5 MHzDynamic range > 20 dB chip

Φ0/2

MICROGRAPH OF JOSEPHSON SUPERCONDUCTING CIRCUIT

6.2 GHz

100µm

500 nmPump1.6 GHz

CHIP DESIGN: MEANDER COPLANARSTRIPLINE RESONATORS

6.2 GHz

1.6 GHz

Pump @ 7.8 GHz

5 mm

MEASUREMENT SETUP

JPCChip

Pump line LF lineHF lineIn In

300mK

1K

4K

300K OutOut

-20 dB

50 Ω 50 Ω

+28 dB

-20 dB

-30 dB

-20 dB

-20 dB

-30 dB

50 Ω 50 Ω

+50dB +50dB

LOCATINGTHE HALF

FLUX-QUANTUMWORKING

POINT

color: phase of reflected signal

PRELIMINARY DATA: MEASUREMENTOF REFLECTED SIGNAL

42dB

30dB

No pump

With pump

PRELIMINARY DATA: DYNAMIC RANGE

CONCLUSIONS AND PERSPECTIVES

We have built a ultra-low noise practical microwaveamplifier operating in the quantum regime

Construction is simpler than the microstrip SQUID

Noise should be only limited by quantum fluctuations

Measurement of noise temperature is in progress

This amplifier is useful for:- minimally invasive readout of solid-state qubits- metrology of ampere (detection of Bloch osc.)- detection of very weak signals in astrophysics

TWO CASES

3 1 212 2

1 2

2 ;1

Q QG

χτ ττ ω ω

= =−

12 2

21

G ττ

=+

SPECTROSCOPYReadoutSpectroscopy pulse

Varying frequency

Fit:

Ecp = 17.0GHz

EJ0 = 15.02GHz

RELAXATION TIME, T1

Readoutπ pulse tw

T1=1.4µs↔1.8µs

RAMSEY FRINGESReadoutπ/2 pulse ∆t π/2 pulse

200ns ≤ T2 ≤ 800ns, ∆t

4 401 22 2.10 7.10Q Tϕ πν= = ↔

49


OFF-RESONANCE NMR-TYPEPULSE SEQUENCE

FOR QUBIT MANIPULATION

50


|0>

|1>

READOUTPROBING

PULSEor

~ ADCIN OUT

|0>

|1>


~ ADCIN OUT

AWG

40ns40ns200ns

IMPLEMENTATIONS

Lumped-element parallel LC oscillator

(JBA)

Distributed element oscillator (CBA)

53

Coplanar waveguide

Coplanar stripline

Parallel LC

(Limits Q-value)

Multiplexed readout and gate lines

Each resonator has different frequencyset by itslength

THIS YEAR: COUPLED STRIPLINE NON-LINEAR RESONATOR

Optical image of device

200µm

Gate

Slotline

SEM image of qubit

4µm

Advantages: 1. Completely fabricated using e-beam lithography2. Gate and readout lines separated

3. Excite ± mode in slotline for readout54

CBA WITH QUANTRONIUMOptical image

Output3m

m

56

10mm

readoutjunction

CPB

1

0

Input

Linear resonance frequency f0=9.64GHzQuality factor: Q=160

SEM image

OBSERVATION OF BISTABILITY

τm = 2µs

2µs 3µs 10ns

counts

Im[V

out]

Re[Vout]

57


2µs 3µs 10ns

counts

Im[V

out]

Re[Vout]

58


2µs 3µs 10ns

counts

Im[V

out]

Re[Vout]

59


2µs 3µs 10ns

counts

Drive amplitude variesonly by 1% thru

bifurcation!

Im[V

out]

Re[Vout]

60


2µs 3µs 10ns

counts

Im[V

out]

QUBIT STATEENCODED IN COMPLEX

AMPLITUDEOF TRANSMITTED PULSE

Re[Vout]

61

HYSTERESIS → LATCHING

0

1

Ω/2π = 4.2GHzT=15mK

1 ms sweep

62

Urf

14.3 GHz

9.5 GHz

πMEASUREMENT OFREADOUT FIDELITY

Urf

63

Urf

14.3 GHz

9.5 GHz


Urf

relaxation

slope3 timestoo small

64

65

Urf

14.3 GHz

9.5 GHz


Urf

F 0

1

10 011 p pF = − −F = 45−61%

on 4 samples

Readout relaxation Reduced contrast

THE AMPLIFIER: THE PHYSICIST’S BASIC TOOL, FROM ASTROPHYSICS TO NANOPHYSICS

RADIO-FREQUENCYPHENOMENON

(MHz-GHz)

DATA RECORD

AMPLI-FIER DETERtic

SIGNALDeterministic signal

++

+

THERMALNOISEThermal noise

ADDEDNOISE

ALTHOUGH NECESSARY, THE AMPLIFIERALWAYS DEGRADES INFORMATION

DET. SIGNAL

+

+

TH. NOISE

ADDEDNOISE

BACKGROUND NOISEAT RECORD LEVEL

>>


DET. SIGNAL

+

+

TH. NOISE

ADDEDNOISE


>>

TH. NOISE<1EFFICIENCY =

TH. NOISE + ADDED NOISE

Statistical Mechanics Information Theory


DET. SIGNAL

+

+

TH. NOISE

ADDEDNOISE


>>

QUANTUM REGIME:ENERGY OF EACH MODE OF

SIGNAL AND THERMAL NOISEIS OF ORDER 1 PHOTON

QUANTUM LIMIT:kBT / ω → 0

TH. NOISE → Z.P. FLUCT.

TH. NOISEEFFICIENCY =

TH. NOISE + ADDED NOISE

Statistical Mechanics Information Theory

WHAT IS A TEMPORAL MODE OF A SIGNAL?

mwpick “window” wavepacket

time

p pω ω= ∆

( ) 1ω −∆

nt n t= ∆

( )1/ 2ω∆

( ),m n p=window index:

2t ω π∆ ⋅ ∆ =

( ) ( )' ' '| dm m m m m mw w w t w t t δ+∞ ∗

−∞= =∫orthonormality:

frequency t∆

ω∆p

n time

WHAT IS A TEMPORAL MODE OF A SIGNAL? (CNT’D)

windowed Fourier decomposition:

( ) ( )1 dm mx X t w t t+∞

−∞= ∫

signal mode m : one degree of freedom;optimize window to deal with fewest modes

x≡

p≡( )X t →

( ) ( )2

dd

dm

mp

w tx X t t

tω+∞

−∞= ∫

This signal “atom” can be thought of as an harmonic oscillator

GEOMETRIC REPRESENTATIONOF A SIGNAL MODE

x2

x1α

E noise fuzzdisc

E = signal mode energyα = signal mode phase

AMPLIFICATION OF A QUANTUM SIGNAL

IN OUT

x2

x1

x2

x1

2FG ωh

α

GE2ωh

α

E

AMPLIFICATION AT THE QUANTUM LIMIT

IN OUT

x2

x1

x2

2ωh

α

E

x1

G ωh

α

GE Fmin=2

AMPLIFICATION AT THE QUANTUM LIMIT

IN OUT

x2

x1

x2

2ωh

α

E

x1

G ωh

α

GE

THE AMPLIFIER ADDS ONLYANOTHER ½ PHOTON !

(Caves, 1982)

NON-LINEAR AMPLIFICATION OF READOUT SIGNAL

Vd

Vdrive

R

C

L

Non-linear LC oscillator

w

|Vou

t|

linear LC oscillator

V

LJ

Vd


Vd

R

C

L


|Vou

t|

Vd

stable

unstable

stable

LJ


Vd

R

C

L


Quantronium Qubit0

1

E/E

c

Energy levels

Cg

Vg

g gC V e

0

1

2

|Vou

t|

Vd

stable

unstable

stable

LJ


Vd

R

C

L


Quantronium Qubit0

1

E/E

c

Energy levels

Cg

Vg

g gC V e

0

1

2

|Vou

t|

Vd

stable

unstable

stable

LJ

Mapping

0

1

RF READOUT OF "QUANTRONIUM" BASED ON BIFURCATION AMPLIFIER (JBA)

Cooper pairbox qubit

U

CHARGE PORT:CONTROL

PHASE PORT: READOUT

junction for non-linearinductance probing (gain)

shunting capacitors

(lowers frequency)


Cooper pairbox qubitQUBIT CONTROL

PULSE SEQUENCE

U


U

Cooper pairbox qubit READOUT

PROBINGRF PULSE


Cooper pairbox qubit

U

QUBITSTATE

ENCODEDIN REFL.PULSEPHASE

|0>

|1>

obeys the "no energyleft behind" principle!

QUANTUM OPTICS WITH CIRCUIT ELEMENTS

( )i t

[ ],Z X

Yiσ σ

σ=†,

1

a a⎡ ⎤⎣ ⎦=

STEER READOUT

( )u t

( )

( ) ( ) ( )( )0

† †4†

1

1

X Z

P Z

u t

a a a a t a

H

ai

ω

ω λ

σ

µ

σ

σ

= −

+ + + −+ +

h

h

4

48

JRJ

RC

EE

E

λ

µ

=

=

( ) ( )

( ) ( )2

g

P

Cu t e U t

C

i t I tCω

Σ

=

=h

can alsobe a cavity mode

(CBA, E. Boaknin et al.)

a

PROBLEM: DIFFICULT TO MAKEGOOD CAPACITORS AT HIGH

FREQUENCIES

SOLUTION: USE CAVITY RESONATOR

"Cavity Bifurcation Amplifier" configuration

very similar, but different from:

"circuit-QED" configuration

analogous to cavity QED expts byHaroche, Raimond, Brune et al.

LONG TERM GOAL: SCALABLE ARCHITECTURE

Cooper-pair box charge qubits

superconductingtransmission-line cavity

as quantum bus

multiplexed cavity Josephson bifurcation amplifiers for

readout of individual qubits

frequency-selectiveRF pulses for

1 and 2-bit operations

module scalable to 10’s of qubits if coherence and fidelity allow(need two superconducting wiring layers and one dielectric isolation layer)

SUPERCONDUCTING CAVITY = FABRY-PEROT

3mm

10mm

100µm

Nb

f = 2,5,10GHz

10µm

CPW ground

ISLAND

Readout junction

CPW ground

SAMPLE OF QUANTRONIUM IN CAVITY

QUANTRONIUM: AN ARTIFICIAL ATOM

Φ

U ΦgC

island

U

orthogonalityof steer andread modes

readsteer

IVion et al. 2002


( )i t

( )u tSTEER


PROBINGRF PULSE

READOUT

|0>

|1>

QUBIT STATEENCODED IN

REFLECTED PULSEPHASE


( )i t

( )u tSTEER


PROBINGRF PULSE

READOUT

QUANTRONIUM IN CAVITY:CAVITY BIFURCATION READOUT (CBA)

Udc

qubit

Urf

photon

-10

-5

0

5

10

V / V

d

5 4 3 2 1

ωd − ω0 / Γ

Log

P/P

c(d

B)

bifurcation critical parametersagree very well with thy

(ωd - ω0) / Γ


τm = 2µs

2µs 3µs 10ns

counts

Im[V

out]

Re[Vout]


2µs 3µs 10ns

counts

Im[V

out]

Re[Vout]


2µs 3µs 10ns

counts

amplitude variesonly by 1% thru

bifurcation!

Im[V

out]

Re[Vout]


2µs 3µs 10ns

counts

Im[V

out]

QUBIT STATEENCODED IN COMPLEX

AMPLITUDEOF TRANSMITTED PULSE

Re[Vout]

HYSTERESIS → LATCHING

0

1

Ω/2π = 4.2GHzT=15mK

1 ms sweep

Urf

14.3 GHz

9.5 GHz


Urf

Urf

14.3 GHz

9.5 GHz


Urf

relaxation

slope3 timestoo small

Urf

14.3 GHz

9.5 GHz


Urf

F 0

1

10 011 p pF = − −F = 45−61%

on 4 samples

Readout relaxation Reduced contrast

CAVITY QUANTRONIUMRABI OSCILLATIONS

M. Metcalfe et al.

f = 14.3GHz

20%

40%

60%

acqu

isiti

on ti

me

(s)

RAMSEYFRINGES

T2 =500ns+-

200ns

what is this dirt?- unpaired electrons- vortex motion- "glassy" two-levels

preparationpulse

analysis pulse

h φTOMOGRAPHY

exp

h φ

thy

0 0 12

+ 0 12− 01

Initial states

MULTIPLEXED CAVITY JBA's

IDEA: N QUBITS READ BY AN ARRAY OF MULTIPLEXEDRESONATORS (HARP PRINCIPLE)

2 mm 2 mm

Goal: frequency domain “MUX” of qubit readouts

MEASUREMENT OF MULTIPLE BIFURCATION

WHY IS IT IMPORTANT TO APPROACHTHE QUANTUM LIMIT OF AMPLIFICATION

AT MICROWAVE FREQUENCIES?

S

NOISE ENERGYIGNAL ENE BANDY HRG WIDT×INFORMATION CAPACITY =

(weak signal limit)

(Shannon 1948)

CAVEAT: WE WANT ALSO MAXIMUM POWER GAIN, QUIETNESS, EASE OF OPERATION, ETC.....

ARE THERE GENERAL GUIDING PRINCIPLESFOR CONSTRUCTING AN OPTIMAL AMPLIFIER?

CAN WE ACTUALLY BUILD ONE?

CAN WE DO A MEASUREMENT BEING ONLYLIMITED BY QUANTUM NOISE?

PIONEERING WORK BY Yurke et al. , 1986

RECENT THEORETICAL RESULTS BY Clerk, Girvin and Stone, 2004

ULTRA-LOW-NOISE AMPLIFICATION FOR THE READOUT …kosborn/index_files/DISQ/Disq_Devor… ·...

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