Amplifying Quantum Signals with the Josephson...
Transcript of Amplifying Quantum Signals with the Josephson...
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