Expt. Andrew Houck David Schuster Hannes Majer Jerry Chow Andreas Wallraff Joseph Schreier Blake Johnson Luigi Frunzio Theory Alexandre Blais Jay Gambetta Jens Koch Lev Bishop Terri Yu David Price PI’s: Rob Schoelkopf Michel Devoret Steven Girvin Introduction to Decoherence and How To Fight It
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Expt.Andrew HouckDavid SchusterHannes Majer
Jerry ChowAndreas WallraffJoseph SchreierBlake JohnsonLuigi Frunzio
TheoryAlexandre BlaisJay Gambetta
Jens KochLev Bishop
Terri YuDavid Price
PI’s:Rob SchoelkopfMichel Devoret Steven Girvin
Introduction to Decoherenceand
How To Fight It
Why is decoherence so difficult?
Because is so small!h
Charge qubits:1510 eV-s (1 )(1nV)(1 s)e µ− =h
1e,2e
Flux qubits: 2(1 nT)(1 nA)(10 m) (1 s)µ µh
1 nA1 nT
10 mµ
SENSITIVITY OF BIAS SCHEMES TO NOISE (EXPD)
junction noises
bias ∆Qoff ∆EJ ∆EC
charge
flux
phase
CHARGED IMPURITYTUNNEL CHANNEL
- +-
ELECTRIC DIPOLES
chargequbit
fluxqubit
phasequbit
What can we do about environmental decoherence?
1. Choose materials and fabrication techniques which minimize 1/f noise, two-level fluctuators,dielectric loss, etc.
2. Use quiet dispersive readouts that leave no energybehind and which do not heat up the dirt or the q.p.’s(And: Develop low noise pre-amps so fewer photons needed for read out.)
3. Design using symmetry principles which immunize qubits against unavoidable environmental influences (e.g. sweet spots, topological protection)
( )0 1 ( ) ( ) ( )2 2
z z x yH Z t X t Y tω σ σ σ σ= + + +
t
E↓
E↑
Review of NMRlanguage
( ) causes transition frequency to fluctuation in time
( ), ( ) cause diabatic transitionsbetween eigenstates
Z t
X t Y t*
2 1
1 1 12T T Tϕ
= +
1
1T ↑ ↓= Γ +Γ
( )0 1 ( ) ( ) ( )2 2
z z x yH Z t X t Y tω σ σ σ σ= + + +
0 ( )Z tω +
t0 0
1 2 1 20 0 0
0
( )
1 ( ) ( )2
1[ (0)]2
( ) (0)
( ) (0)
( ) (0)
t
t t
ZZ
i d Zi t
d d Z Zi t
S ti t
t e e
t e e
t e e
τ τω
τ τ τ τω
ω
ρ ρ
ρ ρ
ρ ρ
−−
↑↓ ↑↓
−−
↑↓ ↑↓
−−↑↓ ↑↓
∫=
∫ ∫≈
≈
1 1 (0)2 ZZS
Tϕ=
Fluctuations in transition frequency make the phaseof superpositions unpredictable.
Gaussian white noise leads tohomogeneous broadening(Lorentzian line shape)
( )0 1 ( ) ( ) ( )2 2
z z x yH Z t X t Y tω σ σ σ σ= + + +
0 ( )Z tω +
t
0 0
0
2 2
0
( )
12
( ) (0) e
( ) (0)
( ) (0)
t
i d Zi t
i t itZ
Z ti t
t e
t e e
t e e
τ τω
ω
ω
ρ ρ
ρ ρ
ρ ρ
−−
↑↓ ↑↓
− −↑↓ ↑↓
−−↑↓ ↑↓
∫=
≈
≈
Low frequency 1/f noise leads toinhomogeneous broadening(gaussian line shape)
Spin echo can help insome cases.
Dephasing of CPB qubit due to gate charge noise
ener
gy
ng
◄ charge fluctuations
gn
22
g g2g g
1( ) ( ) ( ) ...2
Z ZZ t n t n tn n
δ δ∂ ∂≈ + +∂ ∂
0( ) ( )t Z tω ω= +
g g
2
g
1 1 1(0) (0) ...2 2ZZ n n
ZS ST n δ δϕ
⎛ ⎞∂= ≈ +⎜ ⎟⎜ ⎟∂⎝ ⎠
Outsmarting noise: CPB sweet spot
only sensitive to 2nd order fluctuations in gate charge!
ener
gy sweet spot
ng (gate charge)
ener
gy
ng
Vion et al., Science 296, 886 (2002)
◄ charge fluctuations
► Best CPB performance @ sweet spot: A. Wallraff et al., Phys. Rev. Lett. 95, 060501 (2005)
(Schoelkopf Lab)
DISTRIBUTION OF RAMSEY RESULTSat Charge Sweet Spot
(Devoret group, fast CBA readout)Lopsided frequency fluctuations
10
Charge noise!1/f2
3( ) , 1.9 10gNS eαω α
ω−=
value OKEJ/EC = 3.6
DISTRIBUTION OF RAMSEY RESULTSSecond order (curvature) effects limit coherence times to 500-600 ns
consistent with ~ 20 kHz ofresidual charge dispersion at EJ/EC = 50
*2 1
1 1 12T T Tϕ
= +
*2
1
2.05 0.1 s1.5 s
TT
µµ
= ±=
6 sTϕ µ=NO Echo:
consistent with ~ 20 kHz ofresidual charge dispersion at EJ/EC = 50
*2 1
1 1 12T T Tφ
= +
Phase coherence time becomes exponentially largerfor only modest increase in EJ/EC
Quasiparticles plentiful but non-poisoning. See Rob Schoelkopf’s talk.
Is T1 the only remaining problem???
( )0 1 ( ) ( ) ( )2 2
z z x yH Z t X t Y tω σ σ σ σ= + + +
[ ]
[ ]
1
0 0
0 0
1
1 ( ) ( )41 ( ) ( )4
XX YY
XX YY
T
S S
S S
ω ω
ω ω
↑ ↓
↓
↑
= Γ +Γ
Γ = + + +
Γ = − + −
emission into environment
absorption from environment
( )1 2 1 1 tanC C jC C j δ= − = −
Environment = Junction Loss?? 1tan
Qδ
=
( )i t
( )B2( ) 1iiS nR
ω ω= +h 01
1LC
ω =
ω( )0 B
1
1 tan 2 1nT
ω δ= +
Reduce Junction Participation Ratio
1tan
Qδ
=
( )i tCS
S
tan tanCC C
δ δ′ =+
If shunt capacitanceis lossless then:
UCSB: overlap shunt capacitorNori et al. proposal: shunt capacitance in flux qubitsYale: single layer transmon shunt capacitance
Qubit is simply an anharmonic oscillator. A necessary but not sufficient conditionto achieve high Q is to be able to make high Q resonators on the same substrate.
Purcell Effect:Engineering Spontaneous Emission from Cavity
?
?
?
Substrate lossesJunction losses
Shunt capacitance
Density of EM States Seen by Qubit Weakly Coupled to Cavity
cavityω ω
Cavity filtering enhances qubit decay rate
Cavity filtering reduces qubit decay rate
cavitygQ
ωκ =
κ
50 ohm background decay rate
This picture only valid in the ‘bad cavity’ limit:
cavity
qubit
qubit
cavity
2 250 MHzg
2
NR1 1
1 1 gT T
κ⎛ ⎞≈ + ⎜ ⎟∆⎝ ⎠
κ∆
Strong Qubit-Cavity Coupling:‘Good Cavity’ Limit
g∆
With proper engineeringand detuning from cavityresonances, spontaneousfluorescence can be madesmall.
In limit of large detuning:
again...TϕMeasurement Induced Dephasing
Photons intentionally or accidentally introducedinto the cavity cause a light shift (ac Stark shift) of the qubit frequency
eff 01†
2
r†
2 zg aH a aa ωω σ
⎛ ⎞′= +
∆⎜ ⎟⎝
+⎠
hhh
atom-cavity couplingatom-cavity detuning
g∆==
Measurement induced dephasing:g∆
eff 01†
2
r†
2 zg aH a aa ωω σ
⎛ ⎞′= +
∆⎜ ⎟⎝
+⎠
hhh
AC Stark shift of qubit by photons
†
1a a =†
20n a a= =
RMSn nδ =
AC Stark measurements: Schuster et al., PRL 94, 123602 (2005).
Phase shift induced by passage of a single photon
( ) ( )/ 2 / 2in out
2
1 11 12 2
2arctan resonator decay rate2
i ie e
g
θ θ
θ κκ
+ −↑ + ↓ → ↑ + ↓
⎛ ⎞= =⎜ ⎟∆⎝ ⎠
For strong coupling, even a single photon measures the state of the qubitand destroys the superposition:
1 nTϕ
κ
What can we do about environmental decoherence?
1. Choose materials and fabrication techniques which minimize 1/f noise, two-level fluctuators,dielectric loss, etc.
2. Use quiet dispersive readouts that leave no energybehind and which do not heat up the dirt or the q.p.’s(And: Develop low noise pre-amps so fewer photons needed for read out.)
3. Design using symmetry principles which immunize qubits against unavoidable environmental influences (e.g. sweet spots, topological protection)
The End
Coherence Limits for SC QubitsNoise source transmon
[1] A. B. Zorin et al., Phys. Rev. B 53, 13682 (1996).[2] F. C. Wellstood et al., Appl. Phys. Lett. 50, 772 (1987).[3] F. Yoshihara et al., Phys. Rev. Lett. 97, 16001 (2006).
* values evaluated at sweet spots† value away from flux sweet spot at Φ0/4 [4] D. J. Van Harlingen et al., Phys. Rev. B 70, 064517 (2004).
[5] A. Wallraff et al., Phys. Rev. Lett. 95, 060501 (2005).[6] P. Bertet et al., Phys. Rev. Lett. 95, 257002 (2005).[7] M. Steffen et al., Phys. Rev. Lett. 97, 050502 (2006).