introduction to decoherence and how to fight itkosborn/index_files/... · steven girvin...
TRANSCRIPT
![Page 1: Introduction to Decoherence and How To Fight Itkosborn/index_files/... · Steven Girvin Introduction to Decoherence and How To Fight It. Why is decoherence so difficult? ... tan tan](https://reader033.vdocuments.us/reader033/viewer/2022051910/6000737b87c0e900af582f5a/html5/thumbnails/1.jpg)
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
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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
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SENSITIVITY OF BIAS SCHEMES TO NOISE (EXPD)
junction noises
bias ∆Qoff ∆EJ ∆EC
charge
flux
phase
CHARGED IMPURITYTUNNEL CHANNEL
- +-
ELECTRIC DIPOLES
chargequbit
fluxqubit
phasequbit
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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)
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( )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
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( )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)
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( )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.
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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
⎛ ⎞∂= ≈ +⎜ ⎟⎜ ⎟∂⎝ ⎠
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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)
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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
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DISTRIBUTION OF RAMSEY RESULTSSecond order (curvature) effects limit coherence times to 500-600 ns
Need larger EJ/EC for less curvature
Lopsided frequency fluctuations
Charge noise!1/f2
3( ) , 1.9 10gNS eαω α
ω−=
value OK11
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Comparison of superconducting qubitsEJ/EC ~ 0.1-10 EJ/EC ~ 30-100 EJ/EC ~ 10,000
Cooper pair box Transmon Phase qubit
100 µm
5 µm
12
Ng
E
50 µm
60 µm
sweet spoteverywhere!E
Ng
EgV
Φbias cI I≈
Large junction
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Transmon qubit: Sweet Spot EverywhereE
nerg
y
Ng (gate charge)
EJ/EC = 1 EJ/EC = 5 EJ/EC = 10 EJ/EC = 50
charge dispersion Exponentially small charge dispersion!
290 µm
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quantum rotor(charged, in constantvector potential )
Offset charge = ‘vector potential’
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T2 and Larmor Frequency Statistics1st generation transmon with on Si
with EJ/EC ~ 50, flux sweet spot20 hours of Ramsey experiments, no retuning
There is no significant drift or 1/f dephasing on these scales!
2 1140 10 ns 2T T= ± = 01 7350495 90 kHzω = ±1 79 3 nsT = ±
15
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Coherence in Second Generation Transmon
12 ns π-pulsesRabi visibility100.4% +- 1%
T1 = 1.5 µs
T2* = 2 µs
Rabi experiment
Ramsey experiment
T1 Measurement
no echo, at flux sweet spot
6 sTϕ µ=
consistent with ~ 20 kHz ofresidual charge dispersion at EJ/EC = 50
*2 1
1 1 12T T Tϕ
= +
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*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???
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( )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
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( )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= +
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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.
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Purcell Effect:Engineering Spontaneous Emission from Cavity
?
?
?
Substrate lossesJunction losses
Shunt capacitance
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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:
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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:
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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∆==
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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).
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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
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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)
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The End
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Coherence Limits for SC QubitsNoise source transmon
EJ/EC=85CPB
EJ/EC=1flux qubit phase
qubit
dephasing 1/f amplitude T2 [ns] T2 [ns] T2 [ns] T2 [ns]
charge 10-4 – 10-3 e [1] 400,000 1,000* 1,500 ∞
flux 10-6–10-5 Φ0 [2,3] 3,600,000*1,000 - 10,000†
1,000,000* 1,000 - 2,000* 300
critical current 10-7 – 10-6 I0 [4] 35,000 17,000 1,500 1,000
measured T2 [ns]
last yearthis year
1402,000
> 500 [5] 4,000 [3,6] 160 [7]
measured T1[ns]
last yearthis year
904,000
~ 7,000 [5] 2,000 - 4,000[3,6]
110 [7]
[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).