Decoherence in flux qubits

Yasunobu Nakamura

NEC Nano Electronics Research LaboratoriesRIKEN Frontier Research SystemCREST-JST

• Measurement of T1, T2 – qubit as a spectrum analyzer• Longer T1 samples• Flux qubit in a cavity

YuriPashkin

AnttiNiskanen

ShenTsai

OlegAstafiev

KhalilHarrabi

MichioWatanabe

TsuyoshiYamamoto

FumikiYoshihara

KazuakiMatsuba

TiefuLi

YasuNakamura

HyunsikIm

FarrukhAbdumalikov

Study of decoherence

= Characterization of environment• Qubit as a tool for investigating its environment

environment

interaction

qubit

tunabletunable

Charge-flux: Cottet 2002, Ithier 2005 (Saclay)Charge: Astafiev 2004 (NEC), Duty 2004 (Chalmers)Flux: Bertet 2005 (Delft), Yoshihara 2006 (NEC), Kakuyanagi 2007 (NTT)Phase: Simmonds 2004, Cooper 2005, Martinis 2005 (NIST/UCSB)

Steffen 2006, Bialczak 2007 (UCSB), Claudon 2006 (Grenoble)

Possible decoherence sources

phonons?

photons?

magnetic-field noise?

charge fluctuations?

paramagnetic/nuclear spins?

trapped vortices?

charge/Josephson-energy fluctuations?

quasiparticletunneling?

environment circuit modes?

Flux qubit: Hamiltonian and energy levels

J.E. Mooij et al. Science 285, 1036 (1999)

0.8 1.0 1.2-100

0

100

Energy (GHz)

γq/πnφ/nφ* nφ*=0.5

Sensitivity to noises

relaxation

dephasing

transverse coupling

longitudinal coupling

nφ-nφ*

Estimation of decoherence time

• EJ-fluctuation can be the largest contribution

4JJ flux qubit @ optimal bias point

preliminaryJ. Koch et al. PRA 76, 042319 (2007)

cf. transmon and CPB

constraints:

Flux qubit: experimental setup

Rabi oscillationsresonant microwave pulse

visibility~79.5%

Energy relaxation

relaxation and excitation

for weak perturbation: Fermi’s golden rule

ex. Johnson noise in ohmic resistor R

spontaneous emission

absorption

zero-point fluctuation of environment

• qubit energy E01 variable• relaxation ∝ S(+E01 ) and excitation ∝ S(-E01 )⇒ quantum spectrum analyzer

U. Gavish et al.R. Aguado and L. KouwenhovenR. Schoelkopf et al.O. Astafiev et al.

T1 vs f: flux bias dependence

80

70

60

50

Switc

hing

pro

babi

lity

(%)

1.61.20.80.40.0Time ( µs)

π ~ 4ns

delay readout pulse

E01 /h (G

Hz)

E01

initialization to ground state is better than 90%⇒ relaxation dominant⇒ classical noise is not important

at qubit frequency ~ 5 GHz

nφ

Γ1 vs E01: qubit energy dependence

• Data from both sides of spectroscopy coincide

• Floor at high-frequency

• Random high-frequency peaks• Broad structure at low frequency

• Depends on SQUID bias pointE01/h (GHz)sample3

E01/h (GHz)sample5

Gamma_1 at different flux bias

Dephasing

free evolution of the qubit phase

dephasing

sensitivity of qubit energy to the fluctuations of external parameter

tunable

information of S(ω) at low frequencies

tunablefor Gaussian fluctuations

Dephasing: T2Ramsey, T2echo measurement

π/2~2ns π/2

t

correspond to detuning

readout pulse

Ramsey interference (free induction decay)

0.01 0.1 1 10 100freq.

0.20.40.60.8

1

thgiew

[1/t]

π/2π ~ 4ns

t/2

readout pulse

π/2~2ns

t/2

spin echo

0.01 0.1 1 10 100freq.

0.20.40.60.8

1

thgiew

[1/t]

Optimal point to minimize dephasing

Ib

nφ• two bias parameters– External flux: nφ=Φex/Φ0

– SQUID bias current Ib

nφ

E01 (GHz)

Ib

G. Burkard et al. PRB 71, 134504 (2005); P. Bertet et al. PRL 95, 257002 (2005).

T1 and T2echo at optimal point nφ=nφ*, Ib=Ib*

T1=545±16ns

Echo decay time is limited by relaxation

Pure dephasing due to high frequency noise (>MHz) is negligible

Echo at nφ≠nφ*, Ib=Ib*

consistent with 1/f flux noise

do not fit

No high-frequency cut-off (soft nor hard)below ~1 MHz

1/f noise cut off dependence

ΓϕRamsey, Γϕecho vs nφ : flux bias dependence

Red lines: fit

For

Flux noise, not charge noise nor critical current noise

F. Yoshihara et al. PRL 97, 167001 (2006)

Dephasing due to photon number fluctuations in SQUID plasma mode

D.I. Schuster et al. PRL 94, 123602 (2005); P. Bertet et al. Phys. Rev. Lett. 95, 257002 (2005).

thermal fluctuation of photon number in resonator ⇒ dephasing of qubit

κ: cavity decay

exponential decay

Red: dephasing due to 1/f flux noisequbit + resonator

1/f flux noise: sample dependence

3 4.58 242.9 11.0 1.63

5 5.08 246.4 9.68 1.406 3.85 229.5 18.7 2.90

11 6.07 232.6 10.1 1.5514 5.45 132 4.9 1.32Loop area ~3 µm2

7±3x10-6 [Φ0] SQUID~2500-160000 µm2 F.C.Wellstood et al. APL50, 772 (1987)1.5x10-6 [Φ0] phase qubit ~10000 µm2 (gradiometer) R.C. Bialczak et al. PRL 99, 187006 (2007)~ 1x10-6 [Φ0] flux qubit ~1000 µm2 (Berkeley, unpublished)~ 1x10-6 [Φ0] flux qubit ~ 25 µm2 K. Kakuyanagi et al. PRL 98, 047004 (2007)

Loop size independent?

Optimal point to minimize dephasing

Ib

nφ• two bias parameters– External flux: nφ=Φex/Φ0

– SQUID bias current Ib

nφ

E01 (GHz)

Ib

G. Burkard et al. PRB 71, 134504 (2005); P. Bertet et al. PRL 95, 257002 (2005).

Γ1, ΓϕRamsey, Γϕecho vs Ib : bias current dependence

relaxation:

Increase |Ib-Ib*| ⇒ selectively introduce Ib noise coupling

F. Yoshihara et al. PRL 97, 167001 (2006).

•exponential decay

dephasing:

•inefficient echo

Yu. Makhlin and A. Shnirman, PRL92, 178301 (2004);G. Burkard et al. PRB71, 134504 (2005).

Summary• T1, T2 measurement in flux qubit, T1,T2echo~ several µs• dependence on flux bias and SQUID-current bias conditions⇒ characterization of environment

Optimal point nφ=nφ*, Ib=Ib*

T1 limited echo decayPure dephasing due to low freq. noise

nφ=nφ*, Ib≠Ib*

‘white’ Ib noise dominant

nφ≠nφ*, Ib=Ib*

1/f flux noise dominant

Open questions: -T1 vs flux bias-residual dephasing at optimal point-origin of 1/f flux noise

Effect of environment circuit design

R-environmentwith large Cshunt

LC-environmentwith less Cshunt

Single qubit 06-06-06 with on-chip LC filter

SQUIDplasmamode

Res

onan

ce in

the

LC

filte

r

Rabi measurements at optimal point

0 1 2 3 4-5

0

5

t(µ s)0 1 2 3 4

-5

0

5

t(µ s)

0 1 2 3 4-5

0

5

t(µ s)0 1 2 3 4

-5

0

5

t(µ s)

0 1 2 3 470

75

80

t(µ s)0 1 2 3 4

80

85

90

t(µ s)

Psw

(%)

strong driving

weak driving

T2Rabi ~ 6 µs(corrected for drift)

Relaxation at optimal point last logs of T1T2 B=opt Ipre=0.311opt2.lvd

0 5 10 15 20 25 3029

30

31

32

33

34

35

36

37

38

time (µ s)

Psw

(%)

T1 = 6.3 µs

Ramsey at optimal point last logs of T1T2 B=opt Ipre=0.311opt2.lvd

0 0.5 1 1.5 2 2.5 331

32

33

34

35

36

37

38

39

time (µ s)

Psw

(%)

T2Ramsey = 2.7 µs

Echo at optimal point last logs of T1T2 B=opt Ipre=0.311opt2.lvd

0 5 10 15 20 25 3031.5

32

32.5

33

33.5

34

34.5

35

35.5

36

time (µ s)

Psw

(%)

T2echo = 3.7 µs

Sample with best coherence

On-chip resistors were replaced by superconducting leads by mistake

∆/h=2.557 GHz, IP=157 nA2.3 µΦ0/Hz1/2 @ 1Hz

A. Abdumalikov, Jr.O. AstafievFlux qubit in a cavity: sample design

Nb – main part of the resonator

Qubit

SOG – isolator, used only for test structures

Al – adjust coupling of the resonator and qubit

Resonator quality factor is defined by the form of this Al island

chip size: 2.5 × 5 mm

Spectroscopy

• Plot shows the change of the phasedip when peak when

Vacuum Rabi splitting

fit:

Relaxation time (continuous measurement)

• measured by sweeping the pulse period– Pulse width was 10 ns

• T1= 0.73 µs – Qubit frequency

E01/h = 8.4 GHz– Coupling to cavity

gsinθ/h = 30 MHz

• E01 dependence

Remarks

•Qubit is powerful tool to analyze its environment

What we have tried and we have been trying

• Flux bias point dependence (nφ*=0.5, 1.5, 2.5; up to 20 Gs)• T1 depends on bias point – coupling to the SQUID is different• T2echo, T2Ramsey are almost independent ~ 20% variation

• Area dependence• 4 times larger qubit – flux noise 3.6 µΦ0/Hz-1/2

• Qubit with small ∆/h~50 MHz• Long T1 ~ 5 ms• Consistent with flux noise contribution• However, does not necessarily mean flux noise contribution

• Spin locking• Temperature dependence of T1• Qubit with variable ∆• Superconducting leads