Decoherence in flux

Yasunobu Nakamura

NEC Nano Electronics Research Laboratories RIKEN Frontier Research System CREST-JST

• Measurement of T1, T2 – as a spectrum analyzer •Longer T1 samples •Flux qubitin a cavity Hyunsik Im Farrukh Abdumalikov

Yuri Shen Khalil Tsuyoshi Kazuaki Yasu Pashkin Tsai Harrabi Yamamoto Matsuba Nakamura

Antti Oleg Michio Fumiki Tiefu Niskanen Astafiev Watanabe Yoshihara Li Study of decoherence

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

environment

interaction

qubit

tunable tunable

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

magnetic-field noise?

trapped vortices?

paramagnetic/nuclear spins?

charge fluctuations? environment circuit modes?

phonons? tunneling?

?

charge/Josephson-energy fluctuations? : Hamiltonian and energy levels

100 ) z GH ( 0 y

g r e En

-100 0.81.01.2 γ /π nqφ/nφ* nφ*=0.5

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

relaxation

transverse coupling

dephasing

longitudinal coupling

nφ-nφ* Estimation of decoherence time

4JJ flux qubit @ optimal bias point constraints:

•EJ-fluctuation can be the largest contribution cf. transmon and CPB

J. Koch et al. PRA 76, 042319 (2007) preliminary Flux qubit: experimental setup

Rabi oscillations resonant microwave pulse

visibility~79.5% Energy relaxation

relaxation and excitation

for weak perturbation: Fermi’s golden rule

•qubitenergy E01 variable • relaxation ∝ S(+E01 ) and excitation ∝ S(-E01 ) ⇒ quantum spectrum analyzer U. Gavish et al. R. Aguado and L. Kouwenhoven R. Schoelkopf et al. O. Astafiev et al. zero-point fluctuation of

environment ex. Johnson noise in ohmic resistor R spontaneous absorption emission

T1 vs f: flux bias dependence

80 π ~ 4ns 70

delay readout pulse 60

50

Switching probability (%) 0.0 0.4 0.8 1.2 1.6 Time ( µs)

initialization to ground state is better than 90%

E01 ⇒ relaxation dominant ⇒ classical noise is not important at qubit frequency ~ 5 GHz E 01 /h (G Hz)

nφ Γ1 vs E01: qubit energy dependence

• Data from both sides of spectroscopy coincide • Floor at high-frequency

• Random high-frequency peaks sample3 E /h (GHz) • Broad structure at low frequency 01 • Depends on SQUID bias point

sample5 E01/h (GHz) Gamma_1 at different flux bias Dephasing

free evolution of the qubit phase

dephasing

for Gaussian fluctuations tunable tunable sensitivity of qubit energy to the fluctuations of external parameter

information of S(ω) at low frequencies Dephasing: T2Ramsey, T2echo measurement Ramsey interference (free induction decay) correspond to detuning π/2~2ns π/2

readout pulse

t 1 0.8 t h g

i 0.6 e

w 0.4 0.2

0.01 0.1 1 10 100 freq. [1/t] spin echo π/2~2ns π ~ 4ns π/2

readout pulse

t/2 t/2 1 0.8 t h g

i 0.6 e

w 0.4 0.2

0.01 0.1 1 10 100 freq. [1/t] Optimal point to minimize dephasing

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

– SQUID bias current Ib

E01 (GHz)

I b

nφ

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 number fluctuations in SQUID plasma mode

qubit + resonator Red: dephasing due to 1/f flux noise

thermal fluctuation of photon number in resonator ⇒ dephasing of qubit

exponential decay

κ: cavity decay

D.I. Schuster et al. PRL 94, 123602 (2005); P. Bertet et al. Phys. Rev. Lett. 95, 257002 (2005). 1/f flux noise: sample dependence

3 4.58 242.9 11.0 1.63 5 5.08 246.4 9.68 1.40 6 3.85 229.5 18.7 2.90 11 6.07 232.6 10.1 1.55

Loop area ~3 µm2 14 5.45 132 4.9 1.32

-6 2 7±3x10 [Φ0] SQUID~2500-160000 µm F.C.Wellstood et al. APL50, 772 (1987) -6 2 1.5x10 [Φ0] phase qubit ~10000 µm (gradiometer) R.C. Bialczak et al. PRL 99, 187006 (2007) -6 2 ~ 1x10 [Φ0] flux qubit ~1000 µm (Berkeley, unpublished) -6 2 ~ 1x10 [Φ0] flux qubit ~ 25 µm K. Kakuyanagi et al. PRL 98, 047004 (2007) Loop size independent? Optimal point to minimize dephasing

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

– SQUID bias current Ib

E01 (GHz)

I b

nφ

G. Burkard et al. PRB 71, 134504 (2005); P. Bertet et al. PRL 95, 257002 (2005). Γ1, ΓϕRamsey, Γϕecho vs Ib : bias current dependence F. Yoshihara et al. PRL 97, 167001 (2006). * Increase |Ib-Ib | ⇒ selectively introduce Ib noise coupling

•exponential decay

•inefficient echo

relaxation: dephasing:

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* nφ=nφ*, Ib≠Ib*

T1 limited echo decay Pure dephasing due to low freq. noise

‘white’ Ib noise dominant

nφ≠nφ*, Ib=Ib*

Open questions:

-T1 vs flux bias -residual dephasing at optimal point 1/f flux noise dominant -origin of 1/f flux noise Effect of environment circuit design

R-environment

with large Cshunt

LC-environment

with less Cshunt Single qubit 06-06-06 with on-chip LC filter sonance in the LC filter Re

SQUID plasma mode Rabi measurements at optimal point

(corrected for drift) T2Rabi ~6µs 5 5 strong driving

0 0

-5 -5 0 1 2 3 4 0 1 2 3 4 t(µ s) t(µ s) 5 5 %) ( 0 0 Psw -5 -5 0 1 2 3 4 0 1 2 3 4 t(µ s) t(µ s) 80 90 weak driving

75 85

70 80 0 1 2 3 4 0 1 2 3 4 t(µ s) t(µ s) Relaxation at optimal point last logs of T1T2 B=opt Ipre=0.311opt2.lvd

38

37

36

35 T1 =6.3µs

34 %) ( 33 Psw 32

31

30

29 0 5 10 15 20 25 30 time (µ s) Ramsey at optimal point last logs of T1T2 B=opt Ipre=0.311opt2.lvd

39

38 T2Ramsey =2.7µs

37

36 %) ( 35

Psw 34

33

32

31 0 0.5 1 1.5 2 2.5 3 time (µ s) Echo at optimal point last logs of T1T2 B=opt Ipre=0.311opt2.lvd

36

35.5

35

34.5

34 %) (

33.5 T2echo = 3.7 µs Psw 33

32.5

32

31.5 0 5 10 15 20 25 30 time (µ s) Sample with best

On-chip resistors were replaced by superconducting leads by mistake

∆/h=2.557 GHz, IP=157 nA 1/2 2.3 µΦ0/Hz @ 1Hz A. Abdumalikov, Jr. Flux qubit in a cavity: sample design O. Astafiev

Qubit

Nb – main part of the resonator SOG – isolator, used only for test structures Resonator quality factor is defined by the form of Al – adjust coupling of the resonator and qubit this Al island chip size: 2.5 × 5 mm Spectroscopy

• Plot shows the change of the phase dip 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 -1/2 • 4 times larger qubit – flux noise 3.6 µΦ0/Hz • 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 •Qubitwith variable ∆ • Superconducting leads