Two Level Systems and Kondo-like traps as possible sources of decoherence in superconducting qubits Lara Faoro and Lev Ioffe Rutgers University (USA)

Two Level Systems and Kondo-like traps as possible sources of

decoherence in superconducting qubits

Lara Faoro and Lev Ioffe

Rutgers University (USA)

Outline

• Decoherence in superconducting qubit [ experimental state of the art ]:• low frequency noise (1/f noise)• high frequency noise (f noise)

• We discuss two possible microscopic mechanisms for the fluctuators• weakly interacting quantum Two Level Systems (TLSs)• environment made by Kondo-like traps

• TLSs model: • significant source of noise• detailed characteristics of the noise power spectrum are in a qualitative and quantitative disagreement with the data

• Kondo-like traps model:• significant source of noise• agreement with most features observed in the experiments

What are the sources of noise?

There are several experiments in different frequency regimes butthe dominant source of noise is yet to be identified!

Electromagnetic fluctuationsof the circuit (gaussian)

Discrete noise due tofluctuating background charges (BC)trapped in the substrate or in thejunction

S

?

1

Experimental picture ofthe noise power spectrum

Zimmerli et al. 1992Visscher et al. 1995 Zorin et al. 1996 Kenyon et al. 2000Nakamura et al. 2001Astafiev et al. 2004 Wellstood et al. 2004

T

Origin of both types of noise are the same ?

Low frequency noise ( 1/f )

• 1/f spectrum up to frequency ~ 100-1000 Hz. [ where is the upper cut-off ??? ] The intensity is in the range of at f=10Hz

• some samples clearly produce a telegraph noise but 1/f spectrum points to numerous charges participating in generating the noise.

• This noise dominates and it is greatly reduced by echo technique.

Hze43 1010

2T

• - Temperature dependence of the noise 2T

S

high frequency noise ( f )

Theoretical analysis

Upper level: use a proper model to study decoherence. “fluctuators model” and not spin boson model Paladino, Faoro, Falci and Fazio (2002) Galperin, Altshuler, Shantsev (2003)

Lower level: understanding which is the microscopic mechanism of decoherence that originate the fluctuators Faoro, Bergli, Altshuler and Galperin (2004)

Faoro and Ioffe (2005)

Quantum TLSs modelxzTLS tEH

4322

1010

de

tt,EP with

eVcm3

2010

i

zii

i ij ij

iijiijjiint pp̂

r

p̂r̂p̂r̂p̂p̂H

34

3

dep

The effective strength of the interactions is controlled by and it is always very weak.

2p

• Many TLSs interacts via dipole-dipole interactions:

23

3

2 prdEP

r

pEE ji

• interaction with low energy phonons T>100 mk

Relaxations for TLSs

Dipole and qubit interaction

L

pVCQ

Q

EpV g

nmL 3

nmL 300

tiggq eQtQdtS 0

iiizii deppp̂

i

tiiz

iz etdtG 0

ixi

izi

iz sincos 22

iii

i

ii

i

ii

tEE

E

tsinθ

E

Eθcos

Each dipole induces a change in the island potential or in the gate charge

i.e.

barrier

substrate

Charge Noise Power Spectrum:

Rotated basis:

+++

---

Q

Dephasing rates for the dipoles

i

ixi

izii

effint sincosthH

ij j

jijci Ecoshcoskh

222 1

Tp

2pure dephasing:

The weak interaction• causes a width in each TLS• at low frequency some of the TLSs become classical

Effective electric field

34

3

ij

jijiijjiij r

pr̂pr̂ppk

N.B: density of thermally activated TLSs enough (Continuum)

T 310

Relaxation rates for the dipoles

Tp

sin ii

2221

jiijj ji

i sinsinkEE

222

221

Fermi Golden Rule

0 ji EE

But in presence of large disorder, some of TLSs:

These dipoles become classical and will be responsible for 1/f noise

qS at high frequency

22

2

20

i

iii

tiiz

iz

EsinetdtG

222

2

eLe

VpSq

white!

Tp

2

In the barrier...3

710

AV The density of TLSs ~ too low! K/.10

Astafiev et al. 2004

Edet

EnE

HHHH

zxzxJ

zgC

ITLSQ

22

214

22 tedEE

eVEE

GHzEeVEnm.d

E

E

L

dEE

optopt

optC

opt

Coptopt

2

3013010

12

1

1

2

2

2

12

Strongly coupled TLS21gn

23gn

E

gn

In the substrate...

3910

AV

222

2

eLe

VpSq

HzeSq

21817 1010

• Comparison with experiments :

Astafiev et al. 2004

mKTC 120

2862

1010 eSq 2

Hze

TS

Cq

217152

1010

qS at low frequency

21

2

12 20

i

i

iii

tiiz

iz cosetdtG

222

2

eT

Le

VpSq

• it has a 1/f dependence for

• it has only linear dependence on Temperature

• it has intensity in agreement with experimental data

T310

What did we learn from the dipole picture?

qS

f1

2T dependence

Search for fluctuators of different nature ...

CT

eVcm3

2010

Number of thermally activated TLSs

T

eVWVW

TnTLS 10

NW

TnTLS

2

dependence

VVT

WN 0

60 10

Andreev fluctuators model

qubit

v

• correlations are short range• amplitude of oscillations increases with increasing

Faoro, Bergli, Altshuler and Galperin (2004)

ccccTHccH

HT

T~ccvH

TE

zTI

0

0

2

0

2 gdg 2T dependence

T 110 06

0 VVW

TN mKT 20

Kondo-like traps model

dididi

i kdikkisd

dii

didii

didd

kkkkk

kkBCS

sddBCS

ccn

.c.hccVH

nnUccH

.c.hccccH

HHHH

0

Uexp

UT d

i

d

ii

iK

00

122

202 ii VN

Kondo Temperature

U

0d

Properties of the ground state and the localized excited state

30.TTT *K

*KKK

KT KT

Weak coupling Strong coupling

KT

ds EE

doublet

singlet

0sHd 30.T *

K

“Physics” of the Kondo-like traps

*K

*KK

K

KKKK

T

TTT

dTd

0

0

0

0

0

242

3

220 10

1 *K

*K

Al

*K TTTA

r

eAA

0

Slow processes

Fast processes

0d

KTw

barrier

superconductor

Superconductor coherence lenght

Density of states closeto the Fermi energy

bare density

weight of the Kondo resonance

L

HzW

Hz.T *K

14

10

10

1030

ji tjit

ATransition amplitude:

at high frequency qS

2

cothRS

20

2

021 AT

VweGR

*K

• This noise is dominated by fast tunneling processes between traps• effectively the motion of electrons between trap acts as resistor R

From the conductance G we calculate the resistance R

The noise power spectrum raises linearly with the frequency!

NB: Andreev fluctuators have the same but … and

12

1 2

at low frequency qS

22

02

2 T

T

V

L

rweS

*K

q

*KT

TV

L

rw

0

410w

e32 1010

e43 1010

• in the barrier :

3710

AV

22

2

0i

i

i

tiggq L

rweeQtQdtS

HzA?,d

Ai

iii

80 10 but maxmin

g

33

0 10

A

experimental value:

estimates :

• We have discussed a novel microscopic mechanism (Kondo-like traps) that might be the dominant source of noise for dephasing

• But the “physics” of the device is complex : Kondo-like + TLSs

• TLSs are “killed” by the T-dependence!

• Our analysis cannot be done in greater details, due to the lack of an analytical theory of kondo-like impurites with superconductor

• Try to measure 1/f noise after suppressing the superconductivity. We expect reduction of 1/f noise

• Reasonable level of noise even only in the barrier. • Different substrates no changes in the intensity of the noise (NEC)• relevant for phase qubit.

Conclusions