Two Level Systems in Phase Qubits: Tunnel Barriers & Wiring Dielectrics

Jeff Kline

March 6, 2008

Josephson Junctions1||1ie 2||2

ie

: complex pair wavefunction: phase of Cooper pairs = 1 - 2 is the phase difference across the junction

Josephson Inductance

cos2 o

oJO IL

•The phase changes according to the potential U•The motion of has an exact correspondence with the motion of a particle moving in the potential U•It is easier to visualize the particle’s motion, so we speak in terms of the fictitious “particle” in the washboard potential

e

ho 2 “Flux quantum”

Tilted Washboard Potential

sinoS II Ve

Vdt

d

o 22

Josephson Relations

o

oo

I

IIU cos

2)(

S1 S2I

Phase Qubits

32/6

)2/)(()(

oooo

IIIU

Nonlinearity•Unlike other qubits, the phase qubit must be current-biased with Ibias~Io and ~/2•This is necessary to obtain a large nonlinearity in the Josephson inductance•This nonlinearity is what produces the unequal energy level spacing required for unique level addressability

Ibias JJ

A phase qubit is simply a current biased JJ in parallel with its “self capacitance”

For Ibias~Io & ~/2

•It is a cubic potential (i.e., 3), so QM energy levels have unequal spacing•Avg. Slope of U() is –I/Io •For I<Io, U() has relative minima, and particle can be trapped

•When particle is trapped, JJ is in zero-voltage state

•When particle escapes from well, JJ makes transition to non-zero voltage state (a.k.a. running state)

CJ

“self-capacitance”

Trapped state Running state

QM Energy levels

Ibias ~ Io

U()

|0>

|1>ħ10

Qubit Spectroscopy-Theory

Ibias JJ

Qubit Spectroscopy-Theory

Ibias’ > Ibias

U()

|0>

|1>

|0’>

|1’>ħ10

’

ħ10

10

(GHz)

Ibias (a.u.)

Ibias JJ

Qubit Spectroscopy-Experiment

“Splittings”

Spurious Two Level Systems

Displacement• Transverse• Bond direction• Rotational

SiO2

U

ħ

12

1 2

d

(displacement)

Isolated Harmonic Potentials

ħ

U

Eo

E1

tunneling

Spurious Two Level Systems

Displacement• Transverse• Bond direction• Rotational

SiO2

0

1

d

Dipole moment

+ -

- +

Overlapped Harmonic Potentials

Spurious TLS coupled to qubit

S

S

I + -

+ -

Microwave +

TLS||TLS

• TLSII

– Can align with electric field– Lowers energy state

• TLS– Cannot align– No preferred orientation

• TLS fluctuates with microwave field– Resonant effect, only when

TLS energy matches microwave energy

– Dissipates microwave power

• Resonant interaction between TLS and qubit– Only occurs when TLS and

qubit energies matchS

S

I - +

+ - ~

Microwave -

TLS||TLS

Vac

+ + +

- - -

- - -

+ + +

~ Vac

Raw data-multiple valued

“Splittings”

Smoothed data-single valued

-40 -30 -20 -10 0 10 20 30

6

6.2

6.4

6.6

6.8

7

7.2

7.4

7.6

Flux bias (mV)

Fre

quen

cy

(GH

z)

2 4 6 8 10 12 14 16

7

7.05

7.1

7.15

7.2

7.25

7.3

7.35

7.4

Sizes of splittings

Integrated splittings

N/G

Hz

(.01

GH

z <

S <

S’)

Splitting size S’ (GHz)10

-210

-110

00

2

4

6

8

10

• Integrate splittings and display on semi-log graph

• Normalize to 1 GHz bandwidth

Density of splittings S:

SAdE

dNlog

Integrate w.r.t S:

A: junction area: materials constant related to defect density

Slope =

ASMax

1

Maximum splitting size

Smax

Ntot

SA

dEdS

dN 1

Integrated splittings-material comparisons

0.01 0.1 10

10

20

30

40

50

Normalized to 49 m2 JJ area

N/G

Hz

Splitting size (GHz)

amorph-AlOx epi-MgO epi-Al2O3

epi-Al2O3

epi-MgO

amorph-AlOx

= 20

= 60

= 60

Min-SiO2 Re/MgO/Al Qubit• Splitting density

– Similar to AlOx

• T1 = 80 ns– Worse than Al2O3 &

AlOx

– Phonon loss?

P1

(%)

t (ns)

P1

(%) T1 = 80 ns

t (ns)

Flux bias (mV)

Fre

q (G

Hz)

SpectroscopyRabi Osc.

Spurious TLS in wiring dielectrics

S

S

I + -

+ -

Microwave +

TLS||TLS

• TLSII

– Can align with electric field– Lowers energy state

• TLS– Cannot align– No preferred orientation

• TLS fluctuates with microwave field– Resonant effect, only when

TLS energy matches microwave energy

– Dissipates microwave power

• Resonant interaction between TLS and qubit– Only occurs when TLS and

qubit energies match

+ + +

- - -

~ Vac

Insulator thickness

Tunnel barrier Wiring Dielectric

2 nm 200nm

•Dielectric loss decreases at high T or high power

Schickfus 1977

Future Directions• Re/Al2O3/Al qubit with Re wiring

– Avoid trap states in native oxide of Al wiring

• Try atomic oxygen for Al2O3 barrier growth– Fix pinhole problem?

• Try annealing finished chip in hydrogen– Passivate surface states?

• Try rf-sputt MgO and AlOx t-barrier– Could be pinhole free

• Try Nb/Al2O3/Al JJ– University of Illinois failed, but could be tool-specific

• Try ALD of dielectrics– Conformal coverage can decrease thickness!