Spectroscopy of material defects using superconducting qubits · Alexey Ustinov Two-level fluctuators in Josephson junctions. Spectroscopy of material defects using superconducting

Alexey UstinovPhysikalisches Institut

Karlsruhe Institute of TechnologyGermany

10

2 nmAlOX

Al

Al

Spectroscopy of material defects using superconducting qubits

Alexey Ustinov Two-level fluctuators in Josephson junctions

Spectroscopy of material defects using superconducting qubits

J. Lisenfeld, P. Bushev, A. Lukashenko (KIT, experiment)

C. Müller, J. H. Cole, A. Shnirman (KIT, theory)

J. M. Martinis, M. Ansmann (UCSB, sample fab)

Karlsruhe experimental team


Outline

Josephson qubitMicrowave spectroscopyTwo-level fluctuators (TLFs)Manipulating a TLF by the qubitDirect driving of TLFs by microwavesEntangling two or more TLFs

10

2 nmAlOX

Al

Al


Josephson tunnel junction

electricalfield

-+ - +

Nb or Al

AlOX

Nb or Al

equivalent circuit

-

+

two-level fluctuator (TLF)

electrical dipole

Josephson junction: mapping to a pendulum

Alexey Ustinov Two-level fluctuators in Josephson junctions 5

+

Φ−= ϕϕ

πϕ cos

2)( 0

c

c

IIIU

0)(1=

∂∂

++ϕϕϕϕ U

RCmm

Dynamics of a small Josephson junction is equivalent to a motion of a particle

in a washboard potential

20

2

Φ

=π

Cmwith mass

ϕ0 2π 4π 6π

ener

gy

U(ϕ

)

I

current

phase

Macroscopic quantum system

Alexey Ustinov Two-level fluctuators in Josephson junctions 6

By reducing the capacitance Cthe ´mass`

can be made small

Theory:A. J. Leggett, Prog. Theor. Phys. Suppl. 69, 80 (1980).A. J. Leggett and A. Garg, Phys. Rev. Lett. 54, 857(1985).

ϕ0 2π 4π 6π

ener

gy

U(ϕ

)

phase

Experiment:J.M. Martinis, M. H. Devoret, and J. Clarke, Phys. Rev. B 35, 4682 (1987).

20

2

Φ

=π

Cm

7

J. M. Martinis et al., Phys. Rev. Lett. 89, 117901 (2002).

ener

gy

phase

R. McDermott et al., Science 307, 1299 (2005)

01ω0

1Rω

22

1=SxB

ϕ

I

current

0

1

Josephson phase qubit

01ω Rω


Reducing dissipation by placing the junction in a loop

ϕ0 2π 4π

ener

gy

U(ϕ

)

−−

Φ= ϕϕ

πϕ cos

2)( 0

c

c

IIIU

L Ren

ergy

U

(ϕ)

ϕ0 2π

I

current current

0

1

−

ΦΦ

−Φ

= ϕπϕβπ

ϕ cos22

12

)(2

0

0

L

cIU

Φ

01

85.00

≈ΦΦ


Phase qubit readout: Tunneling from the excited state

ener

gy

phaseϕ

Readout by applying a tilt (current) pulse

tunneling rate

0Γ

03

1 10 Γ⋅≈Γ

current

time

tunneling event

I

current

01ω Rω

0

1

10

L R

steps:inter-welltransitions

DC-SQUIDreadout

switching currenthistogram

threshold treshI

rf-SQUIDqubit

flux biascontrol

SQ

UID

crit

ical

cur

rent

(µA

)

Φext/Φ0

Readout using a DC-SQUID


Josephson phase qubit

readout SQUID qubit loop

fluxline

microwave line

1 µmqubit junction

An example of a Nb phase qubit made at PTB Braunschweig (R. Dolata and A. Zorin)


exponential fit

Josephson junction as a quantum system- an artificial ‘atom’

01ω

I

current

ener

gy

phase

Rω

2

ϕ

01ω Rω

0

1

J. Lisenfeld et al.,Phys. Rev. Lett. 99, 170504 (2007)


Origin of decoherence in phase qubits: microscopic two-level fluctuators

AS 1

max ∝

spectroscopy

S

K. B. Cooper, et al., Phys.Rev.Lett. 93, 180401 (2004).

A is the junction area

Two-level fluctuators

SiO2 - crystalline (quartz) amorphous modification

see e.g.Ch. Enss and S. Hunklinger Low Temperature PhysicsChap. 9

20

2 ∆+∆=−=∆ −+ EEE λ−Ω≈∆ e0

mUd 22

≈λ

∆−∆

∆∆=

0

0

21

TLSH(WKB)

15

Capacitively shunted phase qubit fabricated at UCSB

M.Steffen et al. Phys.Rev.Lett. 97, 050502 (2006)

DC-SQUID readoutflux biascontrol

qubit

16

Phase qubit fabricated at UCSB

M.Steffen et al. Phys.Rev.Lett. 97, 050502 (2006)

TdRabi ~ 140 ns

T1 ~ 110 ns

SiO2 replaced by SiNx

DC-SQUID readoutflux biascontrol

qubit


Spectroscopic signatures of individual two-level fluctuators (TLFs)

-

+

two-level fluctuator (TLF)

electrical dipole

10

2 nmAlOX

Al

Al mic

row

ave

frequ

ency

, G

Hz

external flux cext / ΦΦ

45 MHz

201 eg +

201 eg −

g1

e0

microscopictwo-level fluctuators

Pesc


Swapping a quantum state of qubit with the state of a two-level fluctuator

∆t

external flux cext / ΦΦ

40 MHz

Pes

c

∆t

Pe

scg1

e0

g1

e0

g1

2MHz22

2vac S

≈=π

ω

∆t

mic

row

ave

frequ

ency

, G

Hz

swapping a photon between qubit and TLF

Alexey Ustinov Two-level fluctuators in Josephson junctions19

ns850T TLF,1 ≈

see also:M. Neeley, M. Ansmann, J. Martinis, et. al.,Nature Physics 4, 523 (2008)

ss,s, n210T2.1Tn400T TLF,2TLF,1Qubit,1 ≈≈≈ µ

ns110T Qubit,1 ≈

Using a two-level fluctuator as a quantum memory


an excited multi-level system could absorb additional photons

Is TLF really a two-level system ?Yes, it is.

Outcome: no oscillations when both TLF and qubit arein their excited states and coupled


time domain data frequency domain data

Rabi oscillations of the qubit in the vicinity of a TLF: Data

Sweeping flux through splitting, at each flux adjusting microwave frequency to qubit resonance and recording a Rabi oscillation trace.


xxzzqs SH τστεσε 21

f21

21 +−−=emHHHH Is ++=

( ) ( )−+

+−+

+ +Ω++Ω= ττσσ aaaaH qI f21

21( )2

1em += +aaH dω

qubit TLF qubit-TLF coupling

field:

Hamiltonian:

qubit-field coupling TLF-field coupling

symmetric0f =Ω

Transitions in the driven 4-level system: qubit coupled to TLF

not symmetric1.0f =Ω

Theory: C. Müller, J. H. Cole, andA. Shnirman (Karlsruhe)


Rabi oscillations of the qubit in the vicinity of TLF: Comparison in time domain

experiment theory

J. Lisenfeld, C. Müller, J. H. Cole, A. Lukashenko, A. Shnirman, and A. Ustinov arXiv:0909.3425


Dipole size fit from theory:

nm12.0d06.0 ≈≈p

nm2d ≈with dielectric thickness

Asymmetric pictureindicates direct coupling of TLF tothe driving field

experiment theory

Rabi oscillations of the qubit in the vicinity of TLF: Comparison in frequency domain


Direct excitation of a TLF by applying microwaves

Rabi oscillations in TLF


Two-level fluctuator has much longer T1 time than the JJ qubit

Rabi oscillations of TLF

Rabi oscillations of the qubit

TLF is a better qubit than JJ ...


Migration of fluctuators due to thermal annealing

Center: 7.82 GHzMagnitude: 24 MHz

Center: 7.65 GHzMagnitude: 24 MHz

Data taken on 18.02.09after annealing at 1.8 Kfor a few hours

Data taken on 12.02.09


Conclusions

TLFs may have longer coherence times than qubits

they can be used as a built-in quantum memorythey allow to entangle a macroscopic object with a microscopic system and study a coupled quantum system

TLFs show direct coupling to the electrical ac field in the junction

they can be directly controlled by microwavesa qubit is only necessary to measure them

Full quantum control and characterization of individual TLFs

10

2 nmAlOX

Al

Al

Documents

Spectroscopy of material defects using superconducting qubits · Alexey Ustinov Two-level fluctuators in Josephson junctions. Spectroscopy of material defects using superconducting