Josephson junction as a tool to manipulate microscopic two ... · Alexey Ustinov Two-level...

Alexey Ustinov Two-level fluctuators in Josephson junctions

Josephson junction as a tool to manipulate microscopic two-level systemsJ. Lisenfeld, P. Bushev, A. Lukashenko

C. Müller, A. Shnirman, J. H. Cole, A. V. Ustinov

Universität Karlsruhe, Germany

10

2 nmAlOX

Al

Al

I.F. Schegolev Memorial Conference “Low-Dimensional Metallic and Superconducting Systems”

October 11-16, 2009 - Chernogolovka


Outline

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

J. Lisenfeld, C. Mueller, J. H. Cole, A. Lukashenko, A. Shnirman, and A. V. Ustinov. ArXiv:0909.3425


Josephson tunnel junction

electricalfield

-+ - +

Nb or Al

AlOX

Nb or Al

equivalent circuit

-

+

two-level fluctuator (TLF)

electrical dipole


Spectroscopic evidences of 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

e0

swapping a photon from qubit to TLF

Pesc

g1


Phase qubit readout: Tunneling from the excited state

ener

gy

phase

0

1

ϕ

Readout by applying a tilt (current) pulse

tunneling rate

0Γ

03

1 10 Γ⋅≈Γ

current

time

tunneling event

I

current


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 cos221

2)(

2

0

0

L

cIU

Φ

01

85.00

≈ΦΦ


Josephson phase qubit

readout SQUID qubit loop

fluxline

microwave line

1 μmqubit junction 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


exponential fit

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

01ωh

I

current

ener

gy

phase

Rω

2

ϕ

01ω Rω

analog of a two-level atom

0

1

1

0


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

Δt

external flux cext / ΦΦ

40 MHz

Pes

c

Δt

time for SWAP gate: 23ns(half period of coupled osc.)

Pe

scg1

e0

g1

e0

g1

2MHz22

2vac S

≈=π

ω

Δt

mic

row

ave

frequ

ency

, G

Hz

Alexey Ustinov Two-level fluctuators in Josephson junctions11

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 dωh

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)


Theory: C. MüllerJ. H. ColeA. Shnirman(Karlsruhe)

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

experiment theory


Dipole size fit from theory:

nm12.0d06.0 ≈≈p

nm2d ≈with dielectric thickness

Asymmetric pictureindicates direct coupling of TLF todriving 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


220, Δ+= =ΔRR ωω

220

20

Δ+=

AAA

Rabi oscillations in a directly driven TLF : Dependence on driving field detuning


Ramsey oscillations in a directly driven two-level fluctuator: Dephasing time T2


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 ...


Rabi oscillation in TLF versus qubit ‘parking’ position

microwave field strength ‘seen’ by TLF depends on the qubit resonance frequency

qubit ‘parking’


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


ns50ns129ns150

2

1

≈≈≈

TTTd

MHz25GHz656.710

==

Sf

ns110ns715ns600

2

1

≈≈≈

TTTd

MHz21GHz845.710

==

Sf

ns300~ns150ns250

2

1

TTTd

≈≈

MHz21GHz021.810

==

Sf

Possibility to entangle two or more TLFs

magnetic flux (arb. units)

Data taken after annealing at 400 mKfor several minutes


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 microscopic defect 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 is readily possible

10

2 nmAlOX

Al

Al


Thanks to my collaborators

J. Lisenfeld, P. Bushev, A. Lukashenko (experiment)C. Müller, J. H. Cole, A. Shnirman (Karlsruhe, theory) J. M. Martinis, M. Ansmann (UCSB, sample fab)

Karlsruhe experimental team

J. Lisenfeld, C. Mueller, J. H. Cole, A. Lukashenko, A. Shnirman, and A. V. Ustinov. ArXiv:0909.3425

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