experimental investigation of quantum phenomena in a ...quantenelektronik 2 contents 1. introduction...

Quantenelektronik

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Experimental Investigation of Quantum Phenomena in a Persistent Current Qubit

E. Il‘ichev, N. Oukhanski, A. Izmalkov, U. Hübner, T. May, Th. Wagner, I. Zhylaev, Ya. S. Greenberg,H. E. Hoenig, H.-G MeyerInstitute for Physical High Technology, P.O. Box 100239, D-07702 Jena, Germany

M. Grajcar, W. KrechInstitute of Solid State Physics, Friedrich Schiller University, D-07743 Jena, Germany

M. H. S. Amin, A. Smirnov, Alec Maassen van den Brink, A. M. ZagoskinD-Wave System, Inc., 320-1985 West Broadway, Vancouver, B.C., Canada

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Contents

1. Introduction – single junction interferometer2. Idea of measurements:classical case3. Idea of measurements:quantum case4. Technology5. Response of the qubit to nonresonant

excitation. 6. Response of the qubit to resonant excitation. 7. Rabi spectroscopy 8. Summary and outlook

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Single-junction interferometer

Intern. flux

Extern. flux

-2

-1

1

2

3

-2 -1 0 1 2 3

β=0.8

ϕ /π

ϕext/πβ=1.5

Φ 0-Φ 0

Φ=Φext−LI

ϕ=ϕext-βsinϕ, where

β=2πLIC/Φ0

ϕ π= 20

ΦΦ

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Single-junction interferometer

-1 0 1 2 3-2

0

2

4

6

8

Magnetic flux

Ener

gy

U∝ (ϕ-ϕx)2/2-βcosϕ,

where β=2πLIc/Φ0

Intern. flux

Extern. flux

-2

-1

1

2

3

-2 -1 0 1 2 3

β=0.8

ϕ /π

ϕext/πβ=1.5

Φ 0-Φ 0

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FCEBDA

UJ

energy vs phase at different external fluxes

Idea of measurements: single-junction interferometer in classical case

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FCEBDA

UJ

energy at different external fluxes


M

L LT CT

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FCEBDA

UJ



M

L LT CT

Φ

Φe

A

D

B

E

C

F

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FCEBDA

UJ



M

L LT CT

Φ

Φe

A

D

B

E

C

F

ΦdcExternal flux Φrf + Φdc

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FCEBDA

UJ



M

L LT CT

Φ

Φe

A

D

B

E

C

F


Φdc

V

Voltage across the tank vs Φdc

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FCEBDA

UJ



M

L LT CT

Φ

Φe

A

D

B

E

C

F


Φdc

V


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FCEBDA

UJ



M

L LT CT

Φ

Φe

A

D

B

E

C

F


Φdc

V


E.Il’ichev et al. Rev. Sci. Instrum. 72, 1882, 2001

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Idea of measurements – quantum case

FCEBDA

UJ


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FCEBDA

UJ


Φe

B E

F

C

A

D

Φ0/2

UJ

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Φ

Φe

A

D

B

E

C

FFCEBDA

UJ


Φe

B E

F

C

A

D

Φ0/2

UJ

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Φ

Φe

Φdc

Φdc

V

External flux Φrf + Φdc


A

D

B

E

C

FFCEBDA

UJ


Φe

B E

F

C

A

D

Φ0/2

UJ

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Φ

Φe

Φdc

Φdc

V



A

D

B

E

C

FFCEBDA

UJ


Φe

B E

F

C

A

D

Φ0/2

UJ

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Φ

Φe

Φdc

Φdc

V



A

D

B

E

C

F


Ya. S. Greenberg et al. PRB 66, 214525, 2002

Ya. S. Greenberg et al. PRB 66, 224511, 2002

FCEBDA

UJ


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Nb technology for the coil of the tank circuit.

T. May, et al. Rev. Sci. Instrum., 74; March 2003

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•Nb coil is prepared on oxidized Si substrates lithographically.•The line width of the coil windings was 2 µm, with a 2 µm spacing. •Various square-shape coils with between 20 and 150 µm windings were designed.•We use an external capacitance CT.

Nb coil without concentrator.

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Al qubit

•Material: Aluminium, Shadow-evaporation tecnique•Two contacts ~600x200nm, (IC ≈ 600 nA), the third is smaller, so that α=EJ1 /EJ2,3 ~0.9•Inductance L ≈ 20 pH•J.E. Mooij et al., Science 285, 1036, 1999.

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Nonresonant excitation of the qubit - setup

Amp Lock In Amplifier

RF Generator5-100MHz

DC Generator0.1-10Hz

Oscilloscope

QUBIT

T=2K T=300K

Amp

T=10mK

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Tank voltage vs external flux – large Φac

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Tank voltage vs external flux near Φdc= Φ0/2 – small Φac

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Idea of Rabi spectroscopy - resonant excitation

M

L LT CT

hΩ

Ω

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Idea of Rabi spectroscopy - resonant excitation

Resonant circuit

Rabi spectra

Voltage

Frequency

ωR∼ Ahf

<Sx> ∼ sin(ωRt)sin(Ω t)

<Sy> ∼ sin(ωRt)cos(Ω t)

<Sz> ∼ cos(ωRt)

H

S

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Resonant excitation of the qubit - setup

HF Generator 0.1-3GHz

Amp Amp

DC source

QUBIT Spectrum Analyzer

T=2K T=300KT=10mK

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The voltage spectral density on the tank circuit at different microwave amplitude at 868 ± 2 MHz

2/ toclose 0ΦΦ

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0.96 0.98 1 1.02 1.04

(P/P0)1/2

0.9

1

1.1

ωR/ω

T

(b)

0.96 0.98 1 1.02 1.04

(P/P0)1/2

0

0.5

1S V

,max

/S0

(a) b

ca

bac

Decoherence time

τRabi~2.5µs

22222

2

22222

22

22

2

2

)()()()(2),(

TT

T

R

R

TRV C

LIkSγωωω

ωωωωω

ωωωεωω+−

×Γ+−

ΓΩ

=

E.Il’ichev et al., preprint , cond-mat /0303433, 2003

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Summary and outlook

Response of the single qubit to nonresonant and resonant excitation

Nonresonant response is macroscopic quantum tunneling

• Resonant response is similar to NMR for the single spin

• In contrast to quantum optics experiments, where Ω ± ωR were detected, we detected ωR

experimental investigation of quantum phenomena in a ...quantenelektronik 2 contents 1. introduction...

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