MOTIVATION

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GDR Physique Quantique Mésoscopique - Aussois
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Introduction

• Last decade new experiments in quantum
  mechanics using superconducting quantum circuits
• two level system superconducting qubit
• multi quantum levels systems
• qubit coupled to high Q cavity

• Last decade new experiments in quantum
  mechanics using superconducting quantum circuits
• two level system superconducting qubit
• multi quantum levels systems

• Last decade new experiments in quantum
  mechanics using superconducting quantum circuits
• two level system superconducting qubit
• multi quantum levels systems
• qubit coupled to high Q cavity
• fixe coupling between two qubits

• Last decade new experiments in quantum
  mechanics using superconducting quantum circuits
• two level system superconducting qubit

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Motivation for a tunable coupling
Quantum algorithm
Tunable coupling
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Outline

• Description of the circuit
• dc-SQUID phase qubit
• Asymmetric transistor charge qubit
• Tunable coupling between the charge and phase
  qubit
• Summary

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Outline

• Description of the circuit
• dc-SQUID phase qubit
• Asymmetric transistor charge qubit
• Tunable coupling between the charge and phase
  qubit
• Summary

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Hybrid superconducting two-qubits system
dc-SQUID superconducting loop interrupted by 2
Josephson junctions
Asymmetric Cooper pair transistor
(ACPT) Superconducting island 0.12 µm2
Nanofab
200 nm
Ibias
Vg
Phase qubit
Charge qubit
10 mm
3-angle shadow evaporation
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Outline

• Description of the circuit
• dc-SQUID phase qubit
• Asymmetric transistor charge qubit
• Tunable coupling between the charge and phase
  qubit
• Summary

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dc-SQUID phase qubit
Ib
V 0
V 2DAl
J. Claudon et al., Phys. Rev. Lett. 91, 187003
(2004)
Strong anharmonicity
level quantization
DU (Ib,FS)
np (Ib,FS)
E. Hoskinson et al., cond-mat/0810.2372v1 (2008)
quantum tunneling
Escape probability
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Phase qubit spectroscopy
Nanosecond flux pulse
Microwave flux
Ic
Ib (µA)
FS 0.02 F0
Ibias 1890 nA
nS (GHz)
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Outline

• Description of the circuit
• dc-SQUID phase qubit
• Asymmetric transistor charge qubit
• Tunable coupling between the charge and phase
  qubit
• Summary

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Charge qubit spectroscopy
ng CgVg/2e
d(FT, FS,Ib)
Micro-wave (mW)
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Charge qubit frequency versus ng
C2
ng
C1
ng 0.5
nT (GHz)
Pesc
n (GHz)
ng - 0.5
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Charge qubit frequency versus d
Ej2
d(FT, FS,Ib)
ng 0.5
Ej1
optimal point (d 0, ng 0.5)
nT (GHz)
optimal point (d p, ng 0.5)
Josephson asymmetry
p/2
p
0
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Rabi oscillations (charge qubit)
Vg
mwave duration
Amw
T2Rabi 110 ns
Pesc
mw duration (ns)
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Relaxation (charge qubit)
T1 0.8 ms
Pesc
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Outline

• Description of the studied circuit
• dc-SQUID phase qubit
• Asymmetric transistor charge qubit
• Tunable coupling between the charge and phase
  qubit
• Summary

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Coupled qubits spectroscopy
Spectroscopy at Ibias 1890 nA
Charge qubit
I50 (µA)
Phase qubit
Frequency (GHz)
Frequency (GHz)
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Entangled qubits
g 110 MHz
SQUID 1,-gt
Pesc
g
Frequency (GHz)
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Spectroscopy versus ng
ACPT
nT
Resonant coupling at ng 0.5
nS does not depend on ng
dc-SQUID
nS
nr 18.98 GHz
g 110 MHz
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Spectroscopy versus flux
Spectroscopy at Ibias 1890 nA
Spectroscopy at Ibias 2140 nA
Spectroscopy at Ibias 107 nA
nr 10.4 GHz
g 900 MHz
I50 (mA)
Frequency (GHz)
Frequency (GHz)

• Two qubits can be in resonance from 9 GHz to 20
  GHz.
• Strong variation of the coupling strength.

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Resonant coupling
Coupling varies from 60 MHz to 1100 MHz
factor of 18
g (GHz)
nr (GHz)
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Electrical schematic of the circuit
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Hamiltonian of the coupled qubits
Josephson energy asymmetry
Capacitance asymmetry
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Resonant coupling
A. Fay et al., PRL 100, 187003 (2008)
We consider ? ? ? ? ???6?
g (GHz)
nr (GHz)
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Resonant coupling
A. Fay et al., PRL 100, 187003 (2008)
We consider ? ? 37.7? and ? ? ???6?
g (GHz)
nr (GHz)
If transistor was symmetric (lm0) coupling
would be zero
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Outline

• Description of the studied circuit
• dc-SQUID phase qubit
• Asymmetric transistor charge qubit
• Tunable coupling between the charge and phase
  qubit
• Summary

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Summary

• Two different qubits
• Strong tunable coupling between
• a charge and phase qubit (x18)
• Zero coupling and non-zero coupling

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Outline

• Description of the studied circuit
• dc-SQUID phase qubit
• Asymmetric transistor charge qubit
• Tunable coupling between the charge and phase
  qubit
• Measurement of the charge qubit
• Summary

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Energy levels
Measurement
I50 (mA)
Flux pulse
Flux pulse
Measurement
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Landau-Zener and adiabatic passage
coupling
speed
Eb
Er
LZ passage PLZ 1
2g
Adiabatic passage PLZ 0
x
Eb
Er
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Measurement of the ACPT
Flux pulse
Adiabatic passage
g 800 MHz
Phase qubit
Charge qubit