P' Bertet

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Photon-noise induced dephasing in a flux-qubit
A. ter Haar A. Lupascu J. Plantenberg F.
Paauw J. Eroms C.J.P.M. Harmans J.E. Mooij
P. Bertet
I. Chiorescu Y. Nakamura
G. Burkard D. DiVicenzo

Quantum Transport Group, Kavli Institute for
Nanoscience, TU Delft, Lorentzweg 1, 2628CJ
Delft, The Netherlands
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Introduction
(weak coupling)
Dephasing ?
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Qubit dephased by photon noise
Temperature T
Quality factor Q
Dispersive regime
Shift of oscillator frequency
Coupling
Shift of qubit frequency
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Qubit dephased by photon noise
Photon fluctuations
around
Qubit frequency
Phase shift
Dephasing factor
with
A. Blais et al., PRA 69, 062320 (2004)
Dephasing time Tf
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Flux-qubit coupled to SQUID plasma mode
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The flux-qubit
Al/AlOx/Al junctions by shadow evaporation
e-beam lithography
Josephson junctions
1 control parameter
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Qubit energy levels
EJ225GHz EC7.2GHz a0.76
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Persistent-current
Property of states 0gt and 1gt
0gt
1gt
Useful to measure the qubit state
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Two-level approximation
Flux-noise optimal point
(GHz)
n
(cf Saclay)
Frequency
In the
basis,
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Control of the qubit state
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Persistent-current and detection of the qubit
state
Our detector a hysteretic DC-SQUID as on-chip
comparator
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Persistent-current and detection of the qubit
state
Qubit inductively coupled to SQUID
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Persistent-current and detection of the qubit
state
SQUID shunted by a capacitor
PLASMA MODE
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Coupling of the qubit and the plasma mode
dJ/dIb(Ib)
M
Circ current J
Plasma mode current
qubit
Complex
2 different effects
a) Effective inductive coupling with tunable
mutual inductance
b) Flux dependent SQUID Josephson inductance
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SQUID circulating current
dJ/dIb0
dJ/dIb(Ib)
Ideal symmetric SQUID dJ/dIb(0)0
Decoupling current
Including asymmetries
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Coupling of the qubit and the plasma mode
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The sample
Ib
Microwave antenna
V
Csh
G. Burkard et al., cond-mat/0405273
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The setup
3k
1k
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Qubit spectroscopy
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Plasma mode spectroscopy
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Evaluating the coupling constants
Measure l(Ib)
Spectroscopy
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Evaluating the coupling constants
Measure l(Ib)
Spectroscopy
Ib
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Frequency shift
Frequency shift dn0 due to g1
ac-Zeeman shift. Always gt0
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Frequency shift
Optimal point For flux-noise
Optimal point for photon noise
dn00
Quantitative prediction optimal point for
photon noise
Optimal point for flux/current noise
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Characterizing decoherence (1) spectroscopy
Low-power spectroscopy
Rabi oscillations
5 types of experiments
T1 measurements
Ramsey fringes
Spin-echo measurements
Thermal photon noise  high frequency 
At decoupled optimal point (IbIb,e0)
Strongly coupled 2-level fluctuator
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Characterizing decoherence (2) Rabi oscillations
At decoupled optimal point (IbIb,e0)
nMWnQ
Dt
Non-exponential because low-frequency noise
Pswitch ()
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Characterizing decoherence (3) T1 measurements
At decoupled optimal point (IbIb,e0)
p
Dt
- Exponential decay
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Characterizing decoherence (4) Ramsey fringes
At decoupled optimal point (IbIb,e0)
p/2
p/2
Tp/2
nMW-nQ
Difficult to extract dephasing time
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Characterizing decoherence (5) spin-echo
sequence
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T1 dependence on Ib
Ib
Away from Ib, T1 limited by coupling to
measuring circuit
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Spin-echo and t2 dependence on Ib and e
Techo
t22/p(w1w2)
IbIb
g10
Best coherence e0 (optimal point)
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Decoherence due to qubit-plasma mode coupling
em
dn00
Dephasing minimum for spin-echo and Ramsey when
dn00
Quantum coherence limited by photon noise
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Spin-echo and t2 dependence
T70mK, Q150
IbIb
g10
Ib0mA
g180MHz
Quantitative agreement
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Conclusion
Dephasing due to thermal fluctuations of the
photon number in an underdamped resonator
coupled to the qubit very general situation
Case of a flux-qubit coupled to the plasma mode
of its SQUID detector
By tuning coupling constants, could decouple
qubit from photon noise
Long spin-echo time (4ms) at optimal bias point
Quantitative agreement with simple model for
spin-echo time
2 questions
- mechanism for low-freq noise ? (charge or
critical current noise ?)
- effect of dispersive shifts in usual spin-boson
model ?