PowerPoint-Pr

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On Decoherence in Solid-State Qubits
Gerd Schön Karlsruhe work with Alexander
Shnirman Karlsruhe Yuriy Makhlin Landau
Institute Pablo San José Karlsruhe Gergely
Zarand Budapest and Karlsruhe

• Josephson charge qubits
• Classification of noise, relaxation/decoherence
• Josephson qubits as noise spectrometers
• Decoherence due to quadratic 1/f noise
• Decoherence of spin qubits due to spin-orbit
  coupling

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1. Josephson charge qubits
n
Fx /F0
Cg Vg/2e
2 degrees of freedom
charge and phase
tunable
2 energy scales EC , EJ charging energy,
Josephson coupling
2 states only, e.g. for EC EJ
Shnirman, G.S., Hermon (97)
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Observation of coherent oscillations Nakamura,
Pashkin, and Tsai, 99
top 100 psec, tj 5 nsec
major source of decoherence background charge
fluctuations
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Charge-phase qubit
EC EJ
Quantronium (Saclay)

• Operation at saddle point
• to minimize noise effects
• voltage fluctuations couple transverse
• - flux fluctuations couple quadratically

Cg Vg/2e
Fx /F0
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Decay of Ramsey fringes at optimal point
Vion et al., Science 02,
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Spin echo
500
Free decay
Gaussian noise
100
Coherence times (ns)



10
0.05
0.10
Fx/F0
N
-1/2
Experiments Vion et al.
g
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2. Models for noise and classification

• Sources of noise
• - noise from control and measurement circuit,
  Z(w)
• background charge fluctuations
• Properties of noise
• - spectrum Ohmic (white), 1/f, .
• - Gaussian or non-Gaussian
• coupling

longitudinal transverse quadratic
(longitudinal)
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(No Transcript)
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Relaxation (T1) and dephasing (T2)
Bloch (46,57), Redfield (57)
For linear coupling, regular spectra, T ? 0
Golden rule exponential decay law
pure dephasing
Dephasing due to 1/f noise, T0, nonlinear
coupling ?
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1/f noise, longitudinal linear coupling
? time scale for decay
non-exponential decay of coherence
Cottet et al. (01)
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3. Noise Spectroscopy via JJ Qubits
Astafiev et al. (NEC) Martinis et al.,
Josephson qubit dominant background charge
fluctuations
eigenbasis of qubit
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Relaxation (Astafiev et al. 04)
data confirm expected dependence on
? extract
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Relation between high- and low-frequency noise
same strength for low- and high-frequency
noise
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High- and low-frequency noise from coherent
two-level systems

• Qubit used to probe fluctuations X(t)

• Source of X(t) ensemble of coherent two-level
  systems (TLS)

• each TLS is coupled (weakly) to thermal bath
  Hbath.j at T and/or other TLS
• ? weak relaxation and decoherence

TLS
TLS
qubit
bath
TLS
inter- action
TLS
TLS
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Spectrum of noise felt by qubit
low w random telegraph noise large w absorption
and emission
distribution of TLS-parameters, choose
for linear w-dependence
exponential dependence on barrier height for 1/f
overall factor

• One ensemble of coherent TLS
• Plausible distribution of parameters produces
• - Ohmic high-frequency (f) noise ?
  relaxation
• - 1/f noise ? decoherence
• - both with same strength a
• - strength of 1/f noise scaling as T2
• - upper frequency cut-off for 1/f noise

Shnirman, GS, Martin, Makhlin (PRL 05)
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4. At symmetry point Quadratic longitudinal 1/f
noise
static noise
Paladino et al., 04 Averin et al., 03
1/f spectrum quasi-static
Shnirman, Makhlin (PRL 03)
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Fitting the experiment
G. Ithier, E. Collin, P. Joyez, P.J. Meeson, D.
Vion, D. Esteve, F. Chiarello, A. Shnirman, Y.
Makhlin, J. Schriefl, G.S., Phys. Rev. B 2005
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5. Decoherence of Spin Qubits in Quantum Dots or
Donor Levels with Spin-Orbit Coupling
Coherent Manipulation of Coupled Electron Spins
in Semiconductor Quantum Dots Petta et al.,
Science, 2005
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spin 2 orbital states spin-orbit
coupling noise coupling to orbital degrees of
freedom
Generic Hamiltonian
spin
noise 2 independent fluct. fields coupling to
orbital degrees of freedom
dot 2 orbital states
spin-orbit
strength of s-o interaction direction
depends on asymmetries
published work concerned with large ,
? vanishing decoherence for (Nazarov et al.,
Loss et al., Fabian et al., ) We find the
combination of s-o and Xtx and Ztz leads to
decoherence, based on a random Berry phase.
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Specific physical system Electron spin in double
quantum dot
Rashba Dresselhaus
cubic Dresselhaus
Fluctuations
Spectrum

• Phonons with 2 indep. polarizations
• Charge fluctuators near quantum dot

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For each spin projection we consider orbital
ground state Ground (and excited) states
2-fold degenerate due to spin (Kramers
degeneracy)
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Instantaneous diagonalization introduces extra
term in Hamiltonian
In subspace of 2 orbital ground states for and
- spin state
Gives rise to Berry phase
random Berry phase ? dephasing
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X(t) and Z(t) small, independent, Gaussian
distributed ? effective power spectrum and
dephasing rate
Small for phonons (high power of w and
T) Estimate for 1/f noise or 1/f ? f noise

• Nonvanishing dephasing for zero magnetic field
• due to geometric origin (random Berry phase)
• measurable by comparing G1 and Gj for different
• initial spins

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Conclusions

• Progress with solid-state qubits
• Josephson junction qubits
• spins in quantum dots
• Crucial understanding and control of
  decoherence
• optimum point strategy for JJ qubits tj ? 1
  msec gtgt top 110 nsec
• origin and properties of noise sources (1/f, )
• mechanisms for decoherence of spin qubits
• Application of Josephson qubits
• as spectrum analyzer of noise