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On Decoherence in Solid-State Qubits

Universität Karlsruhe (TH). On Decoherence in Solid-State Qubits. Gerd Schön Karlsruhe work with : Alexander Shnirman Karlsruhe Yuriy Makhlin Landau Institute Pablo San Jos é Karlsruhe Gergely Zarand Budapest and Karlsruhe. Josephson charge qubits

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On Decoherence in Solid-State Qubits

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  1. Universität Karlsruhe (TH) On Decoherence in Solid-State Qubits Gerd Schön Karlsruhe work with: Alexander Shnirman Karlsruhe Yuriy Makhlin Landau Institute Pablo San JoséKarlsruhe Gergely Zarand Budapest and Karlsruhe • Josephson charge qubits • Classification of noise, relaxation/decoherence • Josephson qubits as noise spectrometers • Decoherence due to quadratic 1/fnoise • Decoherence of spin qubits due to spin-orbit coupling

  2. g Fx Vg Vg 2 control fields: Vg and Fx gate voltage, flux 1. Josephson charge qubits n Fx/F0 CgVg/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)

  3. Qg/e Observation of coherent oscillations Nakamura, Pashkin, and Tsai, ‘99 top≈ 100 psec, tj≈ 5 nsec major source of decoherence: background charge fluctuations

  4. gate Charge-phase qubit EC≈EJ Quantronium (Saclay) • Operation at saddle point: • to minimize noise effects • voltage fluctuations couple transverse • - flux fluctuations couple quadratically CgVg/2e Fx/F0

  5. p/2 p/2 Decay of Ramsey fringes at optimal point Vion et al., Science 02, …

  6. 500 Sd SNg 100 1/w 1/w w w 4MHz 0.5MHz 10 -0.3 -0.2 -0.1 0.0 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

  7. 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) …

  8. model noise Bosonic bath Spin bath Ohmic 1/f (Gaussian)

  9. Example: Nyquist noise due to R (fluctuation-dissipation theorem) G * j 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, T=0, nonlinear coupling ?

  10. 1/f noise, longitudinallinear coupling  time scale for decay non-exponential decay of coherence Cottet et al. (01)

  11. transverse component of noise  relaxation longitudinal component of noise  dephasing probed in exp’s  1/f noise 3. Noise Spectroscopy via JJ Qubits Astafiev et al. (NEC) Martinis et al., … Josephson qubit + dominant background charge fluctuations eigenbasis of qubit

  12. Low-frequency noise and dephasing E1/f T 2 dependence of 1/f spectrum observed earlier by F. Wellstood, J. Clarke et al. Relaxation (Astafiev et al. 04) data confirm expected dependence on  extract

  13. Astafiev et al. (PRL 04) 9 10 (s) 2 ћ /2 8 2 10 w/ 2e R ћ SX(w) 2 p E1/f2 w / ћ 7 10 w 1 10 100 c w/2p (GHz) Relation between high- and low-frequency noise same strength for low- and high-frequency noise

  14. 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) • eachTLS is coupled (weakly) to thermal bath Hbath.j at Tand/or other TLS •  weak relaxation and decoherence TLS TLS qubit bath TLS inter- action TLS TLS

  15. 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)

  16. 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)

  17. 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

  18. 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

  19. 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.

  20. 2-state approximation: X(t) e + Z(t) 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

  21. For two projections ± of the spin along z = natural quantization axis for spin -b q b -j j y x For each spin projection ± we consider orbital ground state Ground (and excited) states 2-fold degenerate due to spin (Kramers’ degeneracy)

  22. z q -j j y x 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

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

  24. 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 >> top≈ 1…10 nsec • origin and properties of noise sources (1/f, …) • mechanisms for decoherence of spin qubits • Application of Josephson qubits: • as spectrum analyzer of noise

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