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Phonon-induced relaxation and decoherence times of the hybrid qubit in silicon quantum dots

E. Ferraro, M. Fanciulli, and M. De Michielis
Phys. Rev. B 100, 035310 – Published 19 July 2019
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  • INTRODUCTION
  • THEORY
  • RESULTS
  • CONCLUSIONS
  • ACKNOWLEDGMENTS
    • References

    Abstract

    We study theoretically the phonon-induced relaxation and decoherence processes in the hybrid qubit in silicon. A hybrid qubit behaves as a charge qubit when the detuning is close to zero and as a spin qubit for large detuning values. It is realized starting from an electrostatically defined double quantum dot where three electrons are confined and manipulated through only electrical tuning. By employing a three-level effective model for the qubit and describing the environment bath as a series of harmonic oscillators in the thermal equilibrium states, we extract the relaxation and decoherence times as a function of the bath spectral density and of the bath temperature using the Bloch-Redfield theory. For Si quantum dots the energy dispersion is strongly affected by the physics of the valley, i.e., the conduction band minima, so we also included the contribution of the valley excitations in our analysis. Our results offer fundamental information on the system decoherence properties when the unavoidable interaction with the environment is included and temperature effects are considered.

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    • Received 3 April 2019
    • Revised 3 July 2019

    DOI:https://doi.org/10.1103/PhysRevB.100.035310

    ©2019 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    PhononsQuantum computation
    1. Physical Systems
    Double quantum dotsQuantum dotsSemiconductor microcavities
    Condensed Matter, Materials & Applied PhysicsQuantum Information, Science & Technology

    Authors & Affiliations

    E. Ferraro1,*, M. Fanciulli1,2, and M. De Michielis1,†

    • 1CNR-IMM Agrate Unit, Via Camillo Olivetti 2, 20864 Agrate Brianza (Province of Monza and Brianza), Italy
    • 2Dipartimento di Scienza dei Materiali, University of Milano Bicocca, Via Roberto Cozzi, 55, 20126 Milano, Italy

    • *elena.ferraro@mdm.imm.cnr.it
    • †marco.demichielis@mdm.imm.cnr.it

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    Issue

    Vol. 100, Iss. 3 — 15 July 2019

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    Images

    • Figure 1
      Figure 1

      A sketch of the HQ energy levels. The interdot tunnel couplings are Δ1 and Δ2, ε is the detuning between the two QDs, and ΔR corresponds to the low-energy splitting of the right dot.

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    • Figure 2
      Figure 2

      T1 (red lines) and T2 (blue lines) as a function of the bath temperature T for three different regimes: s=1 (solid lines), s=2 (dot-dashed lines), and s=1/2 (dashed lines). The Si/SiGe HQ parameters are set to ε=225μeV, Δ1=19.27μeV, Δ2=12.20μeV, and ΔR=54.18μeV [22]. The bath parameters are set to η=0.5, ωc=10Δ1, and ωcutoff/2π=1 Hz [27].

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    • Figure 3
      Figure 3

      T1 (top panels), Tϕ (middle panels), and T2 (bottom panels) as a function of ε and ΔR in correspondence to an ohmic bath (s=1) at three different temperatures: T=0.1, 0.3, and 1.6 K. The other qubit and bath parameters are the same as those in Fig. 2.

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    • Figure 4
      Figure 4

      (a) χ102 as a function of ε and ΔR. (b) The power spectrum Sζ(EQ) in the same (ε, ΔR) range of (a) for T=0.1, 0.3, and 1.6 K.

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    • Figure 5
      Figure 5

      (a) Eigenvalues of HS as a function of the detuning ε when Δ2 and ΔR are set. The symbols at the corners of the subplots (circle, triangle, square, and star) denote different qubit parameters (i.e., set of (Δ2,ΔR) values) in correspondence to the range boundaries explored in panels (c) and (d). The colored vertical lines highlight the values of the detuning ε=50μeV (cyan) and ε=225μeV (green) chosen for the plots in panels (c) and (d), respectively. (b) Energy qubit EQ (solid black lines) and dEQ/dε (dashed red lines) as a function of ε for the same qubit parameter sets. (c) T1 (top panel), Tϕ (middle panel), and T2 (bottom panel) as a function of Δ2 and ΔR in correspondence to an ohmic bath (s=1) atT=0.1 K and ε=50μeV. The other parameters are the same as those in Fig. 2. (d) The same as panel (c) at ε=225μeV.

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    • Figure 6
      Figure 6

      Pure dephasing rate as a function of (dEQ/dε)2. The symbols correspond to different qubit parameters highlighted in Fig. 5 (green symbols correspond to ε=50μeV and cyan symbols to ε=225μeV). The bath temperatures are T=1.6 K (solid line), T=0.3 K (dashed line), and T=0.1 K (dotted line).

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