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Coherent tunneling by adiabatic passage of an exchange-only spin qubit in a double quantum dot chain

E. Ferraro, M. De Michielis, M. Fanciulli, and E. Prati
Phys. Rev. B 91, 075435 – Published 26 February 2015
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Abstract
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Article Text
  • TRANSPORT IN A DOUBLE QUANTUM DOT CHAIN
  • CTAP IN A CHAIN OF THREE DOUBLE QUANTUM…
  • CONCLUSIONS
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    A scheme based on coherent tunneling by adiabatic passage (CTAP) of exchange-only spin qubit quantum states in a linearly arranged double quantum dot chain is demonstrated. Logical states for the qubit are defined by adopting the spin state of three electrons confined in a double quantum dot. The possibility to obtain gate operations entirely with electrical manipulations makes this qubit a valuable architecture in the field of quantum computing for the implementation of quantum algorithms. The effect of the external control parameters as well as the effect of the dephasing on the coherent tunneling in the chain is studied. During adiabatic transport, within a constant energy degenerate eigenspace, the states in the double quantum dots internal to the chain are not populated, while transient populations of the mixed states in the external ones are predicted.

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    • Received 8 September 2014
    • Revised 23 January 2015

    DOI:https://doi.org/10.1103/PhysRevB.91.075435

    ©2015 American Physical Society

    Authors & Affiliations

    E. Ferraro1,*, M. De Michielis1, M. Fanciulli1,2, and E. Prati1,3

    • 1Laboratorio MDM, IMM-CNR, Via Olivetti 2, I-20864 Agrate Brianza, Italy
    • 2Dipartimento di Scienza dei Materiali, University of Milano Bicocca, Via R. Cozzi, 53, 20126 Milan, Italy
    • 3Istituto di Fotonica e Nanotecnologia, Consiglio Nazionale delle Ricerche, Piazza Leonardo da Vinci 32, I-20133 Milan, Italy

    • *Present address: Istituto Nazionale di Ricerca Metrologica, Strada delle Cacce 91, 10135 Turin, Italy; e.ferraro@inrim.it

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    Issue

    Vol. 91, Iss. 7 — 15 February 2015

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    Images

    • Figure 1
      Figure 1

      Schematic of the tunneling in the quantum channel with N double quantum dots. The black dots in (a) and (b) denote the electrons before and after the tunneling. The quantities indicated by ωi, ω, and ωf are the pulses that have to be furnished by external gates in order to make the tunneling possible.

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    • Figure 2
      Figure 2

      Gaussian pulses as a function of t, for tmax=10π/ωmax, σ=tmax/8, and ωSmax=10ωmax.

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    • Figure 3
      Figure 3

      Probability ρff of finding the three electrons at the tail of the chain in the double quantum dot N as a function of tmax for σ=tmax/8 and ωmax=10. Each family of curves represents a different value of the dephasing parameter Γ for a different number of double quantum dots composing the chain.

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    • Figure 4
      Figure 4

      Eigenvalues of three double quantum dots system as a function of time. The state at zero energy is triple degenerate.

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    • Figure 5
      Figure 5

      Populations of the density matrix ρ as a function of time for N=3, ωmax=1, tmax=25π/ωmax, σ=tmax/8, and Γ=0.

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    • Figure 6
      Figure 6

      Probability ρP3S3 of finding the three electrons at the tail of the chain for N=3 as a function of tmax and Γ for σ=tmax/8 and ωmax=10.

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    • Figure 7
      Figure 7

      Probability ρP3S3 of finding the three electrons at the tail of the chain for N=3 as a function of tmax and ωmax for σ=tmax/8. Each plot illustrates a different value of the dephasing Γ.

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    • Figure 8
      Figure 8

      Absolute value of the difference between ρff and ρideal as a function of tmax for two different variations (+1% and +10%) on the amplitude of ωi(t) and ωf(t) for N=3.

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    • Figure 9
      Figure 9

      Absolute value of the difference between ρff and ρideal as a function of tmax for two different variations (+1% and +10%) on the amplitude of ωi(t), ω(t) and ωf(t) for N=5.

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    • Figure 10
      Figure 10

      Same as Fig. 9 with N=7.

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    • Figure 11
      Figure 11

      Same as Fig. 9 with N=9.

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    • Figure 12
      Figure 12

      Absolute value of the difference between ρff and ρideal as a function of tmax for two different variations (+1% and +10%) on the peak time of ωi(t) and ωf(t) for N=3.

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    • Figure 13
      Figure 13

      Absolute value of the difference between ρff and ρideal as a function of tmax for two different variations (+1% and +10%) on the peak time of ωi(t), ω(t), and ωf(t) for N=5.

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    • Figure 14
      Figure 14

      Same as Fig. 13 with N=7.

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    • Figure 15
      Figure 15

      Same as Fig. 13 with N=9.

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    • Figure 16
      Figure 16

      (a) Scheme of the qubit chain where performing successive SWAP operations. Note that every qubit must be filled with three electrons. (b) Comparison between the transfer time for CTAP and successive SWAPs as a function of the chain length N for three different values of the tunneling rate ωmax.

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