Transfer of a quantum state from a photonic qubit to a gate-defined quantum dot

Benjamin Joecker, Pascal Cerfontaine, Federica Haupt, Lars R. Schreiber, Beata E. Kardynał, and Hendrik Bluhm

Phys. Rev. B 99, 205415 – Published 13 May 2019

Abstract

Interconnecting well-functioning, scalable stationary qubits and photonic qubits could substantially advance quantum communication applications and serve to link future quantum processors. Here, we present two protocols for transferring the state of a photonic qubit to a single-spin and to a two-spin qubit hosted in gate-defined quantum dots (GDQD). Both protocols are based on using a localized exciton as intermediary between the photonic and the spin qubit. We use effective Hamiltonian models to describe the hybrid systems formed by the exciton and the GDQDs and apply simple but realistic noise models to analyze the viability of the proposed protocols. Using realistic parameters, we find that the protocols can be completed with a success probability ranging between $84 - 96 %$ .

Received 13 December 2018
Revised 18 March 2019

DOI:https://doi.org/10.1103/PhysRevB.99.205415

Physics Subject Headings (PhySH)

Excitons Quantum communication Quantum computation Quantum information with solid state qubits

Double quantum dots III-V semiconductors Quantum dots Two-dimensional electron gas

Quantum Information, Science & TechnologyCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Benjamin Joecker^1,2, Pascal Cerfontaine¹, Federica Haupt¹, Lars R. Schreiber¹, Beata E. Kardynał³, and Hendrik Bluhm^1,*

¹JARA-FIT Institute Quantum Information, Forschungszentrum Jülich GmbH and RWTH Aachen University, 52074 Aachen, Germany
²Centre for Quantum Computation and Communication Technology, School of Electrical Engineering & Telecommunications, UNSW, Sydney, NSW, 2052, Australia
³Peter Grünberg Institute, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany

^*bluhm@physik.rwth-aachen.de

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Issue

Vol. 99, Iss. 20 — 15 May 2019

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Images

Figure 1
(a) Schematic of a possible heterostructure realizing a hybrid device with a gate-defined double quantum dot tunnel coupled to a self-assembled quantum dot. A 2DEG emerges in the conduction band minimum at the lower ${Al}_{0.33} {Ga}_{0.67} As$ /GaAs inverted interface. Metallic top gates can be used to deplete the 2DEG and to create gate-defined (lateral) quantum dots. Addition of InAs during the growth of the GaAs layer leads to the formation of SAQDs. (b) Model of a single-level GDQD tunnel coupled to an optically active quantum dot, as discussed in Sec. 2. Here $t_{c}$ represents the tunnel coupling between the GDQD and the OAQD, $ɛ$ the energy detuning between the electronic level in the GDQD and in the exciton, and $H_{ex}$ the excitonic exchange interaction. (c) Model of a double dot tunnel coupled to an OAQD, as discussed in Sec. 3. In addition to the quantities defined before, $ɛ_{DD}$ and $t_{DD}$ represent the detuning and the tunnel coupling in the double dot, respectively.
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Figure 2
Schematic diagram of the information-transfer process from an OAQD to a single spin qubit. Shown are the eigenenergies of the Hamiltonian Eq. (9) as a function of the detuning $ɛ$ for the case of strong tunnel coupling ( $t_{c} = 150 μ eV$ ). All remaining parameters are given in Table 1. The color code indicates the bright-state contribution (BC) of each state, see Eq. (5). The bright spots indicate the detuning at which photoexcitation occurs and the branches chosen as basis states. Once an exciton is created in the OAQD, the photoexcited electron is transferred into the GDQD by adiabatically increasing the detuning $ɛ$ .
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Figure 3
Performance of the protocol for transferring information to a single spin qubit. All plots are for the parameters given in Table 1 with $t_{c} = 50 μ eV$ . (a) Eigenenergies of the coupled GDQD-exciton system, Eq. (9). The color scale indicates the BC of each state. (b) Same as in (a), but now the color scale represents the two independent subspaces of the Hilbert space. The bright spots indicate the detuning $ɛ_{EP}$ at which optical excitation occurs, as well as the branches chosen as basis states for the information transfer process (also labeled as $| Ψ_{1} 〉$ and $| Ψ_{2} 〉$ ). (c) Plot of the inverse maximal sweep speed $1 / v_{ɛ}$ that allows adiabatic evolution along the branches $| Ψ_{1} 〉$ (red) and $| Ψ_{2} 〉$ (blue). (d) Probability that no optical recombination occurs during the adiabatic transfer along the branches $| Ψ_{1} 〉$ (red) and $| Ψ_{2} 〉$ (blue). (e) Probability of completing the adiabatic transfer without dephasing. Different noise sources are separately accounted. The final values are displayed on the right. $t$ is the time elapsed from the beginning of the protocol.
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Figure 4
Schematic of the protocol for transferring information to a singlet-triplet qubit. (a) Energy levels of the subspace sketched in Eq. (18), as a function of the detuning for the parameter set $(t_{c}, t_{DD}, ɛ_{DD}) = (150 μ eV, 50 μ eV, - 2.03 meV)$ . The remaining parameters are given in Table 1. The color scale represents the bright-state contribution of the various branches. The labels close to each branch indicate the main contribution to the eigenstates in the corresponding regime. The bright spots indicate the photoexcited branches. (b) Same as above, with the color scale now representing the vertical-polarization contribution of the relevant protocol branches. (c) Sketch of the pulse sequence involved in the protocol. First the system is detuned to the value $ɛ = ɛ_{EP}$ , where the optical excitation occurs. Then $ɛ$ is adiabatically swept to the driving point $ɛ^{*}$ , where a Rabi $π$ pulse is applied. At the end of the pulse, $ɛ$ is further increased to large positive values, into the regime of separated states. The interdot detuning of the double dot $ɛ_{DD}$ is kept negative until the end of the Rabi pulse to confine the electron initialized in the DD on the left dot. At the end of the pulse, $ɛ_{DD}$ is adiabatically swept to zero.
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Figure 5
Analysis of the protocol presented in Fig. 4. The parameters for these plots are given in Table 1, with the additional choice $(t_{c}, t_{DD}, ɛ_{DD}) = (150 μ eV, 50 μ eV, - 2.03 meV)$ . (a) Energy levels of the subspace sketched in Eq. (18). Different branches are indicated by different colors. The left dashed line marks the excitation point $ɛ_{EP} = 0.09 meV$ and the right line the driving point $ɛ^{*} = 0.17 meV$ . (b) Amplitude of the transition-matrix elements $λ_{a b}$ , from the black ( $T_{+}$ ) branch to the other branches. The color code is the one defined in panel (a). (c) In this panel, the red curve represents the condition $T_{Rabi} = π ℏ / (Δ ɛ λ_{T_{+} S})$ , with $Δ ɛ$ chosen such that the coupling $λ_{T_{+} S}$ does not vary more than 50% in the range $[ɛ - Δ ɛ, ɛ + Δ ɛ]$ . The thin gray curves represent selected levels of constant leakage probability, $P_{Rabi - leak} = P_{Ψ_{T_{+}} \to Ψ_{T_{0}}} = 5 %$ down to $0.25 %$ , calculated according to Eq. (21). (d) Maximal sweep speed allowed for adiabatic transfer along the $T_{+}$ -like branch (black) and along the S- and the $T_{0}$ -like branches (red-blue), calculated according to Eq. (13).
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Figure 6
Performance analysis of the protocol presented in Fig. 4. (a) Schematic evolution of the energies of the relevant protocol branches as a function of time. Dashed lines represent unpopulated branches, while full lines populated ones. The color code is the same as in Fig. 5. (b) Probability of completing the transfer without recombination for the S-like branch (red) and the $T_{0}$ -like branch (blue). (c) Failure probability due to dephasing due to different noise sources.
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