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arXiv:0910.0584 · Physical Review B

Proposals of nuclear spin quantum memory in group-IV elemental and II-VI semiconductors

Özgür Çakır, T. Takagahara

Published Oct 23, 2009• 6 citations
arXivHTMLPDF

Abstract

Schemes for the nuclear spin quantum memory are proposed based on a system composed of two electrons or one electron coupled to a single nuclear spin in isotopically purified group-IV elemental and II-VI compound semiconductors. The qubit consists of the singlet state and one of the triplet states of two electrons or simply of an electron spin. These systems are free from the decoherence due to the nuclear dipole-dipole interaction and are advantageous for the long memory time. In the case of two electrons, the protocol for the quantum state transfer between the electron-spin qubit and the nuclear spin qubit is based on the magnetic or electric field tuning of the singlet-triplet state crossing and on the hyperfine coupling supplemented with a well-defined scheme to initialize the nuclear spin. In the case of a single-electron qubit, the quantum state transfer is driven by the hyperfine interaction itself without the need of the nuclear spin initialization. Many practical systems are considered, e.g., two electrons loaded on a Si or ZnSe quantum dot, a single-electron charged state in a Si quantum dot doped with a P atom, a single-electron charged $^{28}\text{S}\text{i}$ quantum dot doped with an isotope atom of $^{29}\text{S}\text{i}$, and a localized electron system of Si:P and ZnSe:F in the bulk crystal. General aspects of these systems are investigated and a comparison of merits and demerits is made between the two-electron qubit and the single-electron qubit.

DOI
10.1103/physrevb.80.155323

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Quantum physics governs the world at the microscopic scale and determines the properties of matter. While classical computers exploit quantum phenomena passively by relying on transistor technology, the concept of a quantum computer with active control over quantum states promises unprecedented possibilities for information encoding and processing. Already developed quantum algorithms are known to perform certain tasks faster than any existing classical algorithms, and quantum computers also promise the possibility for precise simulations of complex quantum systems, a task infeasible for classical computers. These points emphasize the need for the development of quantum computers. Considering quantum computers, the fundamental unit of information is a qubit, a two-level quantum system. Qubits, in contrast to classical bits which are either in state 0 or 1, can exist in quantum superposition of the states 0 and 1, allowing for more complex and parallel computations. While there are many options to encode a logical qubit in a physical system, spin 1/2 particles are considered a natural choice because their spin degree of freedom defines a qubit intrinsically. Semiconductors are a promising platform for hosting spin qubits, as they enable the confinement of electrons with spin 1/2 either through gate-defined quantum dots (QDs) or donor atoms. Among the possible choices of donor atoms, phosphorous 31P is particularly noteworthy because its nucleus has nuclear spin 1/2. Nuclear spins are prime candidates for qubit implementation because they demonstrated exceptionally long coherence times, but the underlying good isolation from their environment is a challenge when it comes to readout and control. In this thesis, we face this challenge by proposing a hybrid quantum dot-donor (QDD) system consisting of a gate defined silicon (Si) QD and a thereto laterally displaced 31P phosphorous donor atom implanted in the Si host material. A single electron is presumed to be confined in the system, which can be moved between the QD and the donor on demand. If its wave function overlaps with the donor atom, electron spin and the donor nuclear spin interact via the hyperfine interaction and the electron can act as a mediator between the nuclear spin qubit and the environment for readout and control, whereas the nuclear spin qubit can be set in an idling mode by shifting the electron to the QD. Importantly, the proposed system can be embedded in circuit quantum electrodynamics (cQED) architectures enabling strong coupling between the system’s electron spin and microwave resonator photons. This coupling is fundamental for the research presented in this thesis. Analyzing the envisioned system, we first propose a novel method for nuclear-spin readout by probing the resonator transmission. This method is based on the observation that the signature of strong electron spin-photon coupling in the resonator transmission is altered due to the hyperfine interaction, in such a manner that well separated signatures for the electron spin-photon coupling conditioned on the state of the nuclear spin arise. As the next step, we turn our attention to the control of nuclear spin qubits and especially to the challenge of realizing a two-qubit gate between distant nuclear spins. In this course, we derive an effective nuclear spin-photon coupling. While expected to be weak, this interaction can be harnessed to couple the nuclear spins of two distant QDD systems dispersively to a microwave resonator resulting in an entangling nuclear spin two-qubit √iSWAP gate with a gate fidelity approaching 90%. These two key findings represent a significant and valuable contribution to the field of quantum information processing using nuclear spins.
We present a mechanism to protect quantum information stored in an ensemble of nuclear spins in a semiconductor quantum dot. When the dot is charged the nuclei interact with the spin of the excess electron through the hyperfine coupling. If this coupling is made off-resonant, it leads to an energy gap between the collective storage states and all other states. We show that the energy gap protects the quantum memory from local spin-flip and spin-dephasing noise. Effects of nonperfect initial spin polarization and inhomogeneous hyperfine coupling are discussed.
A promising platform for quantum information processing is that of silicon impurities, where the quantum states are manipulated by magnetic resonance. Such systems, in abstraction, can be considered as a nucleus of arbitrary spin coupled to an electron of spin one-half via an isotropic hyperfine interaction. We therefore refer to them as "nuclear-electronic spin systems". The traditional example, being subject to intensive experimental studies, is that of phosphorus doped silicon (Si:P) which couples a spin one-half electron to a nucleus of the same spin, with a hyperfine strength of 117.5 MHz. More recently, bismuth doped silicon (Si:Bi) has been suggested as an alternative instantiation of nuclear-electronic spin systems, differing from Si:P by its larger nuclear spin and hyperfine strength of 9/2 and 1.4754 GHz respectively. The aim of this thesis has been to develop a model that is capable of predicting the magnetic resonance properties of nuclear-electronic spin systems. The theoretical predictions of this model have been tested against experimental data collected on Si:Bi at 4.044 GHz, and have proven quite successful. Furthermore, the larger nuclear spin and hyperfine strength of Si:Bi, compared with that of Si:P, are predicted to offer advantages for quantum information processing. Most notable amongst these is that magnetic field-dependent two-dimensional decoherence free subspaces, called optimal working points, have been identified to exist in Si:Bi, but not Si:P.
The decoherence and fidelity of spin states in a localized single-electron quantum dot in the presence of a dc magnetic field, arising either from the nuclear hyperfine interaction within the dot or due to its coupling with another localized quantum dot, are examined in detail. A general framework for determining the time evolution of the reduced density matrix. for a single dot is presented, which is exact up to the second order in interaction with any reservoir. In particular, it is applied to the problem of nuclear hyperfine coupling, and approximate estimates of coherence decay time are made when the nuclear spins are either polarized or unpolarized and the internal dynamics of nuclear spins is determined mainly by the nuclear magnetic dipole-dipole interaction. The fidelity of a pure unperturbed electronic one-qubit spin state is obtained as a function of time, which is exact even on a very short timescale of logic gate operations. The time variation of the fidelity of the same one-qubit state on the localized dot as a part of the direct product with another one-qubit state on another localized dot arising because of coupling between these quantum dots is also calculated in this paper. In this case, we include both the single-particle tunnelling between the dots as well as the direct and exchange Coulomb interactions, including on-site Coulomb repulsion. This allows for the double occupation of a single dot. It is found that the loss of fidelity of such two-qubit states due to double occupancy and additional phase errors in the presence of appreciable dot-dot coupling can become a more severe limiting factor than that due to the hyperfine interaction in individual dots.
Single electron spin in a semiconductor quantum dot (QD) and single photon wavepacket propagating in an optical waveguide are investigated as carriers of quantum bit (qubit) for information processing. Cavity quantum electrodynamics of the coupled system composed of charged QD, microcavity and waveguide provides a quantum interface for the interplay of stationary spin qubits and flying photon qubits via cavity assisted optical control. This interface forms the basis for a wide range of essential functions of a quantum network, including transferring, swapping, and entangling qubits at distributed quantum nodes as well as a deterministic source and an efficient detector of a single photon wavepacket with arbitrarily specified shape. The cavity assisted optical process also made possible ultrafast initialization and QND readout of the spin qubit in QD. In addition, the strong optical nonlinearity of dot-cavity-waveguide coupled system enables phase gate and entanglement operation for flying single photon qubits in waveguides. The coherence of the electron spin is the wellspring of these quantum applications being investigated. At low temperature and strong magnetic field, the dominant cause of electron spin decoherence is the coupling with the interacting lattice nuclear spins. We present a quantum solution to the coupled dynamics of the electron with the nuclear spin bath. The decoherence is treated in terms of quantum entanglement of the electron with the nuclear pair-flip excitations driven by the various nuclear interactions. A novel nuclear interaction, mediated by virtue spin-flips of the single electron, plays an important role in single spin free-induction decay (FID). The spin echo not only refocuses the dephasing by inhomogeneous broadening in ensemble dynamics but also eliminates the decoherence by electron-mediated nuclear interaction. Thus, the decoherence times for single spin FID and ensemble spin echo are significantly different. The quantum theory of decoherence also leads to a method of coherence recovery of the electron by disentanglement, realized through maneuvering the nuclear bath evolution by control of the electron spin-flip. The studies form the basis to outline the construction of a solid-state quantum network for scalable and distributed processing of quantum information
Recently, an ensemble of nuclear spins in a quantum dot have been proposed as a long-lived quantum memory. A quantum state of an electron spin in the dot can be faithfully transfered into nuclear spins through controlled hyperfine coupling. Here we study the decoherence of this memory due to nuclear spin dipolar coupling and inhomogeneous hyperfine interaction during the storage period. We calculated the maximum fidelity of writing, storing, and reading operations. Our results show that nuclear spin dynamics can severely limit the performance of the proposed device for quantum information processing and storage based on nuclear spins.