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arXiv:0708.2091 · Physical Review B

Spin dynamics in InAs nanowire quantum dots coupled to a transmission line

Mircea Trif, Vitaly N. Golovach, Daniel Loss

Published Jan 31, 2008• 181 citations
arXivHTMLPDF

Abstract

We study theoretically electron spins in nanowire quantum dots placed inside a transmission line resonator. Because of the spin-orbit interaction, the spins couple to the electric component of the resonator electromagnetic field and enable coherent manipulation, storage, and readout of quantum information in an all-electrical fashion. Coupling between distant quantum-dot spins, in one and the same or different nanowires, can be efficiently performed via the resonator mode either in real time or through virtual processes. For the latter case, we derive an effective spin-entangling interaction and suggest means to turn it on and off. We consider both transverse and longitudinal types of nanowire quantum dots and compare their manipulation time scales against the spin relaxation times. For this, we evaluate the rates for spin relaxation induced by the nanowire vibrations (phonons) and show that, as a result of phonon confinement in the nanowire, this rate is a strongly varying function of the spin operation frequency and thus can be drastically reduced compared to lateral quantum dots in GaAs. Our scheme is a step forward to the formation of hybrid structures where qubits of different nature can be integrated in a single device.

DOI
10.1103/physrevb.77.045434

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We study theoretically electron spins in nanowire quantum dots placed inside a transmission line resonator. Because of the spin-orbit interaction, the spins couple to the electric component of the resonator electromagnetic field and enable coherent manipulation, storage, and readout of quantum information in an all-electrical fashion. Coupling between distant quantum-dot spins, in one and the same or different nanowires, can be efficiently performed via the resonator mode either in real time or through virtual processes. For the latter case, we derive an effective spin-entangling interaction and suggest means to turn it on and off. We consider both transverse and longitudinal types of nanowire quantum dots and compare their manipulation time scales against the spin relaxation times. For this, we evaluate the rates for spin relaxation induced by the nanowire vibrations (phonons) and show that, as a result of phonon confinement in the nanowire, this rate is a strongly varying function of the spin operation frequency and thus can be drastically reduced compared to lateral quantum dots in GaAs. Our scheme is a step forward to the formation of hybrid structures where qubits of different nature can be integrated in a single device.
Since the development of microsized devices is moving forward at enormous speed, there is huge amount of new industrial opportunities. However such devices also require high precision and understanding of the operating of their constituent parts up to the quantum level. The device of the purely quantum nature being developed so far is quantum computer. However the physical realization of it is still not performed, as the requirements for it are very rigorous. \n \nIn the pioneering work by Loss and DiVincenzo it was suggested to use a spin of electron placed in a quantum dot as an information qubit. Following this work the study of electron or hole spin qubits developed. Both experimental and theoretical tools for studying them greatly advanced. \n \nIn the first part of the thesis we study the phonon-induced decoherence and relaxation of singlet-triplet qubits in the double quantum dots. First of all we consider AlGaAs/GaAs double quantum dots. The important result we present here is the strong dephasing that occurs at large detuning. This dephasing is due to two-phonon process that affects mainly singlet state of the qubit and consequently changes the splitting between singlet and triplet leading to dephasing. Remarkably at small detuning this dephasing process is suppressed and the decoherence time is by orders of magnitude longer than in case of large detuning and is mainly defined by one-phonon process. We also present the dependence of relaxation time and decoherence time on the strength of spin-orbit interaction and different directions of the system. Our results provide a deeper insight into the recently obtained experimental data. \n \nWe also studied Si/SiGe quantum dots as a potential candidate for a qubit. Apart from the absence of hyperfine interaction and bulk spin-orbit interaction in the isotopically purified 28^{28}28Si, its electron-phonon interaction is different from GaAs that also leads to longer qubit lifetimes. We study SSS-T−T_-T−​ qubit near the anticrossing of the basis states. This particular region is interesting due to possibilities in operating the qubit. We show that the type of singlet plays a crucial role, i.e. whether it is a singlet with each dot singly occupied or a singlet with only one dot doubly occupied. Depending on the type of singlet the qubit lifetimes change by several orders of magnitude. We also study the influence of a micromagnet, usually used in experiments to operate the qubit, on the relaxation time and decoherence time and present the regime where its effect is negligible. We suggest how to test experimentally our theory of one-phonon and two-phonon processes separately. We also show how the relaxation and decoherence time depend on different system parameters for SSS-T0T_0T0​ qubits. \n \nThe second part of the thesis is devoted to the other important constituent part of microsized devices, namely nanowires. We are interested in the dynamic of polarization of localized spins in the nanowires, as it can affect such important device characteristics as e.g. conductance. \n \nWe studied Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction-induced polarization in the nanowire in case when the voltage is applied to it. It was already proposed theoretically that in the ground state the localized spins in 1D systems align in a helix due to RKKY interaction. This polarization is still present until some critical temperature. The presence of such polarization acts as a spin filter for electrons, that most likely affects the conductance of the nanowire. Therefore we studied how this helical polarization changes when the voltage is applied. The key result is the appearance of the uniform polarization perpendicular to the helix plane, that occurs due to backscattering of electrons that is accompanied by flip-flop process with localized spins. When this uniform polarization is formed, the helix starts to rotate as a whole around the direction of the uniform polarization. We present the dependence of polarization of the localized spins on temperature and voltage. Remarkably the uniform polarization grows both with voltage and temperature in the given range of parameters. \n \nWe also considered the electron-induced relaxation of the nuclear spins. As the electron spins and nuclear spins interact via hyperfine interaction, the nuclear relaxation time reflects some properties of electron bath. Namely, we see a strong dependence of nuclear relaxation time on spin-orbit interaction strength. We present here the dependence of the nuclear relaxation time on the external magnetic field and chemical potential of the wire, that can be experimentally varied via gate. The dependences for the strong spin-orbit interaction and for the weak one are substantially different. Moreover, they have distinct peaks, that allow to get the value of spin-orbit interaction amplitude with the high precision.
We propose a setup for universal and electrically controlled quantum information processing with hole spins in Ge/Si core/shell nanowire quantum dots (NW QDs). Single-qubit gates can be driven through electric-dipole-induced spin resonance, with spin-flip times shorter than 100 ps. Long-distance qubit-qubit coupling can be mediated by the cavity electric field of a superconducting transmission line resonator, where we show that operation times below 20 ns seem feasible for the entangling iSWAP\sqrt{i\text{SWAP}}iSWAP​ gate. The absence of Dresselhaus spin-orbit interaction (SOI) and the presence of an unusually strong Rashba-type SOI enable precise control over the transverse qubit coupling via an externally applied, perpendicular electric field. The latter serves as an on-off switch for quantum gates and also provides control over the ggg factor, so single- and two-qubit gates can be operated independently. Remarkably, we find that idle qubits are insensitive to charge noise and phonons, and we discuss strategies for enhancing noise-limited gate fidelities.
Scalable architectures for quantum computing using semiconductor quantum dots require interactions between qubits beyond adjacent quantum dots. Here, we propose using nanowires of electrons to mediate the interaction between two quantum dots. Virtual phonons in the linear chain of electrons can mediate an interaction that gives rise to effective spin-spin coupling of the electrons in distant quantum dots. We find coupling strengths of more than 30 MHz for experimentally realisable parameters in GaAs quantum dots.
Solid state based quantum information processing is focused on physical implementation of all necessary elements of quantum computation and quantum information in solid state systems, mainly due to their scalability compared to e.g. optical systems. Among many proposals to realize these types of devices, such as quantum dots as charge qubits or Josephson junction circuits, we study here one of the most promising candidates, i.e., the spin of an electron confined to a quantum dot as a qubit. Experimentally, it has been shown that the relaxation rate of this two level system can be pushed above few seconds in low magnetic fields. Moreover, using spin echo techniques, \nthe spin dephasing time can be maximized up to milliseconds with the current technology. This long spin decay time is one of the main reasons that make this system desirable for quantum computation and quantum information purposes. \nWe reexamined the recent measurement based proposal called one-way quantum computation which exploits entanglement and local measurements as tools to perform quantum computation on N qubits. Although it was suggested in the original work to entangle the qubits via the nearest neighbor Ising interaction, we investigated how one can generate the so-called cluster states with the Heisenberg interaction. We extended our method to include more general forms of Heisenberg interaction such as asymmetric coupling of adjacent qubits. These forms of couplings, rather than Ising interaction, are more encountered in solid state devices, and therefore make it possible to perform one-way quantum computation with electron spins in quantum dots coupled via exchange interaction to their adjacent spins. \n \nChapters II, III, and IV of my thesis are devoted to the study of the spin-orbit interaction in heterostructure quantum dots and its effect on the spin dynamics. We observed that one can actually use spin-orbit interaction to manipulate the spin state of an electron on time scales much smaller than the spin dephasing time. Specifically, in chapter II, we studied the effect of a nearby functioning quantum point contact (QPC) on the relaxation of the electron spin and show that the charge fluctuations in QPC lead to spin relaxation of the confined electron in the presence of spin-orbit interactiom and an applied magnetic field. We also addressed the relation of this rate to the microscopic parameters of the system and found some geometrical dependence of the spin relaxation time on the orientation of the QPC on the substrate. Moreover, we showed in chapters III and IV that the spin-orbit interaction can play a positive role, in order to rotate the spin around the Bloch sphere. We considered different mechanisms, particularly, Electron Dipole Spin Resonance (EDSR) and holonomic unitary gates in quantum dots. We verified that these mechanisms of spin manipulation can be realized in solid state systems with the state of the art semiconductor technologies. \n \nChapter V of the thesis covers a slightly different topic and focuses on the role of the Coulomb interaction in electronic transport. There, we reviewed the non-analytic corrections to the Fermi liquid behavior and their consequences on the momentum occupation number of the electrons in a two dimensional electron gas (2DEG). As an example, we calculated the tunneling rate from an interacting electron reservoir onto a quantum dot and compared our result to the corresponding case for electron tunneling between bilayer 2DEGs. Moreover, within RPA approximation, we found that the electron-plasmon coupling leads to a quadratic frequency dependence of the electron self-energy at low frequencies at the Fermi surface. This correction suppresses the same order corrections due to the particle-hole bubble. \n \n \n
A nanodevice capable of separating spins of two electrons confined in a quantum dot formed in a gated semiconductor nanowire is proposed. Two electrons confined initially in a single quantum dot in the singlet state are transformed into the system of two electrons confined in two spatially separated quantum dots with opposite spins. In order to separate the electrons' spins we exploit transitions between the singlet and the triplet state, which are induced by resonantly oscillating Rashba spin-orbit coupling strength. The proposed device is all electrically controlled and the electron spin separation can be realized within tens of picoseconds. The results are supported by solving numerically the quasi-one-dimensional time-dependent Schroedinger equation for two electrons, where the electron-electron correlations are taken into account in the exact manner.
We report on the first set of exact orthonormalized states to an ac driven one-dimensional (1D) two-electron nanowire quantum dot with the Rashba-Dresselhaus coexisted spin-orbit coupling (SOC) and the controlled magnetic field orientation and trapping frequency. In the ground state case, it is shown that the spatiotemporal evolutions of probability densities occupying internal spin states and the transfer rates between different spin states can be adjusted by the ac electric field and the intensities of SOC and magnetic field. Effects of the system parameters and initial-state-dependent constants on the mean entanglement are revealed, where the approximately maximal entanglement associated with the stronger SOC and its insensitivity to the initial and parametric perturbations are demonstrated numerically. A novel resonance transition mechanism is found, in which the ladder-like time-evolution process of expected energy and the transition time between two arbitrary exact states are controlled by the ac field strength. Using such maximally entangled exact states to encode qubits can render the qubit control more transparent and robust. The results could be extended to 2D case and to an array of two-electron quantum dots with weak neighboring coupling for quantum information processing.