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Register a new userFrom quantum-mechanical to classical dynamics in the central-spin model
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We discuss the semiclassical and classical character of the dynamics of a single spin 1/2 coupled to a bath of noninteracting spins 1/2. On the semiclassical level, we extend our previous approach presented in D. Stanek, C. Raas, and G. S. Uhrig, Phys. Rev. B 88, 155305 (2013) by the explicit consideration of the conservation of the total spin. On the classical level, we compare the results of the classical equations of motions in absence and presence of an external field to the full quantum result obtained by density-matrix renormalization (DMRG). We show that for large bath sizes and not too low magnetic field the classical dynamics, averaged over Gaussian distributed initial spin vectors, agrees quantitatively with the quantum-mechanical one. This observation paves the way for an efficient approach for certain parameter regimes.
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Using an equations-of-motion method based on analytical representations of spin-operator matrix elements in the XX chain, we obtain exact long-time dynamics of a composite system consisting of a spin-$S$ central spin and an XXZ chain, with the two interacting via inhomogeneous XXZ-type hyperfine coupling. Three types of initial bath states, namely, the Neel state, the ground state, and the spin coherent state are considered. We study the reduced dynamics of both the central spin and the XXZ bath. For the Neel state, we find that strong hyperfine couplings slow down the initial decay but facilitate the long-time relaxation of the antiferromagnetic order. Moreover, for fixed hyperfine coupling a larger $S$ leads to a faster initial decay of the antiferromagnetic order. We then study the purity dynamics of an $S=1$ central spin coupled to an XXZ chain prepared in the ground state. The time-dependent purity is found to reach the highest values at the critical point. We finally study the polarization dynamics of the central spin homogeneously coupled to a bath prepared in the spin coherent state. Under the resonant condition, the polarization dynamics for $S>frac{1}{2}$ exhibits collapse-revival behaviors with fine structures. However, the collapse-revival phenomena is found to be fragile with respect to the anisotropic intrabath coupling.
We analyze a quantum-classical hybrid system of steadily precessing slow classical localized magnetic moments, forming a head-to-head domain wall, embedded into an open quantum system of fast nonequilibrium electrons. The electrons reside within a metallic wire connected to macroscopic reservoirs. The model captures the essence of dynamical noncollinear and noncoplanar magnetic textures in spintronics, while making it possible to obtain the exact time-dependent nonequilibrium density matrix of electronic system and split it into four contributions. The Fermi surface contribution generates dissipative (or damping-like in spintronics terminology) spin torque on the moments, and one of the two Fermi sea contributions generates geometric torque dominating in the adiabatic regime. When the coupling to the reservoirs is reduced, the geometric torque is the only nonzero contribution. Locally it has both nondissipative (or field-like in spintronics terminology) and damping-like components, but with the sum of latter being zero, which act as the counterparts of geometric magnetism force and electronic friction in nonadiabatic molecular dynamics. Such current-independent geometric torque is absent from widely used micromagnetics or atomistic spin dynamics modeling of magnetization dynamics based on the Landau-Lifshitz-Gilbert equation, where previous analysis of Fermi surface-type torque has severely underestimated its magnitude.
The interplay of optical driving and hyperfine interaction between an electron confined in a quantum dot and its surrounding nuclear spin environment produces a range of interesting physics such as mode-locking. In this work, we go beyond the ubiquitous spin 1/2 approximation for nuclear spins and present a comprehensive theoretical framework for an optically driven electron spin in a self-assembled quantum dot coupled to a nuclear spin bath of arbitrary spin. Using a dynamical mean-field approach, we compute the nuclear spin polarization distribution with and without the quadrupolar coupling. We find that while hyperfine interactions drive dynamic nuclear polarization and mode-locking, quadrupolar couplings counteract these effects. The tension between these mechanisms is imprinted on the steady-state electron spin evolution, providing a way to measure the importance of quadrupolar interactions in a quantum dot. Our results show that higher-spin effects such as quadrupolar interactions can have a significant impact on the generation of dynamic nuclear polarization and how it influences the electron spin evolution.
We map electron spin dynamics from time to space in quantum wires with spatially uniform and oscillating Rashba spin-orbit coupling. The presence of the spin-orbit interaction introduces pseudo-Zeeman couplings of the electron spins to effective magnetic fields. We show that by periodically modulating the spin-orbit coupling along the quantum wire axis, it is possible to create the spatial analogue of spin resonance, without the need for any real magnetic fields. The mapping of time-dependent operations onto a spatial axis suggests a new mode for quantum information processing in which gate operations are encoded into the band structure of the material. We describe a realization of such materials within nanowires at the interface of LaAlO3/SrTiO3 heterostructures.
The presence of valley states is a significant obstacle to realizing quantum information technologies in Silicon quantum dots, as leakage into alternate valley states can introduce errors into the computation. We use a perturbative analytical approach to study the dynamics of exchange-coupled quantum dots with valley degrees of freedom. We show that if the valley splitting is large and electrons are not properly initialized to valley eigenstates, then time evolution of the system will lead to spin-valley entanglement. Spin-valley entanglement will also occur if the valley splitting is small and electrons are not initialized to the same valley state. Additionally, we show that for small valley splitting, spin-valley entanglement does not affect measurement probabilities of two-qubit systems; however, systems with more qubits will be affected. This means that two-qubit gate fidelities measured in two-qubit systems may miss the effects of valley degrees of freedom. Our work shows how the existence of valleys may adversely affect multiqubit fidelities even when the system temperature is very low.
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