We show that dynamics in the spin–orbit coupling field simulate the von Neumann measurement of a particle spin. We demonstrate how the measurement influences the spin and coordinate evolution of a particle by comparing two examples of such a procedure. The first example is a simultaneous measurement of spin components, σ x and σ y , corresponding to non-commuting operators, which cannot be accurately obtained together at a given time instant due to the Heisenberg uncertainty ratio. By mapping spin dynamics onto a spatial walk, such a procedure determines measurement-time averages of σ x and σ y , which can already be precisely evaluated in a single short-time measurement. The other, qualitatively different, example is the spin of a one-dimensional particle in a magnetic field. Here, the measurement outcome depends on the angle between the spin–orbit coupling and magnetic fields. These results can be applied to studies of spin–orbit coupled cold atoms and electrons in solids.
We show that dynamics in the spin–orbit coupling field simulate the von Neumann measurement of a particle spin. We demonstrate how the measurement influences the spin and coordinate evolution of a particle by comparing two examples of such a procedure. The first example is a simultaneous measurement of spin components, σ x and σ y , corresponding to non-commuting operators, which cannot be accurately obtained together at a given time instant due to the Heisenberg uncertainty ratio. By mapping spin dynamics onto a spatial walk, such a procedure determines measurement-time averages of σ x and σ y , which can already be precisely evaluated in a single short-time measurement. The other, qualitatively different, example is the spin of a one-dimensional particle in a magnetic field. Here, the measurement outcome depends on the angle between the spin–orbit coupling and magnetic fields. These results can be applied to studies of spin–orbit coupled cold atoms and electrons in solids.
We propose a possible experiment aimed at a joint measurement of two noncommuting spin-1/2 components and analyze its physical meaning. We demonstrate that switching of a strong spin-orbit interaction, e.g., in a solid-state or a cold-atom system, for a short time interval simulates a simultaneous von Neumann measurement of the operators ${\ensuremath{\sigma}}_{x}$ and ${\ensuremath{\sigma}}_{y}$. With the spin dynamics mapped onto the quantum coordinate-space motion, such an experiment determines averages of ${\ensuremath{\sigma}}_{x}$ and ${\ensuremath{\sigma}}_{y}$ over the duration of the measurement, however short the latter may be. These time averages, unlike the instantaneous values of ${\ensuremath{\sigma}}_{x}$ and ${\ensuremath{\sigma}}_{y}$, may be evaluated simultaneously to an arbitrary accuracy.
We report the observation of electron spin interactions between Rydberg atoms, which are driven by spin-orbit coupling through second-order dipole perturbation and exhibit a spatial anisotropy governed by the atomic configuration. Specifically, we observe coherent electron spin exchange dynamics, with the measured coupling strength agreeing well with both numerical calculations and theoretical models. Furthermore, we show that global microwave dressing enables active engineering and dynamical freezing of the spin exchange by introducing a differential AC Stark shift between the participating states. Additionally, we achieve tunability of the interaction by applying a stronger magnetic field, which effectively modifies the energy contributions of the underlying spin-orbit coupling channels. Finally, measuring spin dynamics in one-dimensional multi-atom chains aligned parallel or perpendicular to the magnetic field provides a self-consistent validation of the anisotropic XXZ framework. This electron spin interaction natively features spin-position coupling and enables a natural mapping onto the Heisenberg-Kitaev model. Our findings reveal a new class of electron spin-spin interactions among Rydberg atoms, expanding the scope of quantum simulation with Rydberg atom arrays.
We consider the dynamics of a quantum particle held in a lattice potential and subjected to a time-dependent spin-orbit coupling. Tilting the lattice causes the particle to perform Bloch oscillations, and by suitably changing the Rashba interaction during its motion, the spin of the particle can be gradually rotated. Even if the Rashba coupling can only be altered by a small amount, large spin rotations can be obtained by accumulating the rotation from successive oscillations. We show how the time dependence of the spin-orbit coupling can be chosen to maximize the rotation per cycle, and thus how this method can be used to produce a precise and controllable spin rotator, which we term the Bloch-Rashba rotator, without requiring an applied magnetic field.
Mixed quantum-classical models are widely used to reduce the computational cost of fully quantum simulations. However, their general applicability across different classes of problems remains an open question. Here, we address this issue for systems featuring spin-orbit coupling. In particular, we study the interaction dynamics of quantum spin-1/2 and classical orbital momentum in one-dimensional models of Rashba nanowires. We tackle this problem by resorting to a new quantum-classical Hamiltonian model that, unlike conventional approaches, retains the Heisenberg principle and captures correlation effects beyond the common Ehrenfest method. Based on Koopman wavefunctions in classical mechanics, the new model was recently implemented numerically via a particle scheme -- the koopmon method -- which is extended here to treat spin-orbit coupling. We apply the koopmon method to study the quantum-classical dynamics of nanowire models, with and without the presence of a harmonic potential and in both Rashba-dominated (strong coupling) and Zeeman-dominated (weak coupling) regimes. Considering realistic semiconductor parameters, the results are contrasted with both fully quantum and quantum-classical Ehrenfest dynamics. In the absence of external potential, the koopmon method qualitatively reproduces the features of the fully quantum evolution for all coupling regimes. While it exhibits a slight loss in spin accuracy compared to Ehrenfest simulations, the latter fail to capture the orbital dynamics. In the presence of a harmonic potential, the koopmon scheme reproduces several features of full quantum dynamics with accuracy levels that are unachievable by the Ehrenfest model. We conclude by presenting a test case that exhibits the formation of cat-like states.
In the Dirac theory for the motion of free relativistic electrons, highly oscillatory components appear in the time evolution of physical observables such as position, velocity, and spin angular momentum. This effect is known as zitterbewegung. We present a theoretical analysis of rather different Hamiltonians with gapped and/or spin-split energy spectrum (including the Rashba, Luttinger, and Kane Hamiltonians) that exhibit analogs of zitterbewegung as a common feature. We find that the amplitude of oscillations of the Heisenberg velocity operator v(t) generally equals the uncertainty for a simultaneous measurement of two linearly independent components of v. It is also shown that many features of zitterbewegung are shared by the simple and well-known Landau Hamiltonian, describing the dynamics of two-dimensional (2D) electron systems in the presence of a magnetic field perpendicular to the plane. Finally, we also discuss the oscillatory dynamics of 2D electrons arising from the interplay of Rashba spin splitting and a perpendicular magnetic field.
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