We show that by switching on a spin-orbit interaction in a cold-atom system, experiencing a Zeeman-like coupling to an external field, e.g., in a Bose-Einstein condensate, one can simulate a quantum measurement on a precessing spin. Depending on the realization, the measurement can access both the ergodic and the Zeno regimes, while the time dependence of the spin's decoherence may vary from a Gaussian to an inverse fractional power law. Back action of the measurement forms time- and coordinate-dependent profiles of the atoms' density, resulting in its translation, spin-dependent fragmentation, and appearance of interference patterns.
We show that by switching on a spin-orbit interaction in a cold-atom system, experiencing a Zeeman-like coupling to an external field, e.g., in a Bose-Einstein condensate, one can simulate a quantum measurement on a precessing spin. Depending on the realization, the measurement can access both the ergodic and the Zeno regimes, while the time dependence of the spin's decoherence may vary from a Gaussian to an inverse fractional power law. Back action of the measurement forms time- and coordinate-dependent profiles of the atoms' density, resulting in its translation, spin-dependent fragmentation, and appearance of interference patterns.
Interference of atomic Bose-Einstein condensates, observed in free expansion experiments, is a basic characteristic of their quantum nature. The ability to produce synthetic spin-orbit coupling in Bose-Einstein condensates has recently opened a new research field. Here we theoretically describe interference of two noninteracting spin-orbit coupled Bose-Einstein condensates in an external synthetic magnetic field. We demonstrate that the spin-orbit and the Zeeman couplings strongly influence the interference pattern determined by the angle between the spins of the condensates, as can be seen in time-of-flight experiments. We show that a quantum backflow, being a subtle feature of the interference, is, nevertheless, robust against the spin-orbit coupling and applied synthetic magnetic field.
Atomtronics, a technique to control atoms for an application of devices, has been studied in recent years.The purpose of this thesis is to propose a novel method to control atoms for the application to the atomtronics.To achieve this purpose, we use a spin current in a spin-orbit (SO) coupled cold atoms.The spin current, that is a counterflow of particles with different spins, has attracted attention as a method to control electrons.On the other hand, the artificial SO coupled cold atoms were experimentally realized in 2011 and have been studied theoretically and experimentally.We can expect that a spin current can be formed in the SO coupled cold atoms because the SO coupling is known to induce a spin current and controlled because the cold atoms have various experimentally controllable parameters.However, little has been studied so far on the spin current in the cold atom.Therefore, we studied novel controllability of the spin current in the SO coupled cold atom.An SO coupled Bose-Einstein condensate (BEC) was experimentally realized in 2011 and then an SO coupled degenerate fermions became available in 2012.In these systems, since the SO coupling was engineered in a neutral atom by dressing two atomic spin states with a pair of Raman lasers and an external magnetic field, it is called artificial SO coupling.In addition, some parameters such as intensity of the SO coupling can be experimentally tuned by the lasers and the external magnetic field in the artificial SO coupled cold atoms.Therefore, by investigating parameter dependence of the spin currents, we reveal controllability of the atoms in the artificial SO coupled Bose and Fermi systems.As a result, in the SO coupled Bose system, the spin current changes discontinuously and non-smoothly across the phase boundaries, while in the SO coupled Fermi system, the spin current changes continuously and smoothly at zero temperature.On the other hand, Bose-Fermi mixture was experimentally realized and have been studied from different viewpoints.Therefore, we can expect to realize an artificial SO coupled Bose-Fermi mixture in near future.In this system, since atoms of different quantum statistics coexist under an influence of the SO coupling, novel phenomena can be expected.Based on these ideas, we investigate a ground state and a spin current in a mixture of fermions and SO coupled bosons.The ground states are calculated in the SO coupled Bose-Fermi mixture with high density or low density of the atoms by using a variational method and some approximations such as tight-binding approximation.For the high density, the fermions have a large influence on the Bose system, while, for the low density, the fermions have little influence although the relative amounts of the bosons and the fermions are comparable in the two cases.In addition, we show that the spin current of the i
Dynamical characteristics of internal and external states of a Bose-Einstein condensate are generally different and independent, thus requiring different experimental manipulation techniques. The spin-orbit coupling recently achieved in Bose-Einstein condensates essentially connects spin and motion degree of freedom, endowing spin states with the ability to respond to orbital manipulation, and vice versa. In this work, a dynamical response effect, induced by simultaneously manipulating the internal and external states of a spin-orbit-coupled Bose-Einstein condensate, is predicted. Here, the “simultaneously manipulating the internal and external states” means that the driving field combines the Zeeman field applied to the internal state of the atom and the orbital potential affecting the external states of the atom. Specifically, the Bose-Einstein condensate is assumed to be activated by an abruptly applied Zeeman field and a sudden shake of the trapping potential. After some reasonable simplification and approximation of the model (i.e. neglecting the inter-atomic interactions and modelling the shake of the trapping potential by a short time-dependent pulse), an analytical relationship connecting spin frequency spectrum and the parameters of the driving fields is derived. The numerical calculations based on directly integrating the Gross-Pitaevskii equation are in good agreement with the results from the analytical relationship. The physical origin of the predicted spin dynamical response can be traced back to the quantum interference among different spin-orbit states. Due to the fact that a series of characteristic parameters of the condensate can be manifested in the spin frequency spectrum, the dynamical response effect predicted here provides a candidate method for determining and calibrating various system parameters by measuring the spin frequency spectrum.
We predict a dynamical resonant effect, which is driven by externally applied linear and quadratic Zeeman fields, in a spin-orbit-coupled spin-1 Bose-Einstein condensate. The Bose-Einstein condensate is assumed to be initialized in some superposed state of Zeeman sublevels and subject to a sudden shift of the trapping potential. It is shown that the time-averaged center-of-mass oscillation and the spin polarizations of the Bose-Einstein condensate exhibit remarkable resonant peaks when the Zeeman fields are tuned to certain strengths. The underlying physics behind this resonance can be traced back to the out-of-phase interference of the dynamical phases carried by different spin-orbit states. By analyzing the single-particle spectrum, the resonant condition is summarized as a simple algebraic relation, connecting the strengths of the linear and quadratic Zeeman fields. This property is potentially applicable in quantum information and quantum precision measurement.
Abstract We consider a macroscopic spin qubit based on spin–orbit coupled Bose–Einstein condensates, where, in addition to the spin–orbit coupling (SOC), spin dynamics strongly depends on the interaction between particles. The evolution of the spin for freely expanding, trapped, and externally driven condensates is investigated. For condensates oscillating at the frequency corresponding to the Zeeman splitting in the synthetic magnetic field, the spin Rabi frequency does not depend on the interaction between the atoms since it produces only internal forces and does not change the total momentum. However, interactions and SOC bring the system into a mixed spin state, where the total spin is inside rather than on the Bloch sphere. This greatly extends the available spin space making it three-dimensional, but imposes limitations on the reliable spin manipulation of such a macroscopic qubit. The spin dynamics can be modified by introducing suitable spin-dependent initial phases, determined by the SOC, in the spinor wave function.
Achieving full control of a Bose-Einstein condensate can have valuable applications in metrology, quantum information processing, and quantum condensed matter physics. We propose protocols to simultaneously control the internal (related to its pseudospin-1/2) and motional (position-related) states of a spin-orbit-coupled Bose-Einstein condensate confined in a Morse potential. In the presence of synthetic spin-orbit coupling, the state transition of a noninteracting condensate can be implemented by Raman coupling and detuning terms designed by invariant-based inverse engineering. The state transfer may also be driven by tuning the direction of the spin-orbit-coupling field and modulating the magnitude of the effective synthetic magnetic field. The results can be generalized for interacting condensates by changing the time-dependent detuning to compensate for the interaction. We find that a two-level algorithm for the inverse engineering remains numerically accurate even if the entire set of possible states is considered. The proposed approach is robust against the laser-field noise and systematic device-dependent errors.