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arXiv:1510.06491 · Scientific Reports

The energy-level crossing behavior and quantum Fisher information in a quantum well with spin-orbit coupling

Zhihai Wang, Qiang Zheng, Xiaoguang Wang, Yong Li

Published Mar 2, 2016• 30 citations
arXivHTMLPDF

Abstract

We study the energy-level crossing behavior in a two-dimensional quantum well with the Rashba and Dresselhaus spin-orbit couplings (SOCs). By mapping the SOC Hamiltonian onto an anisotropic Rabi model, we obtain the approximate ground state and its quantum Fisher information (QFI) via performing a unitary transformation. We find that the energy-level crossing can occur in the quantum well system within the available parameters rather than in cavity and circuit quantum eletrodynamics systems. Furthermore, the influence of two kinds of SOCs on the QFI is investigated and an intuitive explanation from the viewpoint of the stationary perturbation theory is given.

DOI
10.1038/srep22347

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We study the energy-level crossing behavior in a two-dimensional quantum well with the Rashba and Dresselhaus spin-orbit couplings (SOCs). By mapping the SOC Hamiltonian onto an anisotropic Rabi model, we obtain the approximate ground state and its quantum Fisher information (QFI) via performing a unitary transformation. We find that the energy-level crossing can occur in the quantum well system within the available parameters rather than in cavity and circuit quantum eletrodynamics systems. Furthermore, the influence of two kinds of SOCs on the QFI is investigated and an intuitive explanation from the viewpoint of the stationary perturbation theory is given.
Abstract In this paper, we study the additivity of quantum Fisher information (QFI) in a coupled system composed by a two-level system and a bosonic mode, which is described by an anisotropic Rabi model. Utilizing a unitary transformation approach, we obtain the approximate ground state for the global state and the reduced density matrix for each subsystem. We find the additivity of QFI, that is, the summation of QFI for two subsystems is always larger than that of the global system. We hope our work will stimulate the studies of quantum metrology in hybrid system.
A system of bosons in a two-dimensional harmonic trap in the presence of Rashba-type spin-orbit coupling is investigated. An analytic treatment of the ground state of a single atom in the weak-coupling regime is presented and used as a basis for a perturbation theory in the interacting two-boson system. The numerical diagonalization of both the single-particle and the two-boson Hamiltonian matrices allows us to go beyond those approximations and obtain not only the ground state, but also the low-energy spectra and the different energy contributions separately. We show that the expectation value of the spin-orbit term is related to the expectation value of ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\sigma}}}_{z}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{L}}_{z}$ for the eigenstates of the system, regardless of the trapping potential. The low-energy states of the repulsively interacting two-boson system are characterized. In the presence of a sufficiently strong interaction and spin-orbit coupling strength, there is a direct energy-level crossing in the ground state of the system between states of different Jz{J}_{z}Jz​, the third component of the total angular momentum, that changes its structure. This is reflected in a discontinuity in the different energy terms and it is signaled in the spatial density of the system.
One of the most dynamic directions in ultracold atomic gas research is the study of low-dimensional physics in quasi-low-dimensional geometries, where atoms are confined in strongly anisotropic traps. Recently, interest has significantly intensified with the realization of synthetic spin–orbit coupling (SOC). As a first step toward understanding the SOC effect in quasi-low-dimensional systems, the solution of two-body problems in different trapping geometries and different types of SOC has attracted great attention in the past few years. In this review, we discuss both the scattering-state and the bound-state solutions of two-body problems in quasi-one and quasi-two dimensions. We show that the degrees of freedom in tightly confined dimensions, in particular with the presence of SOC, may significantly affect system properties. Specifically, in a quasi-one-dimensional atomic gas, a one-dimensional SOC can shift the positions of confinement-induced resonances whereas, in quasitwo- dimensional gases, a Rashba-type SOC tends to increase the two-body binding energy, such that more excited states in the tightly confined direction are occupied and the system is driven further away from a purely two-dimensional gas. The effects of the excited states can be incorporated by adopting an effective low-dimensional Hamiltonian having the form of a two-channel model. With the bare parameters fixed by two-body solutions, this effective Hamiltonian leads to qualitatively different many-body properties compared to a purely low-dimensional model.
The recent experimental realization of spin-orbit coupled Fermi gases provides a unique opportunity to study the interplay between strong interaction and spin-orbit coupling (SOC) in a tunable, disorder-free system. We present here precision ab initio numerical results on the two-dimensional, unpolarized, uniform Fermi gas with attractive interactions and Rashba SOC. Using the auxiliary-field quantum Monte Carlo method and incorporating recent algorithmic advances, we carry out exact calculations on sufficiently large system sizes to provide accurate results systematically as a function of experimental parameters. We obtain the equation of state, the momentum distributions, the pseudospin correlations, and the pair wave functions. Our results help illuminate the rich pairing structure induced by SOC, and provide benchmarks for theory and guidance to future experimental efforts.
We study the system of spin-orbit (SO) coupled Bose–Einstein condensates (BEC) with Rabi coupling in quasi-two dimensions characterized by unequal Rashba and Dresselhaus couplings. The ground state properties and the phase diagram of the system are studied within the mean-field approximation at T = 0. The energy-momentum dispersion relation corresponding to the single-particle ground state exhibits an infinitely degenerate Rashba ring, whose degeneracy is destroyed by the Rabi coupling, leading to a single-point lowest energy. The effect of Rabi coupling and interaction in the system show up three different phases, namely stripe, plane wave and zero momentum phase. At a particular parametric condition, the system admits a critical point separating all three different phases, known as the tri-critical point. For further insight, the momentum distribution, the energy and the longitudinal/transverse spin polarization corresponding to the quantum phases are comprehensively discussed.
We study the role of coupling parameters on the ground state phases of spin-orbit coupled Bose-Einstein condensates with an equal combination of Rashba and Dresselhaus coupling strength with Rabi mixing using quasi-one-dimensional coupled Gross-Pitaevskii equations. By considering weak repulsive inter- and intra-species interactions between the condensate atoms, we investigate the contribution of spin-orbit and Rabi coupling parameters on the phases. We find that for a finite Rabi coupling strength, the system undergoes a phase transition from double plane-wave phase to stripe wave phase at a critical spin-orbit coupling strength.