Energy Band and Josephson Dynamics of Spin-Orbit Coupled Bose——Einstein Condensates

We theoretically investigate the energy band structure and Josephson dynamics of a spin-orbit coupled Bose-Einstein condensate in a double-well potential. We study the energy band structure and the corresponding tunneling dynamics of the system by properly adjusting the SO coupling, Raman coupling, Zeeman field and atomic interactions. The coupled effects of SO coupling, Raman coupling, Zeeman field and atomic interactions lead to the appearance of complex energy band structure including the loop structure. Particularly, the emergence of the loop structure in energy band also depends on SO coupling, Raman coupling, Zeeman field and atomic interactions. Correspondingly, the Josephson dynamics of the system are strongly related to the energy band structure. Especially, the emergence of the loop structure results in complex tunneling dynamics, including suppression-revival transitions and self-trapping of atoms transfer between two spin states and two wells. This engineering provides a possible means for studying energy level and corresponding dynamics of two-species SO coupled BECs.     

Multi-Type Solitons in Spin-Orbit Coupled Spin-1 Bose–Einstein Condensates

Recently, research of solitons in Bose–Einstein condensates has become a popular topic. Here, we mainly study exact analytical solutions of Gross–Pitaevskii equations describing spin-orbit coupled spin-1 Bose–Einstein condensates. To begin with, we show the analytical relation between different types of one-dimensional spin-orbit coupling and Zeeman effect. In addition, we find a transformation that can simplify the three-component Gross–Pitaevskii equations with spin-orbit coupling into the non...     

Interferencing in Coupled Bose–Einstein Condensates

We consider an exactly soluble model of two Bose–Einstein condensates with a Josephson-type of coupling. Its equilibrium states are explicitly found showing condensation and spontaneously broken gauge symmetry. It is proved that the total number and total phase fluctuation operators, as well as the relative number and relative current fluctuation operators form both a quantum canonical pair. The exact relation between the relative current and phase fluctuation operators is established. Also the dynamics of these operators is solved showing the collapse and revival phenomenon.     

Quench Dynamics of Bose–Einstein Condensates in Boxlike Traps

By quenching the interatomic interactions, we investigate the nonequilibrium dynamics of two-dimensional Bose–Einstein condensates in boxlike traps with power-law potential boundaries. We show that ring dark solitons can be excited during the quench dynamics for both concave and convex potentials. The quench’s modulation strength and the steepness of the boundary are two major factors influencing the system’s evolution. In terms of the number of ring dark solitons excited in the condensate, five...     

Spontaneous Symmetry Breaking in Coupled Bose–Einstein Condensates

Journal of Statistical Physics - We study a system of two hardcore bosonic Hubbard models weakly coupled with each other by tunneling. Assuming that the single uncoupled model exhibits off-diagonal...     

Quantum Entanglement in a Spin-Orbit Coupled Bose–Einstein Condensate

We study the spin-field and the spin-spin entanglement in the ground state of a spin-orbit coupled Bose–Einstein condensate. It is found that the spin-field and the spin-spin entanglement can be induced by the spin-orbit coupling. By mapping the system to the Dicke-like model,the system exhibits a quantum phase transition from a normal(spin balanced) phase to superradiant(spin polarized) phase. The Dicke-like phase transition can be captured by the spin-field and the spin-spin entanglement arising from the spin-orbit coupling. The spin-field and the spin-spin entanglement increase as the Raman coupling increases in the superradiant phase,while they decrease with the Raman coupling increasing in the normal phase. We also consider the effect of a finite detuning on these entanglement show that the presence of the detuning suppresses the spin-field and the spin-spin entanglement.     

Stability of Attractive Bose–Einstein Condensates

We propose the critical nonlinear Schrödinger equation with a harmonic potential as a model of attractive Bose–Einstein condensates. By an elaborate mathematical analysis we show that a sharp stability threshold exists with respect to the number of condensate particles. The value of the threshold agrees with the existing experimental data. Moreover with this threshold we prove that a ground state of the condensate exists and is orbital stable. We also evaluate the minimum of the condensate energy.     

Stationary States and Modulational Instability of Coupled Two-Component Bose–Einstein Condensates in a Ring Trap

We investigate modulational instability(MI) of a coupled two-component Bose–Einstein condensates in a rotating ring trap. The excitation spectrum and the MI condition of the system are presented analytically. We find that the coupling between the two components strongly modifies the MI condition, and the MI condition is phase-dependent.Furthermore, we discuss the effect of MI on both density excitation and spin excitation. If the inter- and intra-component interaction strengths are all equal, the MI causes density excitation but not spin excitation, and if the inter- and intracomponent interaction strengths are different, the MI causes both density excitation and spin excitation. Our results provide a promising approach for controlling the stability and excitation of a rotating two-component Bose–Einstein condensates by modulating its coupling strength and interaction strength.     

Dynamics of Analytical Matter-Wave Solutions in Three-Dimensional Bose–Einstein Condensates with Two- and Three-Body Interactions

Using the F-expansion method we present analytical matter-wave solutions to Bose-Einstein condensates with two- and three-body interactions through the generalized three-dimensional Gross-Pitaevskii equation with time- dependent coefficients, for the periodically time-varying interactions and quadratic potential strength. Such solutions exist under certain conditions, and impose constraints on the functions describing potential strength, nonlinearities, and gain （loss）. Various shapes of analytical matter-wave solutions which have important applications of physical interest are s~udied in details.     

Emergent Quantum Euler Equation and Bose–Einstein Condensates

In this paper, proceeding from the recently developed way of deriving the quantum-mechanical equations from the classical ones, the complete system of hydrodynamical equations, including the quantum Euler equation, is derived for a perfect fluid and an imperfect fluid with pairwise interaction between the particles. For the Bose–Einstein condensate of the latter one the Bogolyubov spectrum of elementary excitations is easily reproduced in the acoustic approximation.     

Phase Sensitivity in Bose–Einstein Condensates

We investigate the phase sensitivity of a collection of interacting spins with quantum Fisher information controlled by an external field. By adopting the frozen-spin approximation, we derive the approximate analytical expressions of the maximal quantum Fisher information and the phase sensitivity. It is shown that the maximal quantum Fisher information and the phase sensitivity depend on the strength of the external field. With the increases of the external field, the period of oscillation of quantum Fisher information and phase estimation decrease, while the values of quantum Fisher information and phase sensitivity increase because of the suppress by the external field.     

Exact Temporal Evolution of Two-Species Bose–Einstein Condensates

We construct exact stationary solutions to the one-dimensional coupled Gross–Pitaevskii equations for the two-species Bose–Einstein condensates with equal intraspecies and interspecies interaction constants.Three types of complex solutions as well as their soliton limits are derived.By making use of the SU(2)unitary symmetry,we further obtain analytical time-evolving solutions.These solutions exhibit spatiotemporal periodicity.     

Quantum Dynamics of Cooled Atoms in the Presence of Bose—Einstein Condensates

Under the Markov approximation,the quantum dynamics of cooled atoms in the presence of Bose-Einstein condensates is studied.A master equation governing the evolution of such a system is derved.Using this master equation,the distribution of the atoms in the excited states at finite temperature and the dynamics of the excited atom at zero temperature are given and discussed.     

Solitonic Diffusion of Wavepackets in One-Dimensional Bose–Einstein Condensates

Solitonic characteristics are revealed in the diffusion process of a hump or a notch wave packet in a one-dimensional Bose–Einstein condensate. By numerically solving the time-dependent Gross–Pitaevskii equation, we find completely different spreading behavior for attractive or repulsive condensates. For the attractive condensate, a series of bright solitons are continuously generated one after another at the wave front and they nearly stay at the positions where they are generated in the whole diffusion process. In contrast, for the repulsive condensate,the initial wave packet splits at the beginning into a series of grey solitons that travel at different velocities. The moving velocity of the grey soliton depends on nonlinear interaction strength, as well as the shape of a particular grey soliton.     

Quantum Squeezing of Matter-Wave Solitons in Bose–Einstein Condensates

We investigate the quantum squeezing of matter-wave solitons in atomic Bose–Einstein condensates. By calculating quantum fluctuations of the solitons via solving the Bogoliubov–de Gennes equations, we show that significant quantum squeezing can be realized for both bright and dark solitons. We also show that the squeezing efficiency of the solitons can be enhanced and manipulated by atom–atom interaction and soliton blackness. The results reported here are beneficial not only for understanding q...     

Langevin Equation of Collective Modes of Bose–Einstein Condensates in Traps

A quantum Langevin equation for the amplitudes of the collective modes in Bose–Einstein condensate is derived. The collective modes are coupled to a thermal reservoir of quasi-particles, whose elimination leads to the quantum Langevin equation. The dissipation rates are determined via the correlation function of the fluctuating force and are evaluated in the local-density approximation for the spectrum of quasi-particles and the Thomas–Fermi approximation for the condensate.I take great pleasure in dedicating this paper to Gregoire Nicolis on the occasion of his sixtieth birthday.     

Dynamics of spinor Bose–Einstein condensate subject to dissipation

We investigate the internal dynamics of the spinor Bose–Einstein condensates subject to dissipation by solving the Lindblad master equation. It is shown that for the condensates without dissipation its dynamics always evolve along a specific orbital in the phase space of(n_0, θ) and display three kinds of dynamical properties including Josephson-like oscillation, self-trapping-like oscillation, and ‘running phase'. In contrast, the condensates subject to dissipation will not evolve along the specific dynamical orbital. If component-1 and component-(-1) dissipate at different rates, the magnetization m will not conserve and the system transits between different dynamical regions. The dynamical properties can be exhibited in the phase space of(n_0, θ, m).