The paper presents a survey of some dynamical transitions in nonequilibrium trapped Bose-condensed systems subject to the action of alternating fields. Nonequilibrium states of trapped systems can be implemented in two ways: resonant and nonresonant. Under resonant excitation, several coherent modes are generated by external alternating fields with the frequencies been tuned to resonance with some transition frequencies of the trapped system. A Bose system of trapped atoms with Bose–Einstein condensate can display two types of the Josephson effect, the standard one, when the system is separated into two or more parts in different locations, or the internal Josephson effect, when there are no any separation barriers but the system becomes nonuniform due to the coexistence of several coherent modes interacting one with another. The mathematics in both these cases is similar. We focus on the internal Josephson effect. Systems with nonlinear coherent modes demonstrate rich dynamics, including Rabi oscillations, the Josephson effect, and chaotic motion. Under the Josephson effect, there exist dynamic transitions that are similar to phase transitions in equilibrium systems. The bosonic Josephson effect is shown to be implementable not only for quite weakly interacting systems, but also in superfluids with not necessarily as weak interactions. Sufficiently strong nonresonant excitation can generate several types of nonequilibrium states comprising vortex germs, vortex rings, vortex lines, vortex turbulence, droplet turbulence, and wave turbulence. Nonequilibrium states are shown to be characterized and distinguished by effective temperature, effective Fresnel number, and dynamic scaling laws.
The paper presents a survey of some dynamical transitions in nonequilibrium trapped Bose-condensed systems subject to the action of alternating fields. Nonequilibrium states of trapped systems can be implemented in two ways: resonant and nonresonant. Under resonant excitation, several coherent modes are generated by external alternating fields with the frequencies been tuned to resonance with some transition frequencies of the trapped system. A Bose system of trapped atoms with Bose–Einstein condensate can display two types of the Josephson effect, the standard one, when the system is separated into two or more parts in different locations, or the internal Josephson effect, when there are no any separation barriers but the system becomes nonuniform due to the coexistence of several coherent modes interacting one with another. The mathematics in both these cases is similar. We focus on the internal Josephson effect. Systems with nonlinear coherent modes demonstrate rich dynamics, including Rabi oscillations, the Josephson effect, and chaotic motion. Under the Josephson effect, there exist dynamic transitions that are similar to phase transitions in equilibrium systems. The bosonic Josephson effect is shown to be implementable not only for quite weakly interacting systems, but also in superfluids with not necessarily as weak interactions. Sufficiently strong nonresonant excitation can generate several types of nonequilibrium states comprising vortex germs, vortex rings, vortex lines, vortex turbulence, droplet turbulence, and wave turbulence. Nonequilibrium states are shown to be characterized and distinguished by effective temperature, effective Fresnel number, and dynamic scaling laws.
Abstract The review presents the methods of generation of nonlinear coherent excitations in strongly nonequilibrium Bose-condensed systems of trapped atoms and their properties. Non-ground-state Bose–Einstein condensates are represented by nonlinear coherent modes. The principal difference of nonlinear coherent modes from linear collective excitations is emphasized. Methods of generating nonlinear modes and the properties of the latter are described. Matter-wave interferometry with coherent modes is discussed, including such effects as interference patterns, internal Josephson current, Rabi oscillations, Ramsey fringes, harmonic generation, and parametric conversion. Dynamic transition between mode-locked and mode-unlocked regimes is shown to be analogous to a phase transition. Atomic squeezing and entanglement in a lattice of condensed atomic clouds with coherent modes are considered. Nonequilibrium states of trapped Bose-condensed systems, starting from weakly nonequilibrium state, vortex state, vortex turbulence, droplet or grain turbulence, and wave turbulence, are classified by means of effective Fresnel and Mach numbers. The inverse Kibble–Zurek scenario is described. A method for the formation of directed beams from atom lasers is reported.
Abstract The generation of different nonequilibrium states in trapped Bose–Einstein condensates is studied by numerically solving the nonlinear Schrödinger equation. Inducing nonequilibrium states by shaking a trap creates the following states: weak nonequilibrium, the state of vortex germs, the state of vortex rings, the state of straight vortex lines, the state of deformed vortices, vortex turbulence, grain turbulence, and wave turbulence. A characterization of nonequilibrium states is advanced by introducing effective temperature, Fresnel number, and Mach number .
Abstract The paper discusses what characteristic quantities could quantify nonequilibrium states of Bose systems. Among such quantities, the following are considered: effective temperature, Fresnel number, and Mach number. The suggested classification of nonequilibrium states is illustrated by studying a Bose-Einstein condensate in a shaken trap, where it is possible to distinguish eight different nonequilibrium states: weak nonequilibrium, vortex germs, vortex rings, vortex lines, deformed vortices, vortex turbulence, grain turbulence, and wave turbulence. Nonequilibrium states are created experimentally and modeled by solving the nonlinear Schrödinger equation.
In a trapped Bose-Einstein condensate, subject to the action of an alternating external field, coherent topological modes can be resonantly excited. Depending on the amplitude of the external field and detuning parameter, there are two principally different regimes of motion, with mode locking and without it. The change of the dynamic regime corresponds to a dynamic phase transition. This transition can be characterized by an effective order parameter defined as the difference between fractional mode populations averaged over the temporal period of oscillations. The behavior of this order parameter, as a function of detuning, pumping amplitude, and atomic interactions is carefully analyzed. Special attention is paid to numerical calculations for the realistic case of a quadrupole exciting field and the system parameters accessible in current experiments.
The report reviews the problem of topological coherent modes, which are nonlinear collective states of Bose‐condensed atoms. Such modes can be generated by means of alternating external fields, whose frequencies are in resonance with the transition frequencies between the related modes. The Bose gas with generated topological coherent modes is a collective nonlinear analog of a resonant atom. Such systems exhibit a variety of nontrivial effects, e.g.: interference fringes, interference current, mode locking, dynamic transitions, critical phenomena, chaotic motion, harmonic generation, parametric conversion, atomic squeezing, and entanglement production.
The report reviews the problem of topological coherent modes, which are nonlinear collective states of Bose-condensed atoms. Such modes can be generated by means of alternating external fields, whose frequencies are in resonance with the transition frequencies between the related modes. The Bose gas with generated topological coherent modes is a collective nonlinear analog of a resonant atom. Such systems exhibit a variety of nontrivial effects, e.g.: interference fringes, interference current, mode locking, dynamic transitions, critical phenomena, chaotic motion, harmonic generation, parametric conversion, atomic squeezing, and entanglement production. 1