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.
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.
Multiple mode couplings in topological coherent modes of Bose–Einstein condensate are considered, by introducing an external alternating (resonating) field in the system. This analysis is based on the analytical solutions of nonlinear Gross–Pitaevskii equation for a trapped Bose gas at nearly absolute zero temperature. The dynamics of fractional populations of the generated coherent modes are analysed, particularly for a three-level system in the limit of small to large detuning of the intermediate state. These coupled topological modes, though nonlinear, are analogous to a resonant atom and exhibit a variety of significant non-trivial phenomena (effects), like: dynamic phase transitions, interference patterns, critical phenomena, mode-locking and chaotic motion.
Nonlinear coherent modes are the collective states of trapped Bose atoms, corresponding to different energy levels. These modes can be created starting from the ground-state condensate that can be excited by means of a resonant alternating field. A thorough theory for the resonant excitation of the coherent modes is presented. The necessary and sufficient conditions for the feasibility of this process are found. Temporal behavior of fractional populations and of relative phases exhibits dynamic critical phenomena on a critical line of the parametric manifold. The origin of these critical phenomena is elucidated by analyzing the structure of the phase space. An atomic cloud, containing the coherent modes, possesses several interesting features, such as interference patterns, interference current, spin squeezing, and massive entanglement. The developed theory suggests a generalization of resonant effects in optics to nonlinear systems of Bose-condensed atoms.
The population dynamics of a trapped Bose-Einstein condensate, subject to the action of an external field, is studied. This field produces a spatio-temporal modulation of the trapping potential with the frequency close to the transition frequency between the ground state and a higher energy level. For the evolution equations of fractional populations, a critical line is found. It is demonstrated that there exists a direct analogy between dynamical instability at this line and critical phenomena at a critical line of an averaged system. The related critical indices are calculated. The spatio-temporal evolution of atomic density is analyzed.
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 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
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.