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 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 By pumping energy into a trapped Bose-Einstein condensate it is possible to generate nonlinear coherent modes representing non-ground-state condensates. A Bose-condensed system of trapped atoms with nonlinear coherent modes is analogous to a finite-level atom considered in optics which can be excited by applying external fields. The excitation of finite-level atoms produces a variety of optical phenomena. In the similar way, the generation of nonlinear coherent modes in a trapped condensate results in many phenomena studied in what is termed atom optics. For example, there occur such effects as interference patterns, interference current, Rabi oscillations, harmonic generation, parametric conversion, Ramsey fringes, mode locking, and a dynamic transition between Rabi and Josephson regimes. The possibility of creating mesoscopic entangled states of trapped atoms and entanglement production by atomic states in optical lattices are studied.
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.
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.
Abstract Trapped bosonic atoms can be cooled down to temperatures where the atomic cloud experiences Bose–Einstein condensation. Almost all atoms in a dilute gaseous system can be Bose-condensed, which implies that this system is in a coherent state. The coherent atomic system enjoys many properties typical of coherent optical systems. It is possible to generate different condensate coherent modes similarly to the generation of optical modes. Several effects can be observed, such as interference patterns, interference current, Rabi oscillations, harmonic generation, parametric conversion, Ramsey fringes, mode locking, dynamic transition between Rabi and Josephson regimes, and atomic squeezing.
The resonant formation of nonlinear coherent modes in trapped Bose-Einstein condensates is studied. These modes represent nonground-state Bose condensates. The methods of describing the spectrum of the nonlinear modes are discussed. The latter can be created by modulating the trapping potential with a frequency tuned close to the transition frequency between the two chosen modes. The requirement that the transition amplitudes be smaller than the transition frequency implies a constraint on the number of particles that can be transferred to an excited mode. The resonant Bose condensate serves as a collective analog of a single resonant atom. Such a condensate, displaying the coherent resonance, possesses several interesting features, among which are: mode locking, critical dynamics, interference patterns, interference current, atomic squeezing, and multiparticle entanglement.