Generation of compressed sub-poisson Bose condensate by an atom laser

The dynamics of Bose-condensate generation by a cw atom laser with simultaneous stimulated evaporative cooling in a magnetic trap was analyzed using a quantum-mechanical master equation. The model of the atom laser includes irreversible processes of incoherent trap mode pumping and spontaneous atomic transitions due to the interaction of the atomic ensemble with heat reservoirs. The inelastic atomic collisions in the trap and the continual coherent Bose-condensate output coupling from the trap were considered. At certain values of parameters, the Bose condensate created in this laser scheme occurs in a compressed sub-Poisson state. For large Bose condensates with a mean number of atoms ～10⁶, the Fano factor may be as high as ?0.5. The influence of spontaneous transitions from the excited trap modes on the statistics of Bose condensate was analyzed.     

Nonadiabatic effects on population transfer of two Bose－Einstein condensates induced by atomic interaction

We investigate the stimulated Raman adiabatic passage for Bose－Einstein condensate (BEC) states which are trapped in different potential wells or two ground states of BEC in the same trap. We consider that lasers are nearly resonant with the atomic transitions. The difference of population transfer processes between BEC atoms and usual atoms is that the atomic interaction of the BEC atoms can cause some nonadiabatic effects, which may degrade the process. But with suitable detunings of laser pulses, the effects can be remedied to some extent according to different atomic interactions.     

Entangled spin states of a Bose condensate in an electromagnetic field

We consider the formation of entangled quantum states for an atomic Bose condensate interacting with an external electromagnetic field in a single-particle state under conditions of change in various regimes for exchange interaction processes. These states of the Bose system have high phase coherence and are accompanied by the generation of squeezed states of a new type in terms of the parameters defined by a combination of transition operators for the condensate atoms and external-field photons with an appropriate polynomial deformation of the algebra SU(2). We show that localized quantum structures corresponding to stable elementary excitations of the atoms and the field in the condensate can be formed in principle. We also analyze the purely quantum effects of collapse and revival for the level populations of the Bose condensate and the change in atomic statistics as well as determine the conditions for the formation of superstructure of these unsteady states for the Bose system.     

Bose condensate drag in a system of two coupled traps

A system of two plane traps disposed one above the other and confined atomic Bose condensate is considered. The possibility of entraining atoms of one of the traps by the atoms of the other trap upon the rotation of the latter is studied. The average angular momentum induced by the rotation of the first trap is found for the atoms in the second trap.     

原子间相互作用对双模原子激光压缩性质的影响

研究了由单模压缩相干态光场与Ξ型三能级原子玻色爱因斯坦凝聚体(BEC)相互作用系统中耦合输出的双模原子激光的压缩特性,重点讨论了玻色爱因斯坦凝聚体原子间相互作用对原子激光压缩性质的影响,并讨论了原子激光压缩对光场初始压缩因子的依赖关系。结果表明:由光场诱导的双模原子激光呈现周期性的压缩,原子间的相互作用和光场初始压缩因子对原子的压缩性质具有重要影响。原子间的相互作用影响原子激光压缩的振荡频率而不会影响其压缩深度,而初始光场的压缩因子则对原子激光压缩深度产生调制作用,且初始光场的压缩因子越大,则原子激光压缩的时间越短。     

Quantum Statistical Behaviors of Interaction of an Atomic Bose-Einstein Condensate with Laser

We have investigated quantum statistical behaviors of photons and atoms in interaction of an atomic Bose Einstein condensate with quantized laser field. When the quantized laser field is initially prepared in a superposition state which exhibits holes in its photon-number distribution, while the atomic field is initially in a Fock state, it is found that there is energy exchange between photons and atoms. For the input and output states, the photons and atoms may exhibit the sub-Poissonian distribution. The input and output laser fields may exhibit quadrature squeezing, but for the atomic field, only the output state exhibits quadrature squeezing. It is shown that there exists the violation of the Cauchy-Schwartz inequality, which means that the correlation between photons and atoms is nonclassical.``     

Ground-states and rotational properties of a spin–orbit-coupled spin-1 Bose–Einstein condensate in a concentrically coupled toroidal trap

We investigate the ground states of an antiferromagnetic spin-1 Bose–Einstein condensate with spin–orbit coupling in a concentrically coupled toroidal trap. A new necklace-type state with double-ring structure is created in the system due to the spin–orbit coupling. The petal number of the necklace state is increased with enhancing the strength of the spin–orbit coupling. When the rotation is introduced, the condensate can be dragged into the outer trough of the trap by increasing the rotation frequency, which makes it possible to realize the exotic ground state combined by the necklace state at the inner trough and the persistent flow at the outer one. Once the two troughs of the toroidal trap are populated by the persistent flow at the specific effective interactions between atoms, the hidden vortices may occur in the central region of the trap and at the barrier between the two troughs. In addition, the visible vortex with the laminar structure can be generated under the more effective atomic interaction.     

Atomic condensate in an optical trap formed by a cavity mode

It has been shown that an optical trap for an atomic condensate formed by a mode of a ring cavity possesses specific properties. These properties are not featured by a trap formed by free beams and arise owing to quantum correlations (entanglement) between the localized atoms and the optical mode. In particular, there is an effect similar to an optomechanical phenomenon known as an “optical spring” (S. Martellucci et al., Bose–Einstein Condensates and Atom Lasers (Kluwer, Dordrecht, 2002)) and manifested by the emergence of an effective correction to the interaction between the localized atoms. The magnitude and sign of this correction can be controlled by varying the frequency of the source forming the trap.     

Bose-stimulated raman adiabatic passage in photoassociation

We analyze coherent two-color photoassociation of a Bose-Einstein condensate, focusing on stimulated Raman adiabatic passage (STIRAP) in free-bound-bound transitions from atoms to molecules. This problem raises an interest because STIRAP has been predicted to be absent in the nondegenerate case [Javanainen and Mackie, Phys. Rev. A 58, R789 (1998)]. Nevertheless, we find that Bose stimulation enhances the free-bound dipole matrix element for an atomic condensate, and photoassociative STIRAP turns out to be a viable mechanism for converting an atomic condensate to a molecular condensate with near-unit efficiency.     

Superchemistry: dynamics of coupled atomic and molecular bose-einstein condensates

We analyze the dynamics of a dilute, trapped Bose-condensed atomic gas coupled to a diatomic molecular Bose gas by coherent Raman transitions. This system is shown to result in a new type of "superchemistry," in which giant collective oscillations between the atomic and the molecular gas can occur. The phenomenon is caused by stimulated emission of bosonic atoms or molecules into their condensate phases.     

Condensation state of ultra-cold Bose atomic gases with pure gradient interactions with negative coefficient

Within the framework of quantum field theory, we find that uniform Bose atomic gases with pure gradient interactions with negative coefficient can undergo a Bardeen-Cooper-Schrieffer (BCS) condensation below a critical temperature. In the BCS condensation state, bare atoms with opposite wave vectors are bound into pairs, and unpaired bare atoms are transformed into a new kind of quasi-particle, i.e. the dressed atom. The atom-pair system is a condensate or a superfluid and the dressed-atom system is a normal fluid. At absolute zero temperature the condensate possesses a lowest negative energy. When the total interaction strength of atoms is large enough, the energy of the condensate is a monotonically increasing function of temperature and interaction strength. The critical temperature and the effective mass of dressed atoms are derived analytically. The transition from the BCS condensation state to the normal state is a first-order phase transition.     

Photon condensation: A new paradigm for Bose–Einstein condensation

Bose–Einstein condensation is a state of matter known to be responsible for peculiar properties exhibited by superfluid Helium-4 and superconductors. Bose–Einstein condensate (BEC) in its pure form is realizable with alkali atoms under ultra-cold temperatures. In this paper, we review the experimental scheme that demonstrates the atomic Bose–Einstein condensate. We also elaborate on the theoretical framework for atomic Bose–Einstein condensation, which includes statistical mechanics and the Gross–Pitaevskii equation. As an extension, we discuss Bose–Einstein condensation of photons realized in a fluorescent dye filled optical microcavity. We analyze this phenomenon based on the generalized Planck’s law in statistical mechanics. Further, a comparison is made between photon condensate and laser. We describe how photon condensate may be a possible alternative for lasers since it does not require an energy consuming population inversion process.     

Interactions of condensate atoms in the process of velocity-selective coherent population trapping

The properties of a one-dimensional atomic Bose condensate are studied under the assumption that the condensation leads to a state of velocity-selective coherent population trapping. This state is characterized by the quantum correlation (entanglement) between the intrinsic angular momentum of an atom and its translational motion underlying nontrivial features of the condensate. The effects of weak interatomic interaction are taken into account. The steady state of above-condensate atoms corresponding to the slow decay of the state with coherent population trapping is found. The dynamic problem concerning the evolution of the system of above-condensate atoms after switching off the optical field forming the state with coherent population trapping is solved. The solution is found by the diagonalization of the Hamiltonian based on introducing the Bogoliubov quasiparticles with the unusual dispersion law.     

Features of dynamics of stimulated atomic-molecular Raman conversion in a Bose-Einstein condensate

A set of nonlinear evolution equations describing the dynamics of atoms, molecules, and photons in the course of stimulated atomic—molecular conversion in a Bose—Einstein condensate is derived and studied in the mean-field approximation. It is shown that conversion can be periodic or aperiodic in time, the rate of the process being determined to a considerable extent by the initial density of particles and by the initial phase difference. Depending on the initial conditions, various conversion modes can be realized. The possibility of stabilization of a special state (of rest) of the system for nonzero initial number densities of particles is predicted. It is pointed out that coherence of a Bose condensate of atoms, molecules, and photons predetermines the possibility of phase control of the conversion process.     

The quantum acousto-optic effect in Bose-Einstein condensate

We investigate the interaction between a single mode light field and an elongated cigar shaped Bose-Einstein condensate (BEC), subject to a temporal modulation of the trap frequency in the tight confinement direction. Under appropriate conditions, the longitudinal sound like waves (Faraday waves) in the direction of weak confinement acts as a dynamic diffraction grating for the incident light field analogous to the acousto-optic effect in classical optics. The change in the refractive index due to the periodic modulation of the BEC density is responsible for the acousto-optic effect. The dynamics is characterised by Bragg scattering of light from the matter wave Faraday grating and simultaneous Bragg scattering of the condensate atoms from the optical grating formed due to the interference between the incident light and the diffracted light fields. Varying the intensity of the incident laser beam we observe the transition from the acousto-optic effect regime to the atomic Bragg scattering regime, where Rabi oscillations between two momentum levels of the atoms are observed. We show that the acousto-optic effect is reduced as the atomic interaction is increased.     

Expansion dynamics of a two-component quasi-one-dimensional Bose–Einstein condensate: Phase diagram,self-similar solutions,and dispersive shock waves

We investigate the expansion dynamics of a Bose–Einstein condensate that consists of two components and is initially confined in a quasi-one-dimensional trap. We classify the possible initial states of the two-component condensate by taking into account the nonuniformity of the distributions of its components and construct the corresponding phase diagram in the plane of nonlinear interaction constants. The differential equations that describe the condensate evolution are derived by assuming that the condensate density and velocity depend on the spatial coordinate quadratically and linearly, respectively, which reproduces the initial equilibrium distribution of the condensate in the trap in the Thomas–Fermi approximation. We have obtained self-similar solutions of these differential equations for several important special cases and write out asymptotic formulas describing the condensate motion on long time scales, when the condensate density becomes so low that the interaction between atoms may be neglected. The problem on the dynamics of immiscible components with the formation of dispersive shock waves is considered. We compare the numerical solutions of the Gross–Pitaevskii equations with their approximate analytical solutions and numerically study the situations where the analytical method being used admits no exact solutions.     

Interactions of Bose–Einstein-Condensate Oscillons

The interaction of two one-dimensional spatial vector structures of a Bose–Einstein atomic condensate in a trap with significant transverse dimensions and oscillating walls has been simulated numerically. Different types of coupled structures and different scenarios of their collisions are revealed. A comparison is made with the properties of scalar solitons, which are described by the traditional nonlinear Schrödinger equation.     

Dynamics of Hysteresis for a Bose–Einstein Condensate Soliton in a Dynamic Trap

The dynamics of the fundamental soliton of Bose–Einstein atomic condensate is analytically and numerically examined and compared in two schemes: (i) a magnetic or an optical trap with oscillating walls and (ii) a single oscillating atomic mirror in a homogeneous gravitational field. It is demonstrated that the dependence of the degree of excitation of the soliton motion on the rate of scanning of the instantaneous oscillation frequency has a band structure.     

Superfluidity and phase transitions in a resonant Bose gas

The atomic Bose gas is studied across a Feshbach resonance, mapping out its phase diagram, and computing its thermodynamics and excitation spectra. It is shown that such a degenerate gas admits two distinct atomic and molecular superfluid phases, with the latter distinguished by the absence of atomic off-diagonal long-range order, gapped atomic excitations, and deconfined atomic π-vortices. The properties of the molecular superfluid are explored, and it is shown that across a Feshbach resonance it undergoes a quantum Ising transition to the atomic superfluid, where both atoms and molecules are condensed. In addition to its distinct thermodynamic signatures and deconfined half-vortices, in a trap a molecular superfluid should be identifiable by the absence of an atomic condensate peak and the presence of a molecular one.     

Uncondensed atoms in the regime of velocity-selective coherent population trapping

We consider the model of a Bose condensate in the regime of velocity-selective coherent population trapping. As a result of interaction between particles, some fraction of atoms is outside the condensate, remaining in the coherent trapping state. These atoms are involved in brief events of intense interaction with external resonant electromagnetic fields. Intense induced and spontaneous transitions are accompanied by the exchange of momenta between atoms and radiation, which is manifested as migration of atoms in the velocity space. The rate of such migration is calculated. A nonlinear kinetic equation for the many-particle statistical operator for uncondensed atoms is derived under the assumption that correlations of atoms with different momenta are insignificant. The structure of its steady-state solution leads to certain conclusions about the above-mentioned migration pattern taking the Bose statistics into consideration. With allowance for statistical effects, we derive nonlinear integral equations for frequencies controlling the migration. The results of numerical solution of these equations are represented in the weak interatomic interaction approximation.