Application of potential harmonic expansion method to BEC: Thermodynamic properties of trapped23Na atoms

We adopt the potential harmonics expansion method for anab initio solution of the many-body system in a Bose condensate containing interacting bosons. Unlike commonly adopted mean-field theories, our method is capable of handling two-body correlation properly. We disregard three- and higher-body correlations. This simplification is ideally suited to dilute Bose Einstein condensates, whose number density is required to be so small that the interparticle separation is much larger than the range of two-body interaction to avoid three- and higher-body collisions, leading to the formation of molecules and consequent instability of the condensate. In our method we can incorporate realistic finite range interactions. We calculate energies of low-lying states of a condensate containing²³Na atoms and some thermodynamical properties of the condensate.     

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.     

Bose–Einstein condensation in the three-sphere and in the infinite slab: Analytical results

We study the finite size effects on Bose–Einstein condensation (BEC) of an ideal non-relativistic Bose gas in the three-sphere (spatial section of the Einstein universe) and in a partially finite box which is infinite in two of the spatial directions (infinite slab). Using the framework of grand-canonical statistics, we consider the number of particles, the condensate fraction and the specific heat. After obtaining asymptotic expansions for large system size, which are valid throughout the BEC regime, we describe analytically how the thermodynamic limit behaviour is approached. In particular, in the critical region of the BEC transition, we express the chemical potential and the specific heat as simple explicit functions of the temperature, highlighting the effects of finite size. These effects are seen to be different for the two different geometries. We also consider the Bose gas in a one-dimensional box, a system which does not possess BEC in the sense of a phase transition even in the infinite volume limit.     

Diffusion Monte Carlo analysis of the crossover from three to two dimensions for trapped Bose gases

We investigate the crossover from three to two dimensions for harmonically trapped hard-sphere Bose gases by varying the aspect ratio of the trapping potential. The diffusion Monte Carlo method is used to calculate both the ground-state energy and structural properties. The effect of trap anisotropy, interparticle interaction, and number of particles on the ground-state properties is discussed. Our results show that the minimum value of the aspect ratio at which the system reaches an asymptotic equilibrium distribution in the weakly confined direction decreases with increasing scattering length, while the minimum value of the aspect ratio at which the system enters the quasi-two-dimensional (2D) regime increases as both the scattering length and the number of particles increase. Additionally, the role played by particle correlations is proved to be more pronounced in the quasi-2D system than in the three-dimensional (3D) system by directly comparing the ground-state properties for the two cases.     

A microscopic study of the finite two-dimensional trapped bose atomic gas

Using the static fluctuation approximation, finite two-dimensional Bose gas systems, trapped in a harmonic potential, are investigated. The interparticle potential is taken as a δ-function. The chemical potential, condensate fraction, total energy, and heat capacity are calculated as functions of the temperature for different values of the interaction strength and of the number of particles. Our results show that interacting bosons trapped in a harmonic potential have a similar behavior to that of the ideal system. These results conform with those obtained using different many-body theories, such as the semi-classical two-fluid model and the Hartree–Fock approximation.     

Dynamics of Bec Mixtures Loaded into the Optical Lattice in the Presence of Linear Inter-Component Coupling

We consider dynamics of a two-component Bose–Einstein condensate, where the components correspond to different hyperfine states of the same sort of atoms. External microwave radiation leads to resonant transitions between the states. The condensate is loaded into the optical lattice. We invoke the tight-binding approximation and examine the interplay of spatial and internal dynamics of the mixture. We show that internal dynamics qualitatively depends on the intra-component interaction strength and the phase configuration of the initial state. We focus attention on two intriguing phenomena occurring at certain values of the parameters. The first phenomenon is the spontaneous synchronization of Rabi oscillations running inside neighboring lattice sites. The other one is demixing of the condensate with formation of immiscible solitons at sufficiently strong nonlinearity. Demixing is preceded by the transient regime with highly irregular behavior of the mixture.     

Spin dynamics in a one-dimensional ferromagnetic bose gas

We investigate the propagation of spin excitations in a one-dimensional ferromagnetic Bose gas. While the spectrum of longitudinal spin waves in this system is soundlike, the dispersion of transverse spin excitations is quadratic, making a direct application of the Luttinger liquid theory impossible. By using a combination of different analytic methods we derive the large time asymptotic behavior of the spin-spin dynamical correlation function for strong interparticle repulsion. The result has an unusual structure associated with a crossover from the regime of trapped spin wave to an open regime and does not have analogues in known low-energy universality classes of quantum 1D systems.     

On the theory of slowing down gracefully

We discuss the transport of a tracer particle through the Bose?CEinstein condensate of a Bose gas. The particle interacts with the atoms in the Bose gas through two-body interactions. In the limiting regime where the particle is very heavy and the Bose gas is very dense, but very weakly interacting (??mean-field limit??), the dynamics of this system corresponds to classical Hamiltonian dynamics. We show that, in this limit, the particle is decelerated by emission of gapless modes into the condensate (Cerenkov radiation). For an ideal gas, the particle eventually comes to rest. In an interacting Bose gas, the particle is decelerated until its speed equals the propagation speed of the Goldstone modes of the condensate. This is a model of ??Hamiltonian friction??. It is also of interest in connection with the phenomenon of ??decoherence?? in quantum mechanics. This note is based on work we have carried out in collaboration with D Egli, I M Sigal and A Soffer.     

Zero-temperature phases of many-atom Bose systems

We show that a many-atom Bose system at zero temperature has, in general, a liquid phase in addition to its well-known gaseous phase. A universal phase diagram is presented that is applicable to all Bose systems with a -C6/r6 type of interaction at large interparticle separations. We show that the predicted phase structure has implications on the stability of a gaseous Bose-Einstein condensate (BEC) even at dilute densities that are routinely achieved under existing experimental conditions. We also predict that should have a gaseous BEC phase below a critical density of 5.58 x 10(15) 1/cm3.     

Mechanism of the collapse of a low-density Bose gas with strong attraction

It is shown that the Bose condensate of a low-density Bose gas whose interparticle interaction potential possesses a bound state is unstable. The modes with large momenta, of the order of the inverse radius of the bound state, are unstable. Their fluctuations grow exponentially in time. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 10, 678–683 (25 November 1996)     

Interacting bosons in an optical lattice

A strongly interacting Bose gas in an optical lattice is studied using a hard‐core interaction. Two different approaches are introduced, one is based on a spin‐1/2 Fermi gas with attractive interaction, the other one on a functional integral with an additional constraint (slave‐boson approach). The relation between fermions and hard‐core bosons is briefly discussed for the case of a one‐dimensional Bose gas. For a three‐dimensional gas we identify the order parameter of the Bose‐Einstein condensate through a Hubbard‐Stratonovich transformation and treat the corresponding theories within a mean‐field approximation and with Gaussian fluctuations. This allows us to evaluate the phase diagram, including the Bose‐Einstein condensate and the Mott insulator, the density‐density correlation function, the static structure factor, and the quasiparticle excitation spectrum. The role of quantum and thermal fluctuations are studied in detail for both approaches, where we find good agreement with the Gross‐Pitaevskii equation and with the Bogoliubov approach in the dilute regime. In the dense regime, which is characterized by the phase transition between the Bose‐Einstein condensate and the Mott insulator, we discuss a renormalized Gross‐Pitaevskii equation. This equation can describe the macroscopic wave function of the Bose‐Einstein condensate in the dilute regime as well as close to the transition to the Mott insulator. Finally, we compare the results of the attractive spin‐1/2 Fermi gas and those of the slave‐boson approach and find good agreement for all physical quantities.     

Bose–Einstei condensation of dipolar excitons in a ring trap

The temperature of Bose–Einstein condensation and the fraction of particles in a condensate for a system of spatially indirect dipole excitons in an electrostatic ring trap have been found. If only levels of the radial motion close to the bottom of the potential well of the trap are populated considerably, the oscillatory model of the single-particle spectrum is applicable. In this case, even the strong exciton–exciton interaction can be taken into account.     

Thermodynamic properties of a finite Bose gas in a harmonic trap

We have investigated the thermodynamic behaviour of ideal Bose gases with an arbitrary number of particles confined in a harmonic potential. By taking into account the conservation of total number $N$ of particles and using a saddle-point approximation, we derive analytically the simple explicit expression of mean occupation number in any state of the finite system. The temperature dependence of the chemical potential, specific heat, and condensate fraction for the trapped finite-size Bose system is obtained numerically. We compare our results with the usual treatment which is based on the grand canonical ensemble. It is shown that there exists a considerable difference between them at sufficiently low temperatures, specially for the relative small numbers of Bose atoms. The finite-size scaling at the transition temperature for the harmonically trapped systems is also discussed. We find that the scaled condensate fractions for various system sizes and temperatures collapse onto a single scaled form.     

Decay of cosmological constant in self-consistent inflation

The symmetric vacuum state in gauge theories with spontaneous symmetry breaking is symmetric in both internal and space-time variables. We consider this vacuum state as a Bose condensate of physical Higgs particles, defined over an asymmetric vacuum state, and identify the energy density of their self-interaction with the cosmological constant in the Einstein equation. In this picture, spontaneous symmetry breaking proceeds as decay. Decoherence of coherent oscillations of a scalar field in the course of decay provides the effective mechanism for damping of coherent oscillations, leading to the regime of slow evaporation of a Bose condensate. This mechanism is responsible for self-consistent inflation without fine-tuning of the potential parameters. The physical self-consistency in this model is provided by incorporating the origin of the cosmological constant in the dynamics of spontaneous breaking of particle symmetries. Received: 28 September 2000 / Revised version: 16 January 2001 / Published online: 25 April 2001     

Instabilities of a Filled Vortex in a Two-Component Bose–Einstein Condensate

JETP Letters - A two-component Bose–Einstein condensate of cold atoms with a strong intercomponent repulsion leading to the spatial separation of the components has been numerically studied....     

Coherence time of the condensate of a weakly nonideal Bose gas

A system of equations for the density matrix is derived to describe the condensate and quasi-particles of a weakly nonideal spatially homogeneous Bose gas. The equations are used to find the distribution function of the number of particles and the condensate coherence time. A numerical estimate is obtained for a temperature that is significantly lower than the transition temperature. Original Text ? Astro, Ltd., 2009.     

Exciton Condensation in a Two-Dimensional System with Disorder

The Bose–Einstein condensation of excitons in two-dimensional (2D) systems has been studied theoretically, taking into account both the random potential associated with imperfections of the structure and the finite exciton lifetime. It is shown that the disorder existing in the system makes condensation possible. The finite exciton lifetime limits the thermalization of excitons in the disordered system and sets an additional limit on the critical temperature of the transition. The effects of interparticle interaction and pump fluctuations have been analyzed. The phase correlator has been calculated and the failure of the condensate due to the effects of interaction and fluctuations has been analyzed. The propagation of perturbations in the condensate has been investigated.     

Pairing energy of liquid 4He

The two-particle density matrix of a Bose system described by a Jastrow wave function displays off-diagonal long-range order associated with strong correlations between pairs of bosons with non-zero momenta ?q, -?q. In conjunction with the zero-momentum condensate, these correlations give rise to a finite contribution to the energy expectation value per particle, which is calculated for liquid ⁴He at two values of the density.     

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.