Variational self-consistent theory for trapped Bose gases at finite temperature

2014

Phys. Rev. A

We study the properties of a Bose-Einstein condensate (BEC)-impurity mixture at finite temperature employing the time dependent Hartree-Fock Bogoliubov (TDHFB) theory which is a set of coupled nonlinear equations of motion for the condensate and its normal and anomalous fluctuations on the one hand, and for impurity on the other. The numerical solutions of these equations in the static quasi-1D regime show that the thermal cloud and the anomalous density are deformed as happens to the condensate and the impurity becomes less localized at nonzero temperatures. Effects of the BEC fluctuations on the self-trapping state are studied in homogeneous weakly interacting BEC-impurity at low temperature. The self-trapping threshold is also determined in such a system. The formation of solitons in the BEC-impurity mixture at finite temperature is investigated. Our formalism shows several new pictures.

“…Upon introducing these variational parameters into the BV principle, one obtains dynamical equations for the expectation values of the one-and two-boson field operators [21][22][23] …”

Section: Tdhfb Equationsmentioning

confidence: 99%

Self-localized state and solitons in a Bose-Einstein-condensate–impurity mixture at finite temperature

2014

Phys. Rev. A

“…Therefore, the theory is valid even for strong interactions [31,32]. In addition, the TDHFB equations (1) satisfy the total number of particles and the energy conservation law, and they provide a gapless spectrum [27].…”

Section: Formalismmentioning

confidence: 98%

Spontaneous formation of bright solitons in self-localized impurities in Bose–Einstein condensates

Communications in Nonlinear Science and Numerical Simulation

2016

We study the formation of bright solitons in the impurity component of Bose-Einstein condensateimpurity mixture by using the time-dependent Hartree-Fock-Bogoliubov theory. While we assume the boson-boson and impurity-boson interactions to be effectively repulsive, their character can be changed spontaneously from repulsive to attractive in the presence of strong anomalous correlations. In such a regime the impurity component becomes a system of effectively attractive atoms leading automatically to the generation of bright solitons. We find that this soliton decays at higher temperatures due to the dissipation induced by the impurity-host and host-host interactions. We show that after a sudden increase of the impurity-boson strength a train of bright solitons is produced and this can be interpreted in terms of the modulational instability of the time-dependent impurity wave function.

“…The TDHFB equations which we choose to employ here constitute a model well suited to this task because it governs both the dynamics of the condensate and the anomalous density at finite temperature. In this quasi-1D geometry, the TDHFB equations may be represented as [21,23,29,30,[34][35][36][37][38]:…”

Section: Tdhfb Formalismmentioning

confidence: 99%

“…Moreover, in spirit of the mean-field theory, linearized TDHFB equations have been derived in [33] to study the damping and the collective oscillations in the collisionless regime. Our TDHFB formalism is usually given in the form of nonlocal coupled equations for the condensate order parameter and the single particle density matrix [21,23,34]. A striking advantage of such equations would be that they can be solved self-consistently using the exact non-local interaction potential (dipolar, gravitational, etc.…”

Section: Tdhfb Formalismmentioning

confidence: 99%

See 1 more Smart Citation

Collective modes of a one-dimensional trapped Bose gas in the presence of the anomalous density

2016

Phys. Rev. A

We study the collective modes of a one-dimensional (1D) harmonically trapped Bose-Einstein condensate (BEC) in the presence of the anomalous density using the time-dependent-Hartree-FockBogoliubov (TDHFB) theory. Within the hydrodynamic equations, we derive analytical expressions for the mode frequencies and the density fluctuations of the anomalous density which constitutes the minority component at very low temperature and feels an effective external potential exerted by the majority component i.e. the condensate. On the other hand, we numerically examine the temperature dependence of the breathing mode oscillations of the condensate at finite temperature in the weak-coupling regime. At zero temperature, we compare our predictions with available experimental data, theoretical treatments and Monte carlo simulations in all interaction regimes and the remaining hindrances are emphasized. We show that the anomalous correlations have a non-negligible role on the collective modes at both zero and finite temperatures.