Self-Consistent Derivation of the Modified Gross-Pitaevskii Equation with Lee-Huang-Yang Correction

We consider a dilute and ultracold bosonic gas of weakly-interacting atoms. Within the framework of quantum field theory, we derive a zero-temperature modified Gross–Pitaevskii equation with beyond-mean-field corrections due to quantum depletion and anomalous density. This result is obtained from the stationary equation of the Bose–Einstein order parameter coupled to the Bogoliubov–de Gennes equations of the out-of-condensate field operator. We show that, in the presence of a generic external trapping potential, the key steps to get the modified Gross–Pitaevskii equation are the semiclassical approximation for the Bogoliubov–de Gennes equations, a slowly-varying order parameter and a small quantum depletion. In the uniform case, from the modified Gross–Pitaevskii equation, we get the familiar equation of state with Lee–Huang–Yang correction.

Matter-wave solitons of Bose–Einstein condensates with time-dependent complex potentials

To analytically investigate the matter-wave solitons of Bose–Einstein condensates (BECs) in time-dependent complex potential, we consider a cubic-quintic Gross–Pitaevskii (GP) equation with distributed coefficients and a dissipative term. By introducing a suitable ansatz, we establish the criterion of the modulational instability (MI) of the system and present an explicit expression for the growth rate of a purely growing MI. Effects of the parabolic background potential, as well as of the linear potential, the gain/loss parameter, and the two- and three-body interatomic interactions on the MI are investigated. We show how the feeding/loss parameter can be well used to control the instability of the system. The analytical resolution of the considered GP equation leads to exact bright, dark and kink solitary wave solutions which are used to investigate analytically the dynamics of matter-wave solitons in BECs under consideration. These analytical investigations show that the amplitude and the motion of bright, dark and kink solitary waves depend on the strengths of the two- and three-body interatomic interactions, as well as on the strengths of the external trapping potential and the parameter of the gain/loss of atoms in the condensate.

Non-equilibrium scale invariance and shortcuts to adiabaticity in a one-dimensional Bose gas

We present experimental evidence for scale invariant behaviour of the excitation spectrum in phase-fluctuating quasi-1d Bose gases after a rapid change of the external trapping potential. Probing density correlations in free expansion, we find that the temperature of an initial thermal state scales with the spatial extension of the cloud as predicted by a model based on adiabatic rescaling of initial eigenmodes with conserved quasiparticle occupation numbers. Based on this result, we demonstrate that shortcuts to adiabaticity for the rapid expansion or compression of the gas do not induce additional heating.