Many-body effects in the excitations and dynamics of trapped Bose-Einstein condensates

Abstract

This review explores the dynamics and the low-energy excitation spectra of Bose-Einstein condensates (BECs) of interacting bosons in external potential traps putting particular emphasis on the emerging manybody effects beyond mean-field descriptions. To do so, methods have to be used that, in principle, can provide numerically exact results for both the dynamics and the excitation spectra in a systematic manner. Numerically exact results for the dynamics are presented employing the well-established multicongurational time-dependent Hartree for bosons (MCTDHB) method. The respective excitation spectra are calculated utilizing the more recently introduced linear-response theory atop it (LR-MCTDHB). The latter theory gives rise to an, in general, non-hermitian eigenvalue problem. The theory and its newly developed implementation are described in detail and benchmarked towards the exactly-solvable harmonic-interaction model. Several applications to BECs in one-and two-dimensional potential traps are discussed. With respect to dynamics, it is shown that both the out-of-equilibrium tunneling dynamics and the dynamics of trapped vortices are of many-body nature. Furthermore, many-body effects in the excitation spectra are presented for BECs in different trap geometries. It is demonstrated that even for essentially-condensed systems, the spectrum of the lowest-in-energy excitations computed at the many-body level can differ substantially from the standard mean-field description. In general, it is shown that bosons carrying angular momentum are more sensitive to many-body effects than bosons without. These effects are present in both the dynamics and the excitation spectrum.

Entangling lattice-trapped bosons with a free impurity: impact on stationary and dynamical properties

“…This ab-initio method has been successfully applied to solve the time-dependent Schrödinger equation of various experimentally accessible and extensively studied systems. The core idea of this method lies in expanding the many-body wave-function in terms of product states of time-dependent single-particle functions [70,71]. This becomes beneficial, when the number of basis configurations with considerable contribution to the state fluctuates weakly during the time propagation, whereas the configurations themselves do change.…”

“…In these expressions, λ i and |Ψ σ i denote the natural populations and natural orbitals of the spectrally decomposed ρσ , while n σ i and |Φ σ i are the natural populations and natural orbitals of the spectrally decomposed ρσ 1 [59,71]. Also, S and s σ are the number of species orbitals and single-particle functions respectively, N σ is the number of σ component particles and σ = σ.…”

Quantum hydrodynamics of the spinor Bose-Einstein condensate at non-zero temperatures

“…The Gross-Pitaevskii equation can be derived from the microscopic quantum mechanics represented in the second quantization form [7], which is one of realizations for the transition from the microscopic to the macroscopic models. The many-particle quantum hydrodynamics presents another approach giving the representation of the many-particle wave function via the set of hydrodynamic functions [8], [9], [10], [11], [12], [13].…”