玻色-爱因斯坦凝聚气体中激发粒子态占据数的多体涨落量子优越性

迈向最简单的量子霸权模型：盒式陷阱中的原子玻色子采样

Towards the simplest model of quantum supremacy: Atomic boson sampling in a box trap

本文提出盒式陷阱中BEC气体非凝聚部分的原子玻色子采样作为量子霸权新平台，发现压缩和干涉自发生成，无需外部压缩源。

Occupation numbers in a quantum canonical ensemble: a projection operator approach

Recently, we have used a projection operator to fix the number of particles in a second quantization approach in order to deal with the canonical ensemble. Having been applied earlier to handle various problems in nuclear physics that involve fixed particle numbers, the projector formalism was extended to grant access as well to quantum-statistical averages in condensed matter physics, such as particle densities and correlation functions. In this light, the occupation numbers of the subsequent single-particle energy eigenstates are key quantities to be examined. The goal of this paper is 1) to…

Microscopic Treatment of Binary Interactions in the Non-Equilibrium Dynamics of Partially Bose-condensed Trapped Gases

In this paper we use microscopic arguments to derive a nonlinear Schrödinger equation for trapped Bose-condensed gases. This is made possible by considering the equations of motion of various anomalous averages. The resulting equation explicitly includes the effect of repeated binary interactions (in particular ladders) between the atoms. Moreover, under the conditions that dressing of the intermediate states of a collision can be ignored, this equation is shown to reduce to the conventional Gross-Pitaevskii equation in the pseudopotential limit. Extending the treatment, we show first how the …

The saddle-point method for condensed Bose gases

The application of the conventional saddle-point approximation to condensed Bose gases is thwarted by the approach of the saddle-point to the ground-state singularity of the grand canonical partition function. We develop and test a variant of the saddle-point method which takes proper care of this complication, and provides accurate, flexible, and computationally efficient access to both canonical and microcanonical statistics. Remarkably, the error committed when naively employing the conventional approximation in the condensate regime turns out to be universal, that is, independent of the sy…

An exactly solvable phase transition model: generalized statistics and generalized Bose-Einstein condensation

In this paper, we present an exactly solvable phase transition model in which the phase transition is purely statistically derived. The phase transition in this model is a generalized Bose-Einstein condensation. The exact expression of the thermodynamic quantity which can simultaneously describe both gas phase and condensed phase is solved with the help of the homogeneous Riemann-Hilbert problem, so one can judge whether there exists a phase transition and determine the phase transition point mathematically rigorously. A generalized statistics in which the maximum occupation numbers of differe…

Condensate statistics in interacting Bose gases: exact results

Recently, a Quantum Monte Carlo method alternative to the Path Integral Monte Carlo method was developed for the numerical solution of the N-boson problem; it is based on the stochastic evolution of classical fields. Here we apply it to obtain exact results for the occupation statistics of the condensate mode in a weakly interacting trapped one-dimensional Bose gas. The temperature is varied across the critical region down to temperatures lower than the trap level spacing. We verify that the number-conserving Bogoliubov theory gives accurate predictions provided that the non-condensed fraction…