Ideal Bose-Einstein Condensate Research Articles

Matter waves from quantum sources in a force field

Localized scattering phenomena may result in the formation of stationary matter waves originating from a compact region in physical space. Mathematically, such waves are advantageously expressed in terms of quantum sources that are introduced into the Schrodinger equation. The source formalism yields direct access to the scattering wavefunction, particle distribution and total current. As an example, we study emission from three-dimensional Gaussian sources into a homogeneous force field. This model describes the behaviour of an atom laser supplied by an ideal Bose-Einstein condensate under the influence of gravity. We predict a strong dependence of the beam profile on the condensate size and the presence of interference phenomena recently observed in photodetachment experiments.

Influence of boundary conditions on statistical properties of ideal Bose-Einstein condensates.

We investigate the probability distribution that governs the number of ground-state particles in a partially condensed ideal Bose gas confined to a cubic volume within the canonical ensemble. Imposing either periodic or Dirichlet boundary conditions, we derive asymptotic expressions for all its cumulants. Whereas the condensation temperature becomes independent of the boundary conditions in the large-system limit, as implied by Weyl's theorem, the fluctuation of the number of condensate particles and all higher cumulants remain sensitive to the boundary conditions even in that limit. The implications of these findings for weakly interacting Bose gases are briefly discussed.

Master equation vs. partition function: canonical statistics of ideal Bose–Einstein condensates

Within the canonical ensemble, a partially condensed ideal Bose gas with arbitrary single-particle energies is equivalent to a system of uncoupled harmonic oscillators. We exploit this equivalence for deriving a formula which expresses all cumulants of the canonical distribution governing the number of condensate particles in terms of the poles of a generalized Zeta function provided by the single-particle spectrum. This formula lends itself to systematic asymptotic expansions which capture the non-Gaussian character of the condensate fluctuations with utmost precision even for relatively small, finite systems, as confirmed by comparison with exact numerical calculations. We use these results for assessing the accuracy of a recently developed master equation approach to the canonical condensate statistics; this approach turns out to be quite accurate even when the master equation is solved within a simple quasithermal approximation. As a further application of the cumulant formula we show that, and explain why, all cumulants of a homogeneous Bose–Einstein condensate “in a box” higher than the first retain a dependence on the boundary conditions in the thermodynamic limit.

Yang-Lee circle theorem for an ideal pseudospin-1/2 Bose gas in an external magnetic field.

The Yang-Lee circle theorem is extended to an ideal pseudospin-1/2 Bose gas in an external magnetic field. It is found that the zeros of the canonical partition function are located on the unit circle in the complex activity plane if the temperature is above the critical temperature of ideal Bose-Einstein condensation. No zeros exist if the temperature is below the critical temperature.

Manipulating a Bose-Einstein condensate with a single photon

We propose a method to create macroscopic superpositions, so-called Schrodinger cat states, of different motional states of an ideal Bose-Einstein condensate. The scheme is based on the scattering of a freely expanding condensate by the light field of a high-finesse optical cavity in a quantum superposition state of different photon numbers. The atom-photon interaction creates an entangled state of the motional state of the condensate and the photon number, which can be converted into a pure atomic Schrodinger cat state by operations only acting on the cavity field. We discuss in detail the fully quantised theory and propose an experimental procedure to implement the scheme using short coherent light pulses.

Critical nature of ideal Bose-Einstein condensation: Similarity with Yang-Lee theory of phase transition

It is found that the singularity of the thermodynamic potential of an ideal Bose gas is connected with the physical root ${z}_{0}=1$ of the inverse of the grand partition function. The critical nature is determined solely by the behavior of the root distribution of the inverse of the grand partition function near ${z}_{0}=1$. This is quite similar to the situation of phase transition described by Yang-Lee theory.

Condensate Fluctuations in Trapped Bose Gases: Canonical vs. Microcanonical Ensemble

We study the fluctuation of the number of particles in ideal Bose–Einstein condensates, both within the canonical and the microcanonical ensemble. Employing the Mellin–Barnes transformation, we derive simple expressions that link the canonical number of condensate particles, its fluctuation, and the difference between canonical and microcanonical fluctuations to the poles of a Zeta function that is determined by the excited single-particle levels of the trapping potential. For the particular examples of one- and three-dimensional harmonic traps we explore the microcanonical statistics in detail, with the help of the saddle-point method. Emphasizing the close connection between the partition theory of integer numbers and the statistical mechanics of ideal Bosons in one-dimensional harmonic traps, and utilizing thermodynamical arguments, we also derive an accurate formula for the fluctuation of the number of summands that occur when a large integer is partitioned.

Quantum Light Excitation of Atoms in Ideal Bose–Einstein condensate11The project supported in part by National Natural Science Foundation of China and Fok Yin-Tung EducationFoundation

The spectrum shape of atomic radiation in the case of ideal Bose–Einstein condensate (BEC) excited by quantized light is derived through the Wigner–Weisskopf approximation. Besides the split and gap in the excitation spectrum, a doublet structure appears in the emission spectrum with different widths for the non-resonant case and the same widths for the resonant case. The survival probability is found to decrease exponentially for the non-resonant case and with oscillation for the resonant case. A suppressed radiation also appears in the non-resonant case. All these results can be used to detect the existence of BE condensation.