aqora

Bose-Einstein Condensation of Particles with Spin

Александр Сергеевич Пелетминский, S. V. Peletminsky, Yu. V. Slyusarenko

Voprosy Atomnoj Nauki i TekhnikiJan 1, 20070 citations

Large Deviations for the Bose--Einstein Condensate of the Ideal Gas in the Canonical Ensemble

Andreas Deuchert, Xuanyu Li

We consider a non-interacting Bose gas governed by a general one-particle Hamiltonian in the canonical ensemble. Our main results are large-deviation estimates for the number of particles in the Bose--Einstein condensate. We show that the left- and right-tail probabilities decay at different exponential rates as the number of particles tends to infinity.

math-phCross-listedarXiv:2608.26378Aug 28, 20260 citations

On the Bose-Einstein condensation of an ideal gas

Lawrence J. Landau, Ivan F. Wilde

Communications in Mathematical PhysicsFeb 1, 197975 citations

The ideal Bose gas in open harmonic trap systems and its condensation revisited.

Mathieu Beau, Baptiste Savoie

We rigorously revisit a textbook model used to figure out the Bose-Einstein condensation (BEC) phenomenon created by dilute cold alkali atoms gases in a magnetic-optical trap. It consists of a d-dimensional (d=1,2,3) ideal non-relativistic spin-0 Bose gas confined in a box and trapped in an isotropic harmonic potential. Throughout we review and clarify a series of methods involved in the derivation of the thermodynamics in the grand-canonical situation. To make the derivation consistent with the usual rules of the statistical mechanics, we assign through our open-trap limit approach the role of canonical parameter to a rescaled number of particles (instead of an effective density involving the pulsation of the trap). Within this approach, we formulate an Einstein-like and Penrose-Onsager-like criterion of BEC and show their equivalence. Afterwards, we focus on the spatial localization of the condensate/thermal gas. When dealing with the reduced density matrix, our method is similar to the loop path approach.We rigorously revisit a textbook model used to figure out the Bose-Einstein condensation (BEC) phenomenon created by dilute cold alkali atoms gases in a magnetic-optical trap. It consists of a d-dimensional (d=1,2,3) ideal non-relativistic spin-0 Bose gas confined in a box and trapped in an isotropic harmonic potential. Throughout we review and clarify a series of methods involved in the derivation of the thermodynamics in the grand-canonical situation. To make the derivation consistent with the usual rules of the statistical mechanics, we assign through our open-trap limit approach the role of canonical parameter to a rescaled number of particles (instead of an effective density involving the pulsation of the trap). Within this approach, we formulate an Einstein-like and Penrose-Onsager-like criterion of BEC and show their equivalence. Afterwards, we focus on the spatial localization of the condensate/thermal gas. When dealing with the reduced density matrix, our method is similar to the loop path approach.

Jun 16, 20130 citations

Stepwise Bose-Einstein Condensation in a Spinor Gas

Camille Frapolli, Tilman Zibold, Andrea Invernizzi +3 more

We observe multistep condensation of sodium atoms with spin F=1, where the different Zeeman components m_{F}=0,±1 condense sequentially as the temperature decreases. The precise sequence changes drastically depending on the magnetization m_{z} and on the quadratic Zeeman energy q (QZE) in an applied magnetic field. For large QZE, the overall structure of the phase diagram is the same as for an ideal spin-1 gas, although the precise locations of the phase boundaries are significantly shifted by interactions. For small QZE, antiferromagnetic interactions qualitatively change the phase diagram with respect to the ideal case, leading, for instance, to condensation in m_{F}=±1, a phenomenon that cannot occur for an ideal gas with q>0.We observe multistep condensation of sodium atoms with spin F=1, where the different Zeeman components m_{F}=0,±1 condense sequentially as the temperature decreases. The precise sequence changes drastically depending on the magnetization m_{z} and on the quadratic Zeeman energy q (QZE) in an applied magnetic field. For large QZE, the overall structure of the phase diagram is the same as for an ideal spin-1 gas, although the precise locations of the phase boundaries are significantly shifted by interactions. For small QZE, antiferromagnetic interactions qualitatively change the phase diagram with respect to the ideal case, leading, for instance, to condensation in m_{F}=±1, a phenomenon that cannot occur for an ideal gas with q>0.

arXiv:1702.08265Physical Review LettersAug 4, 201726 citations

Bose-Einstein condensation of ideal Bose gases under external conditions

Chapman & Hall/CRC eBooksDec 13, 20010 citations

Bose-Einstein condensation of a non-ideal Bose gas of atoms with large spin

Related papers

Bose-Einstein condensation of a non-ideal Bose gas of atoms with large spin

Related papers