Investigación

BEC transition of a weakly interacting ultracold Bose gas in a linear quadrupolar trap

N. Sandoval–Figueroa and V. Romero–Rochín^*

Instituto de Física, Universidad Nacional Autónoma de México, Apartado Postal 20–364, México, 01000 D.F. Mexico, e–mail: nadia@fisica.unam.mx *romero@fisica.unam.mx, Office: + 52 (55) 5622 – 5096 Fax: + 52 (55) 5622 – 2015

Recibido el 26 de noviembre de 2009
Aceptado el 9 de abril de 2010

Abstract

We discuss the thermal gas to Bose–Einstein Condensation (BEC) transition of an ultracold Bose gas in a linear quadrupolar trap with contact interatomic interactions within the Hartree–Fock (HF) approximation. We briefly review the theoretical framework of the thermodynamics of a gas confined by a non–uniform potential to show how mechanical equilibria must be formulated in term of generalized volume and pressure variables V and P that replace the usual volume and hydrostatic pressure of a uniform system. We solve for the density profile within HF as a function of temperature T and molar volume v = V/N. With this information, we are able to calculate all the thermodynamic properties of the system and analyze the behavior of the gas through the BEC (superfluid) transition. We find that the transition is completely smooth, showing no sign of critical behavior. We emphasize how these predictions can be readily measured with the current experimental setups.

Keywords: Bose–Einstein Condensation in confined systems; weakly interacting ultracold gases; phase transitions.

Resumen

En este trabajo discutimos la transición de gas térmico a la Condensación de Bose–Einstein (BEC) de un gas de Bose ultrafrío confinado en una trampa cuadrupolar lineal, considerando interacciones atómicas de contacto dentro de la aproximación de Hartree–Fock (HF). Revisamos brevemente el marco teórico de la termodinámica de un gas confinado por un potencial no uniforme para mostrar cómo debe formularse el equilibrio mecánico en términos de variables generalizadas de volumen y presión V and P, que reemplazan el volumen usual y la presión hidrostática de un sistema uniforme. Calculamos el perfil de densidad dentro de la aproximación HF como función de la temperatura T y el volumen molar generalizado v = V/N. Con esta información podemos calcular todas las propiedades termodinámicas del sistema y analizamos el comportamiento del gas a través de la transición BEC (superfluido). Hallamos que la transición es completamente suave y que no muestra signos de comportamiento crítico. Enfatizamos cómo estas predicciones pueden ser medidas con los dispositivos experimentales actuales.

Descriptores: Condensación de Bose–Einstein en sistemas confinados; gases ultrafríos débilmente interactuantes; transiciones de fase.

PACS: 05.70.–a; 03.75.Hh

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Acknowledgments

Work supported by UNAM DGAPAIN–114308.

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