The stability of Bose gases near resonance has been a puzzling problem in recent years. In this article, we demonstrate that in addition to generating thermal pressure, thermal atoms enhance the repulsiveness of the scale-dependent interactions between condensed atoms due to a renormalization effect and further stabilize the Bose gases. Consequently, we find that, as a precursor of instability, the compressibility develops an anomalous structure as a function of scattering length and is drastically reduced compared with the mean-field value. Furthermore, the density profile of a Bose gas in a harmonic trap is found to develop a flat top near the center. This is due to the anomalous behavior of compressibility and can be a potential smoking gun for probing such an effect.The stability of Bose gases near resonance has been a puzzling problem in recent years. In this article, we demonstrate that in addition to generating thermal pressure, thermal atoms enhance the repulsiveness of the scale-dependent interactions between condensed atoms due to a renormalization effect and further stabilize the Bose gases. Consequently, we find that, as a precursor of instability, the compressibility develops an anomalous structure as a function of scattering length and is drastically reduced compared with the mean-field value. Furthermore, the density profile of a Bose gas in a harmonic trap is found to develop a flat top near the center. This is due to the anomalous behavior of compressibility and can be a potential smoking gun for probing such an effect.

arXiv:1504.03434Physical Review AJul 14, 20154 citations

Interactions in trapped Bose-Einstein condensates

David A. W. Hutchinson, R. J. Dodd, Nick P. Proukakis +4 more

International Conference on Atomic Physics (ICAP)Jan 1, 19990 citations

Nature of Bose gases near Feshbach resonance : the interplay between few-body and many-body physics

Mohammad Sadegh Mashayekhi

In this thesis, we investigated the physics of two- and three-dimensional ultra cold Bose gases in the strongly interacting regime at zero temperature. This regime can be experimentally accessed using a Feshbach resonance. We applied a self-consistent diagrammatic approach to determine the chemical potential of three-dimensional Bose gases for a wide range of interaction values. We showed that such strongly interacting Bose gases become unstable towards the formation of molecules at a finite positive scattering length. In fact, the interaction between atoms becomes effectively attractive and the system looses its metastability before reaching the unitary limit. We also found that such systems are nearly fermionized close to the instability point. Near this critical point, the chemical potential reaches a maximum and the contribution to the system energy due to three-body forces is estimated to be only a few percent. We also studied the same system using a self-consistent renormalization group method. This approach confirms the existence of an instability point towards the formation of molecules as well as fermionization. We showed that the instability and accompanying maximum are precursors of the sign change of the effective two-body interaction strength from repulsive to attractive near resonance. In addition, we examined the physics of two-dimensional Bose gases near resonance using a similar self-consistent diagrammatic approach as the one introduced for three-dimensional Bose gases. We demonstrated that a competition between three-body attractive interactions and two-body repulsive forces results in the chemical potential of two-dimensional Bose gases to exhibit a maximum at a critical scattering length beyond which these quantum gases possess a negative compressibility. For larger scattering lengths, the increasingly prominent role played by three-body attractive interactions leads to an onset instability at a second critical value. The three-body effects studied for these systems are universal, fully characterized by the effective two-dimensional scattering length and are, in comparison to the three-dimensional case, independent of three-body ultraviolet physics.In this thesis, we investigated the physics of two- and three-dimensional ultra cold Bose gases in the strongly interacting regime at zero temperature. This regime can be experimentally accessed using a Feshbach resonance. We applied a self-consistent diagrammatic approach to determine the chemical potential of three-dimensional Bose gases for a wide range of interaction values. We showed that such strongly interacting Bose gases become unstable towards the formation of molecules at a finite positive scattering length. In fact, the interaction between atoms becomes effectively attractive and the system looses its metastability before reaching the unitary limit. We also found that such systems are nearly fermionized close to the instability point. Near this critical point, the chemical potential reaches a maximum and the contribution to the system energy due to three-body forces is estimated to be only a few percent. We also studied the same system using a self-consistent renormalization group method. This approach confirms the existence of an instability point towards the formation of molecules as well as fermionization. We showed that the instability and accompanying maximum are precursors of the sign change of the effective two-body interaction strength from repulsive to attractive near resonance. In addition, we examined the physics of two-dimensional Bose gases near resonance using a similar self-consistent diagrammatic approach as the one introduced for three-dimensional Bose gases. We demonstrated that a competition between three-body attractive interactions and two-body repulsive forces results in the chemical potential of two-dimensional Bose gases to exhibit a maximum at a critical scattering length beyond which these quantum gases possess a negative compressibility. For larger scattering lengths, the increasingly prominent role played by three-body attractive interactions leads to an onset instability at a second critical value. The three-body effects studied for these systems are universal, fully characterized by the effective two-dimensional scattering length and are, in comparison to the three-dimensional case, independent of three-body ultraviolet physics.

Jan 1, 20140 citations

Renormalization group analysis of a confined, interacting Bose gas

G. Alber, G. Metikas

arXiv:cond-mat/0111507Applied Physics BDec 1, 20016 citations

Universal Bose gases near resonance: A rigorous solution

Shao-Jian Jiang, Wu-Ming Liu, Gordon Walter Semenoff +1 more

We obtain a rigorous solution of universal Bose gases near resonance and offer an answer to one of the long-standing challenges of quantum gases at large scattering lengths, where the standard dilute theory breaks down. The solution was obtained by using an $\ensuremath{\epsilon}$ expansion near four spatial dimensions. In dimension $d=4\ensuremath{-}\ensuremath{\epsilon}$, the chemical potential of Bose gases near resonance is shown to approach the universal value ${\ensuremath{\epsilon}}^{\frac{2}{4\ensuremath{-}\ensuremath{\epsilon}}}{\ensuremath{\epsilon}}_{F}\sqrt{\frac{2}{3}}(1+0.474\ensuremath{\epsilon}\ensuremath{-}i1.217\ensuremath{\epsilon}+\ensuremath{\cdots})$, where ${\ensuremath{\epsilon}}_{F}$ is the Fermi energy defined for a Fermi gas of density $n$ , and the condensation fraction is equal to $\frac{2}{3}(1+0.0877\ensuremath{\epsilon}+\ensuremath{\cdots})$. We also discuss the implications on ultracold gases in physical dimensions.We obtain a rigorous solution of universal Bose gases near resonance and offer an answer to one of the long-standing challenges of quantum gases at large scattering lengths, where the standard dilute theory breaks down. The solution was obtained by using an $\ensuremath{\epsilon}$ expansion near four spatial dimensions. In dimension $d=4\ensuremath{-}\ensuremath{\epsilon}$, the chemical potential of Bose gases near resonance is shown to approach the universal value ${\ensuremath{\epsilon}}^{\frac{2}{4\ensuremath{-}\ensuremath{\epsilon}}}{\ensuremath{\epsilon}}_{F}\sqrt{\frac{2}{3}}(1+0.474\ensuremath{\epsilon}\ensuremath{-}i1.217\ensuremath{\epsilon}+\ensuremath{\cdots})$, where ${\ensuremath{\epsilon}}_{F}$ is the Fermi energy defined for a Fermi gas of density $n$, and the condensation fraction is equal to $\frac{2}{3}(1+0.0877\ensuremath{\epsilon}+\ensuremath{\cdots})$. We also discuss the implications on ultracold gases in physical dimensions.

arXiv:1307.4263Physical Review AMar 11, 201428 citations

n

, and the condensation fraction is equal to $\frac{2}{3}(1+0.0877\ensuremath{\epsilon}+\ensuremath{\cdots})$. We also discuss the implications on ultracold gases in physical dimensions.