Finite-range corrections to the thermodynamics of the one-dimensional Bose gas

Cappellaro, Alberto; Salasnich, Luca

doi:10.1103/physreva.96.063610

Cited by 9 publications

(9 citation statements)

References 48 publications

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“…In figure 3 we report the superfluid fraction n s /n as a function of the scaled temperature T/T BEC for three values of the ratio r e /a s at fixed gas parameter na s 3 by numerically solving equation (47). Figure 3 shows that a positive r e /a s slightly enhances the superfluid fraction while the opposite occurs for negative values.…”

Section: D=3mentioning

confidence: 97%

“…3 we report the superfluid fraction n s /n as a function of the scaled temperature T /T BEC for three values of the ratio r e /a s at fixed gas parameter na 3 s by numerically solving Eq. (47). Fig.…”

Section: =mentioning

confidence: 99%

“…Notice that, while the superfluid fraction n s /n=1 at zero temperature, the condensate fraction is n n 1 0 < due to the quantum depletion. Obviously, equation (56) is reliable only in the deep T/T BEC =1 regime but, more generally, one must consider the full solution of equation (47).…”

Section: D=3mentioning

confidence: 99%

“…Superfluid fraction n s /n in D=3 for the gas parameter value na 10 s -, obtained as the numerical integral of equation(47). The zero-range interaction result is reported as the red dashed line, while the finite-range corrections are reported as the solid blue line (for r e /a s =10 2 ) and the black dotted-dashed line (for r a 10 e -).…”

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Condensation and superfluidity of dilute Bose gases with finite-range interaction

2018

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We investigate an ultracold and dilute Bose gas by taking into account a finite-range two-body interaction. The coupling constants of the resulting Lagrangian density are related to measurable scattering parameters by following the effective-field-theory approach. A perturbative scheme is then developed up to the Gaussian level, where both quantum and thermal fluctuations are crucially affected by finite-range corrections. In particular, the relation between spontaneous symmetry breaking and the onset of superfluidity is emphasized by recovering the renowned Landau's equation for the superfluid density in terms of the condensate one.resulting picture is only qualitative since, for instance, it does not even manage to capture the peculiar rotonic minimum of the excitation spectrum.In 1995, the experimental realization of a Bose-Einstein condensates [13] changed the scenario in a crucial way: for the first time, the predictions of the Bogoliubov theory [16] have been checked in actual weaklyinteracting quantum gases. At the same time, within a field-theory approach, it is possible to recover the Landau main results moving from a microscopic Lagrangian for ultracold atoms.The several successful theoretical studies based on the Bogoliubov framework move from the crucial assumption that the true atom-atom interaction can be replaced by a contact (i.e. zero-range) pseudopotential whose strength is given by the s-wave scattering length a s [17,18]. The resulting thermodynamics is universal since there is no dependence on the potential shape, with only a s playing a relevant role. The same point can be made for transport quantities as the superfluid fraction. Despite the many achievements of this strategy, current experiments deal with higher density setups, reduced dimensionalities and more complex interactions [19,20]. Thus, it is pressing to extend the usual two-body zero-range framework in order to capture more realistic and interesting experimental regimes. Within a functional integration formalism, atoms are represented by a bosonic field whose dynamics is governed by a microscopic interacting Lagrangian density. The coupling constants of the finite-range theory can be determined in terms of the s-wave scattering parameters, namely a s and the corresponding effective range r e . In [21][22][23][24], the finite-range thermodynamics is derived up to the Gaussian level for a three-dimensional uniform Bose gas, while the non-trivial case of two spatial dimensions is addressed in [25,26]. In figure 1 we report a visual summary of the major analytical approaches to modeling bosonic quantum gases.A similar analysis concerning the superfluid properties of a finite-range theory is still missing and it is the main subject of this work. By adopting a functional integration point of view as in [23,25], we are going to show that both condensate and superfluid depletion are modified by the finite-range character of the two-body interaction. Moreover, they are not independent from each other but the familiar Landau equation for t...

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Section: D=3mentioning

confidence: 97%

Section: =mentioning

confidence: 99%

Section: D=3mentioning

confidence: 99%

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confidence: 99%

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Condensation and superfluidity of dilute Bose gases with finite-range interaction

2018

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“…Recent works provide an extension of the Popov approach [11], while the nonuniversal corrections to the equation of state in D = 2, arising from a finite-range interaction between the atoms, have been studied [12,13]. Thank to the tunability of interparticle interactions, it is possible to investigate the static and dynamical properties of homogeneous quantum fluids in D-spatial dimensions in regimes where finite-range corrections are relevant [14][15][16]. In this work, we provide an alternative derivation of the zero-temperature equation of state by adopting an explicit superfluid parametrization of the bosonic field.…”

Section: Introductionmentioning

confidence: 99%

Zero-Temperature Equation of State of a Two-Dimensional Bosonic Quantum Fluid with Finite-Range Interaction

Tononi

2019

Condensed Matter

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We derive the two-dimensional equation of state for a bosonic system of ultracold atoms 1 interacting with a finite-range effective interaction. Within a functional integration approach, we 2 employ an hydrodynamic parametrization of the bosonic field to calculate the superfluid equations 3 of motion and the zero-temperature pressure. The ultraviolet divergences, naturally arising from the 4 finite-range interaction, are regularized with an improved dimensional regularization technique. 5

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