Nonuniversal Equation of State of the Two-Dimensional Bose Gas

Salasnich, Luca

doi:10.1103/physrevlett.118.130402

Cited by 22 publications

(37 citation statements)

References 39 publications

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“…The non-universal 1D equation of state is quite different with respect to the 3D [14] and 2D [24] ones, and its quantum fluctuations crucially depend on the scattering length and the effective range of the interaction potential. Our finiterange analytical results, Eq.…”

Section: Discussionmentioning

confidence: 99%

“…In regimes where r s ≈ a s , deviation from universalities are relevant, and every dynamical picture of the system has to take into account not only quantum fluctuations, but also finite-range corrections modelled around Eq. (24). In the present experiments one can tune the scattering length a s and in turn the adimensional parameter α = 4r e /a s of our theory, because the effective range r e remains practically fixed and quite small (≃ 10 −10 m).…”

Section: A Quantum Fluctuationsmentioning

confidence: 99%

“…Finite-range effects naturally arise by modelling the two-body interactions beyond the unphysical zero-range approximation. As recently shown for the 2D Bose gas [24], since finiterange corrections affect the behavior of quantum and thermal fluctuations, they have to be taken into account also in lower dimensional system, where fluctuations are strongly enhanced (Mermin-Wagner-Hohenberg theorem [25,26]). Improvements in cold-atom experimental techniques are providing a precision benchmark which makes possible to explore in great details beyond-mean-field effects in low-dimensional systems [5,6,27,28].…”

Section: Introductionmentioning

confidence: 99%

“…Within the framework of a local effective action [14,15,23,24,34], we derive a novel equation of state, where the contributions of quantum and thermal fluctuations crucially depend also on the effective range of the interatomic potential. These corrections are computed at Gaussian (one-loop) level, where non-physical divergences are removed by using dimensional regularization.…”

Section: Introductionmentioning

confidence: 99%

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

Cappellaro

Salasnich

2017

Phys. Rev. A

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The Lieb-Liniger equation of state accurately describes the zero-temperature universal properties of a dilute one-dimensional Bose gas in terms of the s-wave scattering length. For weakly-interacting bosons we derive non-universal corrections to this equation of state taking into account finiterange effects of the inter-atomic potential. Within the finite-temperature formalism of functional integration we find a beyond-mean-field equation of state which depends on scattering length and effective range of the interaction potential. Our analytical results, which are obtained performing dimensional regularization of divergent zero-point quantum fluctuations, show that for the onedimensional Bose gas thermodynamic quantities like pressure and sound velocity are modified by changing the ratio between the effective range and the scattering length.

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Section: Discussionmentioning

confidence: 99%

Section: A Quantum Fluctuationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Cappellaro

Salasnich

2017

Phys. Rev. A

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“…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.…”

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confidence: 99%

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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2D Dilute Bose Mixture at Low Temperatures

Konietin

Pastukhov

2017

J Low Temp Phys

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The thermodynamic and superfluid properties of the dilute twodimensional binary Bose mixture at low temperatures are discussed. We also considered the problem of the emergence of the long-range order in these systems. All calculations are performed by means of celebrated Popov's pathintegral approach for the Bose gas with a short-range interparticle potential.Keywords two-dimensional Bose mixtures · superfluid properties · offdiagonal long-range orderThe spatial dimensionality plays a crucial role in the behavior of interacting many-boson systems. Perhaps, the most exciting phase diagram is obtained in the two-dimensional case (for review, see [1,2]), where the ground-state Bose condensate state [3,4,5,6,7,8] is altered by the low-temperature Beresinskii-Kosterlitz-Thouless (BKT) phase with the characteristic power-law [9] decay of the one-particle density matrix. To describe these systems appropriately one needs to extend [10] the standard approach with the separated condensate and to use the phase-density formulation [11], renormalization-group [12,13,14,15, 16,17] or the effective field-theoretic [18,19] treatments. Particularly Popov's theory allows to find out the low-energy structure of one-particle Green's functions [20] and improved version of this approach [21,22] which takes into account phase fluctuations exactly is capable to explain [23] experiments with two-dimensional Bose gases. In contrast to the two-dimensional Bose systems

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Nonuniversal Equation of State of the Two-Dimensional Bose Gas

Cited by 22 publications

References 39 publications

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

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

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

2D Dilute Bose Mixture at Low Temperatures

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