Effective field theory of boson-fermion mixtures and bound fermion states on a vortex of boson superfluid

Nishida, Yusuke; Son, D.

doi:10.1103/physreva.74.013615

Cited by 9 publications

(7 citation statements)

References 46 publications

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“…In the two-dimensional case (for both bosonic and fermionic superfluids) the Berezinsky-Kosterlitz-Thouless critical temperature (Berezinskii, 1971;Kosterlitz and Thouless, 1973) of the superfluidnormal phase transition can be extracted by using the Thouless criterion (Nagaosa, 1999) and an accurate description of the superfluid density which takes into account Gaussian fluctuations in the finite-temperature equation of state. Gaussian contributions to the equation of state are clearly relevant for Bose-Fermi mixtures (Nishida and Son, 2006) and for unbalanced superfluid fermions (Klimin et al, 2012). For superfluid fermionic atoms in three and two dimensions one can also investigate the effects of Gaussian fluctuations on the zero-temperature condensate fraction (Fukushima et al, 2007) comparing with mean-field results (Salasnich et al, 2005;Salasnich, 2007) and available Monte Carlo calculations (Astrakharchik et al, 2005).…”

Section: Discussionmentioning

confidence: 99%

Zero-point energy of ultracold atoms

Salasnich

Toigo

2016

Physics Reports

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We analyze the divergent zero-point energy of a dilute and ultracold gas of atoms in D spatial dimensions. For bosonic atoms we explicitly show how to regularize this divergent contribution, which appears in the Gaussian fluctuations of the functional integration, by using three different regularization approaches: dimensional regularization, momentum-cutoff regularization and convergence-factor regularization. In the case of the ideal Bose gas the divergent zero-point fluctuations are completely removed, while in the case of the interacting Bose gas these zero-point fluctuations give rise to a finite correction to the equation of state. The final convergent equation of state is independent of the regularization procedure but depends on the dimensionality of the system and the two-dimensional case is highly nontrivial. We also discuss very recent theoretical results on the divergent zero-point energy of the D-dimensional superfluid Fermi gas in the BCS-BEC crossover. In this case the zero-point energy is due to both fermionic single-particle excitations and bosonic collective excitations, and its regularization gives remarkable analytical results in the BEC regime of composite bosons. We compare the beyond-mean-field equations of state of both bosons and fermions with relevant experimental data on dilute and ultracold atoms quantitatively confirming the contribution of zero-point-energy quantum fluctuations to the thermodynamics of ultracold atoms at very low temperatures.

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Section: Discussionmentioning

confidence: 99%

Zero-point energy of ultracold atoms

Salasnich

Toigo

2016

Physics Reports

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“…Our determination of ξ 2D is likewise obtained within an exceedingly simple mathematical frame-work, which nevertheless leads to an exact result for the universal factor in two-dimensions. We are aware of no experimental results for the (quasi) 2D Fermi gas in, or near, the appropriate scattering regime and only two recent theoretical studies with the explicit aim of extracting ξ 2D , both agreeing on ξ 2D = 1 [22,23]. It has also been pointed out in passing by Tonini et al [24] that for large scattering length in 2D, the effective interactions are weakly attractive, thereby yielding the non-interacting Fermi gas in the infinite scattering length limit (see footnote 1); this observation plays a critical role in our subsequent determination of ξ 2D .…”

Section: Introductionmentioning

confidence: 99%

Density functional theory of the trapped Fermi gas in the unitary regime

Zyl

Hutchinson

2007

Laser Phys. Lett.

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Abstract:We investigate a density-functional theory (DFT) approach for an unpolarized trapped dilute Fermi gas in the unitary limit. A reformulation of the recent work of T. Papenbrock [1] in the language of fractional exclusion statistics allows us to obtain an estimate of the universal factor, ξ3D, in three dimensions (3D), in addition to providing a systematic treatment of finite-N corrections. We show that in 3D, finite-N corrections lead to unphysical values for ξ 3D , thereby suggesting that a simple DFT applied to a small number of particles may not be suitable in 3D. We then perform an analogous calculation for the twodimensional (2D) system in the infinite-scattering length regime, and obtain a value of ξ2D = 1. Owing to the unique properties of the Thomas-Fermi energy density-functional in 2D our result, in contrast to 3D, is exact and therefore requires no finite-N corrections.

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“…The agreement with very recent experimental data for both the critical temperature 8 and the sound velocity 21 is remarkably good and crucially depends on the inclusion of quantum and thermal Gaussian fluctuations. More generally, Gaussian contributions to the equation of state are relevant for Bose-Fermi mixtures 50 , for unbalanced superfluid fermions 51 , and also to investigate the condensate fraction in the BCS-BEC crossover 43 . Finally, we stress that in addition to ultracold atomic gases there are several other superfluid quantum many-body systems where the methods of functional integration and Gaussian fluctuations play a relevant role to achieve a meaningful and reliable theoretical description.…”

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confidence: 99%

Finite-temperature quantum fluctuations in two-dimensional Fermi superfluids

Bighin

Salasnich

2016

Phys. Rev. B

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In two-dimensional systems with a continuous symmetry, the Mermin-Wagner-Hohenberg theorem precludes spontaneous symmetry breaking and condensation at finite temperature. The Berezinskii-Kosterlitz-Thouless critical temperature marks the transition from a superfluid phase characterized by quasicondensation and algebraic long-range order, to a normal phase in which vortex proliferation completely destroys superfluidity. As opposed to conventional off-diagonal long-range order typical of three-dimensional superfluid systems, algebraic long-range order is driven by quantum and thermal fluctuations strongly enhanced in reduced dimensionality. Motivated by this unique scenario and by the very recent experimental realization of trapped quasi-two-dimensional fermionic clouds, we include one-loop Gaussian fluctuations in the theoretical description of resonant Fermi superfluids in two dimensions demonstrating that first sound, second sound, and also critical temperature are strongly renormalized, away from their mean-field values. In particular, we prove that in the intermediate-and strong-coupling regimes, these quantities are radically different when Gaussian fluctuations are taken into account. Our one-loop theory shows good agreement with very recent experimental data on the Berezinskii-Kosterlitz-Thouless critical temperature [Phys. Rev. Lett. 115, 010401 ( 2015)] and on the first sound velocity, giving predictions for the second sound as a function of interaction strength and temperature that are open for experimental verification

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Effective field theory of boson-fermion mixtures and bound fermion states on a vortex of boson superfluid

Cited by 9 publications

References 46 publications

Zero-point energy of ultracold atoms

Zero-point energy of ultracold atoms

Density functional theory of the trapped Fermi gas in the unitary regime

Finite-temperature quantum fluctuations in two-dimensional Fermi superfluids

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