Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1809.09317 · Physical Review A

Quantum fluctuations of a resonantly interacting p -wave Fermi superfluid in two dimensions

Hui Hu, Brendan C. Mulkerin, Lianyi He, Jia Wang, Xia-Ji Liu

Published Dec 4, 2018• 6 citations
arXivHTMLPDF

Abstract

Using the Gaussian pair fluctuation theory, we investigate quantum fluctuations of a strongly interacting two-dimensional chiral $p$-wave Fermi superfluid at the transition from a Bose-Einstein condensate (BEC) to a topologically nontrivial Bardeen-Cooper-Schrieffer superfluid. Near the topological phase transition at zero chemical potential, $\ensuremath{\mu}=0$, we observe that quantum fluctuations strongly renormalize the zero-temperature equations of state, sound velocity, pair-breaking velocity, and Berezinskii-Kosterlitz-Thouless (BKT) critical temperature of the Fermi superfluid, all of which can be nonanalytic functions of the interaction strength. The indication of nonanalyticity is particularly evident in the BKT critical temperature, which also exhibits a pronounced peak near the topological phase transition. Across the transition and towards the BEC limit we find that the system quickly becomes a trivial interacting Bose liquid, whose properties are less dependent on the interparticle interaction. The qualitative behavior of composite bosons in the BEC limit remains to be understood.

DOI
10.1103/physreva.98.063605

Related papers

Quantum fluctuation effect of a two-dimensional Fermi gas with d -wave pairing

S C Wang, Tingting Shi, Wei Zhang

Abstract We investigate quantum fluctuation effects in a two-dimensional Fermi superfluid with $d_{x^2\textrm{-}y^2}$-wave pairing through an evolution from Bardeen-Cooper-Schrieffer (BCS) limit to Bose-Einstein condensate (BEC) limit. Using the Gaussian pair fluctuation (GPF) theory beyond the mean-field approximation, we derive a modified particle number equation and solve it self-consistently with the gap equation. We find that key physical properties, including the equation of state, the compressibility, and the sound velocity, are strongly renormalized by quantum fluctuations, reflecting their crucial role near the phase transition. Both mean-field and GPF theory reveal a pronounced Lifshitz transition at zero chemical potential $\mu=0$, but occurring at different interaction strengths. As the system evolves from the BCS to BEC regime, the fluctuation-induced particle number grows rapidly and saturates near the transition point, further highlighting the importance of quantum fluctuations. We also analyze the quasiparticle excitation spectrum, which exhibits a transition from a nodal BCS regime with characteristic $C_4$ symmetry to a fully gapped BEC regime, providing direct insight into the interplay between pairing symmetry, phase transition of spectrum topology, and quantum fluctuations.

Chinese Physics B•Apr 27, 2026•0 citations

Kosterlitz-Thouless transition and vortex-antivortex lattice melting in two-dimensional Fermi gases with p - or d -wave pairing

Gaoqing Cao, Lianyi He, Xu-Guang Huang

We present a theoretical study of the finite-temperature Kosterlitz-Thouless (KT) and vortex-antivortex lattice (VAL) melting transitions in two-dimensional Fermi gases with $p$- or $d$-wave pairing. For both pairings, when the interaction is tuned from weak to strong attractions, we observe a quantum phase transition from the Bardeen-Cooper-Schrieffer (BCS) superfluidity to the Bose-Einstein condensation (BEC) of difermions. The KT and VAL transition temperatures increase during this BCS-BEC transition and approach constant values in the deep BEC region. The BCS-BEC transition is characterized by the nonanalyticities of the chemical potential, the superfluid order parameter, and the sound velocities as functions of the interaction strength at both zero and finite temperatures; however, the temperature effect tends to weaken the nonanalyticities compared to the zero-temperature case. The effect of mismatched Fermi surfaces on the $d$-wave pairing is also studied.

arXiv:1708.00124•Physical Review A•Dec 22, 2017•5 citations

Superfluid density and critical velocity near the Berezinskii-Kosterlitz-Thouless transition in a two-dimensional strongly interacting Fermi gas

Brendan C. Mulkerin, Lianyi He, Paul Dyke +3 more

We theoretically investigate superfluidity in a strongly interacting Fermi gas confined to two dimensions at finite temperature. Using a Gaussian pair fluctuation theory in the superfluid phase, we calculate the superfluid density and determine the critical temperature and chemical potential at the Berezinskii-Kosterlitz-Thouless transition. We propose that the transition can be unambiguously demonstrated in cold-atom experiments by stirring the superfluid Fermi gas using a red-detuned laser beam, to identify the characteristic jump in the local Landau critical velocity at the superfluid-normal interface, as the laser beam moves across the cloud.

arXiv:1702.07091•Physical Review A•Nov 6, 2017•31 citations

Finite-temperature quantum fluctuations in two-dimensional Fermi superfluids

Giacomo Bighin, Luca Salasnich

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.

arXiv:1507.07542•Physical review. B./Physical review. B•Jan 28, 2016•42 citations

Gaussian fluctuations in the two-dimensional BCS-BEC crossover: finite temperature properties

Giacomo Bighin, Luca Salasnich

The role of fluctuations is enhanced in lower dimensionality systems: in a two dimensions offdiagonal long-range order is destroyed by the fluctuations at any finite temperature, drastically modifying the critical properties with respect to the three-dimensional counterpart.Recently two-dimensional systems of interacting fermions have been the subject of Montecarlo studies and experimental investigations, in particular an ultracold gas of attractive fermions with a widely tunable interaction due to a Feshbach resonance has been realized and the Berezinskii-Kosterlitz-Thouless transition has been observed.The present work deals with the theoretical description of an ultracold Fermi gas: we discuss the role of Gaussian fluctuations of the order parameter in the equation of state, in particular we take into account the first sound velocity, showing that the inclusion of order parameter fluctuations is needed in order to get the correct composite-boson limit in the strong-coupling regime.The theory is also compared with experimental data.Finally we focus on the superfluid density in the weak-coupling, intermediate and strong-coupling regimes at finite temperature, through which the Berezinskii-Kosterlitz-Thouless critical temperature is obtained.

arXiv:1602.03726•Journal of Physics Conference Series•Feb 1, 2016•3 citations

The Berezinskii–Kosterlitz–Thouless transition in imbalanced 2D Fermi gases: The role of fluctuations

Jacques Tempere, Serghei N. Klimin, J. T. Devreese

Abstract The physics of two-dimensional (2D) quantum gases can be revealed in strongly confining optical lattices. Upon cooling, 2D bosonic quantum gases as well as Fermi gases where pairing is present, become superfluid. The superfluid-to-normal transition is no longer governed by the presence or absence of a condensate, but by the Berezinskii–Kosterlitz–Thouless (BKT) mechanism: above a critical temperature, vortices and antivortices proliferate and destroy phase coherence. We investigate the BKT transition for superfluid 2D Fermi gases in the whole range of the BCS–BEC crossover, from weakly bound Cooper pairing (the BCS state), up to strongly bound molecules (the BEC state). Using a path-integral description, we then focus on the case of imbalanced gases: when the number of ‘spin-up’ and ‘spin-down’ fermions that form the pair is no longer equal. When an excess of one spin species exists, pairing is frustrated and the vortex energetics is strongly affected, influencing the KT mechanism. In the present work we are concentrated on the effect of both phase and amplitude fluctuations on phase diagrams of the fermion system. The amplitude fluctuations only slightly influence the BKT phase transition temperature. However, they lead to a substantial modification of the complete phase diagram for the Fermi gas in 2D with respect to that obtained taking into account only phase fluctuations.

Physica C Superconductivity•Feb 24, 2010•3 citations
Using the Gaussian pair fluctuation theory, we investigate quantum fluctuations of a strongly interacting two-dimensional chiral ppp-wave Fermi superfluid at the transition from a Bose-Einstein condensate (BEC) to a topologically nontrivial Bardeen-Cooper-Schrieffer superfluid. Near the topological phase transition at zero chemical potential, \ensuremathμ=0\ensuremath{\mu}=0\ensuremathμ=0, we observe that quantum fluctuations strongly renormalize the zero-temperature equations of state, sound velocity, pair-breaking velocity, and Berezinskii-Kosterlitz-Thouless (BKT) critical temperature of the Fermi superfluid, all of which can be nonanalytic functions of the interaction strength. The indication of nonanalyticity is particularly evident in the BKT critical temperature, which also exhibits a pronounced peak near the topological phase transition. Across the transition and towards the BEC limit we find that the system quickly becomes a trivial interacting Bose liquid, whose properties are less dependent on the interparticle interaction. The qualitative behavior of composite bosons in the BEC limit remains to be understood.
Abstract We investigate quantum fluctuation effects in a two-dimensional Fermi superfluid with dx2-y2d_{x^2\textrm{-}y^2}dx2-y2​-wave pairing through an evolution from Bardeen-Cooper-Schrieffer (BCS) limit to Bose-Einstein condensate (BEC) limit. Using the Gaussian pair fluctuation (GPF) theory beyond the mean-field approximation, we derive a modified particle number equation and solve it self-consistently with the gap equation. We find that key physical properties, including the equation of state, the compressibility, and the sound velocity, are strongly renormalized by quantum fluctuations, reflecting their crucial role near the phase transition. Both mean-field and GPF theory reveal a pronounced Lifshitz transition at zero chemical potential μ=0\mu=0μ=0, but occurring at different interaction strengths. As the system evolves from the BCS to BEC regime, the fluctuation-induced particle number grows rapidly and saturates near the transition point, further highlighting the importance of quantum fluctuations. We also analyze the quasiparticle excitation spectrum, which exhibits a transition from a nodal BCS regime with characteristic C4C_4C4​ symmetry to a fully gapped BEC regime, providing direct insight into the interplay between pairing symmetry, phase transition of spectrum topology, and quantum fluctuations.
We present a theoretical study of the finite-temperature Kosterlitz-Thouless (KT) and vortex-antivortex lattice (VAL) melting transitions in two-dimensional Fermi gases with ppp- or ddd-wave pairing. For both pairings, when the interaction is tuned from weak to strong attractions, we observe a quantum phase transition from the Bardeen-Cooper-Schrieffer (BCS) superfluidity to the Bose-Einstein condensation (BEC) of difermions. The KT and VAL transition temperatures increase during this BCS-BEC transition and approach constant values in the deep BEC region. The BCS-BEC transition is characterized by the nonanalyticities of the chemical potential, the superfluid order parameter, and the sound velocities as functions of the interaction strength at both zero and finite temperatures; however, the temperature effect tends to weaken the nonanalyticities compared to the zero-temperature case. The effect of mismatched Fermi surfaces on the ddd-wave pairing is also studied.
We theoretically investigate superfluidity in a strongly interacting Fermi gas confined to two dimensions at finite temperature. Using a Gaussian pair fluctuation theory in the superfluid phase, we calculate the superfluid density and determine the critical temperature and chemical potential at the Berezinskii-Kosterlitz-Thouless transition. We propose that the transition can be unambiguously demonstrated in cold-atom experiments by stirring the superfluid Fermi gas using a red-detuned laser beam, to identify the characteristic jump in the local Landau critical velocity at the superfluid-normal interface, as the laser beam moves across the cloud.
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.
The role of fluctuations is enhanced in lower dimensionality systems: in a two dimensions offdiagonal long-range order is destroyed by the fluctuations at any finite temperature, drastically modifying the critical properties with respect to the three-dimensional counterpart.Recently two-dimensional systems of interacting fermions have been the subject of Montecarlo studies and experimental investigations, in particular an ultracold gas of attractive fermions with a widely tunable interaction due to a Feshbach resonance has been realized and the Berezinskii-Kosterlitz-Thouless transition has been observed.The present work deals with the theoretical description of an ultracold Fermi gas: we discuss the role of Gaussian fluctuations of the order parameter in the equation of state, in particular we take into account the first sound velocity, showing that the inclusion of order parameter fluctuations is needed in order to get the correct composite-boson limit in the strong-coupling regime.The theory is also compared with experimental data.Finally we focus on the superfluid density in the weak-coupling, intermediate and strong-coupling regimes at finite temperature, through which the Berezinskii-Kosterlitz-Thouless critical temperature is obtained.
Abstract The physics of two-dimensional (2D) quantum gases can be revealed in strongly confining optical lattices. Upon cooling, 2D bosonic quantum gases as well as Fermi gases where pairing is present, become superfluid. The superfluid-to-normal transition is no longer governed by the presence or absence of a condensate, but by the Berezinskii–Kosterlitz–Thouless (BKT) mechanism: above a critical temperature, vortices and antivortices proliferate and destroy phase coherence. We investigate the BKT transition for superfluid 2D Fermi gases in the whole range of the BCS–BEC crossover, from weakly bound Cooper pairing (the BCS state), up to strongly bound molecules (the BEC state). Using a path-integral description, we then focus on the case of imbalanced gases: when the number of ‘spin-up’ and ‘spin-down’ fermions that form the pair is no longer equal. When an excess of one spin species exists, pairing is frustrated and the vortex energetics is strongly affected, influencing the KT mechanism. In the present work we are concentrated on the effect of both phase and amplitude fluctuations on phase diagrams of the fermion system. The amplitude fluctuations only slightly influence the BKT phase transition temperature. However, they lead to a substantial modification of the complete phase diagram for the Fermi gas in 2D with respect to that obtained taking into account only phase fluctuations.