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arXiv:2107.10391

$\mathcal{PT}$-Symmetry Enhanced Berezinskii-Kosterlitz-Thouless Superfluidity

Yunmei Li, Xi-Wang Luo, Chuanwei Zhang

Published Jul 21, 2021• 0 citations
arXivHTMLPDF

Abstract

Berezinskii-Kosterlitz-Thouless (BKT) transition, the topological phase transition to a quasi-long range order in a two-dimensional (2D) system, is a hallmark of low-dimensional topological physics. The recent emergence of non-Hermitian physics, particularly parity-time ($\mathcal{PT}$) symmetry, raises a natural question about the fate of low-dimensional orders (e.g., BKT transition) in the presence of complex energy spectrum. Here we investigate the BKT phase transition in a 2D degenerate Fermi gas with an imaginary Zeeman field obeying $\mathcal{PT}$-symmetry. Despite complex energy spectrum, $\mathcal{PT}$-symmetry guarantees that the superfluid density and many other quantities are real. Surprisingly, the imaginary Zeeman field enhances the superfluid density, yielding higher BKT transition temperature than that in Hermitian systems. In the weak interaction region, the transition temperature can be much larger than that in the strong interaction limit. Our work showcases a surprising interplay between low-dimensional topological defects and non-Hermitian effects, paving the way for studying non-Hermitian low-dimensional phase transitions.

DOI
10.48550/arxiv.2107.10391

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PT\mathcal{PT}PT-Symmetry Enhanced Berezinskii-Kosterlitz-Thouless Superfluidity
Berezinskii-Kosterlitz-Thouless (BKT) transition, the topological phase transition to a quasi-long range order in a two-dimensional (2D) system, is a hallmark of low-dimensional topological physics. The recent emergence of non-Hermitian physics, particularly parity-time (PT\mathcal{PT}PT) symmetry, raises a natural question about the fate of low-dimensional orders (e.g., BKT transition) in the presence of complex energy spectrum. Here we investigate the BKT phase transition in a 2D degenerate Fermi gas with an imaginary Zeeman field obeying PT\mathcal{PT}PT-symmetry. Despite complex energy spectrum, PT\mathcal{PT}PT-symmetry guarantees that the superfluid density and many other quantities are real. Surprisingly, the imaginary Zeeman field enhances the superfluid density, yielding higher BKT transition temperature than that in Hermitian systems. In the weak interaction region, the transition temperature can be much larger than that in the strong interaction limit. Our work showcases a surprising interplay between low-dimensional topological defects and non-Hermitian effects, paving the way for studying non-Hermitian low-dimensional phase transitions.
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The experimental observation of traditional Zeeman-field induced Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluids has been hindered by various challenges, in particular, the requirement of low dimensional systems. In 2D, finite temperature phase fluctuations lead to an extremely small Berezinskii-Kosterlitz-Thouless (BKT) transition temperature for FFLO superfluids, raising serious concerns regarding their experimental observability. Recently, it was shown that FFLO superfluids can be realized using a Rashba spin-orbit coupled Fermi gas subject to Zeeman fields, which may also support topological excitations such as Majorana fermions in 2D. Here we address the finite temperature BKT transition issue in this system, which may exhibit gapped, gapless, topological, and gapless topological FF phases. We find a large BKT transition temperature due to large effective superfluid densities, making it possible to observe 2D FF superfluids at finite temperature. In addition, we show that gapless FF superfluids can be stable due to their positive superfluid densities. These findings pave the way for the experimental observation of 2D gapped and gapless FF superfluids and their associated topological excitations at finite temperature.
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We numerically study the Berezinskii-Kosterlitz-Thouless (BKT) transition of a spin-1 spinor Bose gas under the quadratic Zeeman effect. A calculation of the mass and spin superfluid densities shows that (i) the BKT transition occurs only when vortices are classified by the integer group Z\mathbb{Z}Z, and Z2\mathbb{Z}_2Z2​ vortices do not contribute to the BKT transition, (ii) the two BKT transition temperatures for mass and spin superfluid densities are different for a positive quadratic Zeeman effect and equal for a negative quadratic Zeeman effect, and (iii) the universal relation of the superfluid densities at the BKT transition temperature is changed when multiple kinds of vortices contribute to the transition. We have further found that (iv) spin-singlet pairs in non-magnetic states show the quasi-off-diagonal-long-range order at the different temperature lower than the BKT transition temperature, giving the new universal relation of the superfluid density.
The Berezinskii-Kosterlitz-Thouless (BKT) transition is the paradigmatic example of a topological phase transition without symmetry breaking, where a quasiordered phase, characterized by a power-law scaling of the correlation functions at low temperature, is disrupted by the proliferation of topological excitations above the critical temperature T_{BKT}. In this Letter, we consider the effect of long-range decaying couplings ∼r^{-2-σ} on the BKT transition. After pointing out the relevance of this nontrivial problem, we discuss the phase diagram, which is far richer than the corresponding short-range one. It features-for 7/4<σ<2-a quasiordered phase in a finite temperature range T_{c}<T<T_{BKT}, which occurs between a symmetry broken phase for T<T_{c} and a disordered phase for T>T_{BKT}. The transition temperature T_{c} displays unique universal features quite different from those of the traditional, short-range XY model. Given the universal nature of our findings, they may be observed in current experimental realizations in 2D atomic, molecular, and optical quantum systems.
The physics in two-dimensional (2D) systems is very different from what we observe in three-dimensional (3D) systems. Thermal fluctuations in 2D systems are enhanced, and they prevent the conventional Bose-Einstein condensation (BEC) at non-zero temperatures by destroying the long-range order. However, a phase transition to a superfluid phase is still expected to occur in a 2D system along with an emergence of a quasi-long-range order, explained by the Berezinskii-Kosterlitz-Thouless (BKT) mechanism. Within the BKT mechanism, a universal jump of the superfluid density in a 2D Bosonic system was theoretically predicted by Nelson and Kosterlitz, and was first observed in 2D \textsuperscript{4}He films by Bishop and Reppy. Recent experiments in trapped ultracold 2D Bose gas systems have shown signatures of the BKT transition, and its superfluidity. However, the universal jump in the superfluid density was not observed in these systems. Here we report the first observation of the universal jump in the superfluid density using an optically trapped ultracold 2D Bose gas. The measured superfluid phase space density at the BKT transition agrees well with the predicted value within our measurement uncertainty. Additionally, we measure the phase fluctuations in our density profiles to show that the BKT transition occurs first, followed by the BEC transition.