We investigate the properties of a two-dimensional \emph{spinor} microcavity polariton system driven by a linearly polarised continuous pump. In particular, we establish the role of the elementary excitations, namely the so-called half-vortices and full-vortices; these objects carry a quantum rotation only in one of the two, or both, spin components respectively. Our numerical analysis of the steady-state shows that it is only the half-vortices that are present in the vortex-antivortex pairing/dissociation responsible for the Berezinskii-Kosterlitz-Thouless transition. These are the relevant elementary excitations close to the critical point. However, by exploring the phase-ordering dynamics following a sudden quench across the transition we prove that full-vortices become the relevant excitations away from the critical point in a deep quasi-ordered state at late times. The time-scales for half-vortices binding into full vortices are much faster than the vortex-antivortex annihilations.
We study the 2d phase transition of a driven-dissipative system of exciton-polaritons under non-resonant pumping. Stochastic calculations are used to investigate the Berezinskii-Kosterlitz-Thouless-like phase diagram for experimentally realistic parameters, with a special attention to the non-equilibrium features.
A system of two dimensional photon gas has recently been realized experimentally. It is pointed out that this setup can be used to observe a universal breathing mode of photon gas. It is shown that a modification in the experimental setup would open up a possibility of observing the Berezinskii-Kosterlitz-Thouless (BKT) phase transition in such a system. It is shown that the universal jump in the superfluid density of light in the output channel can be used as an unambiguous signature for the experimental verification of the BKT transition.
We analyse the Bose-Einstein condensation process and the Berezinskii-Kosterlitz-Thouless phase transition within the Gross-Pitaevskii model and their interplay with wave turbulence theory. By using numerical experiments we study how the condensate fraction and the first order correlation function behave with respect to the mass, the energy and the size of the system. By relating the free-particle energy to the temperature we are able to estimate the Berezinskii-Kousterlitz-Thouless transition temperature. Below this transition we observe that for a fixed temperature the superfluid fraction ap…
We study the Berezinskii-Kosterlitz-Thouless transition of two-dimensional Bose gases in a synthetic magnetic field using the standard Metropolis Monte Carlo method. The system is described by the frustrated XY model and the critical temperature is calculated though the absence of central peak of the wave function in momentum space, which can be directly measured by the time-of-flight absorbing imaging in cold atoms experiments. The results of our work show agreement with former studies on superconducting Josephson arrays.
We observe quasi-long range coherence in a two-dimensional condensate of exciton-polaritons. Our measurements are the first to confirm that the spatial correlation algebraically decays with a slow power-law, whose exponent quantitatively behaves as predicted by the Berezinskii-Kosterlitz-Thouless theory. The exciton-polaritons are created by non-resonant optical pumping of a micro-cavity sample with embedded GaAs quantum-wells at liquid helium temperature. Michelson interference is used to measure the coherence of the photons emitted by decaying exciton-polaritons.
We show that quasi-one dimensional Bose-Einstein condensate under suitable conditions can exhibit a Berezinskii-Kosterlitz-Thouless phase transition. The role played by quantized vortices in two dimensional case, is played in this case by dark solitons. We find that the critical temperature for this transition lies in nano Kelvin range and below, for a wide range of experimentally accessible parameters. It is seen that the high temperature (disordered) phase differs from low temperature (ordered) phase in terms of phase coherence, which can be used as an experimental signature for observing th…
We calculate the temperature dependence of the first and second sound velocities in the superfluid phase of a 2D dilute Bose gas by solving Landau's two fluid hydrodynamic equations. We predict the occurrence of a significant discontinuity in both velocities at the critical temperature, as a consequence of the jump of the superfluid density characterizing the Berezinskii-Kosterlitz-Thouless transition. The key role of the thermal expansion coefficient is discussed. We find that second sound in this dilute Bose gas can be easily excited through a density perturbation, thereby, making the perspe…
We investigate single-particle excitations and strong-coupling effects in a two-dimensional Fermi gas. Including pairing fluctuations within a Gaussian fluctuation theory, we calculate the density of states $ρ(ω)$ near the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature $T_{\rm BKT}$. Near $T_{\rm BKT}$, we show that superfluid fluctuations induce a pseudogap in $ρ(ω)$. The pseudogap structure is very similar to the BCS superfluid density of states, although the superfluid order parameter is absent in the present two-dimensional case. Since a two-dimensional $^{40}$K Fermi gas has…
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-norma…
Assuming that two-component Fermi gases with opposite artificial magnetic fields on a square optical lattice are well-described by the so-called time-reversal-symmetric Hofstadter-Hubbard model, we explore the thermal superfluid properties along with the critical Berezinskii-Kosterlitz-Thouless (BKT) transition temperature in this model over a wide-range of its parameters. In particular, since our self-consistent BCS-BKT approach takes the multi-band butterfly spectrum explicitly into account, it unveils how dramatically the inter-band contribution to the phase stiffness dominates the intra-ba…
We theoretically study the sound propagation in a two-dimensional weakly interacting uniform Bose gas. Using the classical fields approximation we analyze in detail the properties of density waves generated both in a weak and strong perturbation regimes. While in the former case density excitations can be described in terms of hydrodynamic or collisionless sound, the strong disturbance of the system results in a qualitatively different response. We identify observed structures as quasisolitons and uncover their internal complexity for strong perturbation case. For this regime quasisolitons bre…
We study the critical point for the emergence of coherence in a harmonically trapped two-dimensional Bose gas with tuneable interactions. Over a wide range of interaction strengths we find excellent agreement with the classical-field predictions for the critical point of the Berezinskii-Kosterlitz-Thouless (BKT) superfluid transition. This allows us to quantitatively show, without any free parameters, that the interaction-driven BKT transition smoothly converges onto the purely quantum-statistical Bose-Einstein condensation (BEC) transition in the limit of vanishing interactions.
The superfluid to normal fluid transition of dipolar bosons in two dimensions is studied throughout the whole density range using path integral Monte Carlo simulations and summarized in the phase diagram. While at low densities, we find good agreement with the universal results depending only on the scattering length $a_s$, at moderate and high densities, the transition temperature is strongly affected by interactions and the elementary excitation spectrum. The results are expected to be of relevance to dipolar atomic and molecular systems and indirect excitons in quantum wells.
We investigate the general features of the renormalization-group flow at the Berezinskii-Kosterlitz-Thouless (BKT) transition, providing a thorough quantitative description of the asymptotc critical behavior, including the multiplicative and subleading logarithmic corrections. For this purpose, we consider the RG flow of the sine-Gordon model around the renormalizable point which describes the BKT transition. We reduce the corresponding beta-functions to a universal canonical form, valid to all perturbative orders. Then, we determine the asymptotic solutions of the RG equations in various crit…
We perform large-scale, numerically exact calculations on the two-dimensional interacting Fermi gas with a contact attraction. Reaching much larger lattice sizes and lower temperatures than previously possible, we determine systematically the finite-temperature phase diagram of the Berezinskii-Kosterlitz-Thouless (BKT) transitions for interaction strengths ranging from BCS to crossover to BEC regimes. The evolutions of the pairing wavefunctions and the fermion and Cooper pair momentum distributions with temperature are accurately characterized. In the crossover regime, we find that the contact…
The quenched dynamics of an ultracold homogeneous atomic two-dimensional Bose gas subjected to periodic quenches across the Berezinskii-Kosterlitz-Thouless (BKT) phase transition are discussed. Specifically, we address the effect of periodic cycling of the effective atomic interaction strength between a thermal disordered state above, and a highly ordered state below the critical BKT interaction strength, by means of numerical simulations of the stochastic projected Gross-Pitaevskii equation. Probing the emerging dynamics as a function of the frequency of sinusoidal driving from low to high fr…
We study the one-dimensional Bose-Hubbard model describing the superfluid-Mott insulator quantum phase transition of cold atoms in optical lattices. We show that derivatives of the variance of the on-site atom number occupation, computed with respect to the parameter driving the transition, have extrema that are located off the critical point even in the thermodynamic limit. We discuss whether such extrema provide solid evidence of the quantum Berezinskii-Kosterlitz-Thouless transition taking place in this system. The calculations are done for systems with the mean number of atoms per lattice …
We theoretically investigate first and second sound of a two-dimensional (2D) atomic Bose gas in harmonic traps by solving Landau's two-fluid hydrodynamic equations. For an isotropic trap, we find that first and second sound modes become degenerate at certain temperatures and exhibit typical avoided crossings in mode frequencies. At these temperatures, second sound has significant density fluctuation due to its hybridization with first sound and has a divergent mode frequency towards the Berezinskii-Kosterlitz-Thouless (BKT) transition. For a highly anisotropic trap, we derive the simplified o…
We study the superfluid properties of two-dimensional spin-population-imbalanced Fermi gases to explore the interplay between the Berezinskii-Kosterlitz-Thouless (BKT) phase transition and the possible instability towards the Fulde-Ferrell (FF) state. By the mean-field approximation together with quantum fluctuations, we obtain phase diagrams as functions of temperature, chemical potential imbalance and binding energy. We find that the fluctuations change the mean-field phase diagram significantly. We also address possible effects of the phase separation and/or the anisotropic FF phase to the …
We study the superfluid weight $D^s$ and Berezinskii-Kosterlitz-Thouless (BKT) transition temperatures $T_{BKT}$ in case of exotic Fulde-Ferrell (FF) superfluid states in lattice systems. We consider spin-imbalanced systems with and without spin-orbit coupling (SOC) accompanied with in-plane Zeeman field. By applying mean-field theory, we derive general equations for $D^s$ and $T_{BKT}$ in the presence of SOC and the Zeeman fields for 2D Fermi-Hubbard lattice models, and apply our results to a 2D square lattice. We show that conventional spin-imbalanced FF states without SOC can be observed at…
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 spectru…
We study Fermi gases in two dimensions at low temperatures with attractive interactions. Analytical results are derived for the equation of state and the Kosterlitz-Thouless transition temperature as functions of the two-body binding energy and the density of the gas. Our results for the equation of state strongly deviate from the mean field predictions. However, they are in reasonable agreement with Monte-Carlo calculations and recent experiments with cold atomic gases.
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 $\mathbb{Z}$, and $\mathbb{Z}_2$ 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 super…
In a recent article [R. Bombin, F. Mazzanti and J. Boronat, Phys. Rev. A100, 063614 (2019)], it is contended that a two-dimensional system of dipolar bosons, with dipole moments aligned at particular angles with respect to the direction perpendicular to the plane of motion, featuring a "striped" crystalline ground state, in turn undergoes a Berezinskii-Kosterlitz-Thouless superfluid transition at low temperature, making it a two-dimensional supersolid. We show here that the results provided therein, obtained by means of Quantum Monte Carlo simulations, do not actually support such a conclusion…
A two-dimensional quantum system of dipoles, with a polarization angle not perpendicular to the plane, shows a transition from a gas to a stripe phase. We have studied the thermal properties of these two phases using the path integral Monte Carlo (PIMC) method. By simulating the thermal density matrix, PIMC provides exact results for magnitudes of interest such as the superfluid fraction and the one-body density matrix. As it is well known, in two dimensions the superfluid-to-normal phase transition follows the Berezinskii-Kosterlitz-Thouless (BKT) scenario. Our results show that both the anis…
The detection of phase transitions in quantum many-body systems with lowest possible prior knowledge of their details is among the most rousing goals of the flourishing application of machine-learning techniques to physical questions. Here, we train a Generative Adversarial Network (GAN) with the Entanglement Spectrum of a system bipartition, as extracted by means of Matrix Product States ansätze. We are able to identify gapless-to-gapped phase transitions in different one-dimensional models by looking at the machine inability to reconstruct outsider data with respect to the training set. We f…
We study the universal critical behavior of two-dimensional (2D) lattice bosonic gases at the Berezinskii-Kosterlitz-Thouless (BKT) transition, which separates the low-temperature superfluid phase from the high-temperature normal phase. For this purpose, we perform quantum Monte Carlo simulations of the hard-core Bose-Hubbard (BH) model at zero chemical potential. We determine the critical temperature by using a matching method that relates finite-size data for the BH model with corresponding data computed in the classical XY model. In this approach, the neglected scaling corrections decay as …
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 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 topologi…
The Berezinskii-Kosterlitz-Thouless mechanism, in which a phase transition is mediated by the proliferation of topological defects, governs the critical behaviour of a wide range of equilibrium two-dimensional systems with a continuous symmetry, ranging from superconducting thin films to two-dimensional Bose fluids, such as liquid helium and ultracold atoms. We show here that this phenomenon is not restricted to thermal equilibrium, rather it survives more generally in a dissipative highly non-equilibrium system driven into a steady-state. By considering a light-matter superfluid of polaritons…
We discuss the d=2 quantum O(2)xO(2) nonlinear sigma model as a low-energy theory of phase reconstruction near a quantum critical point. We first examine the evolution of the Berezinskii-Kosterlitz-Thouless (BKT) transition as the quantum limit is approached in the usual O(2) nonlinear sigma model. Then we go on to review results on the ground-state phase diagram of the O(2)xO(2) nonlinear sigma model, and on the behaviour of the O(2)xO(M) nonlinear sigma model with M>2 in the classical limit. Finally, we present a conjectured finite-temperature phase diagram for the quantum version of the lat…
We study the dynamical evolution of a two-dimensional Bose gas after a disorder potential quench. Depending on the initial conditions, the system evolves either to a thermal or a superfluid state. Using extensive quasi-exact numerical simulations, we show that the two phases are separated by a Kosterlitz-Thouless transition. The thermalization time is shown to be longer in the superfluid phase, but no critical slowing down is observed at the transition. The long-time phase diagram is well reproduced by a simple theoretical model. The spontaneous emergence of Kosterlitz-Thouless transitions fol…
We experimentally investigate the first-order correlation function of a trapped Fermi gas in the two-dimensional BEC-BCS crossover. We observe a transition to a low-temperature superfluid phase with algebraically decaying correlations. We show that the spatial coherence of the entire trapped system can be characterized by a single temperature-dependent exponent. We find the exponent at the transition to be constant over a wide range of interaction strengths across the crossover. This suggests that the phase transitions in both the bosonic regime and the strongly interacting crossover regime ar…
We propose a realistic experiment to demonstrate a dynamic Kosterlitz-Thouless transition in ultra-cold atomic gases in two dimensions. With a numerical implementation of the Truncated Wigner Approximation we simulate the time evolution of several correlation functions, which can be measured via matter wave interference. We demonstrate that the relaxational dynamics is well-described by a real-time renormalization group approach, and argue that these experiments can guide the development of a theoretical framework for the understanding of critical dynamics.
We investigate strong-coupling properties of a two-dimensional ultracold Fermi gas in the normal state. Including pairing fluctuations within the framework of a $T$-matrix approximation, we calculate the distribution function $n({\boldsymbol Q})$ of Cooper pairs in terms of the center of mass momentum ${\boldsymbol Q}$. In the strong-coupling regime, $n({\boldsymbol Q}=0)$ is shown to exhibit a remarkable increase with decreasing the temperature in the low temperature region, which agrees well with the recent experiment on a two-dimensional $^6$Li Fermi gas [M. G. Ries, {\it et. al.}, Phys. Re…
This is a Reply to the Comment from F. Cinti and M. Boninsegni on our recent work on the Berezinskii-Kosterlitz-Thouless (BKT) phase transition in a two-dimensional dipolar system [R.Bombín, F. Mazzanti and J. Boronat, Physical Review A 100, 063614 (2019)]. The main criticism about our work, expressed in that Comment, is that we did not explicitly report the two spatial contributions to the total superfluid fraction. Here, we analyze our results for a point of the phase diagram corresponding to the stripe phase, close to the gas to stripe transition line, and for a temperature below the BKT cr…
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 wa…
