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arXiv:2404.05460 · Physical Review Letters

Thermal Melting of a Vortex Lattice in a Quasi-Two-Dimensional Bose Gas

Rishabh Sharma, David Rey, Laurent Longchambon, A. Perrin, Hélène Perrin, Romain Dubessy

Published Sep 30, 2024• 13 citations
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Abstract

We report the observation of the melting of a vortex lattice in a fast rotating quasi-two dimensional Bose gas, under the influence of thermal fluctuations. We image the vortex lattice after a time-of-flight expansion, for increasing rotation frequency at constant atom number and temperature. We detect the vortex positions and study the order of the lattice using the pair correlation function and the orientational correlation function. We evidence the melting transition by a change in the decay of orientational correlations, associated with a proliferation of dislocations. Our findings are consistent with the hexatic to liquid transition in the Kosterlitz, Thouless, Halperin, Nelson, and Young scenario for two-dimensional melting.

DOI
10.1103/physrevlett.133.143401

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We report the observation of the melting of a vortex lattice in a fast rotating quasi-two dimensional Bose gas, under the influence of thermal fluctuations. We image the vortex lattice after a time-of-flight expansion, for increasing rotation frequency at constant atom number and temperature. We detect the vortex positions and study the order of the lattice using the pair correlation function and the orientational correlation function. We evidence the melting transition by a change in the decay of orientational correlations, associated with a proliferation of dislocations. Our findings are consistent with the hexatic to liquid transition in the Kosterlitz, Thouless, Halperin, Nelson, and Young scenario for two-dimensional melting.
Abstract We present a classical field simulation study of the thermal melting of a two-dimensional (2D) vortex lattice in a rotating Bose gas, focusing on the role of finite-size effects on the melting temperature. This work constitutes a numerical continuation of the recent experimental investigation reported in (Sharma 2024 Phys. Rev. Lett. 133 143401), which addressed the thermal melting of a vortex lattice in a quasi-2D Bose gas. Using the stochastic projected Gross–Pitaevskii equation in a harmonic plus quartic trap, we simulate the finite-temperature equilibrium state and extract vortex configurations from density snapshots. Clear signatures of the two-step Kosterlitz–Thouless–Halperin–Nelson–Young melting scenario are identified. Our simulations enable a detailed characterization of the crystalline, hexatic, and liquid phases through correlation functions quantifying the translational and orientational order and through defect statistics. Finite-size effects are shown to play a crucial role at lower rotation frequencies, affecting the proliferation of lattice defects.
We present a classical field simulation study of the thermal melting of a two-dimensional vortex lattice in a rotating Bose gas, focusing on the role of finite-size effects on the melting temperature. This work constitutes a numerical continuation of the recent experimental investigation reported in [Physical Review Letters 133, 143401 (2024)], which addressed the thermal melting of a vortex lattice in a quasi-two-dimensional Bose gas. Using the stochastic projected Gross-Pitaevskii equation in a harmonic plus quartic trap, we simulate the finite-temperature equilibrium state and extract vortex configurations from density snapshots. Clear signatures of the two-step Kosterlitz--Thouless--Halperin--Nelson--Young melting scenario are identified. Our simulations enable a detailed characterization of the crystalline, hexatic, and liquid phases through correlation functions quantifying the translational and orientational order and through defect statistics. Finite-size effects are shown to play a crucial role at lower rotation frequencies, affecting the proliferation of lattice defects.
We describe thermal melting of the two-dimensional vortex lattice in a rotating superfluid by generalizing the Halperin and Nelson theory of dislocation-mediated melting and derive a melting temperature proportional to the renormalized shear modulus of the vortex lattice. The rigid-body rotation of the superfluid attenuates the effects of lattice compression on the energy of dislocations and hence the melting temperature, while not affecting the shearing. Finally, we discuss dislocations and thermal melting in inhomogeneous rapidly rotating Bose-Einstein condensates; we delineate a phase diagram in the temperature--rotation rate plane, and infer that the thermal melting temperature should lie below the Bose-Einstein transition temperature.
We study the thermal fluctuations of vortex positions in small vortex clusters in a harmonically trapped rotating Bose-Einstein condensate. It is shown that the order-disorder transition of two-shell clusters occurs via the decoupling of shells with respect to each other. The corresponding ``melting'' temperature depends strongly on the commensurability between numbers of vortices in shells. We show that melting can be achieved at experimentally attainable parameters and very low temperatures. Also studied is the effect of thermal fluctuations on vortices in an anisotropic trap with small quadrupole deformation. We show that thermal fluctuations lead to the decoupling of a vortex cluster from the pinning potential produced by this deformation. The decoupling temperatures are estimated and strong commensurability effects are revealed.
We investigate a shift in the critical temperature of rotating Bose-Einstein condensates mediated by the melting of the vortex lattice. Numerical simulations reveal that this temperature exhibits contrasting behavior depending on the system configuration: a negative shift occurs for fixed trap potentials due to the expansion of the condensate, while a positive shift is observed for fixed volumes, where vortex-lattice rigidity suppresses thermal fluctuations. We introduce a vortex-energy model that captures the role of vortex interactions, the positional energy of the vortex lattice, as well as the phase transition and how the vortex lattice disappears. The findings provide insights into the thermodynamic properties of rotating condensates and the dynamics of vortex-lattice melting, offering potential parallels with other quantum systems such as type-II superconductors.
We discuss the feasibility of quantum Hall states of vortices in trapped low-density two-dimensional Bose gases with large particle interactions. For interaction strengths larger than a critical dimensionless 2D coupling constant g c ≈ 0.6, upon increasing the rotation frequency, the system is shown to spatially separate into vortex lattice and melted vortex lattice (vortex liquid) phases. At a first critical frequency, the lattice melts completely, and strongly correlated vortex and particle quantum Hall liquids coexist in inner and outer regions of the gas cloud, respectively. Finally, at a second critical frequency, the vortex liquid disappears and the strongly correlated particle quantum Hall state fills the whole sample.