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Journal of Physics B Atomic Molecular and Optical Physics

Impurity-induced vortex lattice melting and turbulence in rotating Bose–Einstein condensates

Rony Boral, Swarup K. Sarkar, Paulsamy Muruganandam, Pankaj Kumar Mishra

Published Nov 28, 2024• 0 citations
Publisher

Abstract

Abstract We numerically investigate the impact of various impurities on rotating Bose–Einstein condensates confined within two-dimensional harmonic and Gaussian distributed square lattice potentials. Without impurities, the rotating condensates display an organized square lattice pattern of vortices due to the influence of Gaussian distributed square lattice potential. The introduction of impurity potentials disrupts this lattice structure, inducing a phase transition from an ordered state to a disordered state. Our analysis encompasses both static and dynamic types of impurities. The static impurities are implemented using a randomly varying potential with a spatially random amplitude. The transformation of the vortex lattice structure, in this case, relies on the strength and lattice constant of the impurity potential. For dynamical impurities, we employ a Gaussian obstacle that orbits around the condensate at a specific distance from its center. In this scenario, the vortex lattice melting occurs beyond a certain threshold radius and frequency of oscillation of the rotating obstacle. We characterize the melting of the vortex lattice due to impurities using various quantities, such as the structure factor and angular momentum. Notably, in the vortex-melted state, the angular momentum follows a power-law dependence with an exponent of approximately 1.73, regardless of the type of impurity. Finally, we demonstrate the signature of the presence of a turbulent state within the vortex-melted state generated by both static and dynamical impurities.

DOI
10.1088/1361-6455/ad987c

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Abstract We numerically investigate the impact of various impurities on rotating Bose–Einstein condensates confined within two-dimensional harmonic and Gaussian distributed square lattice potentials. Without impurities, the rotating condensates display an organized square lattice pattern of vortices due to the influence of Gaussian distributed square lattice potential. The introduction of impurity potentials disrupts this lattice structure, inducing a phase transition from an ordered state to a disordered state. Our analysis encompasses both static and dynamic types of impurities. The static impurities are implemented using a randomly varying potential with a spatially random amplitude. The transformation of the vortex lattice structure, in this case, relies on the strength and lattice constant of the impurity potential. For dynamical impurities, we employ a Gaussian obstacle that orbits around the condensate at a specific distance from its center. In this scenario, the vortex lattice melting occurs beyond a certain threshold radius and frequency of oscillation of the rotating obstacle. We characterize the melting of the vortex lattice due to impurities using various quantities, such as the structure factor and angular momentum. Notably, in the vortex-melted state, the angular momentum follows a power-law dependence with an exponent of approximately 1.73, regardless of the type of impurity. Finally, we demonstrate the signature of the presence of a turbulent state within the vortex-melted state generated by both static and dynamical impurities.
We investigate the impact of various impurities on rotating Bose-Einstein condensates confined within two-dimensional harmonic and optical lattice potentials. Without impurities, the rotating condensates display an organized square lattice pattern of vortices due to the influence of a square optical lattice. The introduction of impurity potentials disrupts this lattice structure, inducing a phase transition from an ordered state to a disordered state. Our analysis encompasses both static and dynamic types of impurities. The static impurities are implemented using a randomly varying potential with a spatially random amplitude. The transformation of the vortex lattice structure, in this case, relies on the strength and lattice constant of the impurity potential. For dynamical impurities, we employ a Gaussian obstacle that orbits around the condensate at a specific distance from its center. In this scenario, the vortex lattice melting occurs beyond a certain threshold radius and frequency of oscillation of the rotating obstacle. We characterize the melting of the vortex lattice due to impurities using various quantities, such as the structure factor and angular momentum. Notably, in the vortex-melted state, the angular momentum follows a power-law dependence with an exponent of approximately 1.731.731.73, regardless of the type of impurity. Finally, we demonstrate the signature of the presence of a turbulent state within the vortex-melted state generated by both static and dynamical impurities.
We study the vortex pinning effect on the vortex lattice structure of the rotating two-component Bose-Einstein condensates (BECs) in the presence of impurities or disorder by numerically solving the time-dependent coupled Gross-Pitaevskii equations. We investigate the transition of the vortex lattice structures by changing conditions such as angular frequency, the strength of the inter-component interaction and pinning potential, and the lattice constant of the periodic pinning potential. We show that even a single impurity pinning potential can change the unpinned vortex lattice structure from triangular to square or from triangular to a structure which is the overlap of triangular and square. In the presence of a periodic pinning potential or optical lattice, we observe the structural transition from the unpinned vortex lattice to the pinned vortex lattice structure of the optical lattice. In the presence of a random pinning potential or disorder, the vortex lattice melts following a two-step process by creation of lattice defects, dislocations, and disclinations, with the increase of rotational frequency, similar to that observed for single-component Bose-Einstein condensates. However, for the binary BECs, we show that the two-step vortex lattice melting also occurs with increasing strength of the intercomponent interaction.
We simulate a rotating 2D BEC to study the melting of a vortex lattice in the presence of random impurities. Impurities are introduced either through a protocol in which vortex lattice is produced in an impurity potential or first creating the vortex lattice in the absence of random pinning and then cranking up the (co-rotating) impurity potential. We find that for a fixed strength, pinning of vortices at randomly distributed impurities leads to the new states of the vortex lattice. It is unearthed that the vortex lattice follows a two-step melting via loss of positional and orientational order. Also, the comparisons between the states obtained in two protocols show that the vortex lattice states are metastable states when impurities are introduced after the formation of an ordered vortex lattice. We also show that the existence of metastable states depends on the history of how the vortex lattice is created.
We study the vortex lattice dynamics in the presence of a single impurity as well as random impurities or disorder. We show that in the presence of a single impurity, the vortex lattice gets distorted and the distortion depends on the position of the single impurity with respect to the positions of the vortices in the impurity-free Abrikosov vortex lattice and also on the strength of the impurity potential. We then show that a type of giant hole with hidden vortices inside it can be created in the vortex lattice by a cluster of impurities. In the presence of random impurity potential or disorder, the vortex lattice melts. We show that the vortex lattice also melts in the presence of the pseudorandom potential generated by the superposition of two optical lattices. The absence of long-range order in the melted vortex lattice is demonstrated from the structure factor profile and the histogram of the distances between each pair of vortices.
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.
Abstract Using exact diagonalization, we investigate the many-body ground state for regular vortex patterns in a rotating Bose-condensed gas of N spinless particles, confined in a quasi-two-dimensional harmonic trap and interacting repulsively via finite-range Gaussian potential. The N -body Hamiltonian matrix is diagonalized in given subspaces of quantized total angular momentum L z , to obtain the lowest-energy eigenstate. Further, the internal structure of these eigenstates is analyzed by calculating the corresponding conditional probability distribution. Specifically, the quantum mechanically stable as well as unstable states in a co-rotating frame are examined in the moderately rotating regime corresponding to angular momenta 4 N ≤ L z < 5 N for N = 16 bosons. In response to externally impressed rotation, the patterns of singly quantized vortices are formed, shaping into canonical polygons with a central vortex at the trap center. The internal structure of unstable states reveals the mechanism of entry, nucleation and pattern formation of vortices with structural phase transition, as the condensate goes from one stable vortical state to the other. The stable polygonal vortex patterns having discrete p -fold rotational symmetry with p = 5 and p = 6 are observed. The hexagonal vortex pattern with p = 6 symmetry is a precursor to the triangular vortex lattice of singly quantized vortices in the thermodynamic limit. For unstable states, quantum melting of vortex patterns due to uncertainty in positions of individual vortices, is also briefly discussed.