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Journal of Physics Conference Series

Twist effects on quantum vortex defects

Matteo Foresti

Published Jan 1, 2021• 0 citations
Publisher

Abstract

Abstract We demonstrate that on a quantum vortex in Bose-Einstein condensates can form a new, central phase singularity. We define the twist phase for isophase surfaces and show that if the injection of a twist phase is global this phenomenon is given by an analog of the Aharonov-Bohm effect. We show analytically that the injection of a twist phase makes the filament unstable, that is the GP equation is modified by a new term that makes the Hamiltonian non-Hermitian. Using Kleinert’s theory for multi-valued fields we show that this instability is compensated by the creation of the second vortex, possibly linked with the first one.

DOI
10.1088/1742-6596/1730/1/012016

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Abstract We demonstrate that on a quantum vortex in Bose-Einstein condensates can form a new, central phase singularity. We define the twist phase for isophase surfaces and show that if the injection of a twist phase is global this phenomenon is given by an analog of the Aharonov-Bohm effect. We show analytically that the injection of a twist phase makes the filament unstable, that is the GP equation is modified by a new term that makes the Hamiltonian non-Hermitian. Using Kleinert’s theory for multi-valued fields we show that this instability is compensated by the creation of the second vortex, possibly linked with the first one.
In this paper, we determine the instability effects of a phase twist superposed on a quantum vortex defect governed by the Gross–Pitaevskii equation. For this, we consider the modified form of the equation in two cases: when a uniform phase twist is present everywhere in the condensate, and when the defect is subject to a localized phase twist confined to the defect healing region. In the first case, we show that a secondary, new defect is produced as manifestation of an Aharonov–Bohm type effect. In the second case, we prove that due to energy minimization, the defect changes its configurational energy by converting localized twist to writhe. This mechanism, typical of classical elastic systems, is shown to occur also in quantum defects, and it may find useful applications in science and technology.
In this paper we demonstrate that new phase defects of the Gross-Pitaevskii equation (GPE) can be produced as a Aharonov-Bohm effect resulting from pure phase twist injection on existing defects. This is a phenomenon that has physical justification in the hydrodynamic interpretation of GPE. Here we give an analytical proof of its effects by using Fermi-Walker transport and Biot-Savart induction law. An analytical derivation of the dispersion relation is derived from the superposition of phase twist on the fundamental state. Since the extra twist corresponds to a topological change of the total linking number of the system, we show that the production of new defects is just another manifestation of the Aharonov-Bohm effect. We propose a laboratory experiment for Bose-Einstein condensates to test this phenomenon and to show that it can have useful applications in science and technology.
Abstract In this paper we show that twist, defined in terms of rotation of the phase associated with quantum vortices and other physical defects effectively deprived of internal structure, is a property that has observable effects in terms of induced axial flow. For this we consider quantum vortices governed by the Gross–Pitaevskii equation (GPE) and perform a number of test cases to investigate and compare the effects of twist in two different contexts: (i) when this is artificially superimposed on an initially untwisted vortex ring; (ii) when it is naturally produced on the ring by the simultaneous presence of a central straight vortex. In the first case large amplitude perturbations quickly develop, generated by the unnatural setting of the initial condition that is not an analytical solution of the GPE. In the second case much milder perturbations emerge, signature of a genuine physical process. This scenario is confirmed by other test cases performed at higher twist values. Since the second setting corresponds to essential linking, these results provide new evidence of the influence of topology on physics.
The non-local nonlinearity introduced by the dipole–dipole interaction plays a crucial role in the physics of dipolar Bose–Einstein condensates. In particular, it may distort significantly the stability of straight vortex lines due to the rotonization of the Kelvin-wave spectrum. In the present paper, we analyze this instability, showing that it leads to a second-order-like phase transition from a straight vortex line into novel helical or snake-like configurations, depending on the dipole orientation.
The Bogoliubov-de Gennes equations are used for a number of theoretical works to describe quantum and thermal fluctuations of trapped Bose-Einstein condensates. We consider the case in which the condensate has a highly quantized vortex. It is known that these equations have complex eigenvalues in this case. We give the complete set including a pair of complex modes whose eigenvalues are complex conjugates to each other. The expansion of the quantum fields which represent neutral atoms in terms of the complete set brings the operators associated with the complex modes, which are simply neither bosonic nor fermionic ones. The eigenstate of the Hamiltonian is given. Introducing the notion of the physical states, we discuss the instability of the condensates in the context of Kubo’s linear response theory.