The fundamental mode of rotation in quantum fluids is given by a vortex whose quantized value yields the orbital angular momentum (OAM) per particle. If the vortex is displaced (off-centered) from the reference point for rotation, the angular momentum is reduced and becomes fractional. Such displaced vortices can further exhibit a peculiar dynamics in the presence of confining potentials or couplings to other fields. We study analytically a number of 2D systems where displaced vortices exhibit a noteworthy dynamics, including time-varying self-sustained oscillation of the OAM, complex reshaping of their morphology with possible creation of vortex–antivortex pairs, and peculiar trajectories for the vortex core with sequences of strong accelerations and decelerations that can even send the core to infinity and bring it back. Interestingly, these do not have to occur conjointly, with complex time dynamics of the vortex core and/or their wavepacket morphology possibly taking place without affecting the total OAM. Our results generalize to simple and fundamental systems a phenomenology recently reported with Rabi-coupled bosonic fields, showing their wider relevance and opening prospects for new types of control and structuring of the angular momentum of light and/or quantum fluids.
The fundamental mode of rotation in quantum fluids is given by a vortex whose quantized value yields the orbital angular momentum (OAM) per particle. If the vortex is displaced (off-centered) from the reference point for rotation, the angular momentum is reduced and becomes fractional. Such displaced vortices can further exhibit a peculiar dynamics in the presence of confining potentials or couplings to other fields. We study analytically a number of 2D systems where displaced vortices exhibit a noteworthy dynamics, including time-varying self-sustained oscillation of the OAM, complex reshaping of their morphology with possible creation of vortex–antivortex pairs, and peculiar trajectories for the vortex core with sequences of strong accelerations and decelerations that can even send the core to infinity and bring it back. Interestingly, these do not have to occur conjointly, with complex time dynamics of the vortex core and/or their wavepacket morphology possibly taking place without affecting the total OAM. Our results generalize to simple and fundamental systems a phenomenology recently reported with Rabi-coupled bosonic fields, showing their wider relevance and opening prospects for new types of control and structuring of the angular momentum of light and/or quantum fluids.
The extension of quantum phenomena into macroscopic scales is responsible for a whole class of effects such as superconductivity, superfluidity, and Bose-Einstein condensation, which played central roles in physics throughout the last century.The production of the first Bose-Einstein condensates made possible the realization of experiments involving macroscopic quantum phenomena with an unprecedented level of control of the external parameters.The persistent currents in condensates are intimately related to the nucleation of quantized vortices, which are topological defects as response to transference of quanta of angular momentum.A conventional method for generation of such defects consists in confining the condensed atomic cloud into a rotating trap.It turns out that, for angular velocities higher than a critical value, vortex states become energetically favorable, thus inducing the creation of quantized vortices.Experimental realizations of condensed alkali-metal atoms confined by more general time-dependent potentials allowed the observation not only of vortex lattices but also of quantum turbulence.Since quantum turbulence is characterized by the presence of a self-interacting tangle of quantized vortices, the correct understanding of dynamics, formation, and stability of vortices has shown to be of paramount importance being the subject of many theoretical works.In particular, the role of acoustic excitations generated by decaying multi-charged vortices in the development of turbulence is still an open question.This work aims to provide a set of tools that helps to identify the presence as well as the charge of vortices in non-turbulent clouds observed using time-of-flight pictures.We have done a detailed study of condensates containing multi-charged vortices placed at its center where time-of-flight dynamics is only one point of our interest.Due to the control that this system provides experimentally, the collective modes become an important description since they can be excited using well stablished experimental methods as such as modulation of the s-wave scattering length, and they can also be responsible to vortex decaying.For such purposes we have used the semi-analytical variational method, and the fully numerical calculation of Gross-Pitaevskii equation.Thus we have describes the collective modes that couples dynamics of vortex with the oscillation of external components of condensed atomic cloud as well as the effects in time-of-flight.The angular momentum acts increasing the kinetic energy around the vortex core, which results in a faster expansion of perpendicular direction to it.This situation shifts the frequencies of collective oscillations of a vortex-free state, and generates richer collective modes due the coupling.Now there are four possible modes, being two types of monopole mode and two types of quadrupole modes.The difference among these types is the phase of vortex oscillation.When one considers fluctuations without polar symmetry, their collective modes result in the vortex decaying.In order to control and prevent these processes we have proposed three dynamical mechanisms such as modulation of s-wave scattering length, modulation of frequencies of harmonic trap, and modulation of the amplitude of Laguerre-Gauss potential.The last one has proven to be more effective.
Spin-orbital-angular-momentum (SOAM) coupling has been realized in recent experiments of Bose-Einstein condensates [Chen et al., Phys. Rev. Lett. 121, 113204 (2018)PRLTAO0031-900710.1103/PhysRevLett.121.113204 and Zhang et al., Phys. Rev. Lett. 122, 110402 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.110402], where the orbital angular momentum imprinted upon bosons leads to quantized vortices. For fermions, such an exotic synthetic gauge field can provide fertile ground for fascinating pairing schemes and rich superfluid phases, which are yet to be explored. Here we demonstrate how SOAM coupling stabilizes vortices in Fermi superfluids through a unique mechanism that can be viewed as the angular analog to that of the spin-orbit-coupling-induced Fulde-Ferrell state under a Fermi surface deformation. Remarkably, the vortex size is comparable with the beam waist of Raman lasers generating the SOAM coupling, which is typically much larger than previously observed vortices in Fermi superfluids. With tunable size and core structure, these giant vortex states provide unprecedented experimental access to topological defects in Fermi superfluids.
Methods to generate, manipulate, and measure optical and atomic fields with global or local angular momentum have a wide range of applications in both fundamental physics research and technology development. In optics, the engineering of angular momentum states of light can aid studies of orbital angular momentum (OAM) exchange between light and matter. The engineering of optical angular momentum states can also be used to increase the bandwidth of optical communications or serve as a means to distribute quantum keys, for example. Similar capabilities in Bose-Einstein condensates are being investigated to improve our understanding of superfluid dynamics, superconductivity, and turbulence, the last of which is widely considered to be one of most ubiquitous yet poorly understood subjects in physics. The first part of this two-part dissertation presents an analysis of techniques for measuring and manipulating quantized vortices in BECs. The second part of this dissertation presents theoretical and numerical analyses of new methods to engineer the OAM spectra of optical beams. The superfluid dynamics of a BEC are often well described by a nonlinear Schrodinger equation. The nonlinearity arises from interatomic scattering and enables BECs to support quantized vortices, which have quantized circulation and are fundamental structural elements of quantum turbulence. With the experimental tools to dynamically manipulate and measure quantized vortices, BECs are proving to be a useful medium for testing the theoretical predictions of quantum turbulence. In this dissertation we analyze a method for making minimally destructive in situ observations of quantized vortices in a BEC. Secondly, we numerically study a mechanism to imprint vortex dipoles in a BEC. With these advancements, more robust experiments of vortex dynamics and quantum turbulence will be within reach. A more complete understanding of quantum turbulence will enable principles of microscopic fluid flow to be related to the statistical properties of turbulence in a superfluid. In the second part of this dissertation we explore frequency mixing, a subset of nonlinear optical processes in which one or more input optical beam(s) are converted into one or more output beams with different optical frequencies. The ability of parametric nonlinear processes such as second harmonic generation or parametric amplification to manipulate the OAM spectra of optical beams is an active area of research. In a theoretical and numerical investigation, two complimentary methods for sculpting the OAM spectra are developed. The first method employs second harmonic generation with two non-collinear input beams to develop a broad spectrum of OAM states in an optical field. The second method utilizes parametric amplification with collinear input beams to develop an OAM-dependent gain or attenuation, termed dichroism for OAM, to effectively narrow the OAM spectrum of an optical beam. The theoretical principles developed in this dissertation enhance our understanding of how nonlinear processes can be used to engineer the OAM spectra of optical beams and could serve as methods to increase the bandwidth of an optical signal by multiplexing over a range of OAM states.
Angular momentum plays a central role in quantum mechanics, recurring in every length scale from the microscopic interactions of light and matter to the macroscopic behavior of superfluids. Vortex beams, carrying intrinsic orbital angular momentum (OAM), are now regularly generated with elementary particles such as photons and electrons. Thus far, the creation of a vortex beam of a nonelementary particle has never been demonstrated experimentally. We present vortex beams of atoms and molecules, formed by diffracting supersonic beams of helium atoms and dimers off transmission gratings. This method is general and could be applied to most atomic and molecular gases. Our results may open new frontiers in atomic physics, using the additional degree of freedom of OAM to probe collisions and alter fundamental interactions.
The flux of probability density corresponding to a complex wavefunction, ψ=ψr+iψi, can form vortices which rotate about a nodal region of ψ, and have integer values of the circulation numbers. For one particle wavefunctions (or for approximate natural spin molecular orbitals), the vortices are either axial or toroidal. The axial vortices have angular momentum dipole moments which are usually quantized only if the wave function is an eigenfunction of Lz. The axial vortices interact with homogeneous magnetic fields whereas the toroidal interact with inhomogeneous magnetic fields. Toroidal vortices are easily created or annihilated by a perturbation which moves the nodal surface of ψi relative to the nodal surface of ψr so that these surfaces intersect or become separated. Thus, toroidal vortices are unstable and may be important only near resonance. However, axial vortices are stable since their creation requires (a) photon absorption or emission, (b) a perturbation (such as a magnetic field) which converts a real into a complex wavefunction, or (c) conversion of a toroidal into an axial vortex by expanding the nodal loop until a part of it reaches the boundary of configuration space. Thus, axial vortices should play an important role in energy transfer, photochemical processes, etc., and their circulation numbers should be good quantum numbers. A method for determining generalized first-order density matrices and natural spin–orbitals for use in scattering problems is proposed.
We comment on Ref.[D. Karlovets, D. Grosman, and I. Pavlov, Phys. Rev. Lett. 136, 085002 (2026)], which proposes a BMT-like equation for the mean kinetic orbital angular momentum (OAM) of vortex particles in accelerator fields and draws spin-like conclusions about depolarization, resonances, and control. We show that the proposed closure is not generally valid even at the mean-value level. In the authors' own homogeneous-field model, Eq.(8) already makes ⟨Lz⟩ depend on the packet second moment ⟨ρ2⟩(τ); for an exact family of breathing Landau/LG packets this yields an explicit oscillation incompatible with Eq.(9) except in the nongeneric matched case. Moreover, the Appendix A assumption that mixed correlators are negligible suppresses the transverse kinetic-OAM components themselves, since those correlators are precisely the building blocks of Lx and Ly. We also stress that, even if a closed equation for ⟨L^⟩ were available, it would still not constitute a transport equation for a vortex quantum state. Mean-OAM transport does not determine OAM spectra, inter-mode coherences, or fidelity. State-level claims therefore require a mode-resolved density-matrix treatment rather than an Ehrenfest equation for a low-order moment.