Quantum Vortex States Research Articles

Generation of Quantum Vortex Electrons with Intense Laser Pulses.

Accelerating a free electron to high-energy forms the basis for studying particle and nuclear physics. Here it is shown that the wave function of such an energetic electron can be further manipulated with the femtosecond intense lasers. During the scattering between a high-energy electron and a circularly polarized laser pulse, a regime is found where the enormous spin angular momenta of laser photons can be efficiently transferred to the electron orbital angular momentum (OAM). The wave function of the scattered electron is twisted from its initial plane-wave state to the quantum vortex state. Nonlinear quantum electrodynamics (QED) theory suggests that the GeV-level electrons acquire average intrinsic OAM beyond at laser intensities of 1020Wcm-2 with linear scaling. These electrons emit γ-photons with two-peak spectrum, which sets them apart from the ordinary electrons. The findings demonstrate a proficient method for generating relativistic leptons with the vortex wave functions based on existing laser technology, thereby fostering a novel source for particle and nuclear physics.

Fragmentation and correlations in a rotating Bose–Einstein condensate undergoing breakup

The theoretical investigation of rotating Bose–Einstein condensates has mainly focused on the emergence of quantum vortex states and the condensed properties of such systems. In the present work, we concentrate on other facets by examining the impact of rotation on the ground state of weakly interacting bosons confined in anharmonic potentials computed both at the mean-field level and particularly at the many-body level of theory. For the many-body computations, we employ the well-established many-body method known as the multiconfigurational time-dependent Hartree method for bosons. We present how various degrees of fragmentation can be generated following the breakup of the ground state densities in anharmonic traps without ramping up a potential barrier for strong rotations. The breakup of the densities is found to be associated with the acquisition of angular momentum in the condensate due to the rotation. In addition to fragmentation, the presence of many-body correlations is examined by computing the variances of the many-particle position and momentum operators. For strong rotations, the many-body variances become smaller than their mean-field counterparts, and one even finds a scenario with opposite anisotropies of the mean-field and many-body variances. Further, it is observed that for higher discrete symmetric systems of order k, namely three-fold and four-fold symmetry, breakup to k sub-clouds and emergence of k-fold fragmentation take place. All in all, we provide a thorough many-body investigation of how and which correlations build up when a trapped Bose–Einstein condensate breaks up under rotation.

Finite orbital-angular-momentum carried by the final electron and photon in plane-wave electron-nucleus bremsstrahlung

In quantum-electrodynamics scatterings the transfer of angular momentum between initial and final states can be resolved using the vortex scattering theory, where involved particles are described by quantum vortex states with featured orbital angular momentum (OAM). Here we employ the vortex scattering scenario in bremsstrahlung of a plane-wave electron by describing the final electron and photon in vortex states. We find that, while the total cross-section and angular distribution of the vortex scattering scenario are consistent with those from the ordinary plane-wave scattering, the final states in the former can gain non-negligible OAM values even though the incident electron does not contain any OAM. Moreover, introducing the OAM degree of freedom conserves the total angular momentum in polarized scattering. The dependence of the OAM on the opening angle of the vortex state and the energy ratio of photon to electron are obtained. It is shown that the emitted photon gains higher OAM at larger angles and energy ratios.

The quantum vortex states in extended Bose–Hubbard model: effects of lattice geometries, inter-particle interactions and spatial inhomogeneity

We study quantum vortex states of strongly interacting bosons in a two-dimensional rotating optical lattice. The system is modeled by Bose-Hubbard Hamiltonian with rotation. We consider lattices of different geometries, such as square, rectangular and triangular. Using numerical exact diagonalization method we show how the rotation introduces vortex states of different ground-state symmetries and the transition between these states at discrete rotation frequencies. We show how the geometry of the lattice plays crucial role in determining the maximum number of vortex states as well as the general characteristics of these states such as, the average angular momentum $<L_z>$, the current at the perimeter of the lattice, phase winding, the relation between the maximum phase difference, the maximum current and also the saturation of the current between the two neighboring lattice points. The effect of the two- and three-body interactions between the particles, both attractive and repulsive, also depends on the geometry of the lattice as the current flow or the lattice current depends on the interactions. We also consider the effect of the spatial inhomogeneity introduced by the presence of an additional confining harmonic trap potential. It is shown that the curvature of the trap potential and the position of the minimum of the trap potential with respect to the axis of rotation or the center of the lattice have a significant effect on the general characteristics these vortex states.

Twisted Breit-Wheeler electron-positron pair creation via vortex gamma photons

Particles in quantum vortex states (QVSs) carrying definite orbital angular momenta (OAM) bring different perspectives in various fundamental interaction processes. When unique properties arise in the QVS, understanding how OAM manifests itself between initial particles and the outcome in vortex particle collisions becomes essential. This is made possible by applying the complete vortex description for all involved particles such that angular momenta (AM) are represented by explicit quantum numbers and their connections are naturally retrieved. We demonstrate the full-vortex quantum-electrodynamics (QED) results for the Breit-Wheeler pair creation process and derive the AM-dependent selection rule. The numerically resolved cross sections show antisymmetric spin polarization and, most importantly, the OAM spectra in vortex collision processes. The latter reveals efficient conversion of OAM to created pairs, leading to featured hollow and ring-shaped structure in the density distribution. These results demonstrate a clear picture in understanding the AM physics in the scattering processes of high energy particles.

Impurity effect on order modulations in superconducting systems with mixed singlet-triplet pairing

Based on a model Hamiltonian including the on-site repulsive interaction among the electrons, we investigate the effect induced by nonmagnetic impurities in bulk superconducting systems with mixed singlet-triplet pairing by numerically solving the Bogoliubov-de Gennes equations. For the emergent spin-triplet p-wave as well as coexisted spin-singlet s-wave and d-wave pairing symmetries, the order-parameter patterns for the quantized vortex states with point-like cores can be effectively tuned by the located sites of nonmagnetic impurities. The next-nearest-neighbor hopping effect on the evolution of vortex configurations is also discussed in the presence of vortex pinning by the impurity. Besides the unconventional vortex lattice, several types of topological defects, including the unclosed domain walls and enclosed skyrmionic modes, can be obtained when the impurity position is varied. All these configurations can be resolved by the zero-energy peaks in the local density of states.

Vortical patterns in bulk superconducting systems with mixed pairing orders

Based on a model Hamiltonian including the on-site repulsive interaction among the electrons, we investigate the spatial configurations of mixed spin-triplet (dominant p-wave) and spin-singlet (coexisted s-wave and d-wave) pairing symmetries in bulk superconducting systems by numerically solving the Bogoliubov–de Gennes equations. The influences of the Zeeman field and the next-nearest-neighbor hopping on the order-parameter modulations are mainly discussed. Besides the quantized vortex states with point-like cores, the unclosed vortex chains and enclosed skyrmionic modes can remain stable in the present bulk sample. Furthermore, nonuniform patterns of the vortex lattice and the elliptical-like vortices can be obtained at appropriate applied flux. The corresponding zero-energy local density of states as well as the relative phase differences useful to display the skyrmionic texture are provided

Neutral Vortex Necklace in a Trapped Planar Superfluid

We study quantum vortex states consisting of a ring of vortices with alternating sign, in a homogeneous superfluid confined to a circular domain. We find an exact stationary solution of the point vortex model for the neutral vortex necklace. We investigate the stability of the necklace state within both the point-vortex model and the Gross-Pitaevskii equation describing a trapped atomic Bose-Einstein condensate at low temperature. The point-vortex stationary states are found to also be stationary states of the Gross-Pitaevskii equation provided the finite thickness of the outer fluid boundary is accounted for. Under significant perturbation, the Gross-Pitaevskii evolution and point-vortex model exhibit instability as expected for metastable states. The perturbed vortex necklace exhibits sensitivity to the perturbation, suggesting a route to seeding vortex chaos or quantum turbulence.

Observation of a gel of quantum vortices in a superconductor at very low magnetic fields

A gel consists of a network of particles or molecules formed for example using the sol-gel process, by which a solution transforms into a porous solid. Particles or molecules in a gel are mainly organized on a scaffold that makes up a porous system. Quantized vortices in type II superconductors mostly form spatially homogeneous ordered or amorphous solids. Here we present high-resolution imaging of the vortex lattice displaying dense vortex clusters separated by sparse or entirely vortex-free regions in $\beta$-Bi$_2$Pd superconductor. We find that the intervortex distance diverges upon decreasing the magnetic field and that vortex lattice images follow a multifractal behavior. These properties, characteristic of gels, establish the presence of a novel vortex distribution, distinctly different from the well-studied disordered and glassy phases observed in high-temperature and conventional superconductors. The observed behavior is caused by a scaffold of one-dimensional structural defects with enhanced stress close to the defects. The vortex gel might often occur in type-II superconductors at low magnetic fields. Such vortex distributions should allow to considerably simplify control over vortex positions and manipulation of quantum vortex states.

Vortex and skyrmionic patterns in chiral p-wave superconducting systems

In the framework of the microscopic Bogoliubov-de Gennes theory, we study the spatial configurations of topological defects in chiral p-wave superconducting systems. Besides the quantized vortex states with pointlike cores, the coreless single or multiple skyrmionic structures with the topological charge Q=2 and several types of the skyrmion-vortex coexisting modes can remain stable in the bulk system. Interestingly, the multiskyrmionic patterns containing several separated skyrmionic chains can be obtained at an appropriate flux, accompanied with half-quantum vortex-antivortex pairs in one component of the order parameter. Further, more complex skyrmionic states with Q=6 can also take place when the external magnetic flux becomes stronger.

Superfluidity in nuclear systems and neutron stars

Nuclear matter and finite nuclei exhibit the property of superfluidity by forming Cooper pairs. We review the microscopic theories and methods that are being employed to understand the basic properties of superfluid nuclear systems, with emphasis on the spatially extended matter encountered in neutron stars, supernova envelopes, and nuclear collisions. Our survey of quantum many-body methods includes techniques that employ Green functions, correlated basis functions, and Monte Carlo sampling of quantum states. With respect to empirical realizations of nucleonic and hadronic superfluids, this review is focused on progress that has been made toward quantitative understanding of their properties at the level of microscopic theories of pairing, with emphasis on the condensates that exist under conditions prevailing in neutron-star interiors. These include singlet $S$-wave pairing of neutrons in the inner crust, and, in the quantum fluid interior, singlet-$S$ proton pairing and triplet coupled $P$-$F$-wave neutron pairing. Additionally, calculations of weak-interaction rates in neutron-star superfluids within the Green function formalism are examined in detail. We close with a discussion of quantum vortex states in nuclear systems and their dynamics in neutron-star superfluid interiors.

Einstein–Bose condensation of Onsager vortices

We have studied statistical mechanics of a gas of vortices in two dimensions. We introduce a new observable—a condensate fraction of Onsager vortices—to quantify the emergence of the vortex condensate. The condensation of Onsager vortices is most transparently observed in a single vortex species system and occurs due to a competition between solid body rotation (see vortex lattice) and potential flow (see multiple quantum vortex state). We propose an experiment to observe the condensation transition of the vortices in such a single vortex species system.

Generation and Detection of Continuous Variable Quantum Vortex States via Compact Photonic Devices

A quantum photonic circuit with the ability to produce continuous variable quantum vortex states is proposed. This device produces two single-mode squeezed states which go through a Mach-Zehnder interferometer where photons are subtracted by means of weakly coupled directional couplers towards ancillary waveguides. The detection of a number of photons in these modes heralds the production of a quantum vortex. Likewise, a measurement system of the order and handedness of quantum vortices is introduced and the performance of both devices is analyzed in a realistic scenario by means of the Wigner function. These devices open the possibility of using the quantum vortices as carriers of quantum information.

Engineering continuous and discrete variable quantum vortex states by nonlocal photon subtraction in a reconfigurable photonic chip

We study the production of entangled two- and N-mode quantum states of light in optical waveguides. To this end, we propose a quantum photonic circuit that produces a reconfigurable superposition of photon subtraction on two single-mode squeezed states. Under postselection, continuous variable or discrete variable entangled states with possibilities in quantum information processing are obtained. Likewise, nesting leads to higher-dimension entanglement with a similar design, enabling the generation of non-Gaussian continuous variable cluster states. Additionally, we show the operation of the device through the generation of quantum vortex states of light and propose an integrated device that measures their order and handedness. Finally, we study the non-Gaussianity, nonclassicality, and entanglement of the quantum states generated with this scheme by means of the optical field-strength distribution, Wigner function, and logarithmic negativity.

Gauge potential for neutral atoms in a magnetic quadrupole field

We consider a spinor Bose-Einstein condensate of neutral atoms in a magnetic quadrupole field and investigate the gauge potential derived from the spatially-varying magnetic field. We discuss the critical condition for a singular, quantized vortex state being energetically favored in the spinor condensate and find that it is necessary under experimentally realistic conditions to use atoms with hyperfine spin F > 1 and/or a more spatially-varying magnetic field, e.g., hexapole or octopole fields. Finally, we show that a spinor condensate in a ring geometry is beneficial for observing the gauge potential effects.

Preparing quantum vortex states with odd Schrödinger cat states through a coupled waveguide system

A scheme is proposed for preparing a quantum vortex state with a coupled waveguide, in which a single-mode odd cat state with weak intensity and a single-mode coherent state are inserted in the input ports, respectively. The analytical wavefunction of the resulting state in the quadrature space is derived, and the vortex structure of the output state is analyzed. It is found that the obtained states, which may carry a vortex with topological charge index one, are entangled and nonclassical, depending only on the scaled propagation time and the weak intensity of the input odd cat state instead of the displacement parameter of the input coherent state. The phase distribution, however, in the quadrature space, depends on the displacement parameter of the input coherent state

Interaction of a pair coherent state with a three-level Λ-type atom and generation of a modified Bessel—Gaussian state with a vortex structure

The evolution of a system state is derived based on the nonresonant interaction of a three-level “Λ" type atom with two cavity modes at a pair coherent state and two classic fields, and a cavity field state is analyzed in detail under conditional detecting. It is found that the quantized modified Bessel—Gaussian states as well as the superposition states consisting of the quantized vortex states with different weighted coefficients may be prepared through carefully preparing an initial atomic state and appropriately adjusting the interaction time. The scheme provides an additional choice to realize the two-mode quantized vortex state within the context of cavity quantum electrodynamics (QED).

Crossover from Fulde-Ferrell state to Larkin-Ovchinnikov state in cold fermion gases

We study an effect of rotation on the two component Fermi superfluid gases with population imbalance in a toroidal trap. We investigate how the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state is changed by the rotation using the Bogoliubov-de Gennes equation in the quasi-one-dimensional regime. We find that two novel FFLO phases, i.e., the half quantum vortex state and the intermediate state of Fulde-Ferrell (FF) state and Larkin-Ovchinnikov (LO) state, are stabilized by the rotation. The phase diagram for the FF state, LO state, intermediate state, and half quantum vortex state is shown in T-Φ plane. We show the order parameter of these states.

Wigner function and the entanglement of a quantized Bessel-Gaussian vortex state of a quantized radiation field

A new kind of quantum non-Gaussian state with a vortex structure, termed a Bessel—Gaussian vortex state, is constructed, which is an eigenstate of the sum of squared annihilation operators a2 + b2. The Wigner function of the quantum vortex state is derived and exhibits negativity which is an indication of nonclassicality. It is also found that a quantized vortex state is always in entanglement. And a scheme for generating such quantized vortex states is proposed.

Quantized Vortex State in hcp Solid 4He

The quantized vortex state appearing in the recently discovered new states in hcp 4He since their discovery is discussed. Special attention is given to evidence for the vortex state as the vortex fluid (VF) state and its transition into the supersolid (SS) state. Its features are described. The historical expla- nations for the SS state in quantum solids such as solid 4He were based on the idea of Bose Einstein Condensation (BEC) of the imperfections such as va- cancies, interstitials and other possible excitations in the quantum solids which are expected because of the large zero-point motions. The SS state was proposed as a new state of matter in which real space ordering of the lattice structure of the solid coexists with the momentum space ordering of superfluidity. A new type of superconductors, since the discovery of the cuprate high Tc superconductors, HTSCs, has been shown to share a feature with the vortex state, involving the VF and vortex solid states. The high Tcs of these materials are being discussed in connection to the large fluctuations associated with some other phase transitions like the antiferromagnetic transition in addition to that of the low dimensionality. The supersolidity in the hcp solid 4He, in contrast to the new superconductors which have multiple degrees of freedom of the Cooper pairs with spin as well as angular momentum freedom, has a unique feature of possessing possibly only the momentum fluctuations and vortex ring excitations associated with the possible low dimensional fluctuations of the subsystem(s). The high onset temperature of the VF state can be understood by considering thermally excited low D quantized vortices and it may be necessary to seek low dimensional sub-systems in hcp He which are hosts for vortices.