arXiv subjects

D. M. Jezek

Publications and source records attributed to D. M. Jezek.

At least 19 recordsLinked to original sources

arXiv2025

Self-sustained Josephson dynamics and self-trapping in supersolids

We explore the self-sustained Josephson junction dynamics in dipolar supersolids, predicting the possibility of self-trapping alongside the experimentally observed Josephson oscillations [Biagioni, G. et al., Nature 629, 773 (2024)]. Using an asymmetric two-mode (ATM) model to describe a triangular dipolar supersolid, validated through Gross-Pitaevskii simulations, we demonstrate that the system's symmetry enables a consistent two-mode mapping despite the presence of seven droplets. Hence, the associated Hamiltonian allows us to straightforwardly determine the self-trapping regime. Additionally, we show that bringing the system into rotation preserves its ability to sustain the Josephson junction dynamics across its full range, and we assess the robustness of the ATM model under these conditions. We further find that the off-axis droplets move in the radial direction during the evolution in accordance with the size of the central droplet. Such movements do not interfere with the model predictions.

cond-mat.quant-gas↗

arXiv2025

Modeled vortex dynamics on a Bose-Einstein condensate in a rotating lattice

We study the dynamics of vortices in a Bose-Einstein condensate within a rotating four-site lattice which can be effectively described by a multimode model. Such a vortex dynamics develops along the low-density paths that separate the sites, and it is ruled by the phase differences between them. Hence, by appropriately selecting the initial conditions for on-site populations and phase differences, one can access distinct types of evolutions. We show that, by choosing equal populations in alternate sites, one can construct two-mode model Hamiltonians which allows us to model a large variety of associated vortex orbits. In particular, one can select the type of trajectory of the vortex and predict the creation and annihilation of vortex-antivortex pairs near the trap center. Estimates for the periods of closed vortex orbits and for the times that the vortices spend inside the lattice when dealing with open orbits, are obtained in terms of the two-mode models parameters and the rotation frequency only. We believe that the present study establishes a suitable platform to engineer different vortex dynamics.

cond-mat.quant-gas↗

arXiv2024

Phase-induced vortex pinning in rotating supersolid dipolar systems

We analyze the pinning of vortices for a stationary rotating dipolar supersolid along the low-density paths between droplets as a function of the rotation frequency. We restrict ourselves to the stationary configurations of vortices with the same symmetry as that of the array of droplets. In particular, such an analysis clearly reveals that vortices are not only pinned at local density minima, but instead their coordinates are smooth functions of the rotation frequency. Our approach to explaining such a behavior exploits the fact that the wave function of each rotating droplet acquires a linear phase on the coordinates. Hence, the relative phases between the nearest neighboring droplets allow us to predict the position of the vortices in the intermediate low-density region. Here, we show that for a droplet distribution forming a triangular lattice, the phases of three neighboring droplets are needed for the correct description of the vortex location. In particular, for our confined system, we demonstrate that the estimate accurately reproduces the extended Gross-Pitaevskii results in the spatial regions where the neighboring droplets are well-defined.

cond-mat.quant-gas↗

arXiv2023

Vortex nucleation processes in rotating lattices of Bose-Einstein condensates ruled by the on-site phases

We study the nucleation and dynamics of vortices in rotating lattice potentials where weakly linked condensates are formed with each condensate exhibiting an almost axial symmetry. Due to such a symmetry, the on-site phases acquire a linear dependence on the coordinates as a result of the rotation, which allows us to predict the position of vortices along the low density paths that separate the sites. We first show that, for a system of atoms loaded in a four-site square lattice potential, subject to a constant rotation frequency, the analytical expression that we obtain for the positions of vortices of the stationary arrays accurately reproduces the full three-dimensional Gross-Pitaevskii results. We then study the time-dependent vortex nucleation process when a linear ramp of the rotation frequency is applied to a lattice with sixteen sites. We develop a formula for the number of nucleated vortices which turns to have a linear dependence on the rotation frequency with a smaller slope than that of the standard estimate which is valid in absence of the lattice. From time-dependent Gross-Pitaevskii simulations we further find that the on-site populations remain almost constant during the time evolution instead of spreading outwards, as expected from the action of the centrifugal force. Therefore, the time-dependent phase difference between neighboring sites acquires a running behavior typical of a self-trapping regime. We finally show that, in accordance with our predictions, this fast phase-difference evolution provokes a rapid vortex motion inside the lattice. Our analytical expressions may be useful for describing other vortex processes in systems with the same on-site axial symmetry.

cond-mat.quant-gas↗

arXiv2021

Rotation-driven transition into coexistent Josephson modes in an atomtronic dc-SQUID

By means of a two-mode model, we show that transitions to different arrays of coexistent regimes in the phase space can be attained by rotating a double-well system, which consists of a toroidal condensate with two diametrically placed barriers. Such a configuration corresponds to the atomtronic counterpart of the well-known direct-current superconducting quantum interference device. Due to the phase gradient experimented by the on-site localized functions when the system is subject to rotation, a phase difference appears on each junction in order to satisfy the quantization of the velocity field around the torus. We demonstrate that such a phase can produce a significant change on the relative values of different types of hopping parameters. In particular, we show that within a determined rotation frequency interval, a hopping parameter, usually disregarded in nonrotating systems, turns out to rule the dynamics. At the limits of such a frequency interval, bifurcations of the stationary points occur, which substantially change the phase space portrait that describes the orbits of the macroscopic canonical conjugate variables. We analyze the emerging dynamics that combines the $0$ and $π$ Josephson modes, and evaluate the small-oscillation time-periods of such orbits at the frequency range where each mode survives. All the findings predicted by the model are confirmed by Gross-Pitaevskii simulations.

cond-mat.quant-gas↗

arXiv2020

Blocked populations in ring-shaped optical lattices

We study a special dynamical regime of a Bose-Einstein condensate in a ring-shaped lattice where the populations in each site remain constant during the time evolution. The states in this regime are characterized by equal occupation numbers in alternate wells and non-trivial phases, while the phase differences between neighboring sites evolve in time yielding persistent currents that oscillate around the lattice. We show that the velocity circulation around the ring lattice alternates between two values determined by the number of wells and with a specific time period that is only driven by the onsite interaction energy parameter. In contrast to the self-trapping regime present in optical lattices, the occupation number at each site does not show any oscillation and the particle imbalance does not possess a lower bound for the phenomenon to occur. These findings are predicted with a multimode model and confirmed by full three-dimensional Gross-Pitaevskii simulations using an effective onsite interaction energy parameter.

cond-mat.quant-gas↗

arXiv2019

Collisional dynamics of multiple dark solitons in a toroidal Bose-Einstein condensate: Quasiparticle picture

We study the collisional dynamics of multiple dark solitons in a Bose-Einstein condensate confined by a toroidal trap. We assume a tight enough confinement in the radial direction to prevent possible dissipative effects due to the presence of solitonic vortices. Analytical expressions for the initial order parameters with imprinted phases are utilized to generate different initial arrays of solitons, for which the time-dependent Gross-Pitaevskii equation is numerically solved. Given that the soliton velocity is conserved due to the lack of dissipation, we are able to apply a simple quasiparticle description of the soliton dynamics. In fact, the trajectory equations are written in terms of the velocities and the angular shifts produced at each collision, in analogy to the infinite one-dimensional system. To calculate the angular shifts, we directly extract them from the trajectories given by the Gross-Pitaevskii simulations and, on the other hand, we show that accurate values can be analytically obtained by adapting a formula valid for the infinite one-dimensional system that involves the healing length, which in our inhomogeneous system must be evaluated in terms of the sound velocity along the azimuthal direction. We further show that very good estimates of such a sound velocity can be directly determined by using the ground state density profile and the values of the imprinted phases. We discuss the possible implementation of the system here proposed using the current experimental techniques.

cond-mat.quant-gas↗

arXiv2018

Dynamics in multiple-well Bose-Einstein condensates

We study the dynamics of three-dimensional weakly linked Bose-Einstein condensates using a multimode model with an effective interaction parameter. The system is confined by a ring-shaped four-well trapping potential. By constructing a two-mode Hamiltonian in a reduced highly symmetric phase space, we examine the periodic orbits and calculate their time periods both in the self-trapping and Josephson regimes. The dynamics in the vicinity of the reduced phase space is investigated by means of a Floquet multiplier analysis, finding regions of different linear stability and analyzing their implications on the exact dynamics. The numerical exploration in an extended region of the phase space demonstrates that two-mode tools can also be useful for performing a partition of the space in different regimes. Comparisons with Gross-Pitaevskii simulations confirm these findings and emphasize the importance of properly determining the effective on-site interaction parameter governing the multimode dynamics.

cond-mat.quant-gas↗

arXiv2016

Dark soliton collisions in a toroidal Bose-Einstein condensate

We study the dynamics of two gray solitons in a Bose-Einstein condensate confined by a toroidal trap with a tight confinement in the radial direction. Gross-Pitaevskii simulations show that solitons can be long living objects passing through many collisional processes. We have observed quite different behaviors depending on the soliton velocity. Very slow solitons, obtained by perturbing the stationary solitonic profile, move with a constant angular velocity until they collide elastically and move in the opposite direction without showing any sign of lowering their energy. In this case the density notches are always well separated and the fronts are sharp and straight. Faster solitons present vortices around the notches, which play a central role during the collisions. We have found that in these processes the solitons lose energy, as the outgoing velocity turns out to be larger than the incoming one. To study the dynamics, we model the gray soliton state with a free parameter that is related to the soliton velocity. We further analyze the energy, soliton velocity and turning points in terms of such a free parameter, finding that the main features are in accordance with the infinite one-dimensional system.

cond-mat.quant-gas↗

arXiv2014

Dynamics in asymmetric double-well condensates

The dynamics of Bose-Einstein condensates in asymmetric double-wells is studied. We construct a two-mode model and analyze the properties of the corresponding phase-space diagram, showing in particular that the minimum of the phase-space portrait becomes shifted from the origin as a consequence of the nonvanishing overlap between the ground and excited states from which the localized states are derived. We further incorporate effective interaction corrections in the set of two-mode model parameters. Such a formalism is applied to a recent experimentally explored system, which is confined by a toroidal trap with radial barriers forming an arbitrary angle between them. We confront the model results with Gross-Pitaevskii simulations for various angle values finding a very good agreement. We also analyze the accuracy of a previously employed simple model for moving barriers, exploring a possible improvement that could cover a wider range of trap asymmetries.

cond-mat.quant-gas↗

arXiv2014

Influence of global features of a Bose-Einstein condensate on the vortex velocity

We study the way in which the geometry of the trapping potential affects the vortex velocity in a Bose-Einstein condensate confined by a toroidal trap. We calculate the vortex precession velocity through a simple relationship between such a velocity and the gradient of the numerically obtained vortex energy. We observe that our results correspond very closely to the velocity calculated through time evolution simulations. However, we find that the estimates derived from available velocity field formulas present appreciable differences. To resolve such discrepancies, we further study the induced velocity field, analyzing the effect of global features of the condensate on such a field and on the precession velocity.

cond-mat.quant-gas↗

arXiv2013

Multimode model for an atomic Bose-Einstein condensate in a ring-shaped optical lattice

We study the population dynamics of a ring-shaped optical lattice with a high number of particles per site and a low, below ten, number of wells. Using a localized on-site basis defined in terms of stationary states, we were able to construct a multiple-mode model depending on relevant hopping and on-site energy parameters. We show that in case of two wells, our model corresponds exactly to the latest improvement of the two-mode model. We derive a formula for the self-trapping period, which turns out to be chiefly ruled by the on-site interaction energy parameter. By comparing to time dependent Gross-Pitaevskii simulations, we show that the multimode model results can be enhanced in a remarkable way over all the regimes by only renormalizing such a parameter. Finally, using a different approach which involves only the ground state density, we derive an effective interaction energy parameter that shows to be in accordance with the renormalized one.

cond-mat.quant-gas↗

arXiv2013

Two-mode effective interaction in a double-well condensate

We investigate the origin of a disagreement between the two-mode model and the exact Gross-Pitaevskii dynamics applied to double-well systems. In general this model, even in its improved version, predicts a faster dynamics and underestimates the critical population imbalance separating Josephson and self-trapping regimes. We show that the source of this mismatch in the dynamics lies in the value of the on-site interaction energy parameter. Using simplified Thomas-Fermi densities, we find that the on-site energy parameter exhibits a linear dependence on the population imbalance, which is also confirmed by Gross-Pitaevskii simulations. When introducing this dependence in the two-mode equations of motion, we obtain a reduced interaction energy parameter which depends on the dimensionality of the system. The use of this new parameter significantly heals the disagreement in the dynamics and also produces better estimates of the critical imbalance.

cond-mat.quant-gas↗

arXiv2011

Phase-slippage and self-trapping in a self-induced bosonic Josephson junction

A dipolar condensate confined in a toroidal trap constitutes a self-induced Josepshon junction when the dipoles are oriented perpendicularly to the trap symmetry axis and the s-wave scattering length is small enough. The ring-shaped double-well potential coming from the anisotropic character of the mean-field dipolar interaction is robust enough to sustain self-trapping dynamics, which takes place when the initial population imbalance between the two wells is large. We show that in this system the self-trapping regime is directly related to a vortex-induced phase-slip dynamics. A vortex and antivortex are spontaneously nucleated in the low density regions, before a minimum of the population imbalance is reached, and then cross the toroidal section in opposite directions through the junctions.This vortex dynamics yields a phase slip between the two weakly linked condensates causing an inversion of the particle flux.

cond-mat.quant-gas↗

arXiv2011

Bose-Hubbard model in a ring-shaped optical lattice with high filling factors

The high-barrier quantum tunneling regime of a Bose-Einstein condensate confined in a ring-shaped optical lattice is investigated. By means of a change of basis transformation, connecting the set of `vortex' Bloch states and a Wannier-like set of localized wave functions, we derive a generalized Bose-Hubbard Hamiltonian. In addition to the usual hopping rate terms, such a Hamiltonian takes into account interaction-driven tunneling processes, which are shown to play a principal role at high filling factors, when the standard hopping rate parameter turns out to be negative. By calculating the energy and atomic current of a Bloch state, we show that such a hopping rate must be replaced by an effective hopping rate parameter containing the additional contribution an interaction-driven hopping rate. Such a contribution turns out to be crucial at high filling factors, since it preserves the positivity of the effective hopping rate parameter. Level crossings between the energies per particle of a Wannier-like state and the superfluid ground state are interpreted as a signature of the transition to configurations with macroscopically occupied states at each lattice site.

cond-mat.quant-gas↗

arXiv2011

A dipolar self-induced bosonic Josephson junction

We propose a new scheme for observing Josephson oscillations and macroscopic quantum self-trapping phenomena in a toroidally confined Bose-Einstein condensate: a dipolar self-induced Josephson junction. Polarizing the atoms perpendicularly to the trap symmetry axis, an effective ring-shaped, double-well potential is achieved which is induced by the dipolar interaction. By numerically solving the three-dimensional time-dependent Gross-Pitaevskii equation we show that coherent tunneling phenomena such as Josephson oscillations and quantum self-trapping can take place. The dynamics in the self-induced junction can be qualitatively described by a two-mode model taking into account both s-wave and dipolar interactions.

cond-mat.quant-gas↗

arXiv2011

Winding number dependence of Bose-Einstein condensates in a ring-shaped lattice

We study the winding number dependence of the stationary states of a Bose-Einstein condensate in a ring-shaped lattice. The system is obtained by confining atoms in a toroidal trap with equally spaced radial barriers. We calculate the energy and angular momentum as functions of the winding number and the barrier height for two quite distinct particle numbers. In both cases we observe two clearly differentiated regimes. For low barriers, metastable vortex states are obtained up to a maximum winding number which depends on the particle number and barrier height. In this regime, the angular momentum and energy show, respectively, almost linear and quadratic dependences on the winding number. For large barrier heights, on the other hand, stationary states are obtained up to a maximum winding number which depends only on the number of lattice sites, whereas energy and angular momentum are shown to be sinusoidal functions of the winding number.

cond-mat.quant-gas↗

arXiv2010

Dipolar condensates confined in a toroidal trap: ground state and vortices

We study a Bose-Einstein condensate of 52Cr atoms confined in a toroidal trap with a variable strength of s-wave contact interactions. We analyze the effects of the anisotropic nature of the dipolar interaction by considering the magnetization axis to be perpendicular to the trap symmetry axis. In the absence of a central repulsive barrier, when the trap is purely harmonic, the effect of reducing the scattering length is a tuning of the geometry of the system: from a pancake-shaped condensate when it is large, to a cigar-shaped condensate for small scattering lengths. For a condensate in a toroidal trap, the interaction in combination with the central repulsive Gaussian barrier produces an azimuthal dependence of the particle density for a fixed radial distance. We find that along the magnetization direction the density decreases as the scattering length is reduced but presents two symmetric density peaks in the perpendicular axis. For even lower values of the scattering length we observe that the system undergoes a dipolar-induced symmetry breaking phenomenon. The whole density becomes concentrated in one of the peaks, resembling an origin-displaced cigar-shaped condensate. In this context we also analyze stationary vortex states and their associated velocity field, finding that this latter also shows a strong azimuthal dependence for small scattering lengths. The expectation value of the angular momentum along the z direction provides a qualitative measure of the difference between the velocity in the different density peaks.

cond-mat.quant-gas↗