arXiv subjects

H. M. Cataldo

Publications and source records attributed to H. M. Cataldo.

At least 19 recordsLinked to original sources

arXiv2024

dc atomtronic quantum interference device: quantum superposition of persistent-current states and a parity-protected qubit

A generalized Bose-Hubbard model in a two-mode approximation is applied to study the rotational dynamics of a direct-current atomtronic quantum interference device. Modified values of on-site interaction and pair-tunneling parameters of the Hamiltonian, derived from the small-oscillation periods of the Josephson modes, are shown to provide an excellent agreement to the Gross-Pitaevskii simulation results for the whole rotational frequency range, reaching also the critical values of imbalance and current. This amounts to a full validation of the semiclassical approximation of the modified Hamiltonian, whose quantization is employed to investigate the quantum features of the stationary states. Focusing on the frequency interval where the potential energy presents two minima, it is shown that the central frequency, at which such minima are symmetric, yields an atom number parity-protected qubit with a maximum entanglement of both persistent-current states, similar to those of superconducting circuits threaded by a half-quantum of applied flux. Such a parity protection scheme survives within a small interval around the central frequency, which sets the minimum rotational frequency precision that should be required to implement the qubit. It is found that such a maximum admissible error in the frequency determination turns out to be inversely proportional to the qubit quality factor that measures the gap between the qubit energy levels and the following levels. It is shown that the chemical potential or condensate particle number could be employed as suitable control parameters to achieve the best trade-off between such qubit characteristics.

quant-ph↗

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

dc to ac Josephson transition in a dc atom superconducting quantum interference device

We analyze the effect of the barrier motion on the Bose-Hubbard Hamiltonian of a ring-shaped Bose-Einstein condensate interrupted by a pair of Josephson junctions, a configuration which is the cold atom analog of the well-known dc superconducting quantum interference device (SQUID). Such an effect is also shown to modify the Heisenberg equation of motion of the boson field operator in the two-mode approximation, where a hysteretic contribution that could affect the dynamics for accelerated or overlapping barriers is identified. By studying the energy landscape as a function of order and control parameters, we determine the diagram with the location of the dc and ac Josephson regimes, along with the critical points that are shown to depend on the junctions position. We analyze the dc to ac Josephson transition for adiabatic barrier trajectories that lead to a final uniform velocity, or which perform symmetric velocity paths. We show that such symmetric trajectories may induce, when reaching the critical point, highly hysteretic oscillating return paths within the dc regime, similar to the underdamped hysteresis loops arising from the action of a resistive flow in the ac regime. We also consider nonequilibrium initial conditions resulting from a finite phase difference on either side of the junctions, along with the critical features of such a parameter. An excellent agreement between the Gross-Pitaevskii simulations and the two-mode results is found in all cases.

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

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

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

Mapping onto Electrodynamics of a Two-dimensional Bose-Einstein Condensate

A thorough mapping between the hydrodynamics of a two-dimensional Bose-Einstein condensate and the nonrelativistic classical electrodynamics of a charged material medium is proposed. This is shown to provide a very useful frame to discuss several features of vortex dynamics. Two important local conservation theorems of energy and angular momentum are derived and further applications are summarized.

cond-mat.quant-gas↗

arXiv2010

Mutual friction in helium II: a microscopic approach

We develop a microscopic model of mutual friction represented by the dissipative dynamics of a normal fluid flow which interacts with the helical normal modes of vortices comprising a lattice in thermal equilibrium. Such vortices are assumed to interact with the quasiparticles forming the normal fluid through a pseudomomentum-conserving scattering Hamiltonian. We study the approach to equilibrium of the normal fluid flow for temperatures below 1 K, deriving an equation of motion for the quasiparticle pseudomomentum which leads to the expected form predicted by the HVBK equations. We obtain an expression for the mutual friction coefficient $B$ in terms of microscopic parameters, which turns out to be practically independent of the vortex mass for values arising from diverse theories. By comparing our expression of $B$ with previous theoretical estimates, we deduce interesting qualitative features about the excitation of Kelvin modes by the quasiparticle scattering.

cond-mat.stat-mech↗

arXiv2008

Vortex pseudomomentum and dissipation in a superfluid vortex lattice

We propose an alternative approach to the dissipative vortex dynamics occurring in a superfluid vortex lattice at finite temperatures. Focusing upon the pseudomomentum of a vortex and its surrounding quasiparticles, we derive an equation of motion which, in spite of yielding the same evolution as the usual one for massless vortices, does not involve the vortex mass. This picture could provide further insights into the controversy about the nature of the vortex mass.

cond-mat.stat-mech↗

arXiv2005

Damping of vortex waves in a superfluid

The damping of vortex cyclotron modes is investigated within a generalized quantum theory of vortex waves. Similarly to the case of Kelvin modes, the friction coefficient turns out to be essentially unchanged under such oscillations, but it is shown to be affected by appreciable memory corrections. On the other hand, the nonequilibrium energetics of the vortex, which is investigated within the framework of linear response theory, shows that its memory corrections are negligible. The vortex response is found to be of the Debye type, with a relaxation frequency whose dependence on temperature and impurity concentration reflects the complexity of the heat bath and its interaction with the vortex.

cond-mat.stat-mech↗

arXiv2004

Memory effects in superfluid vortex dynamics

The dissipative dynamics of a vortex line in a superfluid is investigated within the frame of a non-Markovian quantal Brownian motion model. Our starting point is a recently proposed interaction Hamiltonian between the vortex and the superfluid quasiparticle excitations, which is generalized to incorporate the effect of scattering from fermion impurities ($^3$He atoms). Thus, a non-Markovian equation of motion for the mean value of the vortex position operator is derived within a weak-coupling approximation. Such an equation is shown to yield, in the Markovian and elastic scattering limits, a $^3$He contribution to the longitudinal friction coefficient equivalent to that arising from the Rayfield-Reif formula. Simultaneous Markov and elastic scattering limits are found, however, to be incompatible, since an unexpected breakdown of the Markovian approximation is detected at low cyclotron frequencies. Then, a non-Markovian expression for the longitudinal friction coefficient is derived and computed as a function of temperature and $^3$He concentration. Such calculations show that cyclotron frequencies within the range 0.01$-$0.03 ps$^{-1}$ yield a very good agreement to the longitudinal friction figures computed from the Iordanskii and Rayfield-Reif formulas for pure $^4$He, up to temperatures near 1 K. A similar performance is found for nonvanishing $^3$He concentrations, where the comparison is also shown to be very favorable with respect to the available experimental data. Memory effects are shown to be weak and increasing with temperature and concentration.

cond-mat.stat-mech↗

arXiv2002

Friction force on a vortex due to the scattering of superfluid excitations in helium II

The longitudinal friction acting on a vortex line in superfluid $^4$He is investigated within a simple model based on the analogy between such vortex dynamics and that of the quantal Brownian motion of a charged point particle in a uniform magnetic field. The scattering of superfluid quasiparticle excitations by the vortex stems from a translationally invariant interaction potential which, expanded to first order in the vortex velocity operator, gives rise to vortex transitions between nearest Landau levels. The corresponding friction coefficient is shown to be, in the limit of elastic scattering (vanishing cyclotron frequency), equivalent to that arising from the Iordanskii formula. Proposing a simple functional form for the scattering amplitude, with only one adjustable parameter whose value is set in order to get agreement to the Iordanskii result for phonons, an excellent agreement is also found with the values derived from experimental data up to temperatures about 1.5 K. Finite values of the cyclotron frequency arising from recent theories are shown to yield similar results. The incidence of vortex-induced quasiparticle transitions on the friction process is estimated to be, in the roton dominated regime, about 50 % of the value of the friction coefficient, $\sim$8 % of which corresponds to roton-phonon transitions and $\sim$42 % to roton $R^+\leftrightarrow R^-$ ones.

cond-mat↗