Ayan Khan

Effect of disorder in BCS?BEC crossover

In this paper, we have investigated the effect of weak random disorder in the Bardeen?Cooper?Schrieffer to Bose?Einstein condensation (BCS?BEC) crossover region. The disorder is included in the mean field formalism through Nozi?res?Smith-Rink (NSR) theory of superconducting fluctuations. A self-consistent numerical solution of the coupled equations involving the superfluid gap parameter and density as a function of the disorder strength, albeit unaffected in the BCS phase, yields a depleted order parameter in the BEC regime and an interesting nonmonotonic behaviour of the condensate fraction in the vicinity of the unitary region, and a gradual depletion thereafter, as the pairing interaction is continuously tuned across the BCS?BEC crossover. The unitary regime thus demonstrates a robust paradigm of superfluidity even when the disorder is introduced. To support the above feature and shed light on a lingering controversial issue, we have computed the behaviour of the sound mode across the crossover that distinctly reveals a suppression of the sound velocity. We also find the Landau critical velocity that shows similar nonmonotonicity as that of the condensate fraction data, thereby supporting a stable superfluid scenario in the unitary limit.

Tunneling dynamics of correlated bosons in a double well potential

The quantum dynamics of a few bosons in a double well potential is studied using a Bose Hubbard model. We consider both signs for the on-site interparticle interaction and also investigated the situations where they are large and small. Interesting distinctive features are noted for the tunneling oscillations of these bosons corresponding to the above scenarios. Further, the sensitivity of the particle dynamics to the initial conditions has been studied. It is found that corresponding to an odd number of particles, such as three (or five), an initial condition of having unequal number of particles in the wells has interesting consequences, which is most discernible when the population difference between the wells is unity.

Investigating dirty crossover through fidelity susceptibility and density of states

We investigate the BCS–BEC crossover in an ultracold atomic gas in the presence of disorder. The disorder is incorporated in the mean-field formalism through Gaussian fluctuations. We observe evolution to an asymmetric line-shape of fidelity susceptibility (FS) as a function of interaction coupling with increasing disorder strength which may point to an impending quantum phase transition (QPT). The asymmetric line-shape is further analyzed using the statistical tools of skewness and kurtosis. We extend our analysis to density of states (DOS) for a better understanding of the crossover in the disordered environment.

Electron pairing and evidence of a BCS–BEC crossover in d-wave superconductors

Abstract We have demonstrated that it is possible to access a crossover scenario starting with a weak coupling (BCS) d-wave superconductor to a strongly coupled Bose–Einstein condensate (BEC) phase as the exchange interaction is tuned in a two-dimensional system described by a t–J–U model via numerically solving the Bogoliubov–de Gennes (BdG) equations. While in the extreme dilute limit, the electronic pairing phenomenon is independent of the Coulomb repulsion, U, the superconductivity depends on U, and so does the crossover. Further, the effect of variation in the carrier density on the BCS–BEC crossover has also been investigated. The crossover picture is illustrated by computing the chemical potential, which when falls below the noninteracting band minimum, signals the onset of a phase with tightly bound, shorter pairs. As an evidence of the above feature, the Cooper pair radius is calculated which shows a significant shortening at the emergence of a BEC-like phase. Besides, in contrast to the previous work where a crossover was claimed only in the dilute limit, we have demonstrated it at large densities near half filling.

Bell solitons in ultra-cold atomic Fermi gas

We demonstrate the existence of supersonic bell soliton in the Bardeen-Cooper-Schrieffer-Bose-Einstein condensate (BCS-BEC) crossover regime. Starting from the extended Thomas-Fermi density functional theory of superfluid order parameter, a density transformation is used to map the hydrodynamic mean field equation to a Lienard type equation. As a result, bell solitons are obtained as exact solutions, which is further verified by the numerical solution of the dynamical equation. The stability of the soliton is established and its behaviour in the entire crossover domain is obtained. It is found that, akin to the case of vortices, the bell solitons yield highest contrast in the BEC regime.

Emerging novel phases of Bose-Einstein Condensate for various topology

In this work, we realize the solitons negative mass regime, when a Bose-Einstein condensate is subjected to a harmonic confinement. We also discuss that this system is favorable for the formation of a bound state when an additional species is considered. When a time modulated optical lattice potential is introduced, the sinusoidal lattice modes lead to the generation of nonlinear resonances. A classical dynamical phase transition is also identified in this case through a superfluid to the insulating phase transition.

Effect of weak disorder on the BCS–BEC crossover in a two-dimensional Fermi gas

In this paper, we study the two-dimensional (2D) ultracold Fermi gas with weak impurity in the framework of mean-field theory where the impurity is introduced through Gaussian fluctuations. We have investigated the role of the impurity by studying the experimentally accessible quantities such as condensate fraction and equation of state of the ultracold systems. Our analysis reveals that at the crossover, the disorder enhances superfluidity, which we attribute to the unique nature of the unitary region and to the dimensional effect.

A COMPARISON OF HARMONIC CONFINEMENT AND DISORDER IN INDUCING LOCALIZATION EFFECTS IN A SUPERCONDUCTOR

We present a comparative study of the localization effects induced by harmonic trapping and random onsite disorder in a 2D s-wave superconductor. Performing a numeric computation of the Bogoliubov-de Gennes equations in the presence of parabolic trap and random disorder, we obtain the eigensolutions as a function of trap depth and disorder strength. While the wavefunctions demonstrate localization tendencies for moderate disorder strengths, with finally yielding an insulating behavior at large disorder, the harmonic confinement effects are seen to be vastly more drastic in inducing localization effects.