Frontiers in Engineering and Built Environment, 2021
PurposeThe purpose of this paper is to show a comparative study of different direction-of-arrival... more PurposeThe purpose of this paper is to show a comparative study of different direction-of-arrival (DOA) estimation techniques, namely, multiple signal classification (MUSIC) algorithm, delay-and-sum (DAS) beamforming, support vector regression (SVR), multivariate linear regression (MLR) and multivariate curvilinear regression (MCR).Design/methodology/approachThe relative delay between the microphone signals is the key attribute for the implementation of any of these techniques. The machine-learning models SVR, MLR and MCR have been trained using correlation coefficient as the feature set. However, MUSIC uses noise subspace of the covariance-matrix of the signals recorded with the microphone, whereas DAS uses the constructive and destructive interference of the microphone signals.FindingsVariations in root mean square angular error (RMSAE) values are plotted using different DOA estimation techniques at different signal-to-noise-ratio (SNR) values as 10, 14, 18, 22 and 26dB. The RMSAE...
Recent observations of droplets in dipolar and binary Bose-Einstein condensate (BEC) motivates us... more Recent observations of droplets in dipolar and binary Bose-Einstein condensate (BEC) motivates us to study the theory of droplet formation in detail. Precisely, we are interested in investigating the possibility of droplet formation in a quasi-one-dimensional geometry. The recent observations have concluded that the droplets are stabilized by the competition between effective mean-field and beyond mean-field interaction. Hence, it is possible to map the effective equation of motion to a cubic-quartic nonlinear Schrödinger equation (CQNLSE). We obtain two analytical solutions of the modified Gross-Pitaevskii equation or CQNLSE and verified them numerically. Based on their stability we investigate the parameter regime for which droplets can form. The effective potential allows us to conclude about the regions of soliton domination and self-bound droplet formations.
The effect of light-matter interaction is investigated for a situation where counter propagating ... more The effect of light-matter interaction is investigated for a situation where counter propagating laser pulses of localized nature are incident on the atomic condensate. In contrast to the earlier investigations on the similar systems, it's assumed that the laser beams are ultra-fast and they have a $\mathrm{sech}^2$ profile. Specifically, we consider a quasi-homogeneous, later extended to inhomogeneous, Bose-Einstein condensate (BEC), which is exposed to two counter propagating orthogonally polarized ultra-fast laser beams of equal intensity. The electromagnetic field creates an optical potential for the Bose-Einstein condensate, which in turn modifies the optical field. Hence, light and matter are found to contentiously exchange energy and thus to modify themselves dynamically. In the inhomogenous case, a self-similar method is used here to treat a cigar-shaped BEC exposed to light. Our theoretical analysis in a hither to unexplored regime of BEC-light interaction hints at the ...
The recent observations of quantum droplet in ultra-cold atomic gases have opened up new avenues ... more The recent observations of quantum droplet in ultra-cold atomic gases have opened up new avenues of fundamental research. The competition between mean-field and beyond mean-field interactions, in ultra-cold dilute alkali gases, are believed to be instrumental in stabilizing the droplets. These new understanding has motivated us to investigate the analytical solutions of a trapped cubic-quartic nonlinear Schrödinger equation (CQNLSE). The quartic contribution in the NLSE is derived from the beyond mean-field formalism of Bose-Einstein condensate (BEC). To the best of our knowledge, a comprehensive analytical description of CQNLSE is non-existent. Here, we study the existence of the analytical solutions which are of the cnoidal type for CQNLSE. The external trapping plays a significant role in the stabilization of the system. In the limiting case, the cnoidal wave solutions lead to the localized solution of bright solution and delocalized kink-antikink pair. The nonexistence of the sinusoidal mode in the current scheme is also revealed in our analysis.
Exchange of energy by means of light-matter interaction provides a new dimension to various nonli... more Exchange of energy by means of light-matter interaction provides a new dimension to various nonlinear dynamical systems. Here, the effects of light-matter interaction are investigated for a situation, where two counter-propagating, orthogonally polarized laser pulses are incident on the atomic condensate. It's observed that a localized laser pulse profile can induce localized modes in Bose-Einstein condensate. A stability analysis performed using Vakhitov-Kolokolov-like criterion has established that these localized modes are stable, when the atom-atom interaction is repulsive. The cooperative effects of light-matter interactions and atom-atom interactions on the Lieb-mode have been studied in the stable region through atomic dispersion, revealing the signature of bound state formation when the optical potential is Pöschl-Teller type. The energy diagram also indicates a continuous transfer of energy from the laser pulses to the atoms as the light-matter interaction changes its sign. PACS. 03.75.Lm Bose-Einstein condensates in periodic potentials-05.45.Yv SOlitons-32.80.Qk Coherent control of atomic interactions with photons
In this work, we realize the soliton's negative mass regime, when a Bose-Einstein condensate is s... more In this work, we realize the soliton's 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.
In this work, we realize the soliton's negative mass regime, when a Bose-Einstein condensate is s... more In this work, we realize the soliton's 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.
In this paper, we study the two-dimensional (2D) ultracold Fermi gas with weak impurity in the fr... more 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.
The quantum dynamics of a few bosons in a double well potential is studied using a Bose Hubbard m... more 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.
We have investigated the formation of bound state of two electrons in different kind of lattices ... more We have investigated the formation of bound state of two electrons in different kind of lattices using a t-J-U model.
We investigate the BCS–BEC crossover in an ultracold atomic gas in the presence of disorder. The ... more 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.
We have demonstrated that it is possible to access a crossover scenario starting with a weak coup... more 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 phenomena 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.
Of late, the study of BCS-BEC crossover in the presence of weak random impurity is an interesting... more Of late, the study of BCS-BEC crossover in the presence of weak random impurity is an interesting issue. In this proceedings we study the effect of this disorder which is included through the Nozières and Smith-Rink theory of superconducting fluctuations. In the weak regime, the random potential leaves an effect on the superconducting order parameter but it spares the chemical potential. Here we present the exact behavior of the mean field quantities as a function of the disorder by self-consistently solving the coupled equations.
Journal of Superconductivity and Novel Magnetism, 2012
We develop the formalism for BCS-BEC crossover in the presence of weak random impurity and calcul... more We develop the formalism for BCS-BEC crossover in the presence of weak random impurity and calculate the effect of the random potentials on the basic mean-field quantities. The disorder has been included through the Nozières and Schmitt-Rink theory of superconducting fluctuations, and we obtain the disorder induced superfluid order parameter and chemical potential through a self-consistent calculation. We also calculate the condensate fraction which reveals a distinct nonmonotonic behavior. The downturn in the latter result occurs at the crossover regime with gradual depletion on the BEC side. The non-monotonic feature in the condensate fraction data has been measured in clean systems. Motivated by the above result, we discuss the stability of a disordered fermionic superfluid in the crossover regime.
Journal of Physics B: Atomic, Molecular and Optical Physics, 2012
In this article we have investigated the effect of weak random disorder in the BCS-BEC crossover ... more In this article we have investigated the effect of weak random disorder in the BCS-BEC crossover region. The disorder is included in the mean field formalism through 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 behavior 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 behavior 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.
Journal of Physics B: Atomic, Molecular and Optical Physics, 2013
We demonstrate the existence of supersonic bell soliton in the Bardeen-Cooper-Schrieffer-Bose-Ein... more 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 behavior 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.
Solving Bogoliubov-de Gennes (BdG) equations for a two dimensional Hubbard model with random on-s... more Solving Bogoliubov-de Gennes (BdG) equations for a two dimensional Hubbard model with random on-site disorder, we compute the participation ratio and fidelity to establish conviction for a BCS-BEC crossover scenario at intermediate values of disorder proposed earlier [P. Dey, S. Basu, J. Phys.: Condens. Matter 20, 485205 (2008)]. The participation ratio analysis suggests the onset of a phase with shrunk pairs extending over moderate number of lattice sites, which however preserves the superfluid character. The fidelity or the ground state overlap for two different (but closely lying) values of the disorder strength shows an abrupt drop at the immediate neighbourhood of the disorder strength where an onset of a paired (bose-like) phase occurs.
ABSTRACT We carry out a detailed investigation of the Bose glass (BG) phase that interrupts a dir... more ABSTRACT We carry out a detailed investigation of the Bose glass (BG) phase that interrupts a direct transition from a superfluid to a Mott insulating phase in a two dimensional disordered Bose Hubbard Model. The accurate distinction between various phases is done via computing a number of relevant physical quantities such as a ratio of the sites containing integer density of the bosons to that of the total number of sites, compressibility, or a close variant of it, that is the relative fluctuation of the boson density and the entropy. Quite intriguingly, assuming the appearance of a spanning cluster of sites with integer occupancy to signal the onset of the BG phase, we find that the percolation threshold is same as that of random site percolation model in two dimensions. This similarity between two completely different systems is thought to be accidental, but may open up more studies in the future to critically examine the issue. Further, with the data obtained from our analysis, we have been able to obtain a complete phase diagram defined by the local interparticle interaction parameter (U) and the chemical potential (μ) averaged over several random configurations at different disorder values.
We elaborate on a general method to find complex envelope solitons in a cigar shaped Bose-Einstei... more We elaborate on a general method to find complex envelope solitons in a cigar shaped Bose-Einstein condensate in a trap. The procedure incorporates time dependent scattering length, oscillator frequency and loss/gain. A variety of time dependencies of the above parameters, akin to the ones occurring in the experiments can be tackled.
Frontiers in Engineering and Built Environment, 2021
PurposeThe purpose of this paper is to show a comparative study of different direction-of-arrival... more PurposeThe purpose of this paper is to show a comparative study of different direction-of-arrival (DOA) estimation techniques, namely, multiple signal classification (MUSIC) algorithm, delay-and-sum (DAS) beamforming, support vector regression (SVR), multivariate linear regression (MLR) and multivariate curvilinear regression (MCR).Design/methodology/approachThe relative delay between the microphone signals is the key attribute for the implementation of any of these techniques. The machine-learning models SVR, MLR and MCR have been trained using correlation coefficient as the feature set. However, MUSIC uses noise subspace of the covariance-matrix of the signals recorded with the microphone, whereas DAS uses the constructive and destructive interference of the microphone signals.FindingsVariations in root mean square angular error (RMSAE) values are plotted using different DOA estimation techniques at different signal-to-noise-ratio (SNR) values as 10, 14, 18, 22 and 26dB. The RMSAE...
Recent observations of droplets in dipolar and binary Bose-Einstein condensate (BEC) motivates us... more Recent observations of droplets in dipolar and binary Bose-Einstein condensate (BEC) motivates us to study the theory of droplet formation in detail. Precisely, we are interested in investigating the possibility of droplet formation in a quasi-one-dimensional geometry. The recent observations have concluded that the droplets are stabilized by the competition between effective mean-field and beyond mean-field interaction. Hence, it is possible to map the effective equation of motion to a cubic-quartic nonlinear Schrödinger equation (CQNLSE). We obtain two analytical solutions of the modified Gross-Pitaevskii equation or CQNLSE and verified them numerically. Based on their stability we investigate the parameter regime for which droplets can form. The effective potential allows us to conclude about the regions of soliton domination and self-bound droplet formations.
The effect of light-matter interaction is investigated for a situation where counter propagating ... more The effect of light-matter interaction is investigated for a situation where counter propagating laser pulses of localized nature are incident on the atomic condensate. In contrast to the earlier investigations on the similar systems, it's assumed that the laser beams are ultra-fast and they have a $\mathrm{sech}^2$ profile. Specifically, we consider a quasi-homogeneous, later extended to inhomogeneous, Bose-Einstein condensate (BEC), which is exposed to two counter propagating orthogonally polarized ultra-fast laser beams of equal intensity. The electromagnetic field creates an optical potential for the Bose-Einstein condensate, which in turn modifies the optical field. Hence, light and matter are found to contentiously exchange energy and thus to modify themselves dynamically. In the inhomogenous case, a self-similar method is used here to treat a cigar-shaped BEC exposed to light. Our theoretical analysis in a hither to unexplored regime of BEC-light interaction hints at the ...
The recent observations of quantum droplet in ultra-cold atomic gases have opened up new avenues ... more The recent observations of quantum droplet in ultra-cold atomic gases have opened up new avenues of fundamental research. The competition between mean-field and beyond mean-field interactions, in ultra-cold dilute alkali gases, are believed to be instrumental in stabilizing the droplets. These new understanding has motivated us to investigate the analytical solutions of a trapped cubic-quartic nonlinear Schrödinger equation (CQNLSE). The quartic contribution in the NLSE is derived from the beyond mean-field formalism of Bose-Einstein condensate (BEC). To the best of our knowledge, a comprehensive analytical description of CQNLSE is non-existent. Here, we study the existence of the analytical solutions which are of the cnoidal type for CQNLSE. The external trapping plays a significant role in the stabilization of the system. In the limiting case, the cnoidal wave solutions lead to the localized solution of bright solution and delocalized kink-antikink pair. The nonexistence of the sinusoidal mode in the current scheme is also revealed in our analysis.
Exchange of energy by means of light-matter interaction provides a new dimension to various nonli... more Exchange of energy by means of light-matter interaction provides a new dimension to various nonlinear dynamical systems. Here, the effects of light-matter interaction are investigated for a situation, where two counter-propagating, orthogonally polarized laser pulses are incident on the atomic condensate. It's observed that a localized laser pulse profile can induce localized modes in Bose-Einstein condensate. A stability analysis performed using Vakhitov-Kolokolov-like criterion has established that these localized modes are stable, when the atom-atom interaction is repulsive. The cooperative effects of light-matter interactions and atom-atom interactions on the Lieb-mode have been studied in the stable region through atomic dispersion, revealing the signature of bound state formation when the optical potential is Pöschl-Teller type. The energy diagram also indicates a continuous transfer of energy from the laser pulses to the atoms as the light-matter interaction changes its sign. PACS. 03.75.Lm Bose-Einstein condensates in periodic potentials-05.45.Yv SOlitons-32.80.Qk Coherent control of atomic interactions with photons
In this work, we realize the soliton's negative mass regime, when a Bose-Einstein condensate is s... more In this work, we realize the soliton's 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.
In this work, we realize the soliton's negative mass regime, when a Bose-Einstein condensate is s... more In this work, we realize the soliton's 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.
In this paper, we study the two-dimensional (2D) ultracold Fermi gas with weak impurity in the fr... more 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.
The quantum dynamics of a few bosons in a double well potential is studied using a Bose Hubbard m... more 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.
We have investigated the formation of bound state of two electrons in different kind of lattices ... more We have investigated the formation of bound state of two electrons in different kind of lattices using a t-J-U model.
We investigate the BCS–BEC crossover in an ultracold atomic gas in the presence of disorder. The ... more 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.
We have demonstrated that it is possible to access a crossover scenario starting with a weak coup... more 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 phenomena 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.
Of late, the study of BCS-BEC crossover in the presence of weak random impurity is an interesting... more Of late, the study of BCS-BEC crossover in the presence of weak random impurity is an interesting issue. In this proceedings we study the effect of this disorder which is included through the Nozières and Smith-Rink theory of superconducting fluctuations. In the weak regime, the random potential leaves an effect on the superconducting order parameter but it spares the chemical potential. Here we present the exact behavior of the mean field quantities as a function of the disorder by self-consistently solving the coupled equations.
Journal of Superconductivity and Novel Magnetism, 2012
We develop the formalism for BCS-BEC crossover in the presence of weak random impurity and calcul... more We develop the formalism for BCS-BEC crossover in the presence of weak random impurity and calculate the effect of the random potentials on the basic mean-field quantities. The disorder has been included through the Nozières and Schmitt-Rink theory of superconducting fluctuations, and we obtain the disorder induced superfluid order parameter and chemical potential through a self-consistent calculation. We also calculate the condensate fraction which reveals a distinct nonmonotonic behavior. The downturn in the latter result occurs at the crossover regime with gradual depletion on the BEC side. The non-monotonic feature in the condensate fraction data has been measured in clean systems. Motivated by the above result, we discuss the stability of a disordered fermionic superfluid in the crossover regime.
Journal of Physics B: Atomic, Molecular and Optical Physics, 2012
In this article we have investigated the effect of weak random disorder in the BCS-BEC crossover ... more In this article we have investigated the effect of weak random disorder in the BCS-BEC crossover region. The disorder is included in the mean field formalism through 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 behavior 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 behavior 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.
Journal of Physics B: Atomic, Molecular and Optical Physics, 2013
We demonstrate the existence of supersonic bell soliton in the Bardeen-Cooper-Schrieffer-Bose-Ein... more 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 behavior 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.
Solving Bogoliubov-de Gennes (BdG) equations for a two dimensional Hubbard model with random on-s... more Solving Bogoliubov-de Gennes (BdG) equations for a two dimensional Hubbard model with random on-site disorder, we compute the participation ratio and fidelity to establish conviction for a BCS-BEC crossover scenario at intermediate values of disorder proposed earlier [P. Dey, S. Basu, J. Phys.: Condens. Matter 20, 485205 (2008)]. The participation ratio analysis suggests the onset of a phase with shrunk pairs extending over moderate number of lattice sites, which however preserves the superfluid character. The fidelity or the ground state overlap for two different (but closely lying) values of the disorder strength shows an abrupt drop at the immediate neighbourhood of the disorder strength where an onset of a paired (bose-like) phase occurs.
ABSTRACT We carry out a detailed investigation of the Bose glass (BG) phase that interrupts a dir... more ABSTRACT We carry out a detailed investigation of the Bose glass (BG) phase that interrupts a direct transition from a superfluid to a Mott insulating phase in a two dimensional disordered Bose Hubbard Model. The accurate distinction between various phases is done via computing a number of relevant physical quantities such as a ratio of the sites containing integer density of the bosons to that of the total number of sites, compressibility, or a close variant of it, that is the relative fluctuation of the boson density and the entropy. Quite intriguingly, assuming the appearance of a spanning cluster of sites with integer occupancy to signal the onset of the BG phase, we find that the percolation threshold is same as that of random site percolation model in two dimensions. This similarity between two completely different systems is thought to be accidental, but may open up more studies in the future to critically examine the issue. Further, with the data obtained from our analysis, we have been able to obtain a complete phase diagram defined by the local interparticle interaction parameter (U) and the chemical potential (μ) averaged over several random configurations at different disorder values.
We elaborate on a general method to find complex envelope solitons in a cigar shaped Bose-Einstei... more We elaborate on a general method to find complex envelope solitons in a cigar shaped Bose-Einstein condensate in a trap. The procedure incorporates time dependent scattering length, oscillator frequency and loss/gain. A variety of time dependencies of the above parameters, akin to the ones occurring in the experiments can be tackled.
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Papers by Ayan Khan