Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
We consider a quasi-one-dimensional Bose–Einstein condensate with contact and long-range dipolar ... more We consider a quasi-one-dimensional Bose–Einstein condensate with contact and long-range dipolar interactions, under the action of the time-periodic modulation applied to the harmonic-oscillator and optical-lattice trapping potentials. The modulation results in generation of a variety of harmonics in oscillations of the condensate’s width and centre-of-mass coordinate. These include multiple and combinational harmonics, represented by sharp peaks in the system’s spectra. Approximate analytical results are produced by the variational method, which are verified by systematic simulations of the underlying Gross–Pitaevskii equation. This article is part of the theme issue ‘New trends in pattern formation and nonlinear dynamics of extended systems’.
We address dynamics of Bose-Einstein condensates (BECs) loaded into a one-dimensional four-color ... more We address dynamics of Bose-Einstein condensates (BECs) loaded into a one-dimensional four-color optical lattice (FOL) potential with commensurate wavelengths and tunable intensities. This configuration lends system-specific symmetry properties. The analysis identifies specific multi-parameter forms of the FOL potential which admits exact solitary-wave solutions. This newly found class of potentials includes more particular species, such as frustrated double-well superlattices, and bichromatic and three-color lattices, which are subject to respective symmetry constraints. Our exact solutions provide options for controllable positioning of density maxima of the localized patterns, and tunable Anderson-like localization in the frustrated potential. A numerical analysis is performed to establish dynamical stability and structural stability of the obtained solutions, which makes them relevant for experimental realization. The newly found solutions offer applications to the design of sch...
Wave packets are spatially localized, mesoscopic object in quantum mechanics which are known to m... more Wave packets are spatially localized, mesoscopic object in quantum mechanics which are known to manifest interesting phenomena, like revival and fractional revivals, during their course of time evolution when the energy contains nonlinear dependency in the quantum number. Molecular isotope separation from a mixture is experimentally carried out in the literature through different methods: laser isotope separation, wave packet isotope separation, etc. However, the minimum evolution time required for such separation as given by the autocorrelation function is quite long \( ({ \sim }2T_{rev} ) \), which is not favorable for a quantum system due to its unavoidable interaction with the environment. We propose a novel method to separate isotopes of Bromine molecule, 79Br2 and 81Br2, in much smaller time compared to that in the existing literature by introducing an initial time delay between the two lasers while preparing the wave packets. The particular observation time is nothing but a chosen fractional revival instant, coincident for both the isotopes.
We consider Bose–Einstein condensates under an experimentally feasible toroidal trap. Temporal ex... more We consider Bose–Einstein condensates under an experimentally feasible toroidal trap. Temporal expansion of the condensate along the minima of the trap experiences self interference between the counter-propagating constituent parts of the condensate. Condensate density nicely manifests fractional revivals in long time evolution, where the original condensate splits into several subsidiary components at times, rational fractions of the revival time. Upon pointing out this novel phenomenon in this system, we investigate the spatial interference pattern, which requires a careful explanation of the phase distribution among the petals. These features have come out as significantly different from other quantum systems and pave the way to achieve efficient quantum precision measurements in this system.
We present an exact analytical model of a cigar-shaped Bose-Einstein condensate at negative tempe... more We present an exact analytical model of a cigar-shaped Bose-Einstein condensate at negative temperature. This work is motivated by the first experimental discovery of negative temperature in Bose-Einstein condensate by Braun et al. We have considered an external confinement which is a combination of expulsive trap, bi-chromatic optical lattice trap, and linear trap. The present method is capable of providing the exact form of the condensate wavefunction, phase, nonlinearity and gain/loss. One of the consistency conditions is shown to map onto the Schrödinger equation, leading to a significant control over the dynamics of the system. We have modified the model by replacing the optical lattice trap by a bi-chromatic optical lattice trap, which imparts better localization at the central frustrated site, delineated through the variation of condensate fraction. Estimation of temperature and a numerical stability analysis are also carried out. Incorporation of an additional linear trap in...
Abstract We provide an exact analytical model of the 1D Gross-Pitäevskii equation for a composite... more Abstract We provide an exact analytical model of the 1D Gross-Pitäevskii equation for a composite trap, which is capable of producing a variety of potentials: a general power-law, harmonic, tunable double-well etc. We derive a family of exact solitary wave solution for condensate density, which can be controlled by tuning the trap parameters. The fact that the minima positions can be controlled and the potential can also be made asymmetric makes it a favorable candidate for quantum information processing. Coherent control of the condensate profile is investigated, where it shows interesting collapse and revival. Moreover, the obtained two-soliton solution follows periodic and bi-periodic trajectories. A numerical study of the condensate dynamics is carried out to verify our result, which is also supported by a numerical stability analysis. Graphical abstract
International Journal of Quantum Information, 2019
We propose to utilize the Bose–Einstein condensate (BEC) for precision phase sensitive measuremen... more We propose to utilize the Bose–Einstein condensate (BEC) for precision phase sensitive measurement of position and momentum displacements. The controlled two-soliton dynamics can be turned into a quantum probe to measure these parameters with high precision in an experimentally verified system of bright solitary trains. A careful phase space analysis of the dynamics of the mesoscopic wave packet is carried out through Wigner phase space picture for finding out the parameter domain exhibiting sub-Planck structures, required for precision quantum metrology. We propose two experimentally feasible scenarios, one involving the overall phase and the other through the relative phase between the two-solitons when they are oscillating inside the trap. In both the cases, detailed analytical studies are carried out through the overlap functions which reveal the sensitivity issue. A careful analysis is also performed to find the parametric domain relevant for the use of BEC for weak value estim...
We report fractional revivals phenomena in ultracold matter-wave inside a ring-waveguide. The spe... more We report fractional revivals phenomena in ultracold matter-wave inside a ring-waveguide. The specific fractional revival times are precisely identified and corresponding spatial density patterns are depicted. Thorough analyses of the autocorrelation function and quantum carpet provide clear evidences of their occurrence. The exhibited theoretical model is in exact conformity of our numerical results. We also investigate the stability of the condensate and a variation of revival time with the diameter of the ring.
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
We consider a quasi-one-dimensional Bose–Einstein condensate with contact and long-range dipolar ... more We consider a quasi-one-dimensional Bose–Einstein condensate with contact and long-range dipolar interactions, under the action of the time-periodic modulation applied to the harmonic-oscillator and optical-lattice trapping potentials. The modulation results in generation of a variety of harmonics in oscillations of the condensate’s width and centre-of-mass coordinate. These include multiple and combinational harmonics, represented by sharp peaks in the system’s spectra. Approximate analytical results are produced by the variational method, which are verified by systematic simulations of the underlying Gross–Pitaevskii equation. This article is part of the theme issue ‘New trends in pattern formation and nonlinear dynamics of extended systems’.
We address dynamics of Bose-Einstein condensates (BECs) loaded into a one-dimensional four-color ... more We address dynamics of Bose-Einstein condensates (BECs) loaded into a one-dimensional four-color optical lattice (FOL) potential with commensurate wavelengths and tunable intensities. This configuration lends system-specific symmetry properties. The analysis identifies specific multi-parameter forms of the FOL potential which admits exact solitary-wave solutions. This newly found class of potentials includes more particular species, such as frustrated double-well superlattices, and bichromatic and three-color lattices, which are subject to respective symmetry constraints. Our exact solutions provide options for controllable positioning of density maxima of the localized patterns, and tunable Anderson-like localization in the frustrated potential. A numerical analysis is performed to establish dynamical stability and structural stability of the obtained solutions, which makes them relevant for experimental realization. The newly found solutions offer applications to the design of sch...
Wave packets are spatially localized, mesoscopic object in quantum mechanics which are known to m... more Wave packets are spatially localized, mesoscopic object in quantum mechanics which are known to manifest interesting phenomena, like revival and fractional revivals, during their course of time evolution when the energy contains nonlinear dependency in the quantum number. Molecular isotope separation from a mixture is experimentally carried out in the literature through different methods: laser isotope separation, wave packet isotope separation, etc. However, the minimum evolution time required for such separation as given by the autocorrelation function is quite long \( ({ \sim }2T_{rev} ) \), which is not favorable for a quantum system due to its unavoidable interaction with the environment. We propose a novel method to separate isotopes of Bromine molecule, 79Br2 and 81Br2, in much smaller time compared to that in the existing literature by introducing an initial time delay between the two lasers while preparing the wave packets. The particular observation time is nothing but a chosen fractional revival instant, coincident for both the isotopes.
We consider Bose–Einstein condensates under an experimentally feasible toroidal trap. Temporal ex... more We consider Bose–Einstein condensates under an experimentally feasible toroidal trap. Temporal expansion of the condensate along the minima of the trap experiences self interference between the counter-propagating constituent parts of the condensate. Condensate density nicely manifests fractional revivals in long time evolution, where the original condensate splits into several subsidiary components at times, rational fractions of the revival time. Upon pointing out this novel phenomenon in this system, we investigate the spatial interference pattern, which requires a careful explanation of the phase distribution among the petals. These features have come out as significantly different from other quantum systems and pave the way to achieve efficient quantum precision measurements in this system.
We present an exact analytical model of a cigar-shaped Bose-Einstein condensate at negative tempe... more We present an exact analytical model of a cigar-shaped Bose-Einstein condensate at negative temperature. This work is motivated by the first experimental discovery of negative temperature in Bose-Einstein condensate by Braun et al. We have considered an external confinement which is a combination of expulsive trap, bi-chromatic optical lattice trap, and linear trap. The present method is capable of providing the exact form of the condensate wavefunction, phase, nonlinearity and gain/loss. One of the consistency conditions is shown to map onto the Schrödinger equation, leading to a significant control over the dynamics of the system. We have modified the model by replacing the optical lattice trap by a bi-chromatic optical lattice trap, which imparts better localization at the central frustrated site, delineated through the variation of condensate fraction. Estimation of temperature and a numerical stability analysis are also carried out. Incorporation of an additional linear trap in...
Abstract We provide an exact analytical model of the 1D Gross-Pitäevskii equation for a composite... more Abstract We provide an exact analytical model of the 1D Gross-Pitäevskii equation for a composite trap, which is capable of producing a variety of potentials: a general power-law, harmonic, tunable double-well etc. We derive a family of exact solitary wave solution for condensate density, which can be controlled by tuning the trap parameters. The fact that the minima positions can be controlled and the potential can also be made asymmetric makes it a favorable candidate for quantum information processing. Coherent control of the condensate profile is investigated, where it shows interesting collapse and revival. Moreover, the obtained two-soliton solution follows periodic and bi-periodic trajectories. A numerical study of the condensate dynamics is carried out to verify our result, which is also supported by a numerical stability analysis. Graphical abstract
International Journal of Quantum Information, 2019
We propose to utilize the Bose–Einstein condensate (BEC) for precision phase sensitive measuremen... more We propose to utilize the Bose–Einstein condensate (BEC) for precision phase sensitive measurement of position and momentum displacements. The controlled two-soliton dynamics can be turned into a quantum probe to measure these parameters with high precision in an experimentally verified system of bright solitary trains. A careful phase space analysis of the dynamics of the mesoscopic wave packet is carried out through Wigner phase space picture for finding out the parameter domain exhibiting sub-Planck structures, required for precision quantum metrology. We propose two experimentally feasible scenarios, one involving the overall phase and the other through the relative phase between the two-solitons when they are oscillating inside the trap. In both the cases, detailed analytical studies are carried out through the overlap functions which reveal the sensitivity issue. A careful analysis is also performed to find the parametric domain relevant for the use of BEC for weak value estim...
We report fractional revivals phenomena in ultracold matter-wave inside a ring-waveguide. The spe... more We report fractional revivals phenomena in ultracold matter-wave inside a ring-waveguide. The specific fractional revival times are precisely identified and corresponding spatial density patterns are depicted. Thorough analyses of the autocorrelation function and quantum carpet provide clear evidences of their occurrence. The exhibited theoretical model is in exact conformity of our numerical results. We also investigate the stability of the condensate and a variation of revival time with the diameter of the ring.
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Papers by Jayanta Bera