Utpal Roy

Complex solitons in Bose–Einstein condensates with two- and three-body interactions

For the first time, we find the complex solitons for a quasi-one-dimensional Bose-Einstein condensate with two-and three-body interactions. These localized solutions are characterized by a power law behaviour. Both dark and right solitons can be excited in the experimentally allowed parameter domain, when two-and three-body interactions are,respectively, repulsive and attractive. The dark solitons travel with a constant speed, which is quite different from the Lieb mode, where profiles with different speeds, bounded above by sound velocity, can exist for specified interaction strengths. We also study the properties of these solitons in the presence of harmonic confinement with time-dependent nonlinearity and loss. The modulational instability and the Vakhitov-Kolokolov criterion of stability are also studied.

Sub-Planck-scale structures in a vibrating molecule in the presence of decoherence

We study the effect of decoherence on the sub-Planck scale structures of the vibrational wave packet of a molecule. The time evolution of these wave packets is investigated under the influence of a photonic or phononic environment. We determine the master equation describing the reduced dynamics of the wave packet and analyze the sensitivity of the sub-Planck structures against decoherence in the case of a hydrogen iodide (HI) molecule.

Coherent states of the Pöschl–Teller potential and their revival dynamics

A recently developed algebraic approach for constructing coherent states for solvable potentials is used to obtain the displacement operator coherent state of the Poschl–Teller potential. We establish the connection between this and the annihilation operator coherent state and compare their properties. We study the details of the revival structure arising from different time scales underlying the quadratic energy spectrum of this system.

Gapped solitons and periodic excitations in strongly coupled BECs

It is found that localized solitons in the strongly coupled cigar-shaped Bose–Einstein condensates (BECs), in the repulsive domain, form two distinct classes. The one without a background is an asymptotically vanishing, localized soliton, having a wave number, which has a lower bound in magnitude. Periodic soliton trains exist only in the presence of a background, where the localized soliton has a W-type density profile. This soliton is well suited for trapping of neutral atoms and is found to be stable under Vakhitov–Kolokolov criterion, as well as numerical evolution. We identify an insulating phase of this system in the presence of an optical lattice. It is demonstrated that the W-type density profile can be precisely controlled through trap dynamics.

Soliton response to transient trap variations

The response of bright and dark solitons to rapid variations in an expulsive longitudinal trap is investigated. We concentrate on the effect of transient changes in the trap frequency in the form of temporal delta kicks and the hyperbolic cotangent functions. Exact expressions are obtained for the soliton profiles. This is accomplished using the fact that a suitable linear Schr?dinger stationary state solution in time can be effectively combined with the solutions of the nonlinear Schr?dinger equation, for obtaining solutions of the Gross?Pitaevskii equation with a time-dependent scattering length in a harmonic trap. Interestingly, there is rapid pulse amplification in certain scenarios.

Sinusoidal excitations in two-component Bose-Einstein condensates in a trap

The nonlinear coupled Gross-Pitaevskii equation governing the dynamics of the two-component Bose-Einstein condensate (TBEC) is shown to admit sinusoidal, propagating-wave solutions in quasi-one-dimensional geometry in a trap. The solutions exist for a wide parameter range, which illustrates a procedure for coherent control of these modes through temporal modulation of the parameters, like scattering length and oscillator frequency. The effects of time-dependent coupling and the trap variation on the condensate profile are explained. The TBEC has also been investigated in the presence of an optical lattice potential, where the superfluid phase is found to exist under general conditions.

A unified model for an external trap in a cigar-shaped Bose?Einstein condensate

In recent years, the study of cigar shaped Bose?Einstein condensate (BEC) under a variety of external confinements has attracted a great deal of attention, from both theoretical and experimental researchers. We report a unified model for obtaining explicit solutions under various kinds of physically relevant space- and time-modulated external traps and nonlinearities for the cigar shaped BEC. Our novel mechanism paves the way to investigate the system for a family of potential functions unified as a physical parameter of the system. We apply and illustrate our results for a number of exactly solvable quantum mechanical potentials; harmonic, double-well, P?sch?Teller, Morse, Toda lattice and power-law as some of the applications of our model. Expressions of the condensate density are provided for these potentials. In addition, as an application of our model, we have illustrated the condensate dynamics for harmonic, double-well and P?sch?Teller potentials. In the presence of loss/gain for a P?sch?Teller potential, the condensate density shows an interesting collapse and revival.

Bose–Einstein condensate in a bichromatic optical lattice: an exact analytical model

We provide an exact analytical model for the dynamics of a 1D Bose–Einstein condensate loaded in a bichromatic optical lattice. Although a host of exact solutions result from this novel method, we mainly concentrate on the solitonic excitations. The trapping potential and its depth of lattice frustration can be varied by tuning the power and the wavelengths of the two overlaying laser beams. Both attractive and repulsive regimes are thoroughly investigated. In the attractive domain, we obtain bright soliton, which reveals interesting variations with the depth of lattice frustration. Localization of the matter wave density is demonstrated as one of the applications in this regime. In the repulsive domain, dark soliton is obtained when the potential resembles an optical lattice. With appropriate tuning of the potential parameter, the dark soliton becomes modulated with an oscillatory background and gradually transforms to bright solitary trains.

Sub-Planck structures and Quantum Metrology

The significance of sub‐Planck structures in relation to quantum metrology is explored, in close contact with experimental setups. It is shown that an entangled cat state can enhance the accuracy of parameter estimations. The possibilty of generating this state, in dissipative systems has also been demonstrated. Thereafter, the quantum Cramer‐Rao bound for phase estimation through a pair coherent state is calculated, which achieves the maximum possible resolution in an interferometer.

PROPAGATION OF SPIKES IN NONRESONANT ATOMIC MEDIA: THE REDUCED MAXWELL-DUFFING MODEL

We obtain spikes or extremely short pulses for reduced Maxwell-Duffing equations under a general boundary condition, connecting the electric field and electron amplitude, using a Möbius transformation. For a nonzero background, this system is shown to admit two families of exact solutions in the form of solitary waves and kink-type of solutions. Parameter domains are delineated where localized solutions signifying both bright and dark spikes, as also singular solutions indicating self-focusing effect, exist in this dynamical system, in nonresonant atomic media.