arXiv subjects

Bimalendu Deb

Publications and source records attributed to Bimalendu Deb.

At least 37 records · Page 2Linked to original sources

arXiv2022

Electronic structure, spectroscopy, cold ion-atom elastic collision properties and photoassociation formation prediction of (MgCs)$^+$ molecular ion

Studies on the interactions between an alkali atom and an alkaline earth ion at low energy are important in the field of cold chemistry. In this paper we, extensively, study the structure, interactions, and dynamics of (MgCs)$^+$ molecular ion. We use an ab initio approach based on the formalism of non-empirical pseudo-potential for Mg$^{2+}$ and Cs$^+$ cores, large Gaussian basis sets and full valence configuration interaction. In this context, the (MgCs)$^+$ cation is treated as an effective two-electron system. Potential energy curves and their spectroscopic constants for the ground and the first 41 excited states of $^{1,3}Σ^+$, $^{1,3}Π$ and $^{1,3}Δ$ symmetries are determined. Furthermore, we identify the avoided crossings between the electronic states of $^{1,3}Σ^+$ and $^{1,3}Π$ symmetries. These crossings are related to the charge transfer process between the two ionic limits Mg/Cs$^+$ and Mg$^+$/Cs. In addition, vibrational-level spacings, the transition and permanent dipole moments are presented and analysed. Using the produced potential energy data, the ground-state scattering wave functions and elastic cross sections for a wide range of energies are performed. Furthermore, we predict the formation of translationally and rotationally cold molecular ion (MgCs) + in the ground state electronic potential energy by stimulated Raman type process aided by ion-atom cold collision. In the low energy limit (< 1 mK), elastic scattering cross sections exhibit Wigner law threshold behaviour; while in the high energy limit the cross sections as a function of energy E go as E$^{-1/3}$. A qualitative discussion about the possibilities of forming the cold (MgCs)$^+$ molecular ions by photoassociative spectroscopy is presented.

physics.atom-ph↗

arXiv2021

A model study on superfluidity of a unitary Fermi gas of atoms interacting with a finite-ranged potential

We calculate Bardeen-Cooper-Schrieffer (BCS) state of a unitary Fermi gas of atoms interacting with the finite-ranged Jost-Kohn potential which has been recently shown to account for the resonant interactions [2019 {\rm J. Phys. B: At. Mol. Opt. Phys.} {\bf 52}, 165004]. Using exact scattering solution of the potential, we derive two-body ${\mathbf T}$-matrix element which is employed to construct the BCS Hamiltonian in momentum space. We present results on the energy- and range-dependence of the pairing gap and superfluid density and the range-dependence of the chemical potential for a wide variation of the scattering length including the unitary regime. In the zero range limit our calculated gap at the Fermi energy is found to be nearly equal to that calculated in mean-field theory with contact potential. The mean gap averaged over the full width at half maximum of the gap function in the zero range and unitary limits is found to be $0.42 E_F$ which is quite close to the recent result of the quantum Monte Carlo simulation [2018 {\rm Phys. Rev.A} {\bf 97}, 013601]. The chemical potential in the zero range limit also agrees well with that for the contact potential.

cond-mat.quant-gas↗

arXiv2021

Time- and frequency-domain two-particle correlations of a driven dissipative Bose-Hubbard model

We theoretically investigate the time- and frequency-domain two-particle correlations of a driven dissipative Bose-Hubbard model (BHM) at and near a dissipative phase transition (DPT). We compute Hanbury Brown-Twiss (HBT) type two-particle temporal correlation function $g^2(τ)$ which, as a function of time delay $τ$, exhibits oscillations with frequencies determined by the imaginary part of Liouvillian gap. As the gap closes near a transition point, the oscillations at that point dies down. For parameters slightly away from the transition point, the HBT correlations show oscillations from super-bunching to anti-bunching regimes. We show that the Fourier transform of HBT correlations into frequency domain provide information about DPT and Liouvillian dynamics. We numerically solve the many-body Lindblad master equation and calculate Wigner distribution of the system in steady state to ascertain DPT.Below certain drive strength, the Fourier transform shows a two-peak structure while above that strength it exhibits either a Lorenzian-like single-peak structure or a structure with two-dips. The width of the single-peak structure is minimum at the phase transition point and the peak of this structure always lies at zero frequency. The positions of the two symmetrical peaks in case of two-peak structure are given by the imaginary parts of the Liouvillian gap while their half width at half maximum (HWHM) is given by the real part of the gap. The positions and the widths of the two dips are also related to low lying eigenvalues of the Liouvillian operator. We discuss quantum statistical properties of the model in terms of the HBT correlation function and its Fourier transform.

physics.atom-ph↗

arXiv2021

Matter-wave phase operators for quantum atom optics: On the possibility of experimental verification

In early 90's Mandel and coworkers performed an experiment \cite{mandel} to examine the significance of quantum phase operators by measuring the phase between two optical fields. We show that this type of quantum mechanical phase measurement is possible for matter-waves of ultracold atoms in a double well. In the limit of low number of atoms quantum and classical phases are drastically different. However, in the large particle number limit, they are quite similar. We assert that the matter-wave counterpart of the experiment \cite{mandel} is realizable with the evolving technology of atom optics.

quant-ph↗

arXiv2020

Realizing negative index of refraction in an ensemble of ground-state polar molecules with lasers

We propose a coherent optical method for creating negative refractive index (NRI) for a gaseous ensemble of ground-state polar molecules possessing both permanent electric and magnetic moments. Exploiting the pure rotational transition between the two lowest rotational levels of the ground vibrational state one can generate two dressed states of mixed parity using a microwave laser. These dressed states are then used as the two lower states of a Λ-type three-level scheme using two infrared lasers to couple them to another ro-vibrational level in the ground-state manifold. One of the infrared lasers is used as a weak probe and the other as a control field with a fixed detuning. We take into account local-field effects on the dielectric response of the medium at the probe frequency in terms of Clausius-Mossoti relation. We extract magnetic response out of purely dielectric response and calculate the magnetic permeability of the medium in terms of dielectric susceptibility. Our results show that there is a small frequency window near the two-photon resonance where both electric permittivity and magnetic permeability are negative with vanishingly small absorption. The figure of merit for the medium is shown to exceed unity. We interpret our results in terms of the proximity of EIT and quantum interference. We discuss the possible realization of our method using cold polar molecules that are recently experimentally produced.

physics.optics↗

arXiv2020

Parametric oscillations in a dissipative bosonic Josephson junction

We study the dynamics of a nonlinear dissipative bosonic Josephson junction (BJJ) with a time-dependent sinusoidal perturbation in interaction term. We demonstrate parametric resonance where the system undergoes sustained periodic oscillations even in the presence of dissipation. This happens when the frequency of the perturbation is close to twice the frequency of the unperturbed Josephson oscillations and the strength of perturbation exceeds a critical threshold. We have formulated the threshold conditions for parametric oscillations. To explore the nature of the oscillations, we carry out a multiple time scale analysis of the stability boundaries in terms of the V-shaped Arnold's tongue in the parameter space. Full numerical simulations have been performed for the zero-, running- and $π$-phase modes of nonlinear Josephson effect. Our results demonstrate that in $π$-phase mode, the system is capable of making a transition from regular parametric to chaotic parametric oscillations as one crosses the stability boundary. Also, the phase difference undergoes phase slip before executing sustained parametric oscillations.

quant-ph↗

arXiv2019

Fermionic vs. bosonic two-site Hubbard models with a pair of interacting cold atoms

In a recent work, Murmann {\it et. al.} [Phys. Rev. Lett. {\bf114}, 080402 (2015)] have experimentally prepared and manipulated a double-well optical potential containing a pair of Fermi atoms as a possible building block of Hubbard model. Here, we carry out a detailed theoretical study on the properties of both fermionic and bosonic two-site Hubbard models with a pair of interacting atoms in a trap with a double-well structure along z-axis and a 2D harmonic confinement along the transverse directions. We consider fermions as of two-component type and bosons as of spinless as well as of two spin components. We first discuss building up the Hubbard models using the model finite-range interaction potentials of Jost and Kohn. In general, a finite range of interaction leads to on-site, inter-site, exchange and partial-exchange terms. We show that, given the same input parameters for both bosonic and fermionic two-site Hubbard models, many of the statistical properties such as the single- and double-occupancy of a site, and the probabilities for the single-particle and pair tunneling are similar in both fermionic and bosonic cases. But, quantum entanglement and quantum fluctuations are found to be markedly different for the two cases. We discuss atom-atom entanglement in two spatial modes corresponding to the two sites of the double-well. Our results show that the entanglement of a pair of spin-half fermions is always greater than that of spinless bosons; and when the fermions are maximally entangled the fluctuation in the two-mode phase difference is largely squeezed. In contrast, spinless bosons never exhibit phase squeezing, but shows squeezing in two-mode population imbalance depending on the system parameters.

quant-ph↗

arXiv2019

Modeling atom-atom interactions at low energy by Jost-Kohn potentials

More than 65 years ago, Jost and Kohn [R. Jost and W. Kohn, {Phys. Rev.} {\bf 87}, 977 (1952)] derived an explicit expression for a class of short-range model potentials from a given effective range expansion with the $s$-wave scattering length $a_s$ being negative. For $a_s >0$, they calculated another class of short-range model potentials [R. Jost and W. Kohn, { Dan. Mat. Fys. Medd} {\bf 27}, 1 (1953)] using a method based on an adaptation from Gelfand-Levitan theory [I. M. Gel'fand and B. M. Levitan, { Dokl. Akad. Nauk. USSR} {\bf 77}, 557-560 (1951)] of inverse scattering. We here revisit the methods of Jost and Kohn in order to explore the possibility of modeling resonant finite-range interactions at low energy. We show that the Jost-Kohn potentials can account for zero-energy resonances. The $s$-wave phase shift for positive scattering length is expressed in an analytical form as a function of the binding energy of a bound state. We show that, for small binding energy, both the scattering length and the effective range are strongly influenced by the binding energy; and below a critical binding energy the effective range becomes negative provided the scattering length is large. As a consistency check, we carry out some simple calculations to show that Jost-Kohn potentials can reproduce the standard results of contact interaction in the limit of the effective range going to zero.

physics.atom-ph↗

arXiv2019

The effects of trap-confinement and interatomic interactions on Josephson effects and macroscopic quantum self-trapping for a Bose-Einstein Condensate

We theoretically study the effects of trap-confinement and interatomic interactions on Josephson oscillations (JO) and macroscopic quantum self-trapping (MQST) for a Bose-Einstein condensate (BEC) confined in a trap which has a symmetric double-well (DW) potential along z-axis and 2D harmonic potentials along x- and y-axis. We consider three types of model interaction potentials: contact, long-range dipolar and finite-range potentials. Our results show that by changing the aspect ratio between the axial and radial trap sizes, one can induce a transition from JO to MQST for contact interactions with a small scattering length. For long-range dipolar interatomic interactions, we analyze transition from Rabi to Josephson regime and Josephson to MQST regime by changing the aspect ratio of the trap for a particular dipolar orientation. For a finite-range interaction, we study the effects of relatively large scattering length and effective range on JO and MQST. We show that JO and MQST are possible even if scattering length is relatively large, particularly near a narrow Feshbach resonance due to the finite-range effects.

physics.atom-ph↗

arXiv2019

Suppressing deleterious effects of spontaneous emission in creating bound states in cold atom continuum

In a previous paper [B. Deb and G. S. Agarwal, Phys. Rev. A 90, 063417 (2014)], it was theoretically shown that, magneto-optical manipulation of low energy scattering resonances and atom-molecule transitions could lead to the formation of a bound state in continuum (BIC), provided there is no spontaneous emission. We find that even an exceedingly small spontaneous decay from exited molecular states can spoil the BIC. In this paper, we show how to circumvent the detrimental effect of spontaneous emission by making use of vacuum-induced coherence (VIC) which results in the cancellation or suppression of spontaneous emission. VIC occurs due to the destructive interference between two spontaneous decay pathways. An essential condition for VIC is the non-orthogonality of the transition dipole moments associated with the decays. Furthermore, the interference between decay pathways requires that the spacing between the two decaying states must be comparable to or smaller than the square root of the product of the two spontaneous linewidths. We demonstrate that these conditions can be fulfilled by microwave dressing of two appropriately chosen molecular excited states, opening a promising prospect for the experimental realization of BIC of cold atoms.

quant-ph↗

arXiv2018

Photon-photon correlations with a V-type three-level system interacting with two quantized field modes

We carry out a model study on the interaction of a $V$-type three-level emitter with two quantized cavity modes which are weakly driven by two classical fields. The emitter may be an atom or a molecule with nondegenerate upper levels in general. The lifetimes of the two upper levels are assumed to be much longer than the lifetime of the cavity photons. We calculate the two-time second order coherence function, namely Hanbury Brown-Twiss function $g^{(2)}(τ)$ where $τ$ is the time delay between the two modes. We analyze the photon-photon correlations between the two cavity modes in terms of $g^{(2)}(τ)$. The variation of $g^{(2)}(τ)$ as a function of $τ$ exhibits collapse and revival type oscillations as well as quantum beats for relatively short $τ$ while in the limit $τ\rightarrow \infty$, $g^{(2)}(τ) \simeq 1$. We further show that the two cavity field modes are entangled when $g^{(2)}(0) > 2$. We develop a dressed state picture with single photon in each mode to explain the results and use the negativity of the partial transpose of the reduced field density matrix to show the entanglement between field modes. The model presented in this paper may be useful for generating entangled photon pairs, and also manipulating photon-photon correlations with a cavity QED set up.

physics.atom-ph↗

arXiv2018

Structure, spectroscopy and cold collisions of the (SrNa)$^+$ ionic system

We perform a study on extended adiabatic potential energy curves of nearly 38 states of 1,3$Σ^+$, 1,3$Π$ and 1,3$Δ$ symmetries for the (SrNa)$^+$ ion, though only the ground and first two excited states are used for the study of scattering processes. Full Interaction Configuration (CI) calculations are carried out for this molecule using the pseudopotential approach. In this context, it is considered that two active electrons interact with the ionic cores and all single and double excitations were included in the CI calculations. A correction including the core-core electron interactions is also considered. Using the accurate potential energy data, the ground state scattering wave functions and cross sections are obtained for a wide range of energies. We find that, in order to get convergent results for the total scattering cross sections for energies of the order 1 K, one need to take into account at least 87 partial waves. In the low energy limit ( < 1 mK), elastic scattering cross sections exhibit Wigner law threshold law behavior while in the high energy limit the cross sections go as $E^{-1/3}$. A qualitative discussion about the possibility of forming the cold molecular ion by photoassociative spectroscopy is presented.

physics.atom-ph↗

arXiv2018

Spectroscopic properties of the molecular ions BeX^+ (X=Na, K, Rb): Forming cold molecular ions from an ion-atom mixture by stimulated Raman adiabatic process

In this theoretical work, we calculate potential energy curves, spectroscopic pa- rameters and transition dipole moments of molecular ions BeX^+ (X=Na, K, Rb) composed of alkaline ion Be and alkali atom X with a quantum chemistry approach based on the pseudopotential model, Gaussian basis sets, effective core polarization potentials, and full configuration interaction (CI). We study in detail collisions of the alkaline ion and alkali atom in quantum regime. Besides, we study the possibility of the formation of molecular ions from the ion-atom colliding systems by stimu- lated Raman adiabatic process and discuss the parameters regime under which the population transfer is feasible. Our results are important for ion-atom cold collisions and experimental realization of cold molecular ion formation.

physics.atom-ph↗

arXiv2018

Density profiles of two-component Bose-Einstein condensates interacting with a Laguerre-Gaussian Beam

The density profiles of trapped two-component Bose-Einstein condensates (BEC) and its microscopic interaction with Laguerre Gaussian (LG) beam are studied. We consider the $^{87}$Rb BEC in two hyperfine spin components. The wavelength of the LG beam is assumed to be comparable to the atomic de-Broglie wavelength. Competitions between intra- and inter-component interactions produce interesting density structures of the ground state of BEC. We demonstrate vortex-antivortex interference and its dependence on the inter-component interactions and Raman transitions.

physics.atom-ph↗

arXiv2017

Number-phase uncertainty and quantum dynamics of bosons and fermions interacting with a finite range and large scattering length in a double-well potential

We define the standard quantum limit (SQL) for phase and number fluctuations, and describe two-mode squeezing for number and phase variables. When phase is treated as a unitary quantum-mechanical operator, number and phase operators satisfy an uncertainty relation. As a result, the usual definition of number squeezing parameter becomes modified. Two-mode number squeezing occurs when the number fluctuation goes below the SQL at the cost of enhanced phase fluctuation. As an application of number-phase uncertainty, we consider bosons or fermions trapped in a quasi-one dimensional double-well (DW) potential interacting via a 3D finite-range two-body interaction potential with large scattering length $a_s$. Under tight-binding or two-mode approximation, we describe in detail the effects of the range of interaction on the quantum dynamics and number-phase uncertainty in the strongly interacting or unitarity regime $a_s \rightarrow \pm \infty$. Our results show intriguing coherent dynamics of number-phase uncertainty with number-squeezing for bosons and phase squeezing for fermions. Our results may be important for exploring new quantum interferometry, Josephson oscillations, Bose-Hubbard and Fermi-Hubbard physics with ultracold atoms in DW potentials or DW optical lattices. Particularly interesting will be the question of the importance of quantum phase operators in two-atom interferometry and entanglement.

quant-ph↗

arXiv2017

A unified approach to $Λ$-, $Ξ$- and $V$-type systems with one continuum

We present a systematic approach to classify the three-level-like models with two bound states coupled to a continuum. It is shown that, when one of the discrete levels of usual three-level Lambda- ($Λ$), cascade ($Ξ$) or Vee ($V$)-type systems is replaced by a continuum of states, the resulting each model can be classified into three distinct categories with nine possible configurations. We show that all these models are exactly solvable. We obtain and compare the asymmetric Fano line shapes of the spectra for all the models. Our results are important for exploring new coherent effects in a variety of physical systems involving continuum-bound coupling such as photoassociation of cold atoms, plasmonics, quantum dots, photonic crystals, electromagnetic metamaterials and so on.

quant-ph↗

arXiv2017

Interaction of a Laguerre-Gaussian beam with Rydberg atoms

Transfer mechanism of orbital angular moment(OAM) of light to trapped ground-state atoms under paraxial approximation is well known. Here we show how optical OAM of a Laguerre-Gaussian(LG) beam under paraxial approximation can be transferred to trapped Rydberg atoms. Optical OAM is shown to be transferable to a Rydberg electronic state in dipole transition. The Gaussian part of the profile of the LG beam, which is generally neglected , is found to have an important effect on the OAM transfer to the Rydberg atoms. Numerical calculations are calculated based on this theory for Rubidium Rydberg atoms trapped in a harmonic potential. Our results exhibit the mixing of final states of different parities.

quant-ph↗

arXiv2017

Optical cooling of interacting atoms in a tightly confined trap

In a recent paper, we have proposed a novel laser cooling scheme for reducing collisional energy of a pair of atoms by using photoassociative transitions. In that paper, we considered two atoms in free space, that is we have not considered the effects of trap on the cooling process. Here in this paper, we qualitatively discuss the possibility of extending this idea for Raman sideband cooling of a pair of interacting atoms trapped in Lamb-Dicke (LD) regime. Apart from cooling, our method may be important for manipulating on-site interaction of atoms in an optical lattice.

physics.atom-ph↗