arXiv subjects

Tarun Kanti Ghosh

Publications and source records attributed to Tarun Kanti Ghosh.

68 records · Page 4Linked to original sources

arXiv2005

Sound velocity and multibranch Bogoliubov spectrum of an elongated Fermi superfluid in the BEC-BCS crossover

We study properties of excited states of an elongated Fermi superfluid along the BEC-BCS crossover including the unitarity limit. Analytic expressions for the sound velocity in an inhomogeneous as well as homogeneous Fermi superfluid along the crossover are obtained on the basis of the hydrodynamic theory. The complete excitation spectrum of axial quasiparticles with various discrete radial nodes are presented. We discuss the feasibility of measuring the sound velocity and the multibranch Bogoliubov spectrum experimentally.

cond-mat.supr-con↗

arXiv2005

Multibranch Bogoliubov-Bloch spectrum of a cigar shaped Bose condensate in an optical lattice

We study properties of excited states of an array of weakly coupled quasi-two-dimensional Bose condensates by using the hydrodynamic theory. The spectrum of the axial excited states strongly depends on the coupling among the various discrete radial modes in a given symmetry. By including mode-coupling within a given symmetry, the complete excitation spectrum of axial quasiparticles with various discrete radial nodes are presented. A single parameter which determines the strength of the mode coupling is identified. The excitation spectrum in the zero angular momentum sector can be observed by using the Bragg scattering experiments.

cond-mat.other↗

arXiv2005

Bragg spectroscopy of discrete axial quasiparticle modes in a cigar-shaped degenerate Bose gas

We propose an experiment in which long wavelength discrete axial quasiparticle modes can be imprinted in a 3D cigar-shaped Bose-Einstein condensate by using two-photon Bragg scattering experiments, similar to the experiment at the Weizmann Institute [J. Steinhauer {\em et al.}, Phys. Rev. Lett. {\bf 90}, 060404 (2003)] where short wavelength axial phonons with different number of radial modes have been observed. We provide values of the momentum, energy and time duration of the two-photon Bragg pulse and also the two-body interaction strength which are needed in the Bragg scattering experiments in order to observe the long wavelength discrete axial modes. These discrete axial modes can be observed when the system is dilute and the time duration of the Bragg pulse is long enough.

cond-mat.soft↗

arXiv2004

Vortex formation in a slowly rotating Bose-Einstein condensate confined in a harmonic-plus-gaussian laser trap

Motivated by the recent experiment at ENS [ V. Bretin, S. Stock, Y. Seurin and, J. Dalibard, Phys. Rev. Lett. {\bf 92}, 050403 (2004)], we study a rotating (non-)interacting atomic Bose-Einstein condensate confined in a harmonic-plus-gaussian laser trap potential. By adjusting the amplitude of the laser potential, one can make quadratic-plus-quartic potential,purely quartic potential, and quartic-minus-quadratic potential. We show that an interacting Bose-Einstein condensate confined in a harmonic-plus-gaussian laser trap breaks the rotational symmetry of the Hamiltonian when rotational frequency is greater than one-half of the lowest energy surface mode frequency. We also show that by increasing the amplitude of the gaussian laser trap, a vortex appears in a slowly rotating Bose-Einstein condensate. Moreover, one can also create a vortex in non-interacting Bose-Einstein condensate confined in harmonic-plus-gaussian laser potential.

cond-mat.soft↗

arXiv2004

Revisiting the Hanbury Brown-Twiss Setup for Phase Fluctuating Bose Gases

The Hanbury Brown-Twiss experiment has proved to be an effective means of measuring two-point correlation function of identical particles. We analyze experimental observation of stripes formation of a phase fluctuating Bose-Einstein condensates in a highly elongated 3D traps [Dettmer {\em et al.}, Phys. Rev. Lett. {\bf 87}, 160406 (2001)] by means of axial two-point correlation functions. We also predict that the stripes are present in quasi-1D Bose gas in the mean-field as well as in the hard-core bosons regimes. These stripes can be realized by measuring the axial two-point correlation functions by using the Bragg interferometric method which is similar to the original Hanbury Brown and Twiss experimental setup.

cond-mat.soft↗

arXiv2004

Quasi-one dimensional degenerate Bose gas

Motivated by the MIT experiment [Gorlitz {\em et al.}, Phys. Rev. Lett. {\bf 87}, 130402 (2001)], we analytically study the effect of density and phase fluctuations on various observables in a quasi one-dimensional degenerate Bose gases. Quantizing the Gross-Pitaevskii Hamiltonian and diagonalize it in terms of the normal modes associated with the density and phase fluctuations of a quasi-one dimensional Bose gas. We calculate dynamic structure factor $S(q,ω)$ from low-energy condensate density fluctuations and find that there are multiple peaks in $S(q,ω)$ for a given momentum $q$ due to the discrete energy spectrum. These multiple peaks can be resolved by a two-photon Bragg pulse with a long duration which transfer the momentum to the system. We calculate the momentum transferred $ P_z(t)$ by using the phase-density representation of the Bose order parameter. We also calculate the single-particle density matrix, phase coherence length, and momentum distribution by taking care of the phase fluctuations upto fourth-order term as well as the density fluctuations. Our studies on coherence properties shows that 1D Bose gases of MIT experiment do not form a true condensate, but it can be obtained by a moderate changes of the current experimental parameters.

cond-mat.soft↗

arXiv2004

Quantized Hydrodynamic Theory of One-Dimensional Hard Core Bosons

We present a quantized hydrodynamic theory and its applications of one-dimensional hard-core bosons in a harmonic trap. Quantizing the Hamiltonian of a trapped hard-core bosons and diagonalize it in terms of the phase and density fluctuations associated with the Bose field operator. As an applications, we calculate discrete energy spectrum, dynamic structure factor, momentum transferred by a two-photon Bragg pulse, single-particle density matrix, momentum distribution, and two-particle correlation function. The dynamic structure factor has multiple peaks due to the discrete nature of the energy spectrum which can be observed by a two-photon Bragg pulse with long duration. The coherence length at zero temperature is very small due to the "fermionization" of the system. We also compute the momentum distributions which has oscillatory behavior at large momentum. The pair distribution function shows that there are many deep valleys at various relative separations which implies shell structure due to the Pauli blocking in real space.

cond-mat.soft↗

arXiv2004

Vortex formation in a fast rotating Bose-Einstein condensate

We study rotational motion of an interacting atomic Bose-Einstein condensate confined in a quadratic-plus-quartic potential. We calculate the lowest energy surface mode frequency and show that a symmetric trapped (harmonic and quartic) Bose-Einstein condensate breaks the rotational symmetry of the Hamiltonian when rotational frequency is greater than one-half of the lowest energy surface mode frequency. We argue that the formation of a vortex is not possible in a non-interacting as well as in an attractive Bose-Einstein condensate confined in a harmonic trap due to the absence of the spontaneous shape deformation, but it can occur which leads to the vortex formation if we add an additional quartic potential. Moreover, the spontaneous shape deformation and consequently the formation of a vortex in an attractive system depends on the strengths of the two-body interaction and the quartic potential.

cond-mat.soft↗

arXiv2003

Cooperative Ring Exchange and Quantum Melting of Vortex Lattices in Atomic Bose-Einstein Condensates

Cooperative ring-exchange is suggested as a mechanism of quantum melting of vortex lattices in a rapidly-rotating quasi two dimensional atomic Bose-Einstein condensate (BEC). Using an approach pioneered by Kivelson et al. [Phys. Rev. Lett. {\bf 56}, 873 (1986)] for the fractional quantized Hall effect, we calculate the condition for quantum melting instability by considering large-correlated ring exchanges in a two-dimensional Wigner crystal of vortices in a strong `pseudomagnetic field' generated by the background superfluid Bose particles. BEC may be profitably used to address issues of quantum melting of a pristine Wigner solid devoid of complications of real solids.

cond-mat↗

arXiv2002

Collective excitation frequencies and vortices of a Bose-Einstein condensed state with gravity-like interatomic attraction

We study the collective excitations of a neutral atomic Bose-Einstein condensate with gravity-like $1/r $ interatomic attraction induced by electromagnetic wave. Using the time-dependent variational approach, we derive an analytical spectrum for monopole and quadrupole mode frequencies of a gravity-like self-bound Bose condensed state at zero temperature. We also analyze the excitation frequencies of the Thomas-Fermi-gravity (TF-G) and gravity (G) regimes. Our result agrees excellently with that of Giovanazzi {\em et al}. [Europhysics Letters, {\bf 56}, 1 (2001)], which is obtained within the sum-rule approach. We also consider the vortex state. We estimate the superfluid coherence length and the critical angular frequencies to create a vortex around the $ z $-axis. We find that the TF-G regime can exhibit the superfluid properties more prominently than the G-regime. We find that the monopole mode frequency of the condensate decreases due to the presence of a vortex.

cond-mat↗

arXiv2002

Splitting between quadrupole modes of dilute quantum gas in a two dimensional anisotropic trap

We consider quadrupole excitations of quasi-two dimensional interacting quantum gas in an anisotropic harmonic oscillator potential at zero temperature. Using the time-dependent variational approach, we calculate a few low-lying collective excitation frequencies of a two dimensional anisotropic Bose gas. Within the energy weighted sum-rule approach, we derive a general dispersion relation of two quadrupole excitations of a two dimensional deformed trapped quantum gas. This dispersion relation is valid for both statistics. We show that the quadrupole excitation frequencies obtained from both methods are exactly the same. Using this general dispersion relation, we also calculate the quadrupole frequencies of a two dimensional unpolarized Fermi gas in an anisotropic trap. For both cases, we obtain analytic expressions for the quadrupole frequencies and the splitting between them for arbitrary value of trap deformation. This splitting decreases with increasing interaction strength for both statistics. For two dimensional anisotropic Fermi gas, the two quadrupole frequencies and the splitting between them become independent of the particle number within the Thomas-Fermi approach.

cond-mat.soft↗

arXiv2001

Modelling Two-Roton Bound State Formation in Fractional Quantum Hall System

Composite Fermion approach using extensive and parallalized numerical analysis has recently established a two-roton bound state as the lowest energy long wavelength neutral excitation of FQHE for finite particle (N~30) system. By focussing on the "oriented dipole" character of magneto roton, we model the two roton problem and solve it variationally (analytically) to find a two-roton bound state with binding energy which is in good agreement with the composite fermion numerical results.

cond-mat.mes-hall↗

arXiv2001

Universality of monopole mode and time evolution of a d-dimensional trapped interacting Bose gas

We study a generalised Gross-Pitaevskii equation describing a d-dimensional harmonic trapped (with trap frequency $ω_{0}$) weakly interacting Bose gas with a non-linearity of order (2 k + 1) and scaling exponent (n) of the interaction potential. Using the time-dependent variational analysis, we explicitly show that for a particular combination of n, k and d, the generalised GP equation has the universal monopole oscillation frequency $2 ω_{0}$. We also find that the time-evolution of the width can be described universally by the same Hill's equation if the system satisfy that particular combination. We also obtain the condition for the exact self-similar solutions of the Gross-Pitaevskii equation. As an application, we discuss low dimensional trapped Bose condensate state and Calogero model.

cond-mat.soft↗

arXiv2000

Frequencies and Damping rates of a 2D Deformed Trapped Bose gas above the Critical Temperature

We derive the equation of motion for the velocity fluctuations of a 2D deformed trapped Bose gas above the critical temperature in the hydrodynamical regime. From this equation, we calculate the eigenfrequencies for a few low-lying excitation modes. Using the method of averages, we derive a dispersion relation in a deformed trap that interpolates between the collisionless and hydrodynamic regimes. We make use of this dispersion relation to calculate the frequencies and the damping rates for monopole and quadrupole mode in both the regimes. We also discuss the time evolution of the wave packet width of a Bose gas in a time dependent as well as time independent trap.

cond-mat↗