arXiv subjects

R. Ramakumar

Publications and source records attributed to R. Ramakumar.

13 recordsLinked to original sources

arXiv2014

Lattice bosons in a quasi-disordered environment: The effects of a superlattice potential on single particle and many particle properties

In this paper we present a theoretical investigation of the effect of a superlattice potential on some properties of non-interacting bosons in one dimensional lattices with Aubry-And\'re disorder potential. In the first part, we investigate the single particle localization properties. We find a re-entrant localization-delocalization transition and the development of multiple mobility edges for a range of superlattice potential strengths. In the second part, we study the Bose-Einstein condensation with an additional harmonic trapping potential. We find that an increase in the superlattice potential leads to an increase in the depletion of the condensate in the low temperature limit.

cond-mat.quant-gas↗

arXiv2013

Lattice bosons in a quasi-disordered environment: The effects of next-nearest-neighbor hopping on localization and Bose-Einstein condensation

We present a theoretical study of the effects of the next-nearest-neighbor (NNN) hopping ($t_2$) on the properties of non-interacting bosons in optical lattices in the presence of an Aubry-Andr\'{e} quasi-disorder. First we investigate, employing exact diagonalization, the effects of $t_2$ on the localization properties of a single boson. The localization is monitored using an entanglement measure as well as with inverse participation ratio. We find that the sign of $t_2$ has a significant influence on the localization effects. We also provide analytical results in support of the trends found in the localization behavior. Further, we extend these results including the effects of a harmonic potential which obtains in experiments. Next, we study the effects of $t_2$ on Bose-Einstein condensation. We find that, a positive $t_2$ strongly enhances the low temperature thermal depletion of the condensate while a negative $t_2$ reduces it. It is also found that, for a fixed temperature, increasing the quasi-disorder strength reduces the condensate fraction in the extended regime while enhancing it in the localized regime. We also investigate the effects of boundary conditions and that of the phase of the AA potential on the condensate. These are found to have significant effects on the condensate fraction in the localization transition region.

cond-mat.quant-gas↗

arXiv2012

Lattice bosons in a quasi-disordered environment

In this paper, we study non-interacting bosons in a disordered one-dimensional optical lattice in a harmonic potential. We consider the case of deterministic disorder produced by an Aubry-Andr\'{e} potential. Using exact diagonalization, we investigate both the zero temperature and the finite temperature properties. We investigate the localization properties by using an entanglement measure. We find that the extreme sensitivity of the localization properties to the number of lattice sites in finite size closed chains disappear in open chains. This feature continues to be present in the presence of a harmonic confining potential. The disorder is found to strongly reduce the Bose-Einstein condensation temperature and the condensate fraction in open chains. The low temperature thermal depletion rate of the condensate fraction increases considerably with increasing disorder strength. We also find that the critical disorder strength required for localization increases with increasing strength of the harmonic potential. Further, we find that the low temperature condensate fraction undergoes a sharp drop to 0.5 in the localization transition region. The temperature dependence of the specific heat is found to be only marginally affected by the disorder.

cond-mat.quant-gas↗

arXiv2010

Collapse dynamics of a ${}^{176}\textrm{Yb}\,$-${}^{174}\textrm{Yb}$ Bose-Einstein condensate

In this paper, we present a theoretical study of a two-component Bose-Einstein condensate composed of Ytterbium (Yb) isotopes in a three dimensional anisotropic harmonic potential. The condensate consists of a mixture of ${}^{176}\textrm{Yb}$ atoms which have a negative s-wave scattering length and ${}^{174}\textrm{Yb}$ atoms having a positive s-wave scattering length. We study the ground state as well as dynamic properties of this two-component condensate. Due to the attractive interactions between ${}^{176}\textrm{Yb}$ atoms, the condensate of ${}^{176}\textrm{Yb}$ undergo a collapse when the particle number exceed a critical value. The critical number and the collapse dynamics are modified due to the presence of ${}^{174}\textrm{Yb}$ atoms. We use coupled two-component Gross-Pitaevskii equations to study the collapse dynamics. The theoretical results obtained are in reasonable agreement with the experimental results of Fukuhara {\em et al.} [PRA{\bf 79}, 021601(R) (2009)].

cond-mat.quant-gas↗

arXiv2009

Two-step condensation of lattice bosons

We present a theoretical study of Bose-Einstein condensation in highly anisotropic harmonic traps. The bosons are considered to be moving in an optical lattice in an overall anisotropic harmonic confining potential. We find that two-step condensation occurs for lattice bosons at much reduced harmonic potential anisotropy when compared to the case of an ideal bose gas in an anisotropic harmonic confinement. We also show that when the bosons are in an isotropic harmonic confinement but with highly anisotropic hopping in the optical lattice, two-step condensation does not occur. We interpret some of our results using single boson density of energy states corresponding to the potentials faced by the bosons.

cond-mat.quant-gas↗

arXiv2008

Bose-Einstein condensate in a quartic potential: Static and Dynamic properties

In this paper, we present a theoretical study of a Bose-Einstein condensate of interacting bosons in a quartic trap in one, two, and three dimensions. Using Thomas-Fermi approximation, suitably complemented by numerical solutions of the Gross-Pitaevskii equation, we study the ground sate condensate density profiles, the chemical potential, the effects of cross-terms in the quartic potential, temporal evolution of various energy components of the condensate, and width oscillations of the condensate. Results obtained are compared with corresponding results for a bose condensate in a harmonic confinement.

cond-mat.other↗

arXiv2008

The effects of next to nearest neighbor hopping on Bose-Einstein condensation in cubic lattices

In this paper, we present results of our calculations on the effects of next to nearest neighbor boson hopping ($t^{\prime}$) energy on Bose-Einstein condensation in cubic lattices. We consider both non-interacting and repulsively interacting bosons moving in the lowest Bloch band. The interacting bosons are studied making use of the Bogoliubov method. We find that the bose condensation temperature is enhanced with increasing $t^{\prime}$ for bosons in a simple cubic (sc) lattice and decreases for bosons in body-centered cubic (bcc) and face-centered cubic (fcc) lattices. We also find that interaction induced depletion of the condensate is reduced for bosons in a sc lattice while is enhanced for bosons in bcc and fcc lattices.

cond-mat.stat-mech↗

arXiv2008

Lattice bosons in quartic confinement

We present a theoretical study of bose condensation of non-interacting bosons in finite lattices in quartic potentials in one, two, and three dimensions. We investigate dimensionality effects and quartic potential effects on single boson density of energy states, condensation temperature, condensate fraction, and specific heat. The results obtained are compared with corresponding results for lattice bosons in harmonic traps.

cond-mat.other↗

arXiv2007

Studies of bosons in optical lattices in a harmonic potential

We present a theoretical study of bose condensation and specific heat of non-interacting bosons in finite lattices in harmonic potentials in one, two, and three dimensions. We numerically diagonalize the Hamiltonian to obtain the energy levels of the systems. Using the energy levels thus obtained, we investigate the temperature dependence, dimensionality effects, lattice size dependence, and evolution to the bulk limit of the condensate fraction and the specific heat. Some preliminary results on the specific heat of fermions in optical lattices are also presented. The results obtained are contextualized within the current experimental and theoretical scenario.

cond-mat.stat-mech↗

arXiv2006

Polaron cross-overs and d-wave superconductivity in Hubbard-Holstein model

We present a theoretical study of superconductivity of polarons in the Hubbard-Holstein model. A residual kinematic interaction proportional to the square of the polaron hopping energy between polarons and phonons provides a pairing field for the polarons. We find that superconducting instability in the d-wave channel is possible with small transition temperatures which is maximum in the large to small polaron cross-over region. An s-wave instability is found to be not possible when the effective on-site interaction between polarons is repulsive.

cond-mat.supr-con↗

arXiv2005

Specific heat of Bosons in a lattice

We present a theoretical study of specific heat of bosons ($C_v$) in a simple cubic lattice. We have studied the non-interacting bosons and the Tonks gas. For both cases, the $C_v$ above the bose condensation temperature shows considerable temperature dependence compared to that of free bosons. For Tonks gas, we find that the low-temperature specific heat increases as the system gets closer to the Mott transition.

cond-mat.other↗

arXiv2005

Bose-Einstein condensation in tight-binding bands

We present a theoretical study of condensation of bosons in tight binding bands corresponding to simple cubic, body centered cubic, and face centered cubic lattices. We have analyzed non-interacting bosons, weakly interacting bosons using Bogoliubov method, and strongly interacting bosons through a renormalized Hamiltonian approach valid for number of bosons per site less than or equal to unity. In all the cases studied, we find that bosons in a body centered cubic lattice has the highest Bose condensation temperature. The growth of condensate fraction of non-interacting bosons is found to be very close to that of free bosons. The interaction partially depletes the condensate at zero temperature and close to it, while enhancing it beyond this range below the Bose-Einstein condensation temperature. Strong interaction enhances the boson effective mass as the band-filling is increased and eventually localizes them to form a Bose-Mott-Hubbard insulator for integer filling.

cond-mat.other↗

arXiv2003

Jahn-Teller polarons and their superconductivity in a molecular conductor

We present a theoretical study of a possibility of superconductivity in a three dimensional molecular conductor in which the interaction between electrons in doubly degenerate molecular orbitals and an {\em intra}molecular vibration mode is large enough to lead to the formation of $E\otimes \beta$ Jahn-Teller small polarons. We argue that the effective polaron-polaron interaction can be attractive for material parameters realizable in molecular conductors. This interaction is the source of superconductivity in our model. On analyzing superconducting instability in the weak and strong coupling regimes of this attractive interaction, we find that superconducting transition temperatures up to 100 K are achievable in molecular conductors within this mechanism. We also find, for two particles per molecular site, a novel Mott insulating state in which a polaron singlet occupies one of the doubly degenerate orbitals on each site. Relevance of this study in the search for new molecular superconductors is pointed out.

cond-mat.supr-con↗