arXiv subjects

Mohd. Imran

Publications and source records attributed to Mohd. Imran.

6 recordsLinked to original sources

arXiv2023

Novel phases in rotating Bose-condensed gas: vortices and quantum correlation

We present the exact diagonalization study of rotating Bose-condensed gas interacting via finite-range Gaussian potential confined in a quasi-2D harmonic trap. The system of many-body Hamiltonian matrix is diagonalized in given subspaces of quantized total angular momentum to obtain the lowest-energy eigenstate employing the beyond lowest-Landau-level approximation. In the co-rotating frame, the quantum mechanical stability of angular momentum states is discussed for the existence of phase transition between the stable states of interacting system. Thereby analyzing the von Neumann entanglement entropy and degree of condensation provide the information about quantum phase correlation in the many-body states. Calculating the conditional probability distribution, we further probe the internal structure of quantum mechanically stable and unstable states. Much emphasis is put on finding the spatial correlation of bosonic atoms in the rotating system for the formation and entry of singly quantized vortices, and then organizing into canonical polygons with and without a central vortex at the trap center. Results are summarized in the form of a movie depicting the vortex patterns having discrete p-fold rotational symmetry with $p = 2,3,4,5,6$.

cond-mat.quant-gas↗

arXiv2020

Ground state properties of trapped boson system with finite-range Gaussian repulsion: Exact diagonalization study

We use exact diagonalization to study an interacting system of $N$ spinless bosons with finite-range Gaussian repulsion, confined in a quasi-two-dimensional harmonic trap with and without an introduced rotation. The diagonalization of the Hamiltonian matrix using Davidson algorithm in subspaces of quantized total angular momentum $L_{z}$ is carried out to obtain the $N$-body lowest eigenenergy and eigenstate. To bring out the effect of quantum (Bose) statistics and consequent phase stiffness (rigidity) of the variationally obtained many-body wavefunction on various physical quantities, our study spans from few-body ($N=2$) to many-body ($N=16$) systems. Further, to examine the finite-range effect of the repulsive Gaussian potential on many-body ground state properties of the Bose-condensate, we obtain the lowest eigenstate, the critical angular velocity of single vortex state and the quantum correlation (measured) in terms of von Neumann entanglement entropy and degree of condensation. It is found that for small values of the range (measured by the parameter $σ$) of Gaussian potential, the ground state energy increases for few-boson ($2\le N\le 8$) systems but decreases for many-boson ($N>8$) systems. On the other hand for relatively large values of the range of Gaussian potential, the ground state energy exhibits a monotonic decrease, regardless of the number of bosons $N$. For a given $N$, there is found an optimal value of the range of Gaussian potential for which the first vortex (with $L_{z}=N$) nucleates at a lower value of the rotational angular velocity $Ω_{\bf c1}$ compared to the zero-range ($δ$-function) potential. Further, we observe that the inter-particle interaction and the introduced rotation are competing effects with latter being dominant over the former.

cond-mat.quant-gas↗

arXiv2016

Ground and Low-Lying Collective States of Rotating Three-Boson System

The ground and low-lying collective states of a rotating system of $N=3$ bosons harmonically confined in quasi-two-dimension and interacting via repulsive finite-range Gaussian potential is studied in weakly to moderately interacting regime. The $N$-body Hamiltonian matrix is diagonalized in subspaces of quantized total angular momenta $0\le L \le 4N$ to obtain the ground and low-lying eigenstates. Our numerical results show that breathing modes with $N$-body eigenenergy spacing of $2\hbarω_{\perp}$, known to exist in strictly 2D system with zero-range ($δ$-function) interaction potential, may as well exist in quasi-2D system with finite-range Gaussian interaction potential. To gain an insight into the many-body states, the von Neumann entropy is calculated as a measure of quantum correlation and the conditional probability distribution is analyzed for the internal structure of the eigenstates. In the rapidly rotating regime the ground state in angular momentum subspaces $L=\frac{q}{2}N\left(N-1\right)$ with $q=2, 4$ is found to exhibit the anticorrelation structure suggesting that it may variationally be described by a Bose-Laughlin like state. We further observe that the first breathing mode exhibits features similar to the Bose-Laughlin state in having eigenenergy, von Neumann entropy and internal structure independent of interaction for the three-boson system considered here. On the contrary, for eigenstates lying between the Bose-Laughlin like ground state and the first breathing mode, values of eigenenergy, von Neumann entropy and internal structure are found to vary with interaction.

cond-mat.quant-gas↗

arXiv2016

Vortex patterns in moderately rotating Bose-condensed gas

Using exact diagonalization, we investigate the many-body ground state for vortex patterns in a rotating Bose-condensed gas of $N$ spinless particles, confined in a quasi-two-dimensional harmonic trap and interacting repulsively via finite-range Gaussian potential. The $N$-body Hamiltonian matrix is diagonalized in given subspaces of quantized total angular momentum $L_{z}$, to obtain the lowest-energy eigenstate. Further, the internal structure of these eigenstates is analyzed by calculating the corresponding conditional probability distribution. Specifically, the quantum mechanically stable as well as unstable states in a co-rotating frame are examined in the moderately rotating regime corresponding to angular momenta $4N \le L_{z} < 5N$ for $N=16$ bosons. In response to externally impressed rotation, patterns of singly quantized vortices are formed, shaping into canonical polygons with a central vortex at the trap center. The internal structure of unstable states reveals the mechanism of entry, nucleation and pattern formation of vortices with structural phase transition, as the condensate goes from one stable vortical state to the other. The stable polygonal vortex patterns having discrete $p$-fold rotational symmetry with $p=5$ and $p=6$ are observed. The hexagonal vortex pattern with $p=6$ symmetry is a precursor to the triangular vortex lattice of singly quantized vortices in the thermodynamic limit. For unstable states, quantum melting of vortex patterns due to uncertainty in positions of individual vortices, is also briefly discussed.

cond-mat.quant-gas↗

arXiv2016

Breathing Modes in Rotating Bose-Condensed Gas: An Exact Diagonalization Study

We present an exact diagonalization study of the breathing mode collective excitations for a rotating Bose-Einstein condensate of $N=10$ spinless bosons interacting via repulsive finite-range Gaussian potential and harmonically confined in quasi-two-dimension. The yrast state and the low-lying excited states are variationally obtained in given subspaces of the quantized total angular momentum $L$ employing the beyond lowest Landau level approximation in slowly rotating regime with $0 \le L < 2N$. For a given $L$, the low-energy eigenspectra (bands) are obtained in weakly to moderately interacting regime. Further, for a given interaction, the split in low-lying eigenenergies with increasing $L$ is the precursor to spontaneous symmetry breaking of the axisymmetry associated with the entry of the first vortex. With increase in repulsive interaction, the value of the first breathing mode increases for stable total angular momentum states $L=0~\mbox{and}~N$, but decreases for intermediate $0<L<N$ metastable states. The position of the observed first breathing modes in the eigenspectrum remains unchanged as the interaction is varied over several orders of magnitude.

cond-mat.quant-gas↗

arXiv2015

Exact Diagonalization Study of Bose-Condensed Gas with Finite-Range Gaussian Interaction

We investigate a system of $N$ spinless bosons confined in quasi-two-dimensional harmonic trap with repulsive two-body finite-range Gaussian interaction potential of large $s$-wave scattering length. Exact diagonalization of the Hamiltonian matrix is carried out to obtain the $N$-body ground state as well as low-lying excited states, using Davidson algorithm in beyond lowest-Landau-level approximation. We examine the finite-range effects of the interaction potential on the many-body ground state energy as also the degree of condensation of the Bose-condensed gas. The results obtained indicate that the finite-range Gaussian interaction potential enhances the degree of condensation compared to the zero-range interaction potential. We further analyze the effect of finite-range interaction potential on the breathing mode collective excitation. Our theoretical results may be relevant for experiments currently conducted on quasi-two-dimensional Bose gas with more realistic interaction potential.

cond-mat.quant-gas↗