arXiv subjects

Md Hamid

Publications and source records attributed to Md Hamid.

2 recordsLinked to original sources

arXiv2022

Multi-vortex Bose-Einstein condensate: examining the role of interaction range using Gaussian potential

We present exact diagonalization study on a system of $10 \leq N \leq 24$ spinless bosons interacting via repulsive Gaussian potential, harmonically confined in $xy$-plane with an externally impressed rotation about the $z$-axis. The two-body interaction strength in the Gaussian potential is taken in the strongly interacting regime with values of interaction range in the regime $0\leq \sigma \leq 1$. The diagonalization of the $N$-body Hamiltonian matrix, in subspaces of total angular momentum in the regime $0\le L_{z} \le 4N$ corresponds to the filling fraction $\nu\lesssim 3.2$ is carried out to obtain the variationally exact ground-state wavefunction and the corresponding eigenvalue. It is found that an increase in interaction range $\sigma$ leads to (a) a systematic decrease in energy, (b) an increase in the critical angular velocity $\Omega_{c_{i}}$ of the $i${th} vortex state and (c) an increase in the largest eigenvalue $\lambda_{1}$, (condensate fraction), of one-particle reduced density matrix (OPRDM). The von Neumann entropy $S_{1}\left(L_{z},\sigma\right)$, quantifying the quantum entanglement between the particles in the many-body ground state, is largely found to decrease with increase in $\sigma$. Crossings in von Neumann entropy for several of the angular momentum states are observed with variation in $\sigma$. The response of the Bose-Einstein condensate to rotation is examined through $L_{z}\left(\sigma\right)-\Omega\left(\sigma\right)$ stability graph for several values of $\sigma$. A vortex state with larger plateau length on the $L_{z}-\Omega$ graph is considered to be more stable. The internal structure of the condensate, as depicted by the conditional probability distribution (CPD) in the body-fixed frame, exhibits characteristic features with interaction range $\sigma$. One such feature is the merging of the cores of the two-vortex state.

cond-mat.quant-gas↗

arXiv2022

Two rotating particles interacting via two-body Gaussian potential harmonically confined in two spatial dimensions

We study two spinless bosons interacting via two-body Gaussian potential subjected to an externally impressed rotation about an axis confined in a harmonic trap in two-spatial dimensions. We obtain a transcendental equation for the relative angular momentum $|m|$ state with various values of the two-body interaction range $\sigma$ and the two-body interaction strength $g_{2}$ to study the resulting energy spectrum and analyze the role of Hilbert space dimensions $\widetilde{N}$. We compare results for both attractive and repulsive interaction for $\delta$-function potential and Gaussian potential for various values of interaction range. We study the effects of interaction parameters and relative angular momentum on the ground state energy and its various components, namely, kinetic energy, trap potential and interaction potential. For a given $|m|$ and non-interacting case, we observe that the ground state energy becomes independent of interaction range. However, for a given relative angular momentum and interaction strength $g_{2}>0$, there is an increase in ground state energy with an increase in interaction range. Below the interaction strength $g_{2}V(r)\leq -1$, ground state energy diverges to physically unacceptable negative-infinity for $|m|=0$ state. Further, for $|m|=1$, the ground state energy becomes independent of the interaction strength. For a $|m|$, we present a comparative study between the Gaussian interaction potential and the $\delta$-function potential. Further, we observe that for a given $g_{2}$ and $|m|$, for $\delta$-function potential {\it i.e.} $\sigma\to 0$, to achieve the convergence of ground state energy, we require a considerably large critical Hilbert space. Whereas, in the case of Gaussian interaction potential with $\sigma\to 1$, the ground state energy converges for a considerably small critical Hilbert space.

cond-mat.quant-gas↗