arXiv subjects

Projjwal K. Kanjilal

Publications and source records attributed to Projjwal K. Kanjilal.

3 recordsLinked to original sources

arXiv2026

A general variational approach for equilibrium phase boundaries of trapped spin-1 Bose-Einstein condensates

We develop a simple and general variational method to estimate the solutions of the Gross-Pitaevskii equations and obtain the corresponding density profiles for all spin states of a trapped spin-1 Bose-Einstein condensate. We further employ this approach to obtain the complete phase diagram of the system under quasi-one-dimensional harmonic confinement, with ferromagnetic or antiferromagnetic spin interactions. We identify a suitable scaling that collapses all phase diagrams for different system sizes (i.e., total particle number) into a universal (system size-independent) phase diagram. The complete phase diagram for a confined system shows some significant qualitative differences compared to that of a condensate with homogeneous density distribution. The phase diagrams reported here could help identify the important parameter regimes in which phase transitions in the confined system, in general, occur. This knowledge of the region of phase boundaries can enable a reliable investigation of the instabilities near the boundaries that drive phase transitions.

cond-mat.quant-gas↗

arXiv2023

Multi-component states for trapped spin-1 Bose-Einstein Condensates in the presence of magnetic field

In presence of a magnetic field, multi-component ground states appear in trapped spin-1 Bose-Einstein condensates for both ferromagnetic and anti-ferromagnetic types of spin-spin interaction. We aim to produce an accurate analytical description of the multi-component states which is of fundamental importance. Despite being in the so-called regime of Thomas-Fermi approximation (condensates with large particle number), the scenario of multi-component states is problematic under this approximation due to large variation in densities of the sub-components. We generalize the variational method that we have introduced in the article [Eur. Phys. J. Plus 137, 547 (2022)] to overcome the limitations of T-F approximation. We demonstrate that the variational method is crucial in identifying multi-component ground states. A comparison of the results of the variational method, which is multi-modal by construction, with that of single-mode approximation is also presented in this paper to demonstrate a marked improvement in accuracy over single-mode approximation. We have also looked into the phase transition between the phase-matched and polar state in a trapped condensate using the variational method and have identified substantial change in the phase boundary. The correspondence of the phase diagram of the trapped case with the homogeneous one identifies other limitations of T-F approximation as opposed to the more accurate variational method.

cond-mat.quant-gas↗

arXiv2021

A variational approach for the ground state profile of a trapped spinor-BEC: A detailed study of phase transition in spin-1 condensate at zero magnetic field

In this article we introduce a multi-modal variational method to analytically estimate the full number- and corresponding energy-density profile of a spin-1 Bose-Einstein condensate (BEC) for a number of particles as low as 500 under harmonic confinement. To apply this method, we consider a system of spin-1 BEC under three-dimensional isotropic and effective one-dimensional harmonic confinement in the absence (negligible presence) of the magnetic field which has ground state candidates of comparable energy. It should be noted that in such circumstances kinetic energy contribution to the ground state cannot be neglected which puts the applicability of Thomas-Fermi approximation to question. For anti-ferromagnetic condensates, the T-F approximated energy difference between the competing stationary states (ground state and the first excited state) is approximately 0.3\%. As T-F approximation is only good for condensates with a large number of particles, T-F approximated predictions can completely go wrong especially for small condensates. This is where comes the role of a detailed analysis using our variational method, which incorporates the kinetic energy contribution and accurately estimates the number- and energy-density profile even for condensates having a small number of particles. Results of our analytical method are supported by numerical simulation. This variational method is general and can be extended to other similar/higher-dimensional problems to get results beyond the accuracy of the Thomas-Fermi approximation.

cond-mat.quant-gas↗