Please visit the following link for the schedule. http://www.imsc.res.in/~nemani/CSM-2024-schedule.pdf

Nature and Numeracy for Chennai SCERT: 2024-25

Please visit the following link for the schedule. http://www.imsc.res.in/~nemani/CSM-2024-schedule.pdf

We study the neutral excitations in the bulk of the fractional quantum Hall (FQH) fluids generated by acting the Girvin-MacDonald-Platzman (GMP) density operator on the uniform ground state. Creating these density modulations atop the ground state costs energy since any density fluctuation in the FQH system has a gap stemming from the underlying inter-particle interactions. We calculate the GMP density-mode dispersion for many bosonic and fermionic FQH states on the Haldane sphere using the ground state static structure factor computed on the same geometry. Previously, this computation was carried out on the plane. Analogous to the GMP algebra of the lowest Landau level (LLL) projected density operators in the plane, we derive the algebra for the LLL-projected density operators on the sphere, which facilitates the computation of the density-mode dispersion. Contrary to previous results on the plane, we find that in the long-wavelength limit, the GMP mode does provide an accurate description of the dynamics of the primary Jain states.

This study presents a quantum heat engine model [1] that couples an ultracold atomic gas with a vibrating nanomechanical mirror [2]. The mirror’s vibrations generate optomechanical sidebands in the control field, altering the behaviour of the atomic gas and influencing the engine’s radiation output. The model bridges a multi-level atom-laser interaction system with the nanomirror’s mechanical vibrations, operating as a heat engine under electromagnetically induced transparency (EIT) conditions [3], while omitting cavity confinement. Three configurations are explored: (i) a vibration-free three-level $\Lambda$-type system, (ii) the same system with nanomechanical vibrations, and (iii) a composite engine combining both. Vibration reduces the spectral brightness in the three-level system, with a slight brightness peak enhancement in the composite engine, though maximum brightness is achieved without vibration. The model’s entropy analysis, aligned with the second law of thermodynamics, reveals deviations from ideal heat engine behaviour when vibrations are introduced, highlighting the impact of nanomechanical dynamics on the engine’s performance. Using a semiclassical approach, this model shows that the output or gain of a three-level $\Lambda$-type quantum heat engine is optimized when the photon distribution in thermal baths is high and the coupling strength between the nanomechanical mirror and the engine is minimized [4]. The model also suggests that a larger temperature difference between the hot and cold reservoirs leads to a more significant positive gain in output. Thermodynamic analysis confirms that the energy absorbed by the atomic system matches the energy released, satisfying the first law of thermodynamics. However, the engine’s efficiency decreases as the photon distribution in the hot reservoir increases, with a more pronounced drop at higher atom-mirror coupling strengths. References:- [1] H. E. D. Scovil and E. O. Schulz-DuBois, ``Three-level masers as heat engines", Physical Review Letters, vol. 2, pp. 262–263 (1959). [2] Rejjak Laskar, ``Proposal for composite quantum electromagnetically induced transparency heat engine coupled by a nanomechanical mirror", Journal of Physics B: Atomic, Molecular and Optical Physics, vol. 57, pp. 025402 (2024). [3] Stephen E. Harris, J. E. Field, and A. Imamoglu, ``Nonlinear optical processes using electromagnetically induced transparency", Physical Review Letters, vol. 64, pp. 1107 (1990). [4] Rejjak Laskar, ``Nano-mirror induced three-level quantum heat engine", arXiv preprint arXiv:2409.08629 (2024).