arXiv subjects

Vinh N. T. Pham

Publications and source records attributed to Vinh N. T. Pham.

7 recordsLinked to original sources

arXiv2026

A general recursion for integrals involving products of Hermite polynomials and its applications

This study presents the derivation of a recursive formula for integrals of products of $N$ Hermite polynomials, establishing a numerically stable scheme for their accurate evaluation in computer codes. The derivation is notably simple and leverages solely the well-established properties of Hermite polynomials and the method of integration by parts. Importantly, our formulation completely circumvents explicit factorials, thereby preventing potential numerical instabilities and overflows, while facilitating high-precision computations for large indices. These findings are of significant relevance to a variety of areas in physics and mathematics. In particular, they offer an efficient and accurate framework for calculating two- and three-body matrix elements in ab initio simulations of few-body systems under a 1D harmonic confinement using the Configuration Interactions approach. A numerical subroutine implementing the recursive formula is provided as supplemental material.

quant-ph↗

arXiv2025

Competition between heating and cooling effects in an optomechanical oscillator using a squeezed field

Squeezed light is a useful phenomenon that can be exploited to improve the sensitivity of specific classes of detectors based on optomechanical effects. Recently, there has been significant interest in the potential application of a squeezed field in the cooling of an optomechanical oscillator. It has been shown that this field could cool an oscillator below the standard limit of a coherent field. In this study, the effect of squeezed light was evaluated by explicitly examining the role of the squeezing parameters on the final effective temperature of the oscillator. The results show that the observed cooling and heating effects are strongly dependent on the squeezing parameters and the phase. Using an oscillator of 2$π\times$10.1 MHz driven by a 1064-nm laser, the lowest effective temperature and quantum number are three orders of magnitude smaller compared to the case of no squeezing; especially, these minimum values are obtained at the squeezing phase of about 0.8$π$. This study highlighted important insights for the optimization of cooling efficiency using squeezed light.

quant-ph↗

arXiv2025

Tuning the lasing threshold of quantum well exciton-polaritons under a magnetic field in Faraday geometry: a theoretical study

Polariton lasing is a promising phenomenon with potential applications in next-generation lasers that operate without the need for population inversion. Applying a perpendicular magnetic field to a quantum well (QW) significantly alters the properties of exciton-polaritons. In this theoretical study, we investigate how the lasing threshold of QW exciton-polaritons depends on the magnetic field. By modifying the exciton's effective mass and Rabi splitting, the magnetic field induces notable changes in the relaxation kinetics, which directly affect the lasing threshold. For low-energy pumping, an increase in the magnetic field delays the lasing threshold, while for high-energy pumping, the threshold is reached at much lower pump intensities. Furthermore, increasing both the pump energy and the magnetic field enhances relaxation efficiency, leading to a substantially larger number of condensed polaritons. Our result gives insights into the modulation of exciton-polariton condensation through magnetic fields, with potential implications for the design of low-threshold polariton lasers.

cond-mat.mes-hall↗

arXiv2025

Effect of linear and quadratic coupling on dynamical parameters of an optomechanical oscillator

Dynamics of icrocantilevers are of important interest in micro-mechanical systems for enhancing the functionality and applicable range of the cantilevers in vibration transducing and highly sensitive measurement. In this study, using the semi-classical Hamiltonian formalism, we study in detail the modification of the mechanical frequency and damping rate taking into account both the linear and quadratic coupling between the mechanical oscillator and the laser field in an opto-mechanical system. It has been seen that, the linear coupling greatly enhances the modification of the effective mechanical frequency and the effective damping rate while the quadratic coupling reduces these quantities. For a MHz-frequency oscillator, the damping rate could be 10^5 times increased and the frequency is several times modified. These results help clarifying the origin of the modification of the susceptibility function for cooling of the mechanical mode

quant-ph↗

arXiv2024

Impact of cut-off frequency effect on resonance energy transfer and Casimir-Polder interaction

Using the Green's function approach, we investigate the resonance energy transfer (RET) rate between two parallel, identical two-level atoms in the presence of three types of cylindrical system: a distributed Bragg reflector (DBR), a perfectly reflecting wall (PRW), and a two-layer silicon fiber. Our analysis, incorporating the cut-off frequency condition, reveals significant suppression of the RET rate for atoms positioned along the axis of the cylinder with the PRW. In contrast, for atoms located within the DBR, the RET rate is enhanced in the far zone. Additionally, we find that for atoms oriented radially are placed inside or near the surface of the silicon fiber, the RET rate is entirely inhibited. We also investigate the Casimir-Polder (CP) interaction between a cut-off-frequency DBR and an excited atom, discovering a fully attractive potential towards the surface for the atom within the waveguide.

physics.optics↗

arXiv2024

Effect of magnetic field on the Bose-Einstein condensation of quantum well exciton-polaritons

We theoretically investigate the nonlinear effects of a magnetic field on the relaxation process of exciton-polaritons toward Bose-Einstein condensation in GaAs quantum wells. Our study reveals that the modification of the exciton's effective mass, Rabi splitting, and dispersion significantly alters the relaxation rate of polaritons as they approach condensation. By employing a quasi-stationary pump, we clarify the dynamics of the total and condensed polariton populations in response to varying magnetic field strengths. Notably, we demonstrate that under low-energy pumping conditions, the presence of a magnetic field significantly suppresses condensation. This suppression is attributed to the decreased scattering rate between energy levels, which is a consequence of the reduced steepness in the high-energy dispersion. Conversely, increasing both the pump energy and the magnetic field can enhance relaxation efficiency, leading to a substantially larger number of condensed polaritons.

quant-ph↗

arXiv2024

A revisit on the hydrogen atom induced by a uniform static electric field

In this paper, we revisit the Stark effect of the hydrogen atom induced by a uniform static electric field. In particular, a general formula for the integral of associated Laguerre polynomials was derived by applying the method for Hermite polynomials of degree n proposed in the work [Anh-Tai T.D. et al., 2021 AIP Advances \textbf{11} 085310]. The quadratic Stark effect is obtained by applying this formula and the time-independent non-degenerate perturbation theory to hydrogen. Using the Siegert State method, numerical calculations are performed and serve as data for benchmarking. The comparisons are then illustrated for the ground and some highly excited states to provide an insightful look at the applicable limit and precision of the quadratic Stark effect formula for other atoms with comparable properties.

quant-ph↗