Samrat Dey, Yatendra S. Jain
Wave mechanics of a particle in an impenetrable spherical cavity with and without a hard core scattering potential of size $ε$ ($ε$ $\to$ 0) at its center is critically analyzed. It makes marginal but important modifications in our present understanding of the energy eigenvalues of such particles.
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The generalized pseudospectral method is employed to study spherical confinement in two simple Coulombic systems: (i) well celebrated and heavily studied H atom (ii) relatively less explored Hulthén potential. In both instances, arbitrary cavity size, as well as low and higher states are considered. Apart from bound state eigenvalues, eigenfunctions, expectation values, quite accurate estimates of the critical cage radius for H atom for all the 55 states corresponding to $n \leq 10$, are also examined. Some of the latter are better than previously reported values. Degeneracy and energy orderin…
We explore ground-state entanglement properties of helium atom confined at the center of an impenetrable spherical cavity of varying radius by using explicitly correlated Hylleraas-type basis set. Results for the dependencies of the von Neumann and linear entanglement entropic measures on the cavity radius are discussed in details. Some highly accurate numerical results for the von Neumann and linear entropy are reported for the first time. It is found that the transition to the strong confinement regime is manifested by the entropies as an appearance of the inflection points on their variatio…
We calculate the Casimir energy at spherical cavities within a host made up of an arbitrary material described by a possibly dispersive and lossy dielectric response. To that end, we add to the coherent optical response a contribution that takes account of the incoherent radiation emitted by the host in order to guarantee the detailed balance required to keep the system at thermodynamic equilibrium in the presence of dissipation. The resulting boundary conditions allow a conventional quantum mechanical treatment of the radiation within the cavity from which we obtain the contribution of the ca…
We study the hydrogen atom confined to a spherical box with impenetrable walls but, unlike earlier pedagogical articles on the subject, we assume that the nucleus also moves. We obtain the ground-state energy approximately by means of first--order perturbation theory and by a more accurate variational approach. We show that it is greater than the one for the case in which the nucleus is clamped at the center of the box. Present approach resembles the well-known treatment of the helium atom with clamped nucleus.
We demonstrate fiber Fabry-Perot (FFP) cavities with concave mirrors that can be operated at cavity lengths as large as 1.5mm without significant deterioration of the finesse. This is achieved by using a laser dot machining technique to shape spherical mirrors with ultralow roughness and employing single-mode fibers with large mode area for good mode matching to the cavity. Additionally, in contrast to previous FFPs, these cavities can be used over an octave-spanning frequency range with adequate coatings. We also show directly that shape deviations caused by the fiber's index profile lead to …
We report a process for fabricating high quality, defect-free spherical mirror templates suitable for developing high finesse optical Fabry-Perot resonators. The process utilizes the controlled reflow of borosilicate glass and differential pressure to produce mirrors with 0.3 nanometer surface roughness. The dimensions of the mirrors are in the 0.5-5mm range making them suitable candidates for integration with on-chip neutral atom and ion experiments where enhanced interaction between atoms and photons are required. Moreover the mirror curvature, dimension and placement is readily controlled a…
Near-concentric optical cavities of spherical mirrors can provide technical advantages over the conventional near-planar cavities in applications requiring strong atom-light interaction, as they concentrate light in a very small region of space. However, such cavities barely support stable optical modes, and thus impose practical challenges. Here, we present an experiment where we maintain a near-concentric cavity at its last resonant length for laser light at 780 nm resonant with an atomic transition. At this point, the spacing of two spherical mirror surfaces is 207(13) nm shorter than the c…
Defect cavities in 3D photonic crystal can trap and store light in the smallest volumes allowable in dielectric materials, enhancing non-linearities and cavity QED effects. Here, we study inverse rod-connected diamond (RCD) crystals containing point defect cavities using plane-wave expansion and finite-difference time domain methods. By optimizing the dimensions of the crystal, wide photonic band gaps are obtained. Mid-bandgap resonances can then be engineered by introducing point defects in the crystal. We investigate a variety of single spherical defects at different locations in the unit ce…
We investigate the suitability of toroidal microcavities for strong-coupling cavity quantum electrodynamics (QED). Numerical modeling of the optical modes demonstrate a significant reduction of modal volume with respect to the whispering gallery modes of dielectric spheres, while retaining the high quality factors representative of spherical cavities. The extra degree of freedom of toroid microcavities can be used to achieve improved cavity QED characteristics. Numerical results for atom-cavity coupling strength, critical atom number N_0 and critical photon number n_0 for cesium are calculated…
Thermodynamics of free bosons and fermions in the hyperball
本文研究D维球形势阱中无相互作用玻色子与费米子的热力学，通过零边界条件求解薛定谔方程，并利用SO(D)对称性揭示由角动量和能级排序形成的壳层结构，在热力学极限下结果与箱体形状无关。
We introduce a method to compute particle detector transition probability in spacetime regions of general curved spacetimes provided that the curvature is not above a maximum threshold. In particular we use this method to compare the response of two detectors, one in a spherically symmetric gravitational field and the other one in Rindler spacetime to compare the Unruh and Hawking effects: We study the vacuum response of a detector freely falling through a stationary cavity in a Schwarzschild background as compared with the response of an equivalently accelerated detector traveling through an …
Energy transfer between localized emitters in photonic cavities from first principles
本文提出一种超越偶极近似的第一性原理方法，定量预测光子腔中缺陷间能量转移，可增强或抑制特定跃迁，适用于量子信息器件。
We consider a system consisting of an atom in the approximation of a harmonic oscillator of frequency $\barω$, coupled to the scalar potential inside a spherical reflecting cavity of radius R. We use {\it dressed} states introduced in a previous publication [Andion, Malbouisson and Matos Neto, J. Phys. A34, 3735 (2001)], which allow a non-perturbative unified description of the atom radiation process, in both cases, of a finite or an arbitrarily large cavity. We perform a study of the energy distribution in a small cavity, with the initial condition that the atom is in the first excited state …
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