Bound state energies and phase shifts of a non-commutative well

New set of exactly solvable complex potentials giving the real energies

We deform the real potential of Poeschl and Teller by a shift of its coordinate in imaginary direction. We show that the new model remains exactly solvable. Its bound states are constructed in closed form. Wave functions are complex and proportional to Jacobi polynomials. Some of them diverge in the Hermitian limit. In contrast, all their energies prove real and shift-independent. In this sense the lost Hermiticity of our family of Hamiltonians seems replaced by their accidental PT symmetry.

Behavior of three modes of decay channels and their self-energies of elliptic dielectric microcavity

The Lamb shift (self-energy) of an elliptic dielectric microcavity is studied. We show that the size of the Lamb shift, which is a small energy shift due to the system-environment coupling in the quantum regime, is dependent on the geometry of the boundary conditions. It shows a global transition depending on the eccentricity of the ellipsis. These transitions can be classified into three types of decay channels known as whispering-gallery modes, stable-bouncing-ball modes, and unstable-bouncing-ball modes. These modes are manifested through the Poincaré surface of section with the Husimi dist…

The large-g observability of the low-lying energies in the strongly singular potentials $V(x)=x^2+g^2/x^6$ after their PT-symmetric regularization

The elementary quadratic plus inverse sextic interaction containing a strongly singular repulsive core in the origin is made regular by a complex shift of coordinate $x = s-{\rm i}\varepsilon$. The shift $\varepsilon>0$ is fixed while the value of $s$ is kept real and potentially observable, $s \in (-\infty,\infty)$. The low-lying energies of bound states are found in closed form for the large couplings $g$. Within the asymptotically vanishing ${\cal O}(g^{-1/4})$ error bars these energies are real so that the time-evolution of the system may be expected unitary in an {\em ad hoc} physical Hil…

Two-atom interaction energies with one atom in an excited state: van der Waals potentials vs. level shifts

I revisit the problem of the interaction between two dissimilar atoms with one atom in an excited state, recently addressed by the authors of Refs.[1-3], and for which precedent approaches have given conflicting results. In the first place, I discuss to what extent Refs.[1], [2] and [3] provide equivalent results. I show that the phase-shift rate of the two-atom wave function computed in Ref.[1], the van der Waals potential of the excited atom in Ref.[2] and the level shift of the excited atom in Ref.[3] possess equivalent expressions in the quasistationary approximation. In addition, I show t…

Quantum Energies of Interfaces

We present a method for computing the one-loop, renormalized quantum energies of symmetrical interfaces of arbitrary dimension and codimension using elementary scattering data. Internal consistency requires finite-energy sum rules relating phase shifts to bound state energies.

Casimir-Polder shifts on quantum levitation states

An ultracold atom above a horizontal mirror experiences quantum reflection from the attractive Casimir-Polder interaction, which holds it against gravity and leads to quantum levitation states. We analyze this system by using a Liouville transformation of the Schrödinger equation and a Langer coordinate adapted to problems with a classical turning point. Reflection on the Casimir-Polder attractive well is replaced by reflection on a repulsive wall and the problem is then viewed as an ultracold atom trapped inside a cavity with gravity and Casimir-Polder potentials acting respectively as top an…

Far-off resonance conditional phase-shifter using the ac-Stark shift

We propose a simple technique that achieves a conditional phase shift of pi radians between two weak lasers with energies at the 1000-photon level. The key idea is to set up a V-system with two far-off resonant lasers by coupling the ground state to two excited electronic states. The lasers interact through the ac Stark shift of the ground state and thereby acquire a large conditional phase shift.

Scattering and bound states in two-dimensional anisotropic potentials

We propose a framework for calculating scattering and bound state properties in anisotropic two-dimensional potentials. Using our method, we derive systematic approximations of partial wave phase shifts and binding energies. Moreover, the method is suitable for efficient numerical computations. We calculate the s-wave phase shift and binding energy of polar molecules in two layers polarized by an external field along an arbitrary direction. We find that scattering depends strongly on their polarization direction and that absolute interlayer binding energies are larger than thermal energies at …

Non-commutativity and non-inertial effects on the Dirac oscillator in a cosmic string space-time

We examine the non-inertial effects of a rotating frame on a Dirac oscillator in a cosmic string space-time with non-commutative geometry in phase space. We observe that the approximate bound-state solutions are related to the biconfluent Heun polynomials. The related energies cannot be obtained in a closed form for all the bound states. We find the energy of the fundamental state analytically by taking into account the hard-wall confining condition. We describe how the ground-state energy scales with the new non-commutative term as well as with the other physical parameters of the system.

Blackbody radiation shift, multipole polarizabilities, oscillator strengths, lifetimes, hyperfine constants, and excitation energies in Ca+

A systematic study of Ca+ atomic properties is carried out using high-precision relativistic all-order method where all single, double, and partial triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. Reduced matrix elements, oscillator strengths, transition rates, and lifetimes are determined for the levels up to n = 7. Recommended values and estimates of their uncertainties are provided for a large number of electric-dipole transitions. Electric-dipole scalar polarizabilities for the 5s, 6s, 7s, 8s, 4p, 5p, 3d, and 4d states and tensor polari…

通过量子纠缠将涡旋粒子的物理研究拓展至更高能量

Shifting physics of vortex particles to higher energies via quantum entanglement

本研究提出利用末态粒子对的量子纠缠与后选择协议，可在多种高能物理过程中产生任意粒子的涡旋态，大幅放宽束流相干性要求，为高能涡旋束的产生与应用提供新途径。