Analytic stochastic treatment of a nonlinear quantum model with negative diffusion

Analytic treatment of CRIB Quantum Memories for Light using Two-level Atoms

It has recently been discovered that the optical analogue of a gradient echo in an optically thick material could form the basis of a optical memory that is both completely efficient and noise free. Here we present analytical calculation showing this is the case. There is close analogy between the operation of the memory and an optical system with two beam splitters. We can use this analogy to calculate efficiencies as a function of optical depth for a number of quantum memory schemes based on controlled inhomogeneous broadening. In particular we show that multiple switching leads to a net 100…

通过绕过长寿命相干实现量子热化动力学的超加速：一种解析处理

Hyper-acceleration of quantum thermalization dynamics by bypassing long-lived coherences: An analytical treatment

本文提出一种以小能隙为微扰参数的解析方法，用于求解马尔可夫量子耗散动力学，并据此展示通过精心制备初态相干来绕过长寿命相干、实现量子热化超指数加速的姆潘巴类效应。

An Alternative Treatment for Yukawa-Type Potentials

We propose a new approximation scheme to obtain analytic expressions for the bound state energies and eigenfunctions of Yukawa like potentials. The predicted energies are in excellent agreement with the accurate numerical values reported in the literature.

Analytic models of ultra-cold atomic collisions at negative energies for application to confinement-induced resonances

We construct simple analytic models of the $S$-matrix, accounting for both scattering resonances and smooth background contributions for collisions that occur below the s-wave threshold. Such models are important for studying confinement-induced resonances such as those occurring in cold collisions of $^{133}$Cs atoms in separated sites of a polarization-gradient optical lattice. Because these resonances occur at negative energy with respect to the s-wave threshold, they cannot be studied easily using direct numerical solutions of the Schrödinger equation. Using our analytic model, we extend p…

Qubit-oscillator system: An analytical treatment of the ultra-strong coupling regime

We examine a two-level system coupled to a quantum oscillator, typically representing experiments in cavity and circuit quantum electrodynamics. We show how such a system can be treated analytically in the ultrastrong coupling limit, where the ratio $g/Ω$ between coupling strength and oscillator frequency approaches unity and goes beyond. In this regime the Jaynes-Cummings model is known to fail, because counter-rotating terms have to be taken into account. By using Van Vleck perturbation theory to higher orders in the qubit tunneling matrix element $Δ$ we are able to enlarge the regime of app…