EXACT SOLUTION FOR THE REFLECTION AND DIFFRACTION OF ATOMIC DE BROGLIE WAVES BY A TRAVELLING EVANESCENT LASER WAVE
@article{Witte1998EXACTSF, title={EXACT SOLUTION FOR THE REFLECTION AND DIFFRACTION OF ATOMIC DE BROGLIE WAVES BY A TRAVELLING EVANESCENT LASER WAVE}, author={Nicholas S. Witte}, journal={Journal of Physics A}, year={1998}, volume={31}, pages={807-832} }
The exact solution to the problem of reflection and diffraction of atomic de Broglie waves by a travelling evanescent wave is found starting with a bare-state formulation. The solution for the wavefunctions, the tunnelling losses and the non-adiabatic losses are given exactly in terms of hyper-Bessel functions, and are valid for all detuning and Rabi frequencies, thus generalizing previous approximate methods. Furthermore, we give the limiting cases of the amplitudes in the uniform…
Figures from this paper
13 Citations
The reflection of narrow slow quantum packets from mirrors
- Physics
- 2002
We study the reflection of narrow (in space) quantum wavepackets from nonabsorptive mirrors (totally or partially reflecting). If the initial mean value of the momentum component perpendicular to the…
The Sommerfeld enhancement for dark matter with an excited state
- Physics
- 2009
We present an analysis of the Sommerfeld enhancement to dark matter annihilation in the presence of an excited state, where the interaction inducing the enhancement is purely off-diagonal, such as in…
The Sommerfeld enhancement for dark matter with an excited state
- Physics
- 2010
We present an analysis of the Sommerfeld enhancement to dark matter annihilation in the presence of an excited state, where the interaction inducing the enhancement is purely off-diagonal, such as in…
The quench action approach to out-of-equilibrium quantum integrable models
- Physics
- 2015
In this PhD thesis quantum quenches to 1D quantum integrable models are studied by means of the quench action approach. Using the large-system-size scaling of overlaps between the initial state and…
SOME FORMULAS FOR BESSEL AND HYPER-BESSEL FUNCTIONS RELATED TO THE PROPER LORENTZ GROUP
- Mathematics
- 2018
In a representation space of the proper Lorentz group, we consider the so-called spherical and two parabolic bases and compute the matrix elements of restriction of the representation to matrix…
A GENERALIZED MODIFIED BESSEL FUNCTION AND EXPLICIT TRANSFORMATIONS OF CERTAIN LAMBERT SERIES
- Mathematics
- 2020
Abstract. An exact transformation, which we call a master identity, is obtained for the series ∑∞ n=1 σa(n)e −ny for a ∈ C and Re(y) > 0. As corollaries when a is an odd integer, we derive the…
Explicit transformations of certain Lambert series
- MathematicsResearch in the Mathematical Sciences
- 2022
An exact transformation, which we call the master identity , is obtained for the first time for the series $$\sum _{n=1}^{\infty }\sigma _{a}(n)e^{-ny}$$ ∑ n = 1 ∞ σ a ( n ) e - n y for $$a\in…
Singular Values of Products of Ginibre Random Matrices
- Mathematics
- 2016
The squared singular values of the product of M complex Ginibre matrices form a biorthogonal ensemble, and thus their distribution is fully determined by a correlation kernel. The kernel permits a…
Some Formulas for Ordinary and Hyper Bessel–Clifford Functions Related to the Proper Lorentz Group
- MathematicsJournal of Mathematical Sciences
- 2021
In this paper, we show that the matrix elements of some Lorentz group representation operators and bases transform operators acting in the representation space may be expressed in terms of the…
Some Formulas for Ordinary and Hyper Bessel–Clifford Functions Related to the Proper Lorentz Group
- MathematicsJournal of Mathematical Sciences
- 2021
In this paper, we show that the matrix elements of some Lorentz group representation operators and bases transform operators acting in the representation space may be expressed in terms of the…
References
SHOWING 1-10 OF 35 REFERENCES
Reflection and diffraction of atomic de Broglie waves by evanescent laser waves—bare-state method
- Physics
- 1996
We present two results in an investigation of reflection and diffraction of atoms by gratings formed either by standing or travelling evanescent laser waves. Both results use the bare-state rather…
Reflection and diffraction of atomic de Broglie waves by an evanescent laser wave.
- PhysicsPhysical review. A, Atomic, molecular, and optical physics
- 1993
The diffraction theory of a reflection grating for atoms based on a standing light wave is developed in a particular dressed-state approximation. The basis states the into account internal and…
Diffraction of atoms by a standing evanescent light wave — A reflection grating for atoms
- Physics
- 1989
The oblique reflexion of long wireless waves from the ionosphere at the places where the Earth's magnetic field is regarded as vertical
- PhysicsPhilosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
- 1952
The calculation of reflexion coefficients for long wireless waves incident obliquely on the ionosphere requires an exact solution of the differential equations governing the propagation of…
Reflection beam splitter for multilevel atoms.
- PhysicsPhysical review. A, Atomic, molecular, and optical physics
- 1993
We propose a beam splitter for atomic de Broglie waves combining atomic reflection from an evanescent laser wave with induced transitions between ground-state sublevels in a homogeneous magnetic…
Exact analytical solution for coupled time-independent Schrödinger equations with certain model potentials
- Physics, Mathematics
- 1996
An exact analytical solution is obtained for coupled time-independent Schrodinger equations with model potentials: , and . This is made possible by solving a single fourth-order ordinary differential…
Exact analytical solution of the quantum Rosen-Zener-Demkov model.
- PhysicsPhysical review. A, Atomic, molecular, and optical physics
- 1994
An exact analytical solution in terms of the Meijer functions is obtained from the quantum Rosen-Zener-Demkov model for nonadiabatic transitions for elastic and inelastic atomic collision channels.
Steepest descent paths for integrals defining the modified Bessel functions of imaginary order
- Mathematics
- 1993
Abstract. The modified Bessel function of the third kind of purely imaginaryorder:K iν (x) = Z ∞0 e −xcosht cosνtdt,is considered for real values of the parameters ν,x, x > 0. This function playsan…