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arXiv:1510.06996 · Physical Review A

Comparison between two models of absorption of matter waves by a thin time-dependent barrier

Maximilien Barbier, Mathieu Beau, Arseni Goussev

Published Nov 30, 2015• 3 citations
arXivHTMLPDF

Abstract

We report a quantitative, analytical, and numerical comparison between two models of the interaction of a nonrelativistic quantum particle with a thin time-dependent absorbing barrier. The first model represents the barrier by a set of time-dependent discontinuous matching conditions, which are closely related to Kottler boundary conditions used in stationary-wave optics as a mathematical basis for Kirchhoff diffraction theory. The second model mimics the absorbing barrier with an off-diagonal $\ensuremath{\delta}$ potential with a time-dependent amplitude. We show that the two models of absorption agree in their predictions in a semiclassical regime, the regime readily accessible in modern experiments with ultracold atoms.

DOI
10.1103/physreva.92.053630

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We report a quantitative, analytical, and numerical comparison between two models of the interaction of a nonrelativistic quantum particle with a thin time-dependent absorbing barrier. The first model represents the barrier by a set of time-dependent discontinuous matching conditions, which are closely related to Kottler boundary conditions used in stationary-wave optics as a mathematical basis for Kirchhoff diffraction theory. The second model mimics the absorbing barrier with an off-diagonal \ensuremathδ\ensuremath{\delta}\ensuremathδ potential with a time-dependent amplitude. We show that the two models of absorption agree in their predictions in a semiclassical regime, the regime readily accessible in modern experiments with ultracold atoms.
Atom-laser interaction is at the heart of the vibrant field of quantum optics. The dynamical properties of a moving atom submitted to a laser radiation are strongly \ninfluenced by the position- and time-dependence of the latter. The full physical state of the atom must include information about the centre-of-mass motion and the internal structure of the atom. It is challenging to obtain a complete description of the full state of the atom. However, there exists an alternative approach to the dynamics of an atom in the presence of a laser, which is based on the concept of matter-wave absorption. \n \nIn this thesis, we theoretically study the nonrelativistic one-dimensional motion of an electrically neutral quantum particle in the presence of a thin time-dependent absorber, representing the laser radiation. Our aim is to better understand the precise connection between time-dependent matter-wave absorption and the interaction between an atom and a localised time-dependent laser. \n \nOur analysis is based on two different approaches to the problem. The first one describes the moving atom by a two-level system, and represents the laser radiation \nby an off-diagonal δ-potential. The second model treats the atom as a structureless particle, and describes the laser by a time-dependent absorbing barrier. While the \nformer model can be derived from first principles, the treatment of the absorbing barrier in the latter model lacks a rigorous quantum mechanical justification. The \nmain outcome of our work is to provide a solid physical ground for the absorber model, by explicitly connecting it to the δ-potential model. We have thus extended \nthe range of theoretical tools useful for investigating the effects of time-dependent laser radiation on quantum matter.
In recent years, matter-wave interferometry has attracted growing attention due to its unique suitability for high-precision measurements and the study of fundamental aspects of quantum theory. Diffraction and interference of matter waves can be observed not only at a spatial aperture (such as a screen edge, slit, or grating), but also at a time-domain aperture (such as an absorbing barrier, or ``shutter,'' that is being periodically switched on and off). The wave phenomenon of the latter type is commonly referred to as ``diffraction in time.'' Here, we introduce a versatile, exactly solvable model of diffraction in time. It describes time evolution of an arbitrary initial quantum state in the presence of a time-dependent absorbing barrier, governed by an arbitrary aperture function. Our results enable a quantitative description of diffraction and interference patterns in a large variety of setups, and may be used to devise new diffraction and interference experiments with atoms and molecules.
In this study, the scattering of matter waves that accompany to the quantum particles by an absorbing half-plane is examined. A quantum shutter, which is opened at an initial time, is proposed to close the semi-infinite complementary aperture of the half-screen. Hence the matter waves, confined in a determined region of space, transmits to the second region by scattering from the semi-infinite aperture. The mathematical expressions of the scattered fields are plotted numerically and interpreted according to the diffraction theory of Young.
We present a theoretical model of matter-wave diffraction through a material nanostructure. This model is based on the numerical solution of the time-dependent Schrödinger equation, which goes beyond the standard semiclassical approach. In particular, we consider the dispersion force interaction between the atoms and the material, which is responsible for high energy variations. The effect of such forces on the quantum model is investigated, along with a comparison with the semiclassical model. In particular, for atoms at low velocity and close to the material surface, the semiclassical approach fails, while the quantum model accurately describes the expected diffraction pattern. This description is thus relevant for slow and cold atom experiments where increased precision is required, e.g., for metrological applications. Published by the American Physical Society 2024
Abstract The dynamics of absorption is analyzed by using an exactly solvable model that deals with an analytical solution to Schrödinger’s equation for cutoff initial plane waves incident on a complex absorbing potential. A dynamical absorption coefficient which allows us to explore the dynamical loss of particles from the transient to the stationary regime is derived. We find that the absorption process is characterized by the emission of a series of damped periodic pulses in time domain, associated with damped Rabi-type oscillations with a characteristic frequency, ω = ( E + ε )/ℏ, where E is the energy of the incident waves and − ε is energy of the quasidiscrete state of the system induced by the absorptive part of the Hamiltonian; the width γ of this resonance governs the amplitude of the pulses. The resemblance of the time-dependent absorption coefficient with a real decay process is discussed, in particular the transition from exponential to nonexponential regimes, a well-known feature of quantum decay. We have also analyzed the effect of the absorptive part of the potential on the dynamical delay time, which behaves differently from the one observed in attractive real delta potentials, exhibiting two regimes: time advance and time delay.
Abstract An error in the author's previous treatment of the interaction of an absorber with high intensity light is noted. The correct development of Mower is applied to determine the amplitude of the initial state of the radiation‐matter system. Comparison of the quantum theory solution for a damped absorber exposed to a square light pulse with the results of semiclassical theories based on the undamped optical Bloch equations is effected by determining the effective in‐ and out‐of‐phase components of the transition dipole response. In general, the out‐of‐phase (or absorptive) part of the transition dipole is zero at the outset and strongly time‐dependent at short times, evolving to a steady‐state value at longer times. For resonance radiation the system exhibits either overdamped irreversible decay or underdamped oscillations, depending upon the relative magnitudes of the incident light intensity and the radiative damping rate. Specific results are presented for a variety of limiting values of the physical parameters, including light intensity, damping rate, and amount of off‐resonance.