We provide the theoretical basis for understanding the phenomenon in which an ultra cold atom incident on a possibly warm target will not stick, even in the large $n$ limit where $n$ is the number of internal degrees of freedom of the target. Our treatment is non-perturbative in which the full many-body problem is viewed as a scattering event purely within the context of scattering theory. The question of sticking is then simply and naturally identified with the formation of a long lived resonance. One crucial physical insight that emerges is that the many internal degrees of freedom serve to decohere the incident one body wavefunction, thus upsetting the delicate interference process necessary to form a resonance in the first place. This is the physical reason for not sticking.
We provide the theoretical basis for understanding the phenomenon in which an ultra cold atom incident on a possibly warm target will not stick, even in the large n limit where n is the number of internal degrees of freedom of the target. Our treatment is non-perturbative in which the full many-body problem is viewed as a scattering event purely within the context of scattering theory. The question of sticking is then simply and naturally identified with the formation of a long lived resonance. One crucial physical insight that emerges is that the many internal degrees of freedom serve to decohere the incident one body wavefunction, thus upsetting the delicate interference process necessary to form a resonance in the first place. This is the physical reason for not sticking.
We provide a general and nonperturbative theoretical basis for quantum reflection of an ultracold atom incident on a cold or warm surface. Sticking is identified with the formation of a long-lived resonance, from which it emerges that the physical reason for not sticking is that the many internal degrees of freedom of the target serve to decohere the incident one body wave function, thereby upsetting the delicate interference process necessary to form a resonance. We then explore the transition to the post-threshold behavior, when sticking prevails at higher incident energies. Studying the WKB wave functions of the atom provides a quick understanding of our results even in the ultracold regime where WKB is not applicable. Explicit examples are examined in detail and we predict the temperatures required to reach the various regimes.
In paper I (physics/0010068) entitled "The No-sticking Effect in Ultra-cold Collisions", we showed that under very general circumstances, atoms approaching a surface will not stick as its incoming energy approaches zero. This is true of either warm or cold surfaces. Here we explore the transition region from non sticking to sticking as energy is increased. The key to understanding the transition region is the WKB approximation and the nature of its breakdown. Simple rules for understanding the rollover to higher energy, post-threshold behavior, including analytical formulae for some asymptotic forms of the attractive potential are presented. We discuss a practical example of atom-surface pair in various substrate geometries. We also discuss the case of low energy scattering from clusters.
The role of shape resonances and many-body effects on universal quantum sticking of ultracold atoms onto solid surfaces is examined analytically and computationally using an exactly solvable representation of the Dyson equation. We derive the self-energy renormalization of the transition amplitude between an ultracold scattering atom and the bound states on the surface in order to elucidate the role of virtual phonon exchanges in the limiting behavior of the sticking probability. We demonstrate that, to first order in the interactions for finite ranged atom–surface potentials, virtual phonons can only rescale the strength of the atom–surface coupling and do not rescale the range of the coupling. Thus, universal sticking behavior at ultralow energies is to be expected for all finite ranged potentials. We demonstrate that the onset of the universal sticking behavior depends greatly on the position of the shape resonance of the renormalized potential and for sufficiently low energy shape resonances, deviations from the universal s(E)∝√E can occur near these energies. We believe that this accounts for many of the low energy sticking trends observed in the scattering of submillikelvin H atoms from superfluid 4He films.
Collision physics plays a key role in understanding the properties of ultracold gases. First, collisions ensure thermalization in trapped atomic samples, which is essential for the success of evaporative cooling. Second, interactions between atoms determine the equilibrium shape and the dynamics of the condensate once it is formed. Finally collisions limit the achievable spatial densities via inelastic processes, which ultimately determine whether a given atomic species may lead to Bose-Einstein condensation. The purpose of the following lectures is to give a basic introduction to collision physics with a special emphasis on the low temperature aspect of these interactions. We will consider here only binary interactions between atoms since one of the remarkable prop-erties of the physics of ultra-cold dilute gases is that all the macroscopic properties of the system can be directly deduced from the two-body interaction potential. In particular the essential concept of scattering length will be introduced and developped for some simple potentials, using as practical examples experimental results obtained on atomic cesium and rubidium. The present lectures are complementary to the ones given by D. Heinzen where a detailed comparison between the collisional properties of the various alkali atoms will be found, together with explanations of the spectroscopic approaches used in the precise determination of interatomic potentials. 1. – Scattering theory: a brief reminder 1.1. Collision between two particles. – We consider here an elementary collision process between two particles 1 and 2 with the same mass M, interacting through the potential
Among the few lessons that Physics teaches us on a daily basis, one in particular is hard to miss: thermalization processes are ubiquitous. With the same degree of certainty, one can predict an apple to fall onto the ground if its stalk is cut, or a cup of tea to be found cold if left on the table for too long. In this respect, generic classical and quantum mechanical systems seem to behave in the same way. This is also one of the main difficulties in the experimental observation of the bizarre effects predicted from the quantum theory, as several of these are known to disappear at finite temperatures. It has been known for a long time that thermalization is associated with “chaotic” behavior at the microscopic level, but recently systematic efforts, both theoretical and experimental, have allowed us to understand its mechanisms at an unprecedented level of accuracy. Indeed, it has been realized that thermalization generally occurs also in isolated systems, where the absence of interactions with the environment allows for first principle theoretical investigations1. In this case thermalization takes place locally, as the whole system acts as a thermal bath for its own subsystems. Theoretical research has been motivated and paralleled by exciting experimental progress in cold-atom physics, which has provided robust, nearly ideal realizations of several theoretical models2. As an established piece of knowledge, recent research has now confirmed that two outstanding exceptions actually exist in the quantum realm, where thermalization is prevented to occur. These are many-body localized systems3, where disorder plays a crucial role, and integrable ones, which are protected by the existence of higher conservation laws. By their own nature, these systems display exceptional non-equilibrium features, which are not washed out by the onset of thermalization as relaxation occurs. At the core of the present thesis lie the remarkable properties of integrable systems out of equilibrium, with a special attention to physical effects which could be observed in cold-atom realizations. The work collected here is part of a large theoretical effort4 which in the past decade has focused on the study of relatively simple protocols to bring a quantum system out of equilibrium, such as the so-called quantum quench. In these “theoretical laboratories” it has been possible to provide quantitative predictions which helped us to develop an intuition on general questions regarding non-equilibrium and thermalization processes. Furthermore, in some cases these studies have highlighted interesting physical effects which could be directly probed experimentally within cold-atom settings. The contribution of the present thesis is two-fold. On the one hand, we have developed new technical tools for the study of integrable systems out of equilibrium, and for the computation of measurable physical quantities such as correlation functions. The techniques employed are mainly analytical and rooted within the mathematical structures of integrability. On the other hand, we have singled out physically relevant nonequilibrium situations where exotic, non-thermal states of matter emerge after relaxation occurs, and provided quantitative analytical predictions in these cases. A comprehensive discussion of the motivations and results of our work will be presented in Chapter 1, where we provide a complete overview of this thesis and discuss the organization of its content.
The formation process of metastable $\mathrm{dt}\ensuremath{\mu}$ molecules in ${D}_{2}\ensuremath{-}{T}_{2}$ mixtures in investigated. The $\mathrm{dt}\ensuremath{\mu}$ molecule exhibits a series of three-body resonances embedded in the $t\ensuremath{\mu}+d$ scattering continuum just below the $t\ensuremath{\mu}(2s)+d$ threshold. These states can be formed in collisions of excited $t\ensuremath{\mu}(2s)$ atoms with D2 molecules, whereby the excess of binding energy is absorbed by the rovibrational degrees of freedom of D2. We present a scattering-theoretic model for this process, and perform a numerical calculation of its cross section. The essential transition amplitudes are obtained from three-body wave functions for the $\mathrm{dt}\ensuremath{\mu}$ subcluster, and adiabatic wave functions for the entire hybrid system in the final channel. It is found that the effective formation rate is limited by the Auger-transition rates of the molecular complex formed. The calculated cross sections exhibit broad "peaks," with magnitudes large enough for the formation process to favorably compete with deexcitation of $t\ensuremath{\mu}(n=2)$ atoms via radiative and collisional processes. The formation of metastable $\mathrm{dt}\ensuremath{\mu}$ can therefore be one of the fastest processes depleting the n=2 levels of the $t\ensuremath{\mu}$ atom in hydrogen mixtures, of importance for low-energy muon science, electroweak physics, and muon catalyzed fusion.