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arXiv:1008.5187 · The European Physical Journal A

How quantum bound states bounce and the structure it reveals

Dean Lee, M. Pine

Published Mar 1, 2011• 5 citations
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Abstract

We investigate how quantum bound states bounce from a hard surface. Our analysis has applications to ab initio calculations of nuclear structure and elastic deformation, energy levels of excitons in semiconductor quantum dots and wells, and cold atomic few-body systems on optical lattices with sharp boundaries. We develop the general theory of elastic reflection for a composite body from a hard wall. On the numerical side we present ab initio calculations for the compression of alpha particles and universal results for two-body states. On the analytical side we derive a universal effective potential that gives the reflection scattering length for shallow two-body states.

DOI
10.1140/epja/i2011-11041-4

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We investigate how quantum bound states bounce from a hard surface. Our analysis has applications to ab initio calculations of nuclear structure and elastic deformation, energy levels of excitons in semiconductor quantum dots and wells, and cold atomic few-body systems on optical lattices with sharp boundaries. We develop the general theory of elastic reflection for a composite body from a hard wall. On the numerical side we present ab initio calculations for the compression of alpha particles and universal results for two-body states. On the analytical side we derive a universal effective potential that gives the reflection scattering length for shallow two-body states.
Scattering probes the internal structure of quantum systems. We calculate the two-particle elastic scattering phase shift for a short-ranged interaction on a quantum computer. Short-ranged interactions with a large scattering length or shallow bound state describe a universality class that is of interest in atomic, condensed matter, nuclear, and particle physics. The phase shift is calculated by relating it to the ground-state energy of the interacting particles in a harmonic trap. The relaxation method is used as the variational quantum eigensolver for the ground-state calculation. Schmidt decomposition is used to reduce quantum circuits nominally requiring tens of qubits to two-qubit circuits, thus reducing the noise in quantum measurements. Calculations in multiparticle systems with many-body interactions would benefit from this reduction of qubits in noisy quantum processors.
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Few-mode models are a cornerstone of the theoretical work in quantum optics, with the famous singlemode Jaynes-Cummings model being only the most prominent example.In this work, we develop an ab initio few-mode theory, a framework connecting few-mode system-bath models to ab initio methods.We first present a method to derive exact few-mode Hamiltonians for noninteracting quantum potential scattering problems and demonstrate how to rigorously reconstruct the scattering matrix from such few-mode Hamiltonians.We show that, upon inclusion of a background scattering contribution, an ab initio version of the well-known input-output formalism is equivalent to standard scattering theory.On the basis of these exact results for noninteracting systems, we construct an effective few-mode expansion scheme for interacting theories, which allows us to extract the relevant degrees of freedom from a continuum in an open quantum system.As a whole, our results demonstrate that few-mode as well as input-output models can be extended to a general class of problems and open up the associated toolbox to be applied to various platforms and extreme regimes.We outline differences of the ab initio results to standard model assumptions, which may lead to qualitatively different effects in certain regimes.The formalism is exemplified in various simple physical scenarios.In the process, we provide a proof of concept of the method, demonstrate important properties of the expansion scheme, and exemplify new features in extreme regimes.
A theoretical investigation of the He-PH (${}^{3}{\ensuremath{\Sigma}}^{\ensuremath{-}}$) complex is presented. We perform ab initio calculations of the interaction potential energy surface and discuss its error bounds with relevance to cold collisions, and we carry out accurate calculations of bound energy levels of the complex including the molecular fine structure and magnetic-field effect. We find the potential has two shallow minima and supports ten and 13 bound levels in complex with 3{}^{3}3He and 4{}^{4}4He, respectively. Based on the potential the quantum scattering calculations are then implemented for elastic and inelastic cross sections of the magnetically trappable low-field-seeking state of PH (${}^{3}{\ensuremath{\Sigma}}^{\ensuremath{-}}$) in collision with 3{}^{3}3He atom. The cold-collision properties and the influence of the external magnetic field as well as the effect of the uncertainty of interaction potential on the collisionally induced Zeeman relaxation are explored and discussed in detail. The ratio of elastic to inelastic cross sections is large over a wide range of collision energy, magnetic field, and scaling factor of the potential, so that helium buffer-gas loading and evaporative cooling of PH is a good prospect.