Abstract
Few-mode models are a cornerstone of the theoretical work in quantum optics, with the famous single-mode 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.
7 More- Received 21 December 2018
- Revised 9 September 2019
DOI:https://doi.org/10.1103/PhysRevX.10.011008
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
The dynamics of many quantum systems of interest are too complex to be understood in their entirety. Fortunately, for many regimes of interest, such systems can often be modeled with a few dominant degrees of freedom. However, because these “few-mode” approaches are based on model assumptions, researchers have questioned the applicability to more extreme experimental platforms. These feature strong couplings within the system or leakage to the environment, and the resulting changes to the system dynamics have moved them into the focus of current research. Here, we promote few-mode models to a fundamental theory, thereby providing access to exact solutions in extreme parameter regimes.
Specifically, we first show how to derive few-mode Hamiltonians for noninteracting quantum potential scattering problems, and how to reconstruct the full scattering information using a first-principles input-output formalism. On this basis, we develop a systematic effective few-mode expansion for interactions, where the continuum in an open quantum system is boiled down to a few relevant degrees of freedom. Compared to standard phenomenological models, this ab initio treatment provides new predictions for qualitatively different phenomena in extreme parameter regimes.
From a more general perspective, our results make few-mode theory a rigorous tool for quantum scattering systems, allowing the extraction of relevant degrees of freedom or resonances. We therefore expect that our method will find applications for general scattering problems, and so further the exchange of concepts and methods between currently separated fields.