The quest for the understanding of complex quantum systems and their properties occupies a central stage at the frontiers of physics, with applications ranging from material science to black holes. The pursuit of this quest has motivated emergent quantum technologies such as quantum computation. Any system in isolation is described by the celebrated Schrödinger equation, which is hard to solve when the system is complex and involves many degrees of freedom. The challenge is even bigger when considering that any physical system interacts with the surrounding environment.
Quantum systems are often characterized by discrete energy levels and a powerful approach to foster the understanding of complex systems resorts to their characterization. Decades ago, the Nobel laureate Eugene Wigner and Freeman Dyson, another renowned theoretical physicist, proposed a statistical description of energy levels that is today a basic tool, using which one can identify the salient features of a system, whether it is integrable or chaotic, or governed by phenomena such as many-body localization.
Yet, the ubiquitous coupling to the surrounding environment make such an approach of limited use in many experimental scenarios. Indeed, environmental effects are generally believed to suppress quantum features through a process known as decoherence.
This understanding has been challenged by a work published in the Physical Review Letters and led by University of Luxembourg (UL) BSc student Julien Cornelius as first author. Working under the supervision of Prof. Adolfo del Campo at the Department of Physics and Materials Science, he teamed up with Prof. Aurelia Chenu, associate professor in theoretical physics at UL, and Avadh Saxena, theoretical physicist at Los Alamos National Laboratory and Prof. Zhenyu Xu at Soochow University.
The authors have shown that certain environments characterized by “balanced gain and loss” naturally provide a spectral filter that brings out the statistical correlations between energy levels. In turn, this facilitates the identification of physical properties such as chaotic behaviour. The findings establish a bridge between numerical methods for the study of complex quantum systems and their simulation in the laboratory.
Reference: Julien Cornelius, Zhenyu Xu, Avadh Saxena, Aurelia Chenu, Adolfo del Campo, Spectral Filtering Induced by Non-Hermitian Evolution with Balanced Gain and Loss: Enhancing Quantum Chaos, Phys. Rev. Lett. 128, 190402 (2022); arXiv:2108.06784