This report on progress explores recent advances in our theoretical and experimental understanding of the physics of open quantum systems (OQSs). The study of such systems represents a core problem in modern physics that has evolved to assume an unprecedented interdisciplinary character. OQSs consist of some localized, microscopic, region that is coupled to an external environment by means of an appropriate interaction. Examples of such systems may be found in numerous areas of physics, including atomic and nuclear physics, photonics, biophysics, and mesoscopic physics. It is the latter area that provides the main focus of this review, an emphasis that is driven by the capacity that exists to subject mesoscopic devices to unprecedented control. We thus provide a detailed discussion of the behavior of mesoscopic devices (and other OQSs) in terms of the projection-operator formalism, according to which the system under study is considered to be comprised of a localized region (Q), embedded into a well-defined environment (P) of scattering wavefunctions (with Q + P = 1). The Q subspace must be treated using the concepts of non-Hermitian physics, and of particular interest here is: the capacity of the environment to mediate a coupling between the different states of Q; the role played by the presence of exceptional points (EPs) in the spectra of OQSs; the influence of EPs on the rigidity of the wavefunction phases, and; the ability of EPs to initiate a dynamical phase transition (DPT). EPs are singular points in the continuum, at which two resonance states coalesce, that is where they exhibit a non-avoided crossing. DPTs occur when the quantum dynamics of the open system causes transitions between non-analytically connected states, as a function of some external control parameter. Much like conventional phase transitions, the behavior of the system on one side of the DPT does not serve as a reliable indicator of that on the other. In addition to discussing experiments on mesoscopic quantum point contacts that provide evidence of the environmentally-mediated coupling of quantum states, we also review manifestations of DPTs in mesoscopic devices and other systems. These experiments include observations of resonance-trapping behavior in microwave cavities and open quantum dots, phase lapses in tunneling through single-electron transistors, and spin swapping in atomic ensembles. Other possible manifestations of this phenomenon are presented, including various superradiant phenomena in low-dimensional semiconductors. From these discussions a generic picture of OQSs emerges in which the environmentally-mediated coupling between different quantum states plays a critical role in governing the system behavior. The ability to control or manipulate this interaction may even lead to new applications in photonics and electronics.
This report on progress explores recent advances in our theoretical and experimental understanding of the physics of open quantum systems (OQSs). The study of such systems represents a core problem in modern physics that has evolved to assume an unprecedented interdisciplinary character. OQSs consist of some localized, microscopic, region that is coupled to an external environment by means of an appropriate interaction. Examples of such systems may be found in numerous areas of physics, including atomic and nuclear physics, photonics, biophysics, and mesoscopic physics. It is the latter area that provides the main focus of this review, an emphasis that is driven by the capacity that exists to subject mesoscopic devices to unprecedented control. We thus provide a detailed discussion of the behavior of mesoscopic devices (and other OQSs) in terms of the projection-operator formalism, according to which the system under study is considered to be comprised of a localized region (Q), embedded into a well-defined environment (P) of scattering wavefunctions (with Q + P = 1). The Q subspace must be treated using the concepts of non-Hermitian physics, and of particular interest here is: the capacity of the environment to mediate a coupling between the different states of Q; the role played by the presence of exceptional points (EPs) in the spectra of OQSs; the influence of EPs on the rigidity of the wavefunction phases, and; the ability of EPs to initiate a dynamical phase transition (DPT). EPs are singular points in the continuum, at which two resonance states coalesce, that is where they exhibit a non-avoided crossing. DPTs occur when the quantum dynamics of the open system causes transitions between non-analytically connected states, as a function of some external control parameter. Much like conventional phase transitions, the behavior of the system on one side of the DPT does not serve as a reliable indicator of that on the other. In addition to discussing experiments on mesoscopic quantum point contacts that provide evidence of the environmentally-mediated coupling of quantum states, we also review manifestations of DPTs in mesoscopic devices and other systems. These experiments include observations of resonance-trapping behavior in microwave cavities and open quantum dots, phase lapses in tunneling through single-electron transistors, and spin swapping in atomic ensembles. Other possible manifestations of this phenomenon are presented, including various superradiant phenomena in low-dimensional semiconductors. From these discussions a generic picture of OQSs emerges in which the environmentally-mediated coupling between different quantum states plays a critical role in governing the system behavior. The ability to control or manipulate this interaction may even lead to new applications in photonics and electronics.
Open photonic systems provide a versatile platform for non-Hermitian physics, enabling control over complex spectra, transport, and light-matter interactions. Exceptional points (EPs), at which eigenvalues and eigenvectors coalesce and the governing operator becomes defective, play a central role because they combine branch-point spectral topology, nonanalytic perturbative response, and controllable eigenstate conversion. This Review provides a unified framework for EP photonics by systematically distinguishing exceptional degeneracies according to the underlying operator, spectral variable, boundary conditions, and experimentally accessible observables. We discuss Hamiltonian EPs, absorbing EPs associated with scattering zeros, real-frequency scattering-matrix and Jones-matrix EPs, Bloch and Floquet EPs, and Liouvillian EPs in open quantum systems. We review their spectral topology, static and dynamical encircling, higher-order exceptional structures, and coexistence with bound states in the continuum, together with applications in sensing, lasing, coherent absorption, directional scattering, polarization and wavefront control, nonlinear optics, optical storage, nonreciprocal photonics, and quantum photonics. We also critically assess the current limitations, practical challenges, and future perspectives of EP-based photonic technologies, with particular attention to robustness, noise, scalability, and experimentally measurable performance.
Calculations for open quantum systems are performed usually by taking into account their embedding into one common environment, which is mostly the common continuum of scattering wave functions. Realistic quantum systems are coupled however often to more than one continuum. For example, the conductance of an open cavity needs at least two environments, namely the input and the output channel. In the present paper, we study generic features of an open quantum system coupled to two channels. We compare the results with those characteristic of a one-channel system. Of special interest is the parameter range which is influenced by singular (exceptional) points. Here, the states of the system are mixed via the environment and the dynamics is determined, in any case, by nonlinear processes. These processes restore the resonance structure of the cross section in the one-channel case, such that there is no need to consider them in calculations for concrete systems. In the two-channel case, however, they cause new effects. Most interesting is the enhanced conductance of an open cavity in this parameter range. This enhancement follows directly from the properties of the eigenstates of a non-Hermitian Hamilton operator (and is not related to the existence of a superradiant state). The study of the conductance allows, among others, an experimental test of the non-Hermitian quantum physics.
Exceptional points (EPs) are the spectral singularities and one of the central concepts of non-Hermitian physics, originating from the inevitable energy exchange with the surrounding environment. EPs exist in diverse physical systems and give rise to many counterintuitive effects, offering rich opportunities to control the dynamics and alter the properties of optical, electronic, acoustic, and mechanical states. The last two decades have witnessed the flourishing of non-Hermitian physics and associated applications related to coalesced eigenstates at EPs in a plethora of classical systems. While stemming from the quantum mechanism, the implementation of EPs in real quantum systems still faces challenges of tuning and stabilizing the systems at EPs, as well as the additional noises that hinder the observation of relevant phenomena. This review mainly focuses on summarizing the current efforts and opportunities offered by quantum EPs that result from or produce observable quantum effects. We introduce the concepts of Hamiltonian and Liouvillian EPs in the quantum regime and focus on their different properties in connection with quantum jumps and decoherence. We then provide a comprehensive discussion covering the theoretical and experimental advances in accessing EPs in diverse quantum systems and platforms. Special attention is paid to EP-based quantum-optics applications with state-of-art technologies. Finally, we present a discussion on the existing challenges of constructing quantum EPs at the nanoscale and an outlook on the fundamental science and applied technologies of quantum EPs, aiming to provide valuable insights for future research and building quantum devices with high performance and advanced functionalities.
The study of quantum criticality has historically been confined to Hermitian systems, where closed-system approximations neglect environmental interactions. However, a significant portion of quantum phenomena occurs in open systems, necessitating a departure from this conventional framework. This paper explores non-Hermitian quantum criticality in open many-body systems, delving into the unique phases and phase transitions that emerge due to dissipation, gain, and other non-conservative interactions. We establish a comprehensive framework that integrates concepts from biorthogonal quantum mechanics, Liouvillian dynamics, and tensor network methods to characterize critical phenomena, including dynamical quantum phase transitions and the emergence of non-Hermitian quantum many-body scars. Through an extensive literature review, we highlight how the interplay of non-Hermiticity with many-body correlations leads to novel critical behaviors, distinct from their Hermitian counterparts, and in some cases, surprisingly resilient or even enhanced. We discuss the role of exceptional points as hallmarks of non-Hermitian systems, their influence on energy spectra, and their implications for criticality and topological invariants. Furthermore, we examine the methodologies for defining observables and statistical ensembles in these non-Hermitian settings, emphasizing the distinctions and occasional controversies that arise. The findings provide critical insights into the fundamental principles governing quantum criticality in dissipative environments and pave new avenues for engineering and understanding open quantum technologies, from quantum sensing to robust quantum information processing.
In the framework of non-Hermitian quantum physics, the relation between exceptional points,dynamical phase transitions and the counter intuitive behavior of quantum systems at high level density is considered. The theoretical results obtained for open quantum systems and proven experimentally some years ago on a microwave cavity, may explain environmentally induce deffects (including dynamical phase transitions), which have been observed in various experimental studies. They also agree(qualitatively) with the experimental results reported recently in PT symmetric optical lattices.
In recent years, two independent research fields, i.e. non-Hermitian andstrongly correlated systems have been merged, forming an important researchfield in physics. The progress of relevant theories and experiments hasreshaped our understanding of matter. In this field, the research object isnot limited to the influence of non-Hermiticity on the energy spectrum andthe eigenstate properties of many-body systems. Researchers have paid more attentionto the manipulation of quantum states. It is universally received that the exceptional point is the most significant featurethat distinguishes non-Hermitian quantum mechanics from Hermitian quantum mechanics. In addition to the recent advances in non-Hermitian topological band theory and quantum sensing around the exceptional points, this paper concentrates on the non-Hermitian critical dynamical phenomenon and its application to the quantum many-body system. When the system has an exceptional point, an arbitrary initial state belonging to the coalescent subspace will be projected on the coalescent state. Based on the directionality of the evolved quantum state, this paper reviews our several representative researches in recent years, including local-field-induced dynamical magnetization, quantum phase transition in transverse field, Ising model at non-zero temperature, quantum mold casting in the center-environment system, as well as superconducting state preparation in the non-Hermitian strongly correlated system. We also focus on the new preparation methods and detection schemes of non-equilibrium quantum states related to exception points.