Viewing a quantum thermal machine as a non-Hermitian quantum system, we characterize in full generality its analytical time-dependent dynamics by deriving the spectrum of its non-Hermitian Liouvillian for an arbitrary initial state.We show that the thermal machine features a number of Liouvillian exceptional points (EPs) for experimentally realistic parameters, in particular, a third-order exceptional point that leaves signatures both in short-and long-time regimes.Remarkably, we demonstrate that this EP corresponds to a regime of critical decay for the quantum thermal machine towards its steady state, bearing a striking resemblance with a critically damped harmonic oscillator.These results open up exciting possibilities for the precise dynamical control of quantum thermal machines exploiting exceptional points from non-Hermitian physics and are amenable to state-of-the-art solid-state platforms such as semiconducting and superconducting devices.
Viewing a quantum thermal machine as a non-Hermitian quantum system, we characterize in full generality its analytical time-dependent dynamics by deriving the spectrum of its non-Hermitian Liouvillian for an arbitrary initial state.We show that the thermal machine features a number of Liouvillian exceptional points (EPs) for experimentally realistic parameters, in particular, a third-order exceptional point that leaves signatures both in short-and long-time regimes.Remarkably, we demonstrate that this EP corresponds to a regime of critical decay for the quantum thermal machine towards its steady state, bearing a striking resemblance with a critically damped harmonic oscillator.These results open up exciting possibilities for the precise dynamical control of quantum thermal machines exploiting exceptional points from non-Hermitian physics and are amenable to state-of-the-art solid-state platforms such as semiconducting and superconducting devices.
The concepts and tools from the theory of non-Hermitian quantum systems are used to investigate the dynamics of a quantum thermal machine. This approach allows us to characterize in full generality the analytical time-dependent dynamics of an autonomous quantum thermal machine, by solving a non-Hermitian Liouvillian for an arbitrary initial state. We show that the thermal machine features a number of exceptional points for experimentally realistic parameters. The signatures of a third-order exceptional point, both in the short and long-time regimes are demonstrated. As these points correspond to regimes of critical decay towards the steady state, in analogy with a critically damped oscillator, our work opens interesting possibilities for the precise control of the dynamics of quantum thermal machines.
One of the most remarkable features that distinguish open systems from closed ones is the presence of exceptional points (EPs), where two or more eigenvectors of a non-Hermitian operator coalesce, accompanying the convergence of the corresponding eigenvalues. So far, EPs have been demonstrated on a number of platforms, ranging from classical optical systems to fully quantum-mechanical spin-boson models. In these demonstrations, the reservoir that induced the non-Hermiticity was treated as a Markovian one, without considering its memory effect. We here present the first experimental demonstration of non-Markovian quantum EPs, engineered by coupling a Josephson-junction-based qubit to a leaky electromagnetic resonator, which acts as a non-Markovian reservoir. We map out the spectrum of the extended Liouvillian superoperator by observing the quantum state evolution of the qubit and the pseudomode, in which the memory of the reservoir is encoded. We identify a twofold second-order EP and a third-order EP in the Liouvillian spectrum, which cannot be realized with a Markovian reservoir. Our results pave the way for experimental exploration of exotic phenomena associated with non-Markovian quantum EPs.
Usually, when investigating exceptional points (EPs) of an open Markovian bosonic system, one deals with spectral degeneracies of a non-Hermitian Hamiltonian (NHH), which can correctly describe the system dynamics only in the semiclassical regime. A recently proposed quantum Liouvillian framework [Minganti et al., Phys. Rev. A 100, 062131 (2019)] enables the complete determination of the dynamical properties of such systems and their EPs (referred to as Liouvillian EPs, or LEPs) in the quantum regime by taking into account the effects of quantum jumps, which are ignored in the NHH formalism. Moreover, the symmetry and eigenfrequency spectrum of the NHH become a part of much larger Liouvillian eigenspace. As such, the EPs of an NHH form a subspace of the LEPs. Here we show that once an NHH of a dissipative linear bosonic system exhibits an EP of a certain finite order n, it immediately implies that the corresponding LEP can become of any higher order $m\ensuremath{\ge}n$ defined in the infinite Hilbert space. These higher-order LEPs can be identified by the coherence and spectral functions at the steady state. The coherence functions can offer a convenient tool to probe extreme system sensitivity to external perturbations in the vicinity of higher-order LEPs. As an example, we study a linear bosonic system of a bimodal cavity with incoherent mode coupling to reveal its higher-order LEPs; particularly, of second and third order via first- and second-order coherence functions, respectively. Accordingly, these LEPs can be additionally revealed by squared and cubic Lorentzian spectral lineshapes in the power and intensity-fluctuation spectra. Moreover, we demonstrate that these EPs can also be associated with spontaneous parity-time (PT) and anti-PT-symmetry breaking in the system studied. These symmetries can be switched in the output fields (the so-called supermodes) of an additional linear coupler with a properly chosen coupling strength. Thus, we show that the initial loss-loss dynamics for the supermodes can be equivalent to the balanced gain-loss evolution.
Exceptional points, where two or more eigenstates of a non-Hermitian system coalesce, are now of interest across many fields of physics, from the perspective of open-system dynamics, sensing, nonreciprocal transport, and topological phase transitions. In this work, we investigate exceptional points in cavity optomechanics, a platform of interest to diverse communities working on gravitational-wave detection, macroscopic quantum mechanics, quantum transduction, etc. Specifically, we clarify the role of quantum jumps in making a clear distinction between Liouvillian and Hamiltonian exceptional points in optomechanical systems. While the Liouvillian exceptional point arises from the unconditional Lindblad dynamics and is independent of the phonon-bath temperature, the Hamiltonian exceptional point emerges from the conditional no-jump evolution and acquires a thermal shift due to an enhanced conditional damping. Employing the thermofield formalism, we derive a unified spectral framework that interpolates between these regimes via an analytical hybrid-Liouvillian description. Remarkably, in the weak-quantum-jump regime, the exceptional point is perturbed only at the second order, highlighting the robustness of the Hamiltonian exceptional point under small hybrid perturbations. Our work reveals a continuous family of hybrid exceptional points, clarifies the operational and physical differences between the conditional and unconditional dissipative dynamics in optomechanical systems, and provides a probe for thermal baths.
Open quantum systems can be approximately described by non-Hermitian Hamiltonians (NHHs) and Liouvillian superoperators. The two approaches differ by quantum jump terms corresponding to a measurement of the system by its environment. We analyze the emergence of exceptional points (EPs) in NHHs and Liouvillian superoperators. In particular, we show how EPs in NHHs relate to a novel type of EPs -- multi-block EPs -- in the no-jump Liouvillian, i.e. the Liouvillian superoperator in absence of quantum jump terms. We further analyze how quantum jump terms modify the multi-block structure. To illustrate our general findings, we present two prime examples: qubits and qutrits coupled to additional ground state levels that serve as sinks of the population. In those examples, we can navigate through the EP block structure by a variation of physical parameters. We analyze how the dynamics of the population of the states is affected by the order of the EPs. Additionally, we demonstrate that the quantum geometric tensor serves as a sensitive indicator of EPs of different kinds.
Exceptional points in non-Hermitian quantum systems give rise to novel genuine quantum phenomena. Recent explorations of exceptional-point-induced quantum phase transitions have extended from discrete-variable to continuous-variable-encoded quantum systems. However, quantum phase transitions driven by Liouvillian exceptional points (LEPs) in continuous-variable platforms remain largely unexplored. Here, we construct and investigate a Liouvillian exceptional structure based on a driven-dissipative Kerr-cat qubit. Through numerical simulations, we reveal a quantum phase transition occurring at the LEP characterized by a sudden change in dynamical behavior from underdamped oscillations to overdamped relaxations as visualized via Wigner functions and Bloch sphere trajectories. Notably the negativity of the Wigner function serves as a direct signature of genuine quantum coherence unattainable in conventional single-qubit non-Hermitian systems. Furthermore, we introduce the phase difference between the off-diagonal elements of the Liouvillian eigenmatrices as a novel parameter to quantify the transition. Our results establish the Kerr-cat qubit as a novel continuous-variable setting for exploring dissipative quantum criticality and intrinsic non-Hermitian physics.