Higher-order Liouvillian exceptional points in the dissipative dynamics of quadratic fermions
University of Science and Technology of China（中国科学技术大学）；Laboratory of Quantum Information, University of Science and Technology of China（中国科学技术大学量子信息实验室）；Anhui Province Key Laboratory of Quantum Network, University of Science and Technology of China（中国科学技术大学安徽省量子网络重点实验室）；CAS Center For Excellence in Quantum Information and Quantum Physics（中国科学院量子信息与量子物理学前沿卓越中心）；Hefei National Laboratory, University of Science and Technology of China（中国科学技术大学合肥国家实验室）
We propose a general class of open fermionic models where quadratic Liouvillians governing the dissipative dynamics feature analytically characterized higher-order exceptional points (EPs). Invoking the formalism of third quantization, we show that, among the multiple EPs of Liouvillian, an EP with its order approaching the system size arises as the dominant modes of the system at long times, leading to a gapless Liouvillian spectrum. By introducing perturbations, in the form of many-body quantum-jump processes, these higher-order EPs break down, leading to finite Liouvillian gaps with fractional power-law scalings. While the power-law scaling is a signature of the higher-order EP, its explicit form is sensitively dependent on the many-body perturbation. Finally, we discuss the long-time dynamics which can serve as detectable signals for the higher-order Liouvillian EPs.
Open quantum systems interacting with an environment exhibit dynamics described by the combination of dissipation and coherent Hamiltonian evolution. Taken together, these effects are captured by a Liouvillian superoperator. The degeneracies of the (generically non-Hermitian) Liouvillian are exceptional points, which are associated with critical dynamics as the system approaches steady state. We use a superconducting transmon circuit coupled to an engineered environment to observe two different types of Liouvillian exceptional points that arise either from the interplay of energy loss and deco…
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-dorder 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 st…
Multi-block exceptional points in open quantum systems
Institute for Theoretical Physics and Astrophysics, University of Würzburg（维尔茨堡大学理论物理与天体物理研究所）；Würzburg-Dresden Cluster of Excellence ctd.qmat（维尔茨堡-德累斯顿卓越集群 ctd.qmat）
Floquet-Magnus (FM) expansion theory is a powerful tool in periodically driven (Floquet) systems under high-frequency drives. In closed systems, it dictates that their stroboscopic dynamics under a time-periodic Hamiltonian is well captured by the FM expansion, which gives a static effective Hamiltonian. On the other hand, in dissipative systems driven by a time-periodic Liouvillian, it remains an important and nontrivial problem whether the FM expansion gives a static Liouvillian describing continuous-time Markovian dynamics, which we refer to as the Liouvillianity of the FM expansion. We ans…
We theoretically investigate dynamics of classical spins exchange-coupled through an isotropic medium. The coupling is treated at the adiabatic level of the medium's response, which mediates a first-order in frequency dissipative interaction along with an instantaneous Heisenberg exchange. The resultant damped spin precession yields exceptional points (EPs) in the coupled spin dynamics, which should be experimentally accessible with the existing magnetic heterostructures. In particular, we show that an EP is naturally approached in an antiferromagnetic dimer by controlling local damping, while…
We develop a numerical procedure to efficiently model the nonequilibrium steady state of one-dimensional arrays of open quantum systems, based on a matrix-product operator ansatz for the density matrix. The procedure searches for the null eigenvalue of the Liouvillian superoperator by sweeping along the system while carrying out a partial diagonalization of the single-site stationary problem. It bears full analogy to the density-matrix renormalization group approach to the ground state of isolated systems, and its numerical complexity scales as a power law with the bond dimension. The method b…
Following the evolution under a non-Hermitian Hamiltonian (nHH) involves significant probability loss. This makes various nHH effects impractical in the quantum realm. In contrast, Lindbladian evolution conserves probability, facilitating observation and application of exotic effects characteristic of open quantum systems. Here we are concerned with the effect of chiral state conversion: encircling an exceptional point, multiple system states are converted into a single system eigenmode. While for nHH the possible converted-into eigenmodes are pure states, for Lindbladians these are typically …
Liouvillian topology and nonreciprocal dynamics in open Floquet chains
Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Institute of Theoretical Physics, Technische Universität Dresden and Würzburg-Dresden Cluster of Excellence ctd.qmat（德累斯顿工业大学理论物理学院和维尔茨堡-德累斯顿卓越集群ctd.qmat）
The state of a quantum system may be steered towards a predesignated target state, employing a sequence of weak $\textit{blind}$ measurements (where the detector's readouts are traced out). Here we analyze the steering of a two-level system using the interplay of a system Hamiltonian and weak measurements, and show that $\textit{any}$ pure or mixed state can be targeted. We show that the optimization of such a steering protocol is underlain by the presence of Liouvillian exceptional points. More specifically, for high purity target states, optimal steering implies purely relaxational dynamics …
Observation of Non-Hermitian Skin Dynamics in the Liouvillian Regime
The University of Hong Kong（香港大学）；HK Institute of Quantum Science and Technology（香港量子科学研究所）；State Key Laboratory of Optical Quantum Materials（光学量子材料国家重点实验室）
Open systems with gain and loss, described by non-trace-preserving, non-Hermitian Hamiltonians, have been a subject of intense research recently. The effect of exceptional-point degeneracies on the dynamics of classical systems has been observed through remarkable phenomena such as the parity-time symmetry breaking transition, asymmetric mode switching, and optimal energy transfer. On the other hand, consequences of an exceptional point for quantum evolution and decoherence are hitherto unexplored. Here, we use post-selection on a three-level superconducting transmon circuit with tunable Rabi …
We explore the topological properties of non-Hermitian nodal-link semimetals with dissipative cold atoms in a three-dimensional optical lattice. We construct a two-band continuum model in three dimensions with a spin-dependent gain and loss, where the exceptional points in the energy spectrum can comprise a double Hopf link. The topology of the bulk band is characterized by a winding number defined for a one-dimensional loop in the momentum space and a topological transition of the nodal structures emerges as the change of the non-Hermiticity strength. A non-Bloch theory is built to describe t…
The spectral and dynamical properties of dissipative quantum systems, as modeled by a damped oscillator in the Fock space, are investigated from a topological point of view. Unlike a physical lattice system that is naturally under the open boundary condition, the bounded-from-below nature of the Fock space offers a unique setting for understanding and verifying non-Hermitian skin modes under semi-infinity boundary conditions that are elusive in actual physical lattices. A topological characterization based on the complex spectra of the Liouvillian superoperator is proposed and the associated c…
This study aims to provide evidence regarding the emergence of a class of dissipative time crystals when $\mathcal{PT}$ symmetry of the systems is restored in collective spin systems with Lindblad dynamics. First, we show that a standard model of boundary time crystals (BTCs) satisfies the Liouvillian $\mathcal{PT}$ symmetry, and prove that BTC exists only when the stationary state is $\mathcal{PT}$ symmetric in the large-spin limit. Also, a similar statement is confirmed numerically for another BTC model. In addition, the mechanism of the appearance of BTCs is discussed through the developmen…
Critical phenomena arise ubiquitously in various context of physics, from condensed matter, high energy physics, cosmology, to biological systems, and consist of slow and long-distance fluctuations near a phase transition or critical point. Usually, these phenomena are associated with the softening of a massive mode. Here we show that a novel, non-Hermitian-induced mechanism of critical phenomena that do not fall into this class can arise in the steady state of generic driven-dissipative many-body systems with coupled binary order parameters such as exciton-polariton condensates and driven-dis…
