Steering the evolution of single spin systems is crucial for quantum computing and quantum sensing. The dynamics of quantum systems has been theoretically investigated with parity-time-symmetric Hamiltonians exhibiting exotic properties. Although parity-time symmetry has been explored in classical systems, its observation in a single quantum system remains elusive. We developed a method to dilate a general parity-time-symmetric Hamiltonian into a Hermitian one. The quantum state evolutions ranging from regions of unbroken to broken [Formula: see text] symmetry have been observed with a single nitrogen-vacancy center in diamond. Owing to the universality of the dilation method, our result provides a route for further exploiting and understanding the exotic properties of parity-time symmetric Hamiltonian in quantum systems.
Steering the evolution of single spin systems is crucial for quantum computing and quantum sensing. The dynamics of quantum systems has been theoretically investigated with parity-time-symmetric Hamiltonians exhibiting exotic properties. Although parity-time symmetry has been explored in classical systems, its observation in a single quantum system remains elusive. We developed a method to dilate a general parity-time-symmetric Hamiltonian into a Hermitian one. The quantum state evolutions ranging from regions of unbroken to broken [Formula: see text] symmetry have been observed with a single nitrogen-vacancy center in diamond. Owing to the universality of the dilation method, our result provides a route for further exploiting and understanding the exotic properties of parity-time symmetric Hamiltonian in quantum systems.
Physics
The energetics of quantum systems are typically described by Hermitian Hamiltonians. The exploration of non-Hermitian physics in classical parity-time (PT)–symmetric systems has provided fertile theoretical and experimental ground to develop systems exhibiting exotic behavior. Wu et al. now demonstrate that non-Hermitian physics can be found in a solid-state quantum system. They developed a protocol, termed dilation, which transformed a PT-symmetric Hamiltonian into a Hermitian one. This allowed them to investigate PT-symmetric physics with a single nitrogen-vacancy center in diamond. The results provide a starting point for exploiting and understanding the exotic properties of PT-symmetric Hamiltonians in quantum systems.
Science , this issue p. [878][1]
[1]: /lookup/doi/10.1126/science.aaw8205
The concept of parity-time (PT) symmetry originates from the framework of quantum mechanics, where if the Hamiltonian operator satisfies the commutation relation with the parity and time operators, it shows real energy spectrum. Recently, PT symmetry was introduced into various systems, such as optics, electronic circuits, acoustics, and other classical fields to further study the dynamical behaviors of the Hamiltonian and the energies. To focus on the dynamical evolution of the quantum state, here we experimentally studied the dynamical evolution of a two-level quantum system under the PT symmetric Hamiltonian using single-photon system. By enlarging the system using ancillary qubit and encoding the subsystem under the non-Hermitian Hamiltonian with post-selection, the evolution of the state can be characterized with a high fidelity. Owing to the effectively operation of the dilation method, our work provides a route for further exploiting the exotic properties of PT symmetric Hamiltonian for quantum simulation and quantum information processing.
Topological edge states arise in non-Hermitian parity-time ([Formula: see text])-symmetric systems, and manifest themselves as bright or dark edge states, depending on the imaginary components of their eigenenergies. As the spatial probabilities of dark edge states are suppressed during the non-unitary dynamics, it is a challenge to observe them experimentally. Here we report the experimental detection of dark edge states in photonic quantum walks with spontaneously broken [Formula: see text] symmetry, thus providing a complete description of the topological phenomena therein. We experimentally confirm that the global Berry phase in [Formula: see text]-symmetric quantum-walk dynamics unambiguously defines topological invariants of the system in both the [Formula: see text]-symmetry-unbroken and -broken regimes. Our results establish a unified framework for characterizing topology in [Formula: see text]-symmetric quantum-walk dynamics, and provide a useful method to observe topological phenomena in [Formula: see text]-symmetric non-Hermitian systems in general.
Abstract Non-Hermitian parity-time ( PT P T ) and anti-parity-time ( APT APT )-symmetric systems exhibit novel quantum properties and have attracted increasing interest. Although many counterintuitive phenomena in PT P T - and APT APT -symmetric systems were previously studied, coherence flow has been rarely investigated. Here, we experimentally demonstrate single-qubit coherence flow in PT P T - and APT APT -symmetric systems using an optical setup. In the symmetry unbroken regime, we observe different periodic oscillations of coherence. Particularly, we observe two complete coherence backflows in one period in the PT P T -symmetric system, while only one backflow in the APT APT -symmetric system. Moreover, in the symmetry broken regime, we observe the phenomenon of stable value of coherence flow. We derive the analytic proofs of these phenomena and show that most experimental data agree with theoretical results within one standard deviation. This work opens avenues for future study on the dynamics of coherence in PT P T - and APT APT -symmetric systems.
Analysis of fundamentally open systems which exhibit both spatial reflection (parity) and time-reversal symmetry, called PT-symmetric [1] systems, has played an important role in understanding the dynamics of a broad class of non-Hermitian systems. Such systems support distinct regimes of stability and instability respectively, and the transition between these plays an important role in the system dynamics. We investigate a variety of non-Hermitian systems which exhibit a PT-symmetry breaking transition in both classical and quantum contexts using an array of theoretical and numerical approaches which are directly amenable to physical experiments. Organizationally, we divide these studies into those done on classical and quantum systems. Specifically for classical systems we analyze several interesting phenomena in the context of optical waveguide arrays. These provide an important testing ground for much of the discrete, PT-symmetric theory. In our case, we analyze PT-symmetric extensions of several interesting lattice models. Firstly, we explore single gain/loss pair, PT-symmetric extensions of the Su-Schreiffer-Heeger (SSH) model [2] and the Aubry-Andre-Harper (AAH) model [3,4]. In both cases, we find a veiled symmetry which is responsible for the PT-symmetry. Secondly we expand upon the Rudner-Levitov (RL) model [5,6], a non-Hermitian extension of the SSH model with multiple gain/loss pairs, and we explore the dependence of topological phenomena on changes in the initial state as well as their robustness in the presence of gain-induced nonlinearity. For quantum systems, we explore the rich PT-symmetric phase diagram resulting from time-periodic, Floquet PT-symmetry [7,8]. This is experimentally implementable in ultracold atomic systems [9], and features a reentrant PT-symmetric phase. Secondly, we examine quantum multi-photon statistics for a simple non-Hermitian model which is transformed and mapped to a system with unitary evolution via a unitary dilation, and is fully realizable on a small-scale quantum simulator [10].
Theoretical investigation of dynamics and concurrence of entangled PT and anti-PT symmetric polarized photons
Non-Hermitian systems with parity-time [Formula: see text] symmetry and anti-parity-time [Formula: see text] symmetry have exceptional points (EPs) resulting from eigenvector co-coalescence with exceptional properties. In the quantum and classical domains, higher-order EPs for [Formula: see text] symmetry and [Formula: see text]-symmetry systems have been proposed and realized. Both two-qubits [Formula: see text]-[Formula: see text] and [Formula: see text]-[Formula: see text] symmetric systems have seen an increase in recent years, especially in the dynamics of quantum entanglement. However, to our knowledge, neither theoretical nor experimental investigations have been conducted for the dynamics of two-qubits entanglement in the [Formula: see text]-[Formula: see text] symmetric system. We investigate the [Formula: see text]-[Formula: see text] dynamics for the first time. Moreover, we examine the impact of different initial Bell-state conditions on entanglement dynamics in [Formula: see text]-[Formula: see text], [Formula: see text]-[Formula: see text] and [Formula: see text]-[Formula: see text] symmetric systems. Additionally, we conduct a comparative study of entanglement dynamics in the [Formula: see text]-[Formula: see text] symmetrical system, [Formula: see text]-[Formula: see text] symmetrical system, and [Formula: see text]-[Formula: see text] symmetrical systems in order to learn more about non-Hermitian quantum systems and their environments. Entangled qubits evolve in a [Formula: see text]-[Formula: see text] symmetric unbroken regime, the entanglement oscillates with two different oscillation frequencies, and the entanglement is well preserved for a long period of time for the case when non-Hermitian parts of both qubits are taken quite away from the exceptional points.