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arXiv:2103.11496 · Physical Review A

Effective protection of quantum coherence by a non-Hermitian driving potential

Kai-Qian Huang, Wen-Lei Zhao, Zhi Li

Published Nov 8, 2021• 14 citations
arXivHTMLPDF

Abstract

We investigate the effects of non-Hermitian driving potential on quantum coherence in a bipartite system. The results show that the dynamical localization will revive after being destroyed by the Hermitian interaction, which provides evidence of the restoration of quantum coherence by a non-Hermitian driving potential. Besides, the entanglement between the two subsystems also decays with the boosting of non-Hermitian driving strength, which gives more evidence that non-Hermitian driving potential will protect quantum coherence. The physics behind this phenomenon is the domination of the quasieigenstate with maximum imaginary value of the quasieigenvalue over the dynamics of the non-Hermitian system. Our discovery establishes a restoration mechanism of quantum coherence in interacting and dissipative quantum systems which is highly expectable in updated experiments from many-body physics to quantum information.

DOI
10.1103/physreva.104.052405

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We investigate the effects of non-Hermitian driving potential on quantum coherence in a bipartite system. The results show that the dynamical localization will revive after being destroyed by the Hermitian interaction, which provides evidence of the restoration of quantum coherence by a non-Hermitian driving potential. Besides, the entanglement between the two subsystems also decays with the boosting of non-Hermitian driving strength, which gives more evidence that non-Hermitian driving potential will protect quantum coherence. The physics behind this phenomenon is the domination of the quasieigenstate with maximum imaginary value of the quasieigenvalue over the dynamics of the non-Hermitian system. Our discovery establishes a restoration mechanism of quantum coherence in interacting and dissipative quantum systems which is highly expectable in updated experiments from many-body physics to quantum information.
We study the effects of non-Hermiticity on quantum coherence via a noisy quantum kicked rotor (NQKR). The random noise comes from the fluctuations in kick amplitude at each time. The non-Hermitian driving indicates the imaginary kicking potential, representing the environment-induced atom gain and loss. In the absence of gain and loss, the random noise destroys quantum coherence manifesting dynamical localization, which leads to classical diffusion. Interestingly, in the presence of non-Hermitian kicking potential, the occurrence of dynamical localization is highly sensitive to the gain and loss, manifesting the restoration of quantum coherence. Using the inverse participation ratio arguments, we numerically obtain a phase diagram of the classical diffusion and dynamical localization on the parameter plane of noise amplitude and non-Hermitian driving strength. With the help of analysis on the corresponding quasieigenstates, we achieve insight into dynamical localization, and uncover that the origin of the localization is interference between multiple quasi-eigenstates of the quantum kicked rotor. We further propose an experimental scheme to realize the NQKR in a dissipative cold atomic gas, which paves the way for future experimental investigation of an NQKR and its anomalous non-Hermitian properties.
We have constructed a non-Hermitian two-level system (a PT -symmetric system) in dissipative environments, and investigated the quantum coherence in the non-Hermitian two-level system. Our results show that, quantum coherence can be created by PT -symmetric systems, even if the initial state of the twolevel system is incoherent state. Even though two-level system is interacted with dissipative environments, the quantum coherence exhibits a long-lived revival, and can be protected. We find that the two-level system can obtain more coherence with the coupling strength Ω increases. And we should point out that the PT -symmetric system can be regarded as a good candidate system for creation of the long-lived quantum coherence in dissipative environments.
Pure quantum states, as described in quantum mechanics textbooks, are ideal representations inevitably deteriorated in real systems by any dissipative connection to the environment. In this work we derive a unified theoretical frame to study the non-Hermitian dynamics of a driven-dissipative quantum system and validate it by comparison to experimental data of matter-wave diffraction. To highlight the role of dissipation, we perform the comparison in a near-resonant regime of light-matter interaction, where perturbative approaches fail. Here, we show that the developed formalism enables both exact simulations and an intuitive interpretation based on modal analysis. The theoretical analysis is based on the general master equation description of driven-dissipative systems, from which we derive an effective complex potential Veff(Ω,Δ)V_\mathrm{eff}(Ω,Δ)Veff​(Ω,Δ) that depends on control parameters such as the amplitude and detuning of the light matter interaction. Experimentally, we drive a 87^{87}87Rb BEC near resonance using periodic excited-state engineering, mapping the spatially modulated Veff[Ω,Δ(x)]V_{\rm eff}[Ω,Δ(x)]Veff​[Ω,Δ(x)] into momentum space for precise quantification. The experimental results agree with numerical simulations of the master equation and demonstrate the interplay between coherent drive and dissipation, with an exceptional signature: a reduced decay rate with increasing drive. Such dynamics is then interpreted by a modal analysis of the non-Hermitian Hamiltonian Heff=p2/2m+VeffH_\mathrm{eff}=p^2/2m+V_\mathrm{eff}Heff​=p2/2m+Veff​ which provide an intuitive and qualitative explanation for such driven-dissipative system.
Many-body localization at nonzero temperature is a quantum-phase transition that is of very fundamental interest to both many-body quantum physics and statistical mechanics. Non-Hermitian systems possess rich and unique phenomena that never are found in their Hermitian counterparts, such as unidirectional invisibility and enhanced sensitivity. In the present study, we explore many-body localization in periodically driven non-Hermitian lattices. The lattices are one-dimensional, and the drive is designed in a piecewise two-step form that consists of a uniform coherent tunneling and incommensurate onsite gain and loss. We find that the system can be in localized, delocalized, or mixed phases depending on the driving frequency and the phase shift of the complex potential. Two critical driving frequencies are identified; one corresponds to the largest phase shift of the complex potential that keeps all the quasienergy spectra real and the eigenstates extended, and the other one is established by the vanishing of all real spectra. We also find that a very weak complex potential can lead the system to localization, when the driving frequency is lower than the critical frequency. We show that in the high-frequency limit, the critical phase shift that separates the two regions with respectively a real and complex spectrum tends to a constant, and the constant can be determined by an effective non-Hermitian Hamiltonian.
We investigate the quantum coherence and quantum entanglement dynamics of a classical driven single atom coupled to a single-mode cavity. It is shown that the transformation between the atomic coherence and the atom-field entanglement exists, and can be improved by adjusting the classical driving field. The joint evolution of two identical single-body systems is also studied. The results show the quantum coherence transfers among composite subsystems, and the coherence conservation of composite subsystems is obtained. Moreover, the classical driving field can be used to suppress the decay of the coherence and entanglement, owing to considering the leaky cavity. The non-Markovian dynamics of the system is also discussed finally.
We study the dynamics of bosonic atoms in a double well potential under the influence of dissipation. The main effect of dissipation is to destroy quantum coherence and to drive the system towards a unique steady state. We study how the atom-atom interaction affects the decoherence process. We use a systematic approach considering different atomic densities. We show that, for two atoms, the interaction already strongly suppresses decoherence: a phenomenon we refer to as "interaction impeded decoherence". For many atoms, thanks to the increased complexity of the system, the nature of the decoherence process is dramatically altered giving rise to an algebraic instead of exponential decay.