Chiral quantum heating and cooling with an optically controlled ion
Jintao Bu, Jian‐Qi Zhang, G.-Y. Ding, J. C. Li, Jiawei Zhang, Bin Wang, Wenqiang Ding, Wen-Fei Yuan, Liang Chen, Qi Zhong, Muhammed Ali Keçebaş, Şahin Kaya Özdemir, Fei Zhou, Hui Jing, Mang Feng
Quantum heat engines and refrigerators are open quantum systems, whose dynamics can be well understood using a non-Hermitian formalism. A prominent feature of non-Hermiticity is the existence of exceptional points (EPs), which has no counterpart in closed quantum systems. It has been shown in classical systems that dynamical encirclement in the vicinity of an EP, whether the loop includes the EP or not, could lead to chiral mode conversion. Here, we show that this is valid also for quantum systems when dynamical encircling is performed in the vicinity of their Liouvillian EPs (LEPs), which include the effects of quantum jumps and associated noise-an important quantum feature not present in previous works. We demonstrate, using a Paul-trapped ultracold ion, the first chiral quantum heating and refrigeration by dynamically encircling a closed loop in the vicinity of an LEP. We witness the cycling direction to be associated with the chirality and heat release (absorption) of the quantum heat engine (quantum refrigerator). Our experiments have revealed that not only the adiabaticity breakdown but also the Landau-Zener-Stückelberg process play an essential role during dynamic encircling, resulting in chiral thermodynamic cycles. Our observations contribute to further understanding of chiral and topological features in non-Hermitian systems and pave a way to exploring the relation between chirality and quantum thermodynamics.
Quantum heat engines and refrigerators are open quantum systems, whose dynamics can be well understood using a non-Hermitian formalism. A prominent feature of non-Hermiticity is the existence of exceptional points (EPs), which has no counterpart in closed quantum systems. It has been shown in classical systems that dynamical encirclement in the vicinity of an EP, whether the loop includes the EP or not, could lead to chiral mode conversion. Here, we show that this is valid also for quantum systems when dynamical encircling is performed in the vicinity of their Liouvillian EPs (LEPs), which include the effects of quantum jumps and associated noise-an important quantum feature not present in previous works. We demonstrate, using a Paul-trapped ultracold ion, the first chiral quantum heating and refrigeration by dynamically encircling a closed loop in the vicinity of an LEP. We witness the cycling direction to be associated with the chirality and heat release (absorption) of the quantum heat engine (quantum refrigerator). Our experiments have revealed that not only the adiabaticity breakdown but also the Landau-Zener-Stückelberg process play an essential role during dynamic encircling, resulting in chiral thermodynamic cycles. Our observations contribute to further understanding of chiral and topological features in non-Hermitian systems and pave a way to exploring the relation between chirality and quantum thermodynamics.
Abstract Exceptional points are the branch-point singularities of non-Hermitian Hamiltonians and have rich consequences in open-system dynamics. While the exceptional points and their critical phenomena are widely studied in the non-Hermitian settings without quantum jumps, they also emerge in open quantum systems depicted by the Lindblad master equations, wherein they are identified as the degeneracies in the Liouvillian eigenspectrum. These Liouvillian exceptional points often have distinct properties compared to their counterparts in non-Hermitian Hamiltonians, leading to fundamental modifications of the steady states or the steady-state-approaching dynamics. Since the Liouvillian exceptional points widely exist in quantum systems such as the atomic vapors, superconducting qubits, and ultracold ions and atoms, they have received increasing amount of attention of late. Here, we present a brief review on an important aspect of the dynamic consequence of Liouvillian exceptional points, namely the chiral state transfer induced by the parametric encircling the Liouvillian exceptional points. Our review focuses on the theoretical description and experimental observation of the phenomena in atomic systems that are experimentally accessible. We also discuss the ongoing effort to unveil the collective dynamic phenomena close to the Liouvillian exceptional points, as a consequence of the many-body effects therein. Formally, these phenomena are the quantum-many-body counterparts to those in classical open systems with nonlinearity, but hold intriguing new potentials for quantum applications.
Non-Hermitian systems have attracted much interest in recent decades, driven partly by the existence of exotic spectral singularities, known as exceptional points (EPs), where the dimensionality of the system evolution operator is reduced. Among various intriguing applications, the discovery of EPs has suggested the potential for implementing a symmetric mode switch, when encircling them in a system parameter space. However, subsequent theoretical and experimental works have revealed that dynamical encirclement of EPs invariably results in asymmetric mode conversion; namely, the mode switching depends only on the winding direction but not on the initial state. This chirality arises from the failure of adiabaticity due to the complex spectrum of non-Hermitian systems. Although the chirality revealed has undoubtedly made a significant impact in the field, a realization of the originally sought symmetric adiabatic passage in non-Hermitian systems with EPs has since been elusive. In this work, we bridge this gap and theoretically demonstrate that adiabaticity, and therefore a symmetric state transfer, is achievable when dynamically winding around an EP. This becomes feasible by specifically choosing a trajectory in the system parameter space along which the corresponding evolution operator attains a real spectrum. Our findings, thus, offer a promise for advancing various wave manipulation protocols in both quantum and classical domains.
The exceptional point has presented considerably interesting and counterintuitive phenomena associated with nonreciprocity, precision measurement, and topological dynamics. The Liouvillian exceptional point (LEP), involving the interplay of energy loss and decoherence inherently relevant to quantum jumps, has recently drawn much attention due to capability to fully capture quantum system dynamics and naturally facilitate non-Hermitian quantum investigations. It was also predicted that quantum jumps could give rise to third-order LEPs in two-level quantum systems for its high dimensional Liouvillian superoperator, which, however, has never been experimentally confirmed until now. Here we report the first observation of the third-order LEPs emerging from quantum jumps in an ultracold two-level trapped-ion system. Moreover, by combining decay with dephasing processes, we present the first experimental exploration of LEPs involving combinatorial effect of decay and dephasing. In particular, due to non-commutativity between the Lindblad superoperators governing LEPs for decay and dephasing, we witness the movement of LEPs driven by the competition between decay and dephasing occurring in an open quantum system. This unique feature of non-Hermitian quantum systems paves a new avenue for modifying nonreciprocity, enhancing precision measurement, and manipulating topological dynamics by tuning the LEPs.
As branch-point singularities of non-Hermitian matrices, the exceptional points (EPs) exhibit unique spectral topology and criticality, with intriguing dynamic consequences in non-Hermitian settings. In quantum open systems, EPs also emerge in the Liouvillian spectrum, but their dynamic impact often pertains to the transient dynamics and is challenging to demonstrate. Here, using the flexible control afforded by single-photon interferometry, we study the chiral state transfer when the Liouvillian EP is parametrically encircled. Reconstructing the density-matrix evolution by experimentally simulating the quantum Langevin equation, we show that the chirality of the dynamics is only present within an intermediate encircling timescale and dictated by the landscape of the Liouvillian spectrum near the EP. However, the chirality disappears at long times as the system always relaxes to the steady state. We then demonstrate the power-law decay of the chirality in regard to the encircling time with a parameter-dependent exponent. Our experiment confirms the transient nature of chiral state transfer near a Liouvillian EP in quantum open systems, while our scheme paves the way for simulating general open-system dynamics using single photons.
Exceptional points emerge in the complex eigenspectra of non-Hermitian systems, and give rise to rich critical behaviors. An outstanding example is the chiral state transfer, where states can swap under an adiabatic encircling around the exceptional point, but only along one direction. In dissipative quantum systems, such exceptional-point encirclings are often accompanied by decoherence, whose impact is beyond the description of non-Hermitian Hamiltonians. In this paper, we study in detail the effects of dephasing on the encircling dynamics, adopting the full Lindblad master equation. Introducing experimentally relevant quantum-jump processes that account for dephasing, we show that gaps emerge in the eigenspectra landscape of the corresponding Liouvillian superoperator. It follows that the chiral state transfer does not take place in the adiabatic limit, since the system always adiabatically follows the quasisteady state of the Liouvillian regardless of the encircling direction. Nevertheless, the chirality is restored at intermediate encircling times, where the dynamics is nonadiabatic in both encircling directions, distinct from the typical chiral state transfer in non-Hermitian systems. While our results are applicable to several recent experiments, we examine a recent cold-atom experiment in particular, and show that the observed long-time chirality is limited to the special encircling path therein. Our paper provides further insight into the chiral state transfer under experimental conditions, and is helpful for controlling open-system dynamics from the perspective of non-Hermitian physics.
One intriguing property of non-Hermitian systems is the breakdown of adiabatic theorem and chiral state conversion as the system dynamically encircles exceptional points. However, the subtle dependence of the chiral dynamics on the loop geometry, the starting point, the encircling speed and especially the noise has not been studied systematically. Here we propose a non-chirality degree χc to measure the chirality quantitatively and analyze it in dynamics without noise by exact solution and dynamics with noise by numerical integration. The exact dynamics starting from the broken phase show chirality oscillations, which are extremely sensitive to noise when the speed is small. The encircling speed and the noise strength are found to compete with each other in determining χc, resulting in two distinguished limits, namely the noisy limit and the clean limit. The critical boundary between the two limits satisfies a simple scaling law, which could be explained in terms of first-order perturbation theory and the condition number of the transfer matrix. Our findings reveal the essential role played by noise in non-Hermitian dynamics and are relevant for both theoretical and experimental investigations.