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Physical Review Research

Controlling transfer and chirality of topological quantum state through dissipation in quantum walk

Xing Tang, Tian Chen, Xiangdong Zhang

Published Feb 13, 2025• 4 citations
Publisher

Abstract

Dissipation always exists in real environments, and it can cause decoherence during transfer of quantum states. To avoid decoherence, dissipation is usually shielded. However, dissipation is difficult to avoid in real cases. Thus, how to achieve efficient quantum state transfer in dissipation environments, although it will receive great attention, remains a challenge. Here we demonstrate that dissipation can be utilized to realize robust control of quantum state transfer instead of being avoided. Our scheme is realized by constructing Liouvillian exceptional point (LEP). By tuning dissipation, the exchange of eigenvectors and nonadiabatic transition near the LEP can be modulated, thereby controlling transfer and chirality of topological quantum state. Furthermore, we have experimentally validated such a scheme on a quantum walk platform. Our work opens up a different avenue for quantum information process in real systems.

DOI
10.1103/physrevresearch.7.013159

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Dissipation always exists in real environments, and it can cause decoherence during transfer of quantum states. To avoid decoherence, dissipation is usually shielded. However, dissipation is difficult to avoid in real cases. Thus, how to achieve efficient quantum state transfer in dissipation environments, although it will receive great attention, remains a challenge. Here we demonstrate that dissipation can be utilized to realize robust control of quantum state transfer instead of being avoided. Our scheme is realized by constructing Liouvillian exceptional point (LEP). By tuning dissipation, the exchange of eigenvectors and nonadiabatic transition near the LEP can be modulated, thereby controlling transfer and chirality of topological quantum state. Furthermore, we have experimentally validated such a scheme on a quantum walk platform. Our work opens up a different avenue for quantum information process in real systems.
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 decoherence or purely due to decoherence. By dynamically tuning the Liouvillian superoperators in real time we observe a non-Hermiticity-induced chiral state transfer. Our study motivates a new look at open quantum system dynamics from the vantage of Liouvillian exceptional points, enabling applications of non-Hermitian dynamics in the understanding and control of open quantum systems.
. However, it has always been a great challenge to complete such a task because of decoherence and disorder. Here, we propose theoretically and demonstrate experimentally an effective scheme to realize robust operation of quantum entanglement states by designing quadruple degeneracy exceptional points. By encircling the exceptional points on two overlapping Riemann energy surfaces, we have realized a chiral switch for entangled states with high fidelity. Owing to the topological protection conferred by the Riemann surface structure, this switching of chirality exhibits strong robustness against perturbations in the encircling path. Furthermore, we have experimentally validated such a scheme on a quantum walk platform. Our work opens up a new way for the application of non-Hermitian physics in the field of quantum information.
We theoretically investigate the state evolution and decoherence of Bell states in a two-qubit system coupled to local bosonic thermal baths. By employing a hybrid Liouvillian formalism with a tuning parameter , we systematically explore the transition from purely non-Hermitian coherent evolution ( ) to complete Lindblad master equation dynamics ( ) in a bosonic environment. Our results demonstrate that at , dynamically encircling a second-order exceptional point (EP) enables a near-perfect chiral transfer between the Bell states and . This phenomenon is shown to be globally robust against variations in the bosonic thermal occupation numbers of the environment. However, the introduction of quantum jump processes ( ) significantly suppresses the directional selectivity, and the chirality completely disappears in the full Liouvillian limit ( ). Furthermore, we find that the dissipative protocol is unable to generate entanglement starting from a maximally mixed state, highlighting the role of initial state purity. This work elucidates the interplay between non-Hermitian topology and bosonic decoherence, providing insights for state evolution in realistic open quantum systems.
While spin-orbit coupling (SOC), an essential mechanism underlying quantum phenomena from the spin Hall effect to topological insulators, has been widely studied in well-isolated Hermitian systems, much less is known when the dissipation plays a major role in spin-orbit-coupled quantum systems. Here, we realize dissipative spin-orbit-coupled bands filled with ultracold fermions, and observe a parity-time (PT\mathcal{PT}PT) symmetry-breaking transition as a result of the competition between SOC and dissipation. Tunable dissipation, introduced by state-selective atom loss, enables the energy gap, opened by SOC, to be engineered and closed at the critical dissipation value, the so-called exceptional point (EP). The realized EP of the non-Hermitian band structure exhibits chiral response when the quantum state changes near the EP. This topological feature enables us to tune SOC and dissipation dynamically in the parameter space, and observe the state evolution is direction-dependent near the EP, revealing topologically robust spin transfer between different quantum states when the quantum state encircles the EP. This topological control of quantum states for non-Hermitian fermions provides new methods of quantum control, and also sets the stage for exploring non-Hermitian topological states with SOC.
We study the quantum evolution of a non-Hermitian qubit realized as a submanifold of a dissipative superconducting transmon circuit. Real-time tuning of the system parameters to encircle an exceptional point results in nonreciprocal quantum state transfer. We further observe chiral geometric phases accumulated under state transport, verifying the quantum coherent nature of the evolution in the complex energy landscape and distinguishing between coherent and incoherent effects associated with exceptional point encircling. Our work demonstrates an entirely new method for control over quantum state vectors, highlighting new facets of quantum bath engineering enabled through dynamical non-Hermitian control.
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.