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OSA Quantum 2.0 Conference

Observing Non-Hermitian Evolution of a Single Dissipative Qubit Near an Exceptional Point

Maryam Abbasi, Weijian Chen, Kater W. Murch, Yogesh N. Joglekar

Published Jan 1, 2020• 0 citations
Publisher

Abstract

We explore features of a non-Hermitian quantum system in a dissipative superconducting circuit. Using the observed quantum evolution, we characterize static and dynamical features of the system’s exceptional point.
DOI
10.1364/quantum.2020.qw5b.4

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We study the dynamics of a driven non-Hermitian superconducting qubit which is perturbed by quantum jumps between energy levels, a purely quantum effect with no classical correspondence. The quantum jumps mix the qubit states leading to decoherence. We observe that this decoherence rate is enhanced near the exceptional point, owing to the cube-root topology of the non-Hermitian eigenenergies. Together with the effect of non-Hermitian gain or loss, quantum jumps can also lead to a breakdown of adiabatic evolution under the slow-driving limit. Our study shows the critical role of quantum jumps in generalizing the applications of classical non-Hermitian systems to open quantum systems for sensing and control.
Exceptional points in non-Hermitian quantum systems give rise to novel genuine quantum phenomena. Recent explorations of exceptional-point-induced quantum phase transitions have extended from discrete-variable to continuous-variable-encoded quantum systems. However, quantum phase transitions driven by Liouvillian exceptional points (LEPs) in continuous-variable platforms remain largely unexplored. Here, we construct and investigate a Liouvillian exceptional structure based on a driven-dissipative Kerr-cat qubit. Through numerical simulations, we reveal a quantum phase transition occurring at the LEP characterized by a sudden change in dynamical behavior from underdamped oscillations to overdamped relaxations as visualized via Wigner functions and Bloch sphere trajectories. Notably the negativity of the Wigner function serves as a direct signature of genuine quantum coherence unattainable in conventional single-qubit non-Hermitian systems. Furthermore, we introduce the phase difference between the off-diagonal elements of the Liouvillian eigenmatrices as a novel parameter to quantify the transition. Our results establish the Kerr-cat qubit as a novel continuous-variable setting for exploring dissipative quantum criticality and intrinsic non-Hermitian physics.
We propose a theoretical scheme to realize the controllable non-Hermitian qubit–qubit coupling by adding a high-loss resonator in a tunable coupling superconducting quantum circuit. By changing the effective qubit–qubit coupling, the phase and amplitude of resonator–qubit interaction, and the qubits’ quantum states, we can continually tune the energy level attraction, the position of EP (exceptional point), and the non-reciprocity in the non-Hermitian superconducting circuit. The EPs and non-reciprocity can affect the quantum states’ evolutions and exchange efficiencies for two qubits in the non-Hermitian superconducting circuit. The controllable non-Hermitian and non-reciprocal interactions between two qubits provide new insights and methods for exploring the unconventional quantum effects in superconducting quantum circuits.
Exceptional point (EP) is a spectral singularity in non-Hermitian systems. The passing over the EP leads to a phase transition, which endows the system with unconventional features that find a wide range of applications. However, the need of using the dissipation and amplification limits the possible applications of systems with the EP. In this work, we demonstrate an existence of signature of exceptional point phase transition in Hermitian systems that are free from dissipation and amplification. We consider a composite Hermitian system including both two coupled oscillators and their environment consisting only of several tens of degrees of freedom. We show that the dynamics of such a Hermitian system demonstrate a transition, which occurs at the coupling strength between oscillators corresponding to the EP in the non-Hermitian system. This transition manifests itself even in the non-Markovian regime of the system dynamics in which collapses and revivals of the energy occur. Thus, we demonstrate that the phase transition occurring at the passing over the EP in the non-Hermitian system manifests itself in the Hermitian system at all time. We discuss the experimental scheme to observe the signature of EP phase transition in the non-Markovian regime.