Emergent PT symmetry in a double-quantum-dot circuit QED setup

Abstract

Open classical and quantum systems with effective parity-time (PT) symmetry, over the past five years, have shown tremendous promise for advances in lasers, sensing, and nonreciprocal devices. And yet, how such effective PT-symmetric non-Hermitian models emerge out of Hermitian quantum mechanics is not well understood. Here, starting from a fully Hermitian microscopic Hamiltonian description, we show that a non-Hermitian Hamiltonian emerges naturally in a double-quantum-dot (DQD) circuit-QED setup, which can be controllably tuned to the PT-symmetric point. This effective Hamiltonian governs the dynamics of two coupled circuit-QED cavities with a voltage-biased DQD in one of them. Our analysis also reveals the effect of quantum fluctuations on the PT-symmetric system. The PT transition is, then, observed both in the dynamics of cavity observables as well as via an input-output experiment. As a simple application of the PT transition in this setup, we show that loss-induced enhancement of amplification and lasing can be observed in the coupled cavities. By comparing our results with two conventional local Lindblad equations, we demonstrate the utility and limitations of the latter. Our results pave the way for an on-chip realization of a potentially scalable non-Hermitian system with a gain medium in the quantum regime, as well as its potential applications for quantum technology.

Non-Hermitian physics and master equations

“…However, implementing such a system can raise some issues. On the one hand, a gain like the one previously considered is an approximation holding up to not too long times (to avoid insurgence of non-linearities) [19]. On the other hand it is nonsensical when working ab initio with nonlinear systems (such as a two-level atom).…”

“…This system can be implemented in a variety of ways [14], including coupled waveguides [15], microcavities [31] and in double-quantum-dot circuit QED setups [19]. As for the general case of N modes, from Eq.…”

High-order exceptional point in a nanofiber cavity quantum electrodynamics system

“…These points are known as exceptional points (EPs). Owing to the EPs open pathways for new functionalities and performance, so far, various physical systems have been studied the concepts of EPs both theoretically and experimentally, including cavity magnonics systems [22][23][24][25][26][27], cavity optomechanical systems [28][29][30][31], non-Hermitian optical gyroscopes [32], two-level quantum dots (QDs) cavity QED systems [33][34][35] and directly or indirectly coupled microresonators [36][37][38].…”

Emergence of PT-symmetry breaking in open quantum systems

“…Therefore, it is still an unresolved question how to formally define PT -symmetry for dissipative quantum systems [32] and if the breaking of this symmetry can exist at all at a microscopic level [31]. In several previous studies this question has been addressed by looking at coupled quantum oscillators [17,[28][29][30][31][34][35][36][37][38][39] or bosonic atoms [40] with gain and loss, or at equivalent coherent, but unstable systems [41]. In such settings, the symmetry-breaking effect can still be observed in the dynamics of the mean amplitudes, which simply reproduce the classical equations of motion, while quantum effects lead to increased fluctuations.…”