$\mathcal {PT}$-symmetric circuit-QED

TL;DR

This paper proposes a circuit-QED setup with coupled resonators and qubits to realize and study $ ext{PT}$-symmetry in quantum dynamics, enabling exploration of symmetry breaking and instabilities through transmission experiments.

Contribution

It introduces a novel circuit-QED architecture that enables the realization and investigation of $ ext{PT}$-symmetry and its breaking in a quantum system.

Findings

Realization of $ ext{PT}$-symmetry via external driving fields.

Observation of symmetry breaking and instabilities in the system.

Prediction of a non-number conserving dipole-dipole interaction.

Abstract

The Hermiticity axiom of quantum mechanics guarantees that the energy spectrum is real and the time evolution is unitary (probability-preserving). Nevertheless, non-Hermitian but $\mathcal{PT}$-symmetric Hamiltonians may also have real eigenvalues. Systems described by such effective $\mathcal {PT}$-symmetric Hamiltonians have been realized in experiments using coupled systems with balanced loss (dissipation) and gain (amplification), and their corresponding classical dynamics has been studied. A $\mathcal {PT}$-symmetric system emerging from a quantum dynamics is highly desirable, in order to understand what $\mathcal {PT}$-symmetry and the powerful mathematical and physical concepts around it will bring to the next generation of quantum technologies. Here, we address this need by proposing and studying a circuit-QED architecture that consists of two coupled resonators and two qubits (each coupled to one resonator). By means of external driving fields on the qubits, we are able to tune gain and losses in the resonators. Starting with the quantum dynamics of this system, we show the emergence of the $\mathcal {PT}$-symmetry via the selection of both driving amplitudes and frequencies. We engineer the system such that a non-number conserving dipole-dipole interaction emerges, introducing an instability at large coupling strengths. The $\mathcal {PT}$-symmetry and its breaking, as well as the predicted instability in this circuit-QED system can be observed in a transmission experiment.