Non-Hermitian topology in a single driven-dissipative Kerr-Cat qubit

TL;DR

This paper explores non-Hermitian topological phenomena in a driven-dissipative Kerr-cat qubit, revealing exceptional points and topological properties unique to continuous-variable quantum systems, expanding the understanding of non-Hermitian physics.

Contribution

It demonstrates the emergence of third-order Liouvillian exceptional points in a Kerr-cat qubit, showing topological features analogous to Hamiltonian EP3s, a novel finding in continuous-variable quantum systems.

Findings

Discovery of bidirectional jumps in Kerr-cat qubits due to dissipation.

Identification of third-order Liouvillian exceptional points (LEP3s).

LEP3s exhibit topological properties similar to Hamiltonian EP3s.

Abstract

The intriguing physical phenomena associated with exceptional points have established non-Hermitian physics as a frontier of modern research. Recent investigations have extended non-Hermitian physics into the fully quantum domain. However, existing studies predominantly concentrate on discrete-variable quantum systems, while non-Hermitian quantum effects in continuous-variable encoded systems remain largely unexplored. In this work, we investigate the exceptional structure for a driven-dissipative Kerr-cat qubit, realized with a Kerr nonlinear resonator. We find that the dissipation leads to a bidirectional jump between the two basis states of the cat qubit, which is in distinct contrast with the unidirectional jump associated with normal two-level systems. The competition between this jump and a single-photon drive gives arise to the emergence of third-order Liouvillian exceptional points (LEP3s), each corresponds to a crossing point of two lines of LEP2s. We further show that the LEP3 can exhibit the topological character of the Hamiltonian EP3s, which cannot be realized with a single qubit. Our work opens the possibility of realizing non-Hermitian phenomena with continuous-variable quantum systems.