Degeneracy beyond the parity-symmetry protection in one-dimensional spinless models: The parity-violating Kerr parametric oscillator

TL;DR

This paper explores degeneracy phenomena in one-dimensional spinless models, specifically in Kerr parametric oscillators, highlighting how antiunitary symmetries can induce doubly-degenerate levels even without parity symmetry.

Contribution

It demonstrates that Kerr parametric oscillators can exhibit degeneracy due to antiunitary symmetries, extending understanding beyond traditional parity-symmetry protection.

Findings

Kerr parametric oscillators can have doubly-degenerate levels despite broken parity symmetry.

Spectral features suggest additional symmetries in the system.

Potential applications in protected qubits in superconducting circuits.

Abstract

One-dimensional quantum systems that undergo spontaneous symmetry-breaking, having a symmetric (non-degenerate) and a broken-symmetry (doubly-degenerate) phase, have been intensely studied in different branches of physics. In most cases, the spontaneously-broken symmetry is parity. However, it is possible to obtain similar phases in systems without parity symmetry, through an antiunitary symmetry that implies a two-fold symmetry either on momentum or coordinate in the system's classical limit. To illustrate this phenomenon, we use a Kerr parametric oscillator (KPO) with one- and two-photon drives that, despite the breaking of parity symmetry, may have doubly-degenerate levels. Different realizations of squeezed KPOs convey a great deal of attention, as effective Hamiltonians for driven superconducting circuits and the occurrence of degeneracy in such systems could be of practical interest in their application to obtain protected qubits in parity-breaking setups. In addition to this, the reported spectral features strongly indicate the existence of additional symmetries in the system.