Investigation of the Effect of Quantum Measurement on Parity-Time Symmetry

TL;DR

This paper explores how quantum measurement influences parity-time ($ ext{PT}$) symmetry in quantum systems, revealing that measurement frequency and strength can induce symmetry breaking, with implications for quantum control and understanding.

Contribution

It establishes the relationship between quantum measurement parameters and $ ext{PT}$-symmetry breaking, providing experimental insights using $^{40} ext{Ca}^+$ ions.

Findings

High measurement frequencies can break $ ext{PT}$ symmetry.

Strong measurement strength can induce symmetry breaking even at lower frequencies.

The work enhances understanding of measurement-induced symmetry effects in quantum systems.

Abstract

Symmetry, including the parity-time ($\mathcal{PT}$)-symmetry, is a striking topic, widely discussed and employed in many fields. It is well-known that quantum measurement can destroy or disturb quantum systems. However, can and how does quantum measurement destroy the symmetry of the measured system? To answer the pertinent question, we establish the correlation between the quantum measurement and Floquet $\mathcal{PT}$-symmetry and investigate for the first time how the measurement frequency and measurement strength affect the $\mathcal{PT}$-symmetry of the measured system using the $^{40}\mathrm{Ca}^{+}$ ion. It is already shown that the measurement at high frequencies would break the $\mathcal{PT}$ symmetry. Notably, even for an inadequately fast measurement frequency, if the measurement strength is sufficiently strong, the $\mathcal{PT}$ symmetry breaking can occur. The current work can enhance our knowledge of quantum measurement and symmetry and may inspire further research on the effect of quantum measurement on symmetry.