Investigation of Effect of Quantum Measurement on Parity-Time Symmetry

The symmetry acts as a very important role in nature. For example, the parity-time ($\mathcal{PT}$)-symmetry is a striking topic and has been widely discussed and used in many fields. Quantum measurement has some mysterious features. It is well known that quantum measurement would destroy or disturbs quantum systems. Can and how does quantum measurement destroy the symmetry of the measured system? We establish the correlation between the quantum measurement and the Floquet $\mathcal{PT}$-symmetry, and probe for the first time how the measure frequency and measure strength affect the $\mathcal{PT}$-symmetry of the measured system using $^{40}\mathrm{Ca}^{+}$ ion. It is shown that the measurement at high frequencies would break the $\mathcal{PT}$-symmetry and lead to the quantum Zeno effect (QZE). On the other hand, even if the measurement frequency is not fast enough, as long as the measurement strength is strong enough, the $\mathcal{PT}$-symmetry breaking can also occur. These work enlarge our knowledge of quantum measurement and symmetry, and may inspire further research on the effect of quantum measurement on symmetry.