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By embedding a $cal PT$-symmetric (pseudo-Hermitian) system into a large Hermitian one, we disclose the relations between $cal{PT}$-symmetric Hamiltonians and weak measurement theory. We show that the amplification effect in weak measurement on a conventional quantum system can be used to effectively simulate a local broken $cal PT$-symmetric Hamiltonian system, with the pre-selected state in the $cal PT$-symmetric Hamiltonian system and its post-selected state resident in the dilated Hamiltonian system.
We theoretically study the dynamics of typical optomechanical systems, consisting of a passive optical mode and an active mechanical mode, in the $mathcal{PT}$- and broken-$mathcal{PT}$-symmetric regimes. By fully analytical treatments for the dynami
In the last few years, the great utility of PT-symmetric systems in sensing small perturbations has been recognized. Here, we propose an alternate method relevant to dissipative systems, especially those coupled to the vacuum of the electromagnetic f
In this paper, we consider a typical continuous two dimensional $cal PT$-symmetric Hamiltonian and propose two different approaches to quantitatively show the difference between the $eta$-inner products. Despite the continuity of Hamiltonian, the $et
We introduce the notion of a ${cal PT}$-symmetric dimer with a $chi^{(2)}$ nonlinearity. Similarly to the Kerr case, we argue that such a nonlinearity should be accessible in a pair of optical waveguides with quadratic nonlinearity and gain and loss,
The dilation method is an important and useful way in experimentally simulating non-Hermitian, especially $cal PT$-symmetric systems. However, the time dependent dilation problem cannot be explicitly solved in general. In this paper, we consider a sp