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Register a new userHidden PT Symmetry and quantization of coupled-oscillators model of QASER
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Using Maxwell-Bloch equations it has been shown how the superradiance can lead to amplification and gain at a frequency much larger than the pumping frequency. This remarkable effect has been examined in terms of a simpler model involving two coupled oscillators with one of them paramet- rically driven. We show that this coupled oscillator model has a hidden parity-time (PT) symmetry for QASER, we thus bring PT symmetry to the realm of parametrically coupled resonators. More- over, we find that the QASER gain arises from the broken PT symmetry phase. We then quantize the simplified version of the QASER using quantum Langevin equations. The quantum description enables us to understand how the system starts from quantum fluctuations.
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We discuss how introducing an equilibrium frame, in which a given Hamiltonian has balanced loss and gain terms, can reveal PT symmetry hidden in non-Hermitian Hamiltonians of dissipative systems. Passive PT-symmetric Hamiltonians, in which only loss is present and gain is absent, can also display exceptional points, just like PT-symmetric systems, and therefore are extensively investigated. We demonstrate that non-Hermitian Hamiltonians, which can be divided into a PT-symmetric term and a term commuting with the Hamiltonian, possess hidden PT symmetries. These symmetries become apparent in the equilibrium frame. We also show that the number of eigenstates having the same value in an exceptional point is usually smaller in the initial frame than in the equilibrium frame. This property is associated with the second part of the Hamiltonian.
We study the effects of the position of the passive and active cavities on the spontaneous parity-time (PT) symmetry breaking behavior in non-Hermitian coupled cavities array model. We analyze and discuss the energy eigenvalue spectrums and PT symmetry in the topologically trivial and nontrivial regimes under three different cases in detail, i.e., the passive and active cavities are located at, respectively, the two end positions, the second and penultimate positions, and each position in coupled cavities array. The odevity of the number of cavities is further considered to check the effects of the non-Hermitian terms applied on the PT symmetric and asymmetric systems. We find that the position of the passive and active cavities has remarkable impacts on the spontaneous PT symmetry breaking behavior, and in each case the system exhibits distinguishable and novel spontaneous PT symmetry breaking characteristic, respectively. The effects of the non-Hermitian terms on the $mathcal{PT}$ symmetric and asymmetric systems due to the odevity are comparatively different in the first case while qualitatively same in the second case.
The symmetry operators generating the hidden $mathbb{Z}_2$ symmetry of the asymmetric quantum Rabi model (AQRM) at bias $epsilon in frac{1}{2}mathbb{Z}$ have recently been constructed by V. V. Mangazeev et al. [J. Phys. A: Math. Theor. 54 12LT01 (2021)]. We start with this result to determine symmetry operators for the $N$-qubit generalisation of the AQRM, also known as the biased Dicke model, at special biases. We also prove for general $N$ that the symmetry operators, which commute with the Hamiltonian of the biased Dicke model, generate a $mathbb{Z}_2$ symmetry.
In this paper, we derive the symmetry operators ($J$s) in the asymmetric two-photon quantum Rabi models in terms of Bogoliubov operator approaches. $ J^2$ can be expressed as a polynomial in terms of the Hamiltonian, which uncovers the $mathbb{Z}_{2}$ nature of the hidden symmetry in this two-photon model rigorously. The previous symmetry operators in the asymmetric one-photon quantum Rabi models are reproduced readily in terms of Bogoliubov operator approaches, and the obtained operators are expressed much more concisely. It is found that the polynomial degree of $J^2$ in the two-photon model is twice of that in the one-photon model.
As the counterpart of PT symmetry, abundant phenomena and potential applications of anti-PT symmetry have been predicted or demonstrated theoretically. However, experimental realization of the coupling required in the anti-PT symmetry is difficult. Here, by coupling two YIG spheres to a microwave cavity, the large cavity dissipation rate makes the magnons coupled dissipatively with each other, thereby obeying a two-dimensional anti-PT Hamiltonian. In terms of the magnon-readout method, a new method adopted here, we demonstrate the validity of our method in constructing an anti-PT system and present the counterintuitive level attraction process. Our work provides a new platform to explore the anti-PT symmetry properties and paves the way to study multi-magnoncavity-polariton systems.
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