Related papers: Symmetries of Liouvillians of squeeze-driven parametric oscillators

Symmetries of Liouvillians of squeeze-driven parametric oscillators

URL: http://arxiv.org/abs/2409.10744v1
Date: Mon, 16 Sep 2024 21:22:07 GMT
Title: Symmetries of Liouvillians of squeeze-driven parametric oscillators
Authors: Francesco Iachello, Colin V. Coane, Jayameenakshi Venkatraman,
Abstract summary: We find a remarkable quasi-spin symmetry $su(2)$ at integer values of the ratio $eta =omega /K$ of the detuning parameter $omega$ to the Kerr coefficient $K$. Our findings may have applications in the generation and stabilization of states of interest in quantum computing.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: We study the symmetries of the Liouville superoperator of one dimensional parametric oscillators, especially the so-called squeeze-driven Kerr oscillator, and discover a remarkable quasi-spin symmetry $su(2)$ at integer values of the ratio $\eta =\omega /K$ of the detuning parameter $\omega$ to the Kerr coefficient $K$, which reflects the symmetry previously found for the Hamiltonian operator. We find that the Liouvillian of an $su(2)$ representation $\left\vert j,m_{j}\right\rangle$ has a characteristic double-ellipsoidal structure, and calculate the relaxation time $T_{X}$ for this structure. We then study the phase transitions of the Liouvillian which occur as a function of the parameters $\xi =\varepsilon _{2}/K$ and $\eta=\omega /K$. Finally, we study the temperature dependence of the spectrum of eigenvalues of the Liouvillian. Our findings may have applications in the generation and stabilization of states of interest in quantum computing.

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