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arXiv · 2409.10744

Symmetries of Liouvillians of squeeze-driven parametric oscillators

Francesco Iachello·Colin V. Coane·Jayameenakshi Venkatraman
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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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Francesco Iachello, Colin V. Coane, Jayameenakshi Venkatraman. 2024-09-16. Symmetries of Liouvillians of squeeze-driven parametric oscillators. https://doi.org/10.1088/1751-8121/ad7ae6

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