1. Symmetries of Liouvillians of squeeze-driven parametric oscillators
- Author
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Iachello, Francesco, Coane, Colin V., and Venkatraman, Jayameenakshi
- Subjects
Quantum Physics ,Mathematical Physics - 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., Comment: 36 pages, 23 figures, to appear in J. Phys. A: Math. Theor
- Published
- 2024