Symmetries of Liouvillians of squeeze-driven parametric oscillators
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| Format: | Preprint |
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2024
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| _version_ | 1866916544316964864 |
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| author | Iachello, Francesco Coane, Colin V. Venkatraman, Jayameenakshi |
| author_facet | Iachello, Francesco Coane, Colin V. Venkatraman, Jayameenakshi |
| contents | 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 $η=ω/K$ of the detuning parameter $ω$ 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 $ξ=\varepsilon _{2}/K$ and $η=ω/K$. 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_10744 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Symmetries of Liouvillians of squeeze-driven parametric oscillators Iachello, Francesco Coane, Colin V. Venkatraman, Jayameenakshi Quantum Physics Mathematical Physics 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 $η=ω/K$ of the detuning parameter $ω$ 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 $ξ=\varepsilon _{2}/K$ and $η=ω/K$. 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. |
| title | Symmetries of Liouvillians of squeeze-driven parametric oscillators |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2409.10744 |