Symmetries of Liouvillians of squeeze-driven parametric oscillators

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 $|j,m_j⟩$ 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 $\xi ={\epsilon }_2/K$ 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.

37 pages, 24 figures, published in J. Phys. A: Math. Theor; v2 minor updates, improved convergence in squeezed QHO numerics

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Cited by in corpus (3)

• Excited-state quantum phase transitions in constrained systems
• Transient dynamics of the quantum Stuart-Landau oscillator
• Degeneracy beyond the parity-symmetry protection in one-dimensional spinless models: The parity-violating Kerr parametric oscillator