Symmetries of the squeeze-driven Kerr oscillator

Abstract

We study the symmetries of the static effective Hamiltonian of a driven superconducting nonlinear oscillator, the so-called squeeze-driven Kerr Hamiltonian, and discover a remarkable quasi-spin symmetry $su(2)$ at integer values of the ratio $\eta =\Delta /K$ of the detuning parameter $\Delta$ to the Kerr coefficient $K$. We investigate the stability of this newly discovered symmetry to high-order perturbations arising from the static effective expansion of the driven Hamiltonian. Our finding may find applications in the generation and stabilization of states useful for quantum computing. Finally, we discuss other Hamiltonians with similar properties and within reach of current technologies.

19 pages, 14 figures

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• Simulating Chemistry on Bosonic Quantum Devices
• Entangling Schrödinger's cat states by bridging discrete- and continuous-variable encoding
• A Roadmap for Simulating Chemical Dynamics on a Parametrically Driven Bosonic Quantum Device
• Fast elementary gates for universal quantum computation with Kerr parametric oscillator qubits
• Symmetries of Liouvillians of squeeze-driven parametric oscillators
• Impact of chaos on the excited-state quantum phase transition of the Kerr parametric oscillator
• Excited-state quantum phase transitions in constrained systems
• Phase transitions, symmetries, and tunneling in Kerr parametric oscillators
• Degeneracy beyond the parity-symmetry protection in one-dimensional spinless models: The parity-violating Kerr parametric oscillator
• Quantum signatures and semiclassical limitations in the transmission of Fock states