Schrödinger cats and steady states in subharmonic generation with Kerr nonlinearities

Abstract

We discuss general properties of the equilibrium state of parametric down-conversion in superconducting quantum circuits with detunings and Kerr anharmonicities, in the strongly nonlinear regime. By comparing moments of the steady state and those of a Schrödinger cat, we show that true Schrödinger cats cannot survive in the steady state if there is any single-photon loss. A delta-function 'cat-like' steady-state distribution can be formed, but this only exists in the limit of an extremely large nonlinearity. The steady state is a mixed state, which is more complex than a mixture or linear combination of delta-functions, and whose purity is reduced by driving. We expect this general behaviour to occur in other driven, dissipative quantum subharmonic non-equilibrium open systems.

arXiv comment10 pages, 4 figures

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• Fast generation of Cat states in Kerr nonlinear resonators via optimal adiabatic control
• The coherent Ising machine with quantum feedback: the total and conditional master equation methods
• Initial states and apodisation for quantum field simulations in phase-space
• Phase-space simulations of feedback coherent Ising machines
• Symmetric quantum states: a review of recent progress
• Proposal of ensemble qubits with two-atom decay
• On the early-time behavior of quantum subharmonic generation
• Beating the 3 dB Limit for Intracavity Squeezing and Its Application to Nondemolition Qubit Readout