Pairwise exponential level kissing in the Kerr-cat eigenspectrum: part 2/2*

Schrödinger cat states, superpositions of coherent states in an oscillator, can be stabilized by a driven effective Hamiltonian thanks to the interplay between Kerr nonlinearity and single-mode squeezing. The pair of resulting degenerate Kerr-cat states form a qubit whose coherence along one Bloch sphere axis increases exponentially with the average photon number, while decreasing only linearly along the other axes. The qubit protection arises from the progressive pairwise kissing of consecutive levels as the average photon number is increased--a quantum manifestation of robust period doubling in this system. We experimentally observe the pairwise kissing via spectroscopy, and the associated increase in the period-doubled coherent state lifetime, which reaches 1 ms, a factor of 480 improvement over the bare lifetime of the constituent SNAIL-transmon circuit. In the second part of this two-part presentation, we discuss the spectroscopy and the lifetime scaling for the coherent states and their superpositions in our system.