Nonlinear response of a transmon using the Schwinger oscillator model of angular momentum

As an alternative to the Jaynes-Cummings model of a qubit, we consider the Schwinger oscillator model of angular momentum [1] to define the pseudo spin of a transmon. Specifically, we treat the transmon as a strong anharmonic oscillator capacitively coupled to a readout resonator, itself represented by a linear oscillator. We then calculate the nonlinear frequency response of the Schwinger pseudo spin in the presence of a driving sinusoidal voltage and surrounding heat bath. We discuss the coherence of the resulting nonlinear many-body state that underlies the pseudo spin, as it arises in the steady state, and consider its broader application to quantum computation. 1) J. Schwinger, On Angular Momentum, U. S. Atomic Energy Commission Report NYO-3071 (1952).