Engineering Cooper pair bunching using an anharmonic environment

The electromagnetic environment of superconducting circuits provides exciting opportunities to engineer the tunneling of Cooper pairs. The simplest example is a dc biased Josephson junction in series with a microwave cavity. There has been extensive work showing that when the dc bias is chosen to be resonant with a well-defined cavity mode, the transport of Cooper pairs has the same statistics in the long time limit as that of the photon emission from the cavity mode [1].

In my poster, I extend this study to the case when the cavity mode is anharmonic. I investigate the case when the voltage bias is detuned from the transition between Fock states 0 and 1. Due to the anharmonicity however, this voltage can be resonant with half the transition between Fock states 0 and 2. Therefore, the process of coherent two-Cooper pair tunneling accompanied by two-photon creation is favored compared to single Cooper pair tunneling and single photon creation. This results in bunched Cooper pair tunneling, with Fano factor approaching 2 and in a squeezed cavity state. I also compare this effect to a similar and competing inelastic co-tunneling process arising from second-order rotating wave approximation.

[1] M. Hofheinz, et. al. Phys. Rev. Lett. 106, 217005 (2011).