Mesoscopic electrons driven by quantum microwave states I: squeezed states

Motivated by recent experiments where superconducting microwave circuits have been coupled to electrons in semiconductor nanostructures [1-3], we consider theoretically the general problem of a mesoscopic conductor (such as a quantum point contact) driven by quantum states of a microwave field in a cavity. We show that even in the simplest case of a coherent state, there are significant corrections to the dc current over the completely classical treatment used in standard photon-assisted tunnelling theory. The case of a squeezed microwave field leads to even more striking deviations. Our calculations incorporate both the use of quantum-optics phase-space methods, and also a general Keldysh formalism that allows a more complete description. \\[4pt] [1] K. D. Petersson, L. W. McFaul, M. D. Schroer, M. Jung, J. M. Taylor, A. A. Houck, and J. R. Petta, Nature \textbf{490}, 380 (2012). \\[0pt] [2] T. Frey, P. Leek, M. Beck, A. Blais, T. Ihn, K. Ensslin, and A. Wallraff, Phys. Rev. Lett. \textbf{108}, (2012). \\[0pt] [3] M. Delbecq, V. Schmitt, F. Parmentier, N. Roch, J. Viennot, G. Feve, B. Huard, C. Mora, A. Cottet, and T. Kontos, Phys. Rev. Lett. \textbf{107}, 256804 (2011).