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State-dependent photon blockade via quantum-reservoir engineering

An arbitrary initial state of an optical or microwave field in a lossy driven nonlinear cavity can be changed, in the steady-state limit, into a partially incoherent superposition of only the vacuum and the single-photon states. This effect is known as single-photon blockade, which is usually analyzed for a Kerr-type nonlinear cavity parametrically driven by a single-photon process assuming single-photon loss mechanisms. We study photon blockade engineering via a squeezed reservoir, i.e., a quantum reservoir, where only two-photon absorption is allowed. Namely, we analyze a lossy nonlinear cavity parametrically driven by a two-photon process and allowing two-photon loss mechanisms, as described by the master equation derived for a two-photon absorbing reservoir. The nonlinear cavity engineering can be realized by a linear cavity with a tunable two-level system via the Jaynes-Cummings interaction in the dispersive limit. We show that by tuning properly the frequencies of the driving field and the two-level system, the steady state of the cavity field can be the single-photon Fock state or a partially incoherent superposition of several Fock states with photon numbers, e.g., (0,2), (1,3), (0,1,2), or (0,2,4). We observe that an arbitrary initial coherent or incoherent superposition of Fock states with an even (odd) number of photons can be changed into a partially incoherent superposition of a few Fock states of the same photon-number parity. A general solution for an arbitrary initial state is a weighted mixture of the above two solutions with even and odd photon numbers, where the weights are given by the probabilities of measuring the even and odd numbers of photons of the initial cavity field, respectively. Thus, in contrast to the standard photon blockade, we prove that the steady state in the engineered photon blockade, can depend on its initial state.