Photon blockade, in analogy to Coulomb's or phonon blockades, is a phenomenon when a single photon in a nonlinear cavity blocks the transmission of a second photon. This effect can occur in Kerr-type systems driven by a laser due to strong nonlinear photon-photon interactions. We predict the occurrence of higher-order photon blockades where the transmission of more than two photons is effectively blocked by single- and two-photon states. This photon blockade can be achieved by tuning the frequency of the laser driving field to be equal to the sum of the Kerr nonlinearity and the cavity resonance frequency. We refer to this phenomenon as two-photon blockade or two-photon state truncation via nonlinear scissors, and can also be interpreted as photon-induced tunneling. We also show that, for a driving-field frequency fulfilling another resonance condition and for higher strengths of the driving field, even a three-photon blockade can occur but less clearly than in the case of single- and two-photon blockades. We demonstrate how various photon blockades can be identified by analyzing photon-number correlations, coherence and entropic properties, Wigner functions, and spectra of squeezing. We show that two- and three-photon blockades can, in principle, be observed in various cavity and circuit quantum electrodynamical systems for which the standard single-photon blockade was observed without the need of using higher-order driving interactions or Kerr media exhibiting higher-order nonlinear susceptibility.Comment: 11 pages, 11 figure

An arbitrary initial state of an optical or microwave field in a lossy driven nonlinear cavity can be changed 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 nonlinear 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). At the right (now fixed) frequencies, we observe that an arbitrary initial coherent or incoherent superposition of Fock states with an even (odd) number of photons is changed into a partially incoherent superposition of a few Fock states of the same photon-number parity. We find analytically approximate formulas for these two kinds of solutions for several differently-tuned systems. 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. This can be interpreted as two separate evolution-dissipation channels for even and odd-number states. Thus, in contrast to the standard predictions of photon blockade, we prove that the steady state of the cavity field, in the engineered photon blockade, can depend on its initial state. To make our results more explicit, we analyze photon blockades for some initial infinite-dimensional quantum and classical states via the Wigner and photon-number distributions.

Conventional Glauber coherent states (CS) can be defined in several equivalent ways, e.g., by displacing the vacuum or, explicitly, by their infinite Poissonian expansion in Fock states. It is well known that these definitions become inequivalent if applied to finite d-level systems (qudits). We present a comparative Wigner-function description of the qudit CS defined (i) by the action of the truncated displacement operator on the vacuum and (ii) by the Poissonian expansion in Fock states of the Glauber CS truncated at (d − 1)-photon Fock state. These states can be generated from a classical light by its optical truncation using nonlinear and linear quantum scissors devices, respectively. We show a surprising effect that a macroscopically distinguishable superposition of two qudit CS (according to both definitions) can be generated with high fidelity by displacing the vacuum in the qudit Hilbert space. If the qudit dimension d is even (odd) then the superposition state contains Fock states with only odd (even) photon numbers, which can be referred to as the odd (even) qudit CS or the female (male) Schrödinger cat state. This phenomenon can be interpreted as an interference of a single CS with its reflection from the highest-energy Fock state of the Hilbert space, as clearly seen via phase-space interference of the Wigner function. We also analyze nonclassical properties of the qudit CS including their photon-number statistics and nonclassical volume of the Wigner function, which is a quantitative parameter of nonclassicality (quantumness) of states. Finally, we study optical tomograms, which can be directly measured in the homodyne detection of the analyzed qudit cat states and enable the complete reconstructions of their Wigner functions.

No abstract

No abstract