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arXiv:1212.4365 · Physical Review A

Two-photon and three-photon blockades in driven nonlinear systems

Adam Miranowicz, Małgorzata Paprzycka, Yu-xi Liu, J. Bajer, Franco Nori

Published Feb 8, 2013• 208 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.87.023809

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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.
We study the photon blockade effect in a coupled cavity system, which is formed by a linear cavity coupled to a Kerr-type nonlinear cavity via a photon-hopping interaction. We explain the physical phenomenon from the viewpoint of the conventional and unconventional photon blockade effects. The corresponding physical mechanisms of the two kinds of photon blockade effects are based on the anharmonicity in the eigenenergy spectrum and the destructive quantum interference between two different transition paths, respectively. In particular, we find that the photon blockade via destructive quantum interference also exists in the conventional photon blockade regime and that the unconventional photon blockade occurs in both the weak- and strong-Kerr nonlinearity cases. The photon blockade effect can be observed by calculating the second-order correlation function of the cavity field. This model is general and hence it can be implemented in various experimental setups such as coupled optical-cavity systems, coupled photon-magnon systems, and coupled superconducting-resonator systems. We present some discussions on the experimental feasibility.
We demonstrate multiphoton blockades (PB) in the pulsed regime by using a Kerr-nonlinear dissipative resonator driven by a sequence of Gaussian pulses. It is shown that the results obtained for single-photon, two-photon, and three-photon blockades in the pulsed excitation regime differ considerably from analogous results obtained for the case of continuous-wave (cw) driving. We strongly demonstrate that for the case of cw pumping of the Kerr-nonlinear resonator there are fundamental limits on populations of lower photonic number states (with n=0n=0n=0, 1, 2, 3). Thus, such detailed comparison demonstrates that PB due to excitation with a suitable photon pulses is realized beyond the fundamental limits established for cw excitations. We analyze photon-number effects and investigate the phase-space properties of PB on the base of photon number populations, the second-order correlation functions, and the Wigner functions in phase space. The generation of Fock states due to PB in the pulsed regime is analyzed in details.
Abstract Photon statistics in a weakly driven optomechanical cavity, with Kerr-type nonlinearity, are analyzed both analytically and numerically. The single-photon blockade effect is demonstrated via calculations of the zero-time-delay second-order correlation function g (2) (0). The analytical results obtained by solving the Schrödinger equation are in complete conformity with the results obtained through numerical solution of the quantum master equation. A systematic study on the parameter regime for observing photon blockade in the weak coupling regime is reported. The parameter regime where the photon blockade is not realizable due to the combined effect of nonlinearities owing to the optomechanical coupling and the Kerr-effect is demonstrated. The experimental feasibility with state-of-the-art device parameters is discussed and it is observed that photon blockade could be generated at the telecommunication wavelength. An elaborate analysis of the thermal effects on photon antibunching is presented. The system is found to be robust against pure dephasing-induced decoherences and thermal phonon number fluctuations.
Abstract The single‐ and two‐photon blockade effects in an optical cavity with a nonlinear Kerr medium, which is coupled with a three‐level atom, forming a Δ‐type transition configuration and closed‐loop coupling are investigated by introducing two driving fields in the atom‐cavity system. It is found that single‐ and two‐photon blockades can be remarkably enhanced by the Kerr nonlinearity, however, the parameter regimes governing two blockades are distinctly different. It is demonstrated that a large Kerr nonlinearity makes more contribution to the single‐photon blockade, as compared to the two‐photon blockade effect. Furthermore, by varying the atom‐cavity coupling strength, single‐ and two‐photon blockades can alternatingly occur. Additionally, the region where two‐photon blockade occurs is widened at the cost of increased Kerr nonlinearity and atom‐cavity coupling. This work provides an alternative way to manipulate the few‐photon states and has potential applications in generating single‐photon or two‐photon sources.
We study multiphoton blockade and photon-induced tunneling effects in the two-photon Jaynes-Cummings model, where a single-mode cavity field and a two-level atom are coupled via a two-photon interaction. We consider both the cavity-field-driving and the atom-driving cases and find that single-photon blockade and photon-induced tunneling effects can be observed when the cavity mode is driven, while the two-photon blockade effect appears when the atom is driven. For the atom-driving case (the two-photon transition process), we present a criterion of the correlation functions for the multiphoton blockade effect. Specifically, we show that quantum interference can enhance the photon blockade effect in the single-photon cavity-field-driving case. Our results are confirmed by analytically and numerically calculating the correlation function of the cavity-field mode. Our work has potential applications in quantum information processing and paves the way for the study of multiphoton quantum coherent devices.
Analogous to Coulomb blockade for electrons, photon blockade is a key quantum optical effect in which the presence of one photon prevents the transmission of subsequent ones through a nonlinear medium. Beyond its fundamental interest, photon and multi-photon blockade are actively studied as mechanisms for generating technologically-relevant quantum states of light. Although photon blockade typically requires achieving strong light-matter coupling, increasing the number of atoms fails to enhance antibunching. Here, we analyze the optical transmission properties of a quantum resonator that embeds a two-photon-coupled ensemble of emitters, combining an approximate analytical approach with full quantum numerical simulations. We show that when light and matter are coupled via a two-photon interaction, both single- and multi-photon blockade can benefit from a collective enhancement. We propose different driving schemes in which the second or third-order correlation functions are strongly suppressed with increasing atom number. Differently from established methods, this collective enhancement of non-classical properties occurs with unitary transmission and is ultimately constrained only by decoherence. This demonstrates that collective two-photon couplings are a powerful mechanism for realizing photon blockade even in platforms where individual strong coupling is not achievable.