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arXiv:1007.0384 · Physical Review A

Photon correlations in a two-site nonlinear cavity system under coherent drive and dissipation

Sara Ferretti, Lucio Claudio Andreani, Hakan E. Türeci, Dario Gerace

Published Jul 30, 2010• 91 citations
arXivHTMLPDF

Abstract

We calculate the normalized second-order correlation function for a system of two tunnel-coupled photonic resonators, each one exhibiting a single-photon nonlinearity of the Kerr type. We employ a full quantum formulation: The master equation for the model, which takes into account both a coherent continuous drive and radiative as well as nonradiative dissipation channels, is solved analytically in steady state through a perturbative approach, and the results are compared to exact numerical simulations. The degree of second-order coherence displays values between $0$ and $1$, and divides the diagram identified by the two energy scales of the system---the tunneling and the nonlinear Kerr interaction---into two distinct regions separated by a crossover. When the tunneling term dominates over the nonlinear one, the system state is delocalized over both cavities, and the emitted light is coherent. In the opposite limit, photon blockade sets in, and the system shows an insulatorlike state with photons locked on each cavity, identified by antibunching of emitted light.

DOI
10.1103/physreva.82.013841

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We calculate the normalized second-order correlation function for a system of two tunnel-coupled photonic resonators, each one exhibiting a single-photon nonlinearity of the Kerr type. We employ a full quantum formulation: The master equation for the model, which takes into account both a coherent continuous drive and radiative as well as nonradiative dissipation channels, is solved analytically in steady state through a perturbative approach, and the results are compared to exact numerical simulations. The degree of second-order coherence displays values between 000 and 111, and divides the diagram identified by the two energy scales of the system---the tunneling and the nonlinear Kerr interaction---into two distinct regions separated by a crossover. When the tunneling term dominates over the nonlinear one, the system state is delocalized over both cavities, and the emitted light is coherent. In the opposite limit, photon blockade sets in, and the system shows an insulatorlike state with photons locked on each cavity, identified by antibunching of emitted light.
This study systematically investigates unconventional photon blockade in two coupled Kerr nonlinear cavities at resonance. By solving the master equation in the steady-state limit and calculating the equal-time second-order correlation function, the photon antibunching effect within the nonlinear regime is revealed. Through analytical derivations, four sets of optimal antibunching conditions are obtained and validated through numerical simulations, unveiling new characteristics of photon blockade. Furthermore, the influence of system parameters on photon blockade is discussed, providing valuable theoretical support for optimizing the design and implementation of single-photon sources.
We investigate spin squeezing, quantum entanglement, and second-order coherence in two coupled, driven, dissipative, nonlinear cavities. We compare these quantum statistical properties for the cavities coupled with either single- or two-photon exchange. Solving the quantum optical master equation of the system numerically in the steady state, we calculate the zero-time delay second-order correlation function for the coherent, genuine two-mode entanglement parameters, an optimal spin squeezing inequality associated with particle entanglement, concurrence, quantum entropy, and logarithmic negativity. We identify regimes of distinct quantum statistical character depending on the relative strength of photon exchange and nonlinearity. Moreover, we examine the effects of weak and strong drives on these quantum statistical regimes.
By solving the master equation in the steady-state limit and calculating the zero-delay-time second-order correlation function, a strong photon antibunching is found in two coupled cavities with weak nonlinearity χ(2). An optimal antibunching condition is derived that is complementary to the result in a recent publication [Phys. Rev. A89, 031803(R) (2014)]. Numerical simulations confirm the optimal condition. These results are extended from the case with a single drive to the case with two drives. We find that the parameter added to the system due to the second drive can lift the restriction on the detuning for the antibunching to occur. This may open a new door towards the application of the antibunching into single photon sources.
This work investigates photon blockade control in a hybrid quantum system containing a Kerr-nonlinear cavity coupled to an optical parametric amplifier (OPA). The dynamics are governed by a master equation derived from an effective Hamiltonian that includes cavity decay. To obtain analytical solutions, the system's quantum state is expanded in the Fock basis up to the two-photon level. Solving the steady-state Schrodinger equation yields probability amplitudes and the analytical conditions for optimal photon blockade. Results confirm that photon blockade is achievable with suitable parameters. Excellent agreement is found between the analytical solutions and numerical simulations for the steady-state, equal-time second-order correlation function, validating both the analytical method and the blockade effect. Numerically, the average intracavity photon number increases significantly under resonance, providing a theoretical pathway for enhancing single-photon source brightness. Furthermore, the driving phase is shown to regulate the optimal blockade region: it shifts the parabolic region within the two-dimensional parameter space of driving strength and OPA nonlinearity and can even reverse its opening direction. The influence of Kerr nonlinearity is also examined. Photon blockade remains robust across a wide range of Kerr strengths. Physical analysis attributes the effect to destructive quantum interference between two distinct excitation pathways that suppress two-photon states. While Kerr nonlinearity shifts the system's energy levels, it does not disrupt this interference mechanism, explaining the effect's stability over a broad parameter range.
The photon blockade is a key quantum-nonlinear effect in which the admission of a second photon to a resonator is inhibited, enabling on-demand single-photon emission. Its practical use is limited by the weak intrinsic nonlinearity of most optical platforms. We address this limitation in a coupled-cavity architecture by engineering two-photon dissipation as a control resource rather than a detrimental loss. Within a quantum-master-equation framework, we model single-photon loss, engineered two-photon decay, and pure dephasing, and analyze their joint impact on the steady-state statistics of the driven cavities. We track the zero-delay correlation, photon populations, and detuning/drive dependences under distinct driving schemes (both cavities driven vs. single-cavity drive with. The results show that adding two-photon dissipation (i) suppresses multiphoton occupation and strengthens antibunching, (ii) broadens the operating window in detuning and drive amplitude, and (iii) improves robustness against moderate dephasing and device imperfections. A mechanism analysis attributes these gains to interference between coherent second-order processes and dissipative selection that stabilizes the odd-photon manifold. The study yields design guidelines for realizing stable, cavity-based single-photon sources using dissipation engineering.
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.