A mixed Ising-Heisenberg spin system consisting of triangular XXZ-Heisenberg spin clusters assembled into a chain by alternating with Ising spins interacting to all three spins in the triangle is considered. The exact solution of the model is given in terms of the generalized decoration-iteration map and within the transfer-matrix technique. Exact expressions for thermodynamic functions are derived. Ground state phase diagrams, thermodynamic and magnetic properties of the system are examined.

It has been a longstanding goal in quantum optics to realize controllable sources generating joint multiphoton states, particularly, photon triplet with arbitrary spectral characteristics. We demonstrate that such sources can be realized via cascaded parametric down-conversion (PDC) in superlattice structures of nonlinear and linear segments. We consider scheme that involves two parametric processes: ω0 → ω1 + ω2, ω2 → ω1 + ω1 under pulsed pump and investigate spontaneous creation of photon triplet as well as generation of high-intensity mode in intracavity three-photon splitting. We show preparation of Greenberger-Horne-Zeilinger polarization entangled states in cascaded type-II and type-I PDC in framework of consideration dual-grid structure that involves two periodically-poled crystals. We demonstrate the method of compensation of the dispersive effects in non-linear segments by appropriately chosen linear dispersive segments of superlattice for preparation heralded joint states of two polarized photons. In the case of intracavity three-photon splitting, we concentrate on investigation of photon-number distributions, third-order photon-number correlation function as well as the Wigner functions. These quantities are observed both for short interaction time intervals and in over transient regime, when dissipative effects are essential.

We describe the process of parametric amplification in a directional coupler of quadratically nonlinear and lossy waveguides, which belong to a class of optical systems with spatial parity-time (PT) symmetry in the linear regime. We identify a distinct spectral parity-time anti-symmetry associated with optical parametric interactions, and show that pump-controlled symmetry breaking can facilitate spectrally selective mode amplification in analogy with PT lasers. We also establish a connection between breaking of spectral and spatial mode symmetries, revealing the potential to implement unconventional regimes of spatial light switching through ultrafast control of PT breaking by pump pulses.PACS numbers: 42.25. Bs, 42.82.Et, 42.65.Yj, 11.30.Er Light propagation in waveguiding structures with spatially distributed sections of loss and gain can be analogous to quantum wavepacket dynamics governed by a parity-time (PT) symmetric Hamiltonian [1]. Below a certain gain/loss level, such systems support PTsymmetric optical modes, which then exhibit the same average loss or gain [2,3]. However when gain or loss is increased, the PT-symmetry of modes breaks, and a mode with the strongest gain (or smallest loss) dominates, as demonstrated experimentally [1,4]. The phase transition associated with such PT-symmetry breaking opens new possibilities for light manipulation, such as PT-symmetric lasers [5,6]. Such lasers can achieve single-mode operation, where small difference in medium gain leads to a dramatic difference in mode amplification below and above the PT breaking threshold.Parametric amplifiers are commonly used as an integral part of optical setups enabling flexible wavelength conversion and tunable signal gain, extending the range of lasers where gain media are limited to particular wavelengths. Wave amplification is efficiently realized in the regime of difference-frequency generation in media with quadratic optical nonlinearity [7]. Importantly, the amplification rate is determined by the pump, enabling ultrafast all-optical tunability. In this work, we reveal the potential of PT-symmetric systems for optical parametric amplification, and identify a new regime of spectral PT anti-symmetry in such devices. Such devices can, on one hand, realize ultrafast spatial signal switching through pump-controlled breaking of PT symmetry, and on the other hand enable spectrally-selective mode amplification in analogy with PT lasers.We consider a directional coupler composed of two waveguides in quadratically nonlinear medium, where modes exhibit different loss in each waveguide. It can be realized experimentally based on LiNbO 3 couplers where parametric gain was demonstrated [8], as well as other platforms with χ (2) nonlinearity. The loss can be introduced, for example, by depositing a thin layer of metal on top of th waveguide [1]. An illustration of such structure with loss in one waveguide is presented in Fig. 1. In the linear regime, at low light intensities, such coupler realizes PT-symmetric optical system [1]. How...

Abstract. We describe theoretically the process of spontaneous parametric downconversion in quadratic nonlinear waveguide arrays in the presence of linear loss. We derive a set of discrete Schrodinger-type equations for the biphoton wave function, and the wave function of one photon when the other photon in a pair is lost. We demonstrate effects arising from loss-affected interference between the generated photon pairs and show that nonlinear waveguide arrays can serve as a robust losstolerant integrated platform for the generation of entangled photon states with nonclassical spatial correlations.

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Integrated nonlinear waveguide structures enable generation of quantum entangled photons. We describe theoretically the effects of spatially inhomogeneous loss on the creation of photon pairs through spontaneous parametric down-conversion in quadratically nonlinear directional couplers, where photons experience effective parity-time (PT) symmetric potential due to the presence of optical loss in one of the waveguides. We show that for losses below the PT-breaking threshold, the quantum photon states can be flexibly tuned similarly to conservative couplers, whereas for stronger losses, the correlations between two waveguide modes are suppressed. We also formulate a quantum-classical correspondence with sum-frequency generation for fast evaluation of device performance. These results can be applied for the design of quantum plasmonic circuits.

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We describe the process of parametric amplification in a directional coupler of quadratically nonlinear and lossy waveguides, which belong to a class of optical systems with spatial parity-time (PT) symmetry in the linear regime. We identify a distinct spectral parity-time anti-symmetry associated with optical parametric interactions, and show that pump-controlled symmetry breaking can facilitate spectrally selective mode amplification in analogy with PT lasers. We also establish a connection between breaking of spectral and spatial mode symmetries, revealing the potential to implement unconventional regimes of spatial light switching through ultrafast control of PT breaking by pump pulses.PACS numbers: 42.25. Bs, 42.82.Et, 42.65.Yj, 11.30.Er Light propagation in waveguiding structures with spatially distributed sections of loss and gain can be analogous to quantum wavepacket dynamics governed by a parity-time (PT) symmetric Hamiltonian [1]. Below a certain gain/loss level, such systems support PTsymmetric optical modes, which then exhibit the same average loss or gain [2,3]. However when gain or loss is increased, the PT-symmetry of modes breaks, and a mode with the strongest gain (or smallest loss) dominates, as demonstrated experimentally [1,4]. The phase transition associated with such PT-symmetry breaking opens new possibilities for light manipulation, such as PT-symmetric lasers [5,6]. Such lasers can achieve single-mode operation, where small difference in medium gain leads to a dramatic difference in mode amplification below and above the PT breaking threshold.Parametric amplifiers are commonly used as an integral part of optical setups enabling flexible wavelength conversion and tunable signal gain, extending the range of lasers where gain media are limited to particular wavelengths. Wave amplification is efficiently realized in the regime of difference-frequency generation in media with quadratic optical nonlinearity [7]. Importantly, the amplification rate is determined by the pump, enabling ultrafast all-optical tunability. In this work, we reveal the potential of PT-symmetric systems for optical parametric amplification, and identify a new regime of spectral PT anti-symmetry in such devices. Such devices can, on one hand, realize ultrafast spatial signal switching through pump-controlled breaking of PT symmetry, and on the other hand enable spectrally-selective mode amplification in analogy with PT lasers.We consider a directional coupler composed of two waveguides in quadratically nonlinear medium, where modes exhibit different loss in each waveguide. It can be realized experimentally based on LiNbO 3 couplers where parametric gain was demonstrated [8], as well as other platforms with χ (2) nonlinearity. The loss can be introduced, for example, by depositing a thin layer of metal on top of th waveguide [1]. An illustration of such structure with loss in one waveguide is presented in Fig. 1. In the linear regime, at low light intensities, such coupler realizes PT-symmetric optical system [1]. How...