Hong-Ou-Mandel interference mediated by the magnetic plasmon waves in a three-dimensional optical metamaterial

Effects of nonlinearity and a new nonlinear resonance in two-path phonon transmittance in lattices with two-dimensional arrays of atomic defects

The paper is devoted to analytical and numerical studies of the effects of nonlinearity on the two-path phonon interference in the transmission through two-dimensional arrays of atomic defects embedded in a lattice. The emergence of transmission antiresonance (transmission node) in the two-path system is demonstrated for the few-particle nanostructures, which allow us to model both linear and nonlinear phonon transmission antiresonances. The universality of destructive-interference origin of transmission antiresonances of waves of different nature, such as phonons, photons, and electrons, in two-path nanostructures and metamaterials is emphasized. Generation of the higher harmonics as a result of the interaction of lattice waves with nonlinear two-path atomic defects is considered, and the full system of nonlinear algebraic equations is obtained to describe the transmission through nonlinear two-path atomic defects with an account for the generation of second and third harmonics. Expressions for the coefficients of lattice energy transmission through and reflection from the embedded nonlinear atomic systems are derived. It is shown that the quartic interatomic nonlinearity shifts the antiresonance frequency in the direction determined by the sign of the nonlinear coefficient and enhances in general the transmission of high-frequency phonons due to third harmonic generation and propagation. The effects of the quartic nonlinearity on phonon transmission are described for the two-path atomic defects with a different topology. Transmission through the nonlinear two-path atomic defects is also modeled with the simulation of the phonon wave packet, for which the proper amplitude normalization is proposed and implemented. It is shown that the cubic interatomic nonlinearity red shifts in general the antiresonance frequency for longitudinal phonons independently of the sign of the nonlinear coefficient, and the equilibrium interatomic distances (bond lengths) in the atomic defects are changed by the incident phonon due to cubic interatomic nonlinearity. For longitudinal phonons incident on a system with the cubic nonlinearity, the new narrow transmission resonance on the background of a broad antiresonance is predicted to emerge, which we relate to the opening of the additional transmission channel for the phonon second harmonic through the nonlinear defect atoms. Conditions of the existence of the new nonlinear transmission resonance are determined and demonstrated for different two-path nonlinear atomic defects. A two-dimensional array of embedded three-path defects with an additional weak transmission channel, in which a linear analog of the nonlinear narrow transmission resonance on the background of a broad antiresonance is realized, is proposed and modeled. The presented results provide better understanding and detailed description of the interplay between the interference and nonlinearity in phonon propagation through and scattering in two-dimensional arrays of two-path anharmonic atomic defects with a different topology.

Quantum Optical Effective-Medium Theory for Layered Metamaterials at Any Angle of Incidence

The quantum optics of metamaterials starts with the question of whether the same effective-medium theories apply as in classical optics. In general, the answer is negative. For active plasmonics but also for some passive metamaterials, we show that an additional effective-medium parameter is indispensable besides the effective index, namely, the effective noise-photon distribution. Only with the extra parameter can one predict how well the quantumness of states of light is preserved in the metamaterial. The fact that the effective index alone is not always sufficient and that one additional effective parameter suffices in the quantum optics of metamaterials is both of fundamental and practical interest. Here, from a Lagrangian description of the quantum electrodynamics of media with both linear gain and loss, we compute the effective noise-photon distribution for quantum light propagation in arbitrary directions in layered metamaterials, thereby detailing and generalizing our previous work. The effective index with its direction and polarization dependence is the same as in classical effective-medium theories. As our main result, we derive both for passive and for active media how the value of the effective noise-photon distribution too depends on the polarization and propagation directions of the light. Interestingly, for s-polarized light incident on passive metamaterials, the noise-photon distribution reduces to a thermal distribution, but for p-polarized light it does not. We illustrate the robustness of our quantum optical effective-medium theory by accurate predictions both for power spectra and for balanced homodyne detection of output quantum states of the metamaterial.

Tailoring Nonlinear Metamaterials for the Controlling of Spatial Quantum Entanglement

The high designability of metamaterials has made them an attractive platform for devising novel optoelectronic devices. The demonstration of nonlinear metamaterials further indicates their potential in developing quantum applications. Here, we investigate designing nonlinear metamaterials consisting of the 3-fold (C3) rotationally symmetrical nanoantennas for generating and modulating entangled photons in the spatial degrees of freedom. Through tailoring the geometry and orientation of the nanoantennas, the parametric down conversion process inside the metamaterials can be locally engineered to generate entangled states with desired spatial properties. As the orbital angular momentum (OAM) states are valuable for enhancing the data capacity of quantum information systems, the photonic OAM entanglement is practically considered. With suitable nanostructure design, the generation of OAM entangled states is shown to be effectively realized in the discussed nonlinear metamaterial system. The nonlinear metamaterials present a perspective to provide a flexible platform for quantum photonic applications.

Two-photon interference: the Hong-Ou-Mandel effect

Nearly 30 years ago, two-photon interference was observed, marking the beginning of a new quantum era. Indeed, two-photon interference has no classical analogue, giving it a distinct advantage for a range of applications. The peculiarities of quantum physics may now be used to our advantage to outperform classical computations, securely communicate information, simulate highly complex physical systems and increase the sensitivity of precise measurements. This separation from classical to quantum physics has motivated physicists to study two-particle interference for both fermionic and bosonic quantum objects. So far, two-particle interference has been observed with massive particles, among others, such as electrons and atoms, in addition to plasmons, demonstrating the extent of this effect to larger and more complex quantum systems. A wide array of novel applications to this quantum effect is to be expected in the future. This review will thus cover the progress and applications of two-photon (two-particle) interference over the last three decades.

A quantum phase gate capable of effectively collecting photons based on a gap plasmon structure

The realization of a quantum phase gate in micro-nano structures is beneficial to the miniaturization and integration of on-chip quantum circuits. Surface plasmons are well known for ultra-small mode volumes, which can further reduce the size of quantum devices. However, high fidelity quantum phase gates using surface plasmon nanocavities in a strong coupling regime have not been proposed yet. Here, based on a metallic nanocone-nanowire structure, we theoretically demonstrate a quantum phase gate, simultaneously achieving an arbitrary phase shift and effective photon collection at the nanoscale. The gate can reach 88.8% fidelity due to combining the enhanced coupling coefficient achievable by gap plasmons with low cavity loss resulting from gain medium. Meanwhile, emitted photons can be guided via the nanowire with collection efficiency over 30%. The system may act as universal quantum nodes that can process and store quantum information. It also holds promise for the physical implementation of on-chip multifunctional quantum gates and novel quantum circuits.

Phase matching in hyperbolic wire media for nonlinear frequency conversion

Efficient nonlinear frequency conversion requires a phase matching condition to be satisfied. We analyze the dispersion of the modes of hyperbolic wire metamaterials and demonstrate that phase matching at infrared wavelengths can be achieved with a variety of constituent materials, such as GaAs, in which phase matching cannot easily be achieved by conventional means. Our finding promises access to many materials with attractive nonlinear properties.

Distillation of photon entanglement using a plasmonic metamaterial

Plasmonics is a rapidly emerging platform for quantum state engineering with the potential for building ultra-compact and hybrid optoelectronic devices. Recent experiments have shown that despite the presence of decoherence and loss, photon statistics and entanglement can be preserved in single plasmonic systems. This preserving ability should carry over to plasmonic metamaterials, whose properties are the result of many individual plasmonic systems acting collectively, and can be used to engineer optical states of light. Here, we report an experimental demonstration of quantum state filtering, also known as entanglement distillation, using a metamaterial. We show that the metamaterial can be used to distill highly entangled states from less entangled states. As the metamaterial can be integrated with other optical components this work opens up the intriguing possibility of incorporating plasmonic metamaterials in on-chip quantum state engineering tasks.

The Hong-Ou-Mandel effect in the context of few-photon scattering

The Hong-Ou-Mandel effect is studied in the context of two-photon transport in a one-dimensional waveguide with a single scatterer. We numerically investigate the scattering problem within a time-dependent, wave-function-based framework. Depending on the realization of the scatterer and its properties, we calculate the joint probability of finding both photons on either side of the waveguide after scattering. We specifically point out how Hong-Ou-Mandel interferometry techniques could be exploited to identify effective photon-photon interactions which are mediated by the scatterer. The Hong-Ou-Mandel dip is discussed in detail for the case of a single two-level atom embedded in the waveguide, and dissipation and dephasing are taken into account by means of a quantum jump approach.