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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Generation of quantum entangled states in nonlinear plasmonic structures and metamaterials (Presentation Recording)

Alexander N. Poddubny, Andrey A. Sukhorukov

Published Sep 2, 2015• 0 citations
Publisher

Abstract

The practical development of quantum plasmonic circuits incorporating non-classical interference [1] and sources of entangled states calls for a versatile quantum theoretical framework which can fully describe the generation and detection of entangled photons and plasmons. However, majority of the presently used theoretical approaches are typically limited to the toy models assuming loss-less and nondispersive elements or including just a few resonant modes. Here, we present a rigorous Green function approach describing entangled photon-plasmon state generation through spontaneous wave mixing in realistic metal-dielectric nanostructures. Our approach is based on the local Huttner-Barnett quantization scheme [2], which enables problem formulation in terms of a Hermitian Hamiltonian where the losses and dispersion are fully encoded in the electromagnetic Green functions. Hence, the problem can be addressed by the standard quantum mechanical perturbation theory, overcoming mathematical difficulties associated with other quantization schemes. We derive explicit expressions with clear physical meaning for the spatially dependent two-photon detection probability, single-photon detection probability and single-photon density matrix. In the limiting case of low-loss nondispersive waveguides our approach reproduces the previous results [3,4]. Importantly, our technique is far more general and can quantitatively describe generation and detection of spatially-entangled photons in arbitrary metal-dielectric structures taking into account actual losses and dispersion. This is essential to perform the design and optimization of plasmonic structures for generation and control of quantum entangled states. [1] J.S. Fakonas, H. Lee, Y.A. Kelaita and H.A. Atwater, Nature Photonics 8, 317(2014) [2] W. Vogel and D.-G. Welsch, Quantum Optics, Wiley (2006). [3] D.A. Antonosyan, A.S. Solntsev and A.A. Sukhorukov, Phys. Rev. A 90 043845 (2014) [4] L.-G. Helt, J.E. Sipe and M.J. Steel, arXiv: 1407.4219

DOI
10.1117/12.2186869

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We develop a general theoretical framework of integrated paired photon-plasmon generation through spontaneous wave mixing in nonlinear plasmonic and metamaterial nanostructures, rigorously accounting for material dispersion and losses in the quantum regime through the electromagnetic Green function. We identify photon-plasmon correlations in layered metal-dielectric structures with 70% internal heralding quantum efficiency and reveal a novel mechanism of broadband generation enhancement due to topological transition in hyperbolic metamaterials.
Frontier quantum engineering tasks require reliable control over light-matter interaction dynamics, which could be obtained by introducing electromagnetic structuring. Initiated by the Purcell's discovery of spontaneous emission acceleration in a cavity, the concept of electromagnetic modes' design have gained a considerable amount of attention due to development of photonic crystals, micro-resonators, plasmonic nanostructures and metamaterials. Those approaches, however, offer qualitatively different strategies for tailoring light-matter interactions and are based on either high quality factor modes shaping, near field control, or both. Remarkably, rigorous quantum mechanical description might address those processes in a different fashion. While traditional cavity quantum electrodynamics tools are commonly based on mode decomposition approach, few challenges rise once dispersive and lossy nanostructures, such as noble metals (plasmonic) antennas or metamaterials, are involved. The primary objective of this review is to introduce key methods and techniques while aiming to obtain comprehensive quantum mechanical description of spontaneous, stimulated and higher order emission and interaction processes, tailored by nanostructured material environment. The main challenge and the complexity here are set by the level of rigorousity, up to which materials should be treated. While relatively big nanostructured features (10 nm and larger) could be addressed by applying fluctuation–dissipation theorem and corresponding Green functions' analysis, smaller objects will require individual approach. Effects of material granularity, spatial dispersion, tunneling over small gaps, material memory and others will be reviewed. Quantum phenomena, inspired and tailored by nanostructured environment, plays a key role in development of quantum information devices and related technologies. Rigorous analysis is required for both examination of experimental observations and prediction of new effects.
We review the latest advances in the generation of quantum light with nonlinear nanoresonators in metasurfaces, which act both as sources of quantum states and nanoantennas shaping the emitted photons. We outline a general quantum theory of spontaneous photon-pair generation in arbitrary nonlinear photonic structures, including nanoresonators and metasurfaces, which provides an explicit analytical solution for the photon state expressed through the classical Green function. We formulate the correspondence between the quantum photon-pair generation and classical sum-frequency process in nonlinear media, and discuss its application in various contexts, including waveguide circuits and nanostructures. We also discuss the first experimental results demonstrating photon-pair generation in a single nonlinear nanoantenna.
We introduce a scheme for generating entanglement between two quantum dots using a plasmonic waveguide made from an array of metal nanoparticles. We show that the scheme is robust to loss, enabling it to work over long distance plasmonic nanoparticle arrays, as well as in the presence of other imperfections such as the detuning of the energy levels of the quantum dots. The scheme represents an alternative strategy to the previously introduced dissipative driven schemes for generating entanglement in plasmonic systems. Here, the entanglement is generated by using dipole-induced interference effects and detection-based postselection. Thus, contrary to the widely held view that loss is major problem for quantum plasmonic systems, we provide a robust-to-loss entanglement generation scheme that could be used as a versatile building block for quantum state engineering and control at the nanoscale.
In the field of quantum information and quantum computing, entanglement plays an essential role. Entanglement preservation is an important issue as realistic quantum systems are affected by decoherence and entanglement losses due to the interaction with their environment. For example, in spite of an exponential decay of a single qubit, the entanglement between two qubits may completely disappear at a finite time; a phenomenon known as “entanglement sudden death” [1]. Recently, interest has been given in cases that qubits can be strongly coupled to plasmonic nanostructures, like, for example, an one-dimensional plasmonic waveguide [2] or a two-dimensional lattice of metal-coated dielectric nanoparticles [3]. In such systems the strong interaction with the surface plasmons leads to significant entanglement between the two qubits. Here, we consider the interaction of two initially entangled qubits interacting individually with a two-dimensional lattice of metal-coated dielectric nanoparticles. We consider two cases for the qubits, a pair of regular two-level systems and a pair of V-type systems where one transition is the qubit and the other level acts as an umbrella level [4]. We consider the entanglement dynamics for different initial conditions of the qubits. The specific plasmonic nanostructure leads to strongly modified spontaneous emission rates of individual quantum systems (strong suppression in certain cases) and, in addition, to strongly anisotropic Purcell effect for orthogonal dipoles, that in turn can be used for simulating quantum interference in spontaneous emission [5]. We use these effects for significantly prolonging entanglement dynamics near the plasmonic nanostructure in both cases, in comparison to the cases that the qubits are in free space. 1. T. Yu and J. H. Eberly, Phys. Rev. Lett. 93, 140404 (2004). 2. A. Gonzalez-Tudela, D. Martin-Cano, E. Moreno, L. Martin-Moreno, C. Tejedor, and F. J. Garcia-Vidal, Phys. Rev. Lett. 106, 020501 (2011). 3. N. Iliopoulos, A. F. Terzis, V. Yannopapas, and E. Paspalakis, Ann. Phys. 365, 38 (2016). 4. S. Das and G. S. Agarwal, Phys. Rev. A 81, 052341 (2010). 5. V. Yannopapas, E. Paspalakis, and N. V. Vitanov, Phys. Rev. Lett. 103, 063602 (2009).