Entangled‐photon generation via biexcitons in nano‐structures

Abstract

We have constructed quantum electrodynamics theory for excitons whose center-of-mass motion is confined in arbitrary-structured dielectrics with considering their nonlocal optical susceptibility. We systematically investigate entangled-photon generation via biexcitons in nano-to-macro scale materials by this theory. It is revealed that nano-structured materials provide scattering spectra explicitly reflecting quantum states of confined exciton-polaritons and are promising sources of entangled photons from the viewpoints of both efficiency and signal-to-noise ratio.1 Introduction Entangled-photon pairs, which play an important role in quantum information technology, are usually generated by parametric-down conversion (PDC). On the other hand, it is reported that hyper-parametric scattering (HPS) in CuCl also generates ultraviolet entangled photons [1]. In the HPS process, resonantly created biexcitons with no angular momentum collapse with the generation of polarization-correlated photon pairs conserving the angular momentum. This scheme shows much higher efficiency than the usual method by PDC because of the giant two-photon absorption in CuCl. Although the bulk crystal was used in Ref.[1], it is worth investigating the HPS process in nano-structures such as quantum dots [2,3], because manipulating the excitonic confinement has a potential to control characteristics of the entangled-photon generation. The purpose of our study is the investigation of HPS in nano-to-macro scale materials, where center-of-mass motions of excitons and biexcitons are confined.

QED of excitons with nonlocal susceptibility in arbitrarily structured dielectrics

“…I, there is a growing interest in the QED of elementary excitations in condensed matters. For example, theoretical studies on entangled-photon generation via biexcitons have already been performed by Savasta et al 49,50 ͑although the nonlocality was not sufficiently considered in these calculations͒ and, by extending our QED theory reported in the present paper, we discuss it in the excitonic system weakly confined in nanostructures, 36 which are known to exhibit anomalous nonlinear optical phenomena. [27][28][29][30][31] In addition, Scheel and Welsch 14,15 discussed the QED of nonlinear media with absorption and dispersion ͑but without the nonlocality͒.…”

“…Based on the self-consistent equation set ͑57͒ or ͑79͒, as discussed in the present paper, the new objective is to solve the equation set with nonlinear terms originating from nonlinear processes, as we have done. 36 On the other hand, based on the Maxwell wave equation ͓Eq. ͑45͔͒ with the nonlocal susceptibility, as discussed in the previously discussed QED theories, 16,17,[38][39][40][41] we must solve the wave equation with nonlinear and nonlocal susceptibility.…”

“…26 Furthermore, we have already applied our QED theory with the RWA for the analysis of the entangledphoton generation from a semiconductor film with a thickness of a few hundred nanometers. 36 In this numerical calculation, we considered 200 exciton states. In this manner, our QED theory is definitely feasible for practical applications.…”

“…Further, we have already applied the present theory to the practical calculation of entangledphoton generation via biexcitons in nanostructures. 36 In Sec. II, we explain the previously discussed QED theories with the nonlocality.…”

QED theory for excitons with microscopic nonlocality

“…Our theory keeps good correspondences with them. Although only the linear process has been discussed in this paper, we can phenomenologically extend our theory to describe nonlinear processes, such as the entangled-photon generation via biexcitons in nano-structures [19]. In addition, our theory has a potential to systematically investigate higher order nonlinear processes of elementary excitations in condensed matters by using the Feynman diagram technique with correlation functions derived in the present paper.…”