Nonlocalized Generation of Correlated Photon Pairs in Degenerate Down-Conversion

Abstract

The achievement of optimum conversion efficiency in conventional spontaneous parametric downconversion requires consideration of quantum processes that entail multisite electrodynamic coupling, actively taking place within the conversion material. The physical mechanism, which operates through virtual photon propagation, provides for photon pairs to be emitted from spatially separated sites of photon interaction; occasionally pairs are produced in which each photon emerges from a different point in space. The extent of such nonlocalized generation is influenced by individual variations in both distance and phase correlation. Mathematical analysis of the global contributions from this mechanism provides a quantitative measure for a degree of positional uncertainty in the origin of down-converted emission. DOI: 10.1103/PhysRevLett.118.133602 Spontaneous parametric down-conversion (SPDC) is a process in which light passing through an optically nonlinear medium can generate double-wavelength output. At a fundamental level, the process entails the conversion of pump photons into conascent, phase-matched pairs, executed by material interactions that entail the secondorder nonlinear optical susceptibility: a third-order electric dipole response. Each generated pair of photons has a combined energy and momentum equal to that of the corresponding annihilated photon, and they also exhibit correlated polarization. When the emergent photons equally share the energy of the input, the process is known as degenerate down-conversion (DDC); an alternative perspective is to regard the conversion as an exact time reversal of second-harmonic generation [1,2]. Much work has been carried out on correlated photon pairs, including their generation [3][4][5], manipulation [6][7][8][9], and application [10][11][12]. The entanglement of the quantum states in each pair has important applications in quantum computing and communication [13], and potential utilization clinically [14].In this Letter we develop an expanded theory of SPDC, highlighting and quantifying an important contribution from nonlocalized couplings. While SPDC is one of the main sources of entangled photon pairs [15], an exact location for the creation of each output photon cannot of course be inferred by direct observation-although pump photon annihilation and down-converted photon emission are generally assumed to be colocated. Of course, the diffuse nature of atomic and molecular orbitals precludes exact identification of the location for any photon creation event; equally, even the emission of two correlated photons cannot be considered as precisely colocated in origin. However, the spatial extent of the region from within which a pair of down-converted photons may emerge is considerably larger than may usually be supposed.In fact, there is a possibility that for each input photon the process may entail correlated photon interactions at two separate locations, creating one down-converted photon at each as indicated in Fig. 1. Accounting for such delocalized interact...

Quantum delocalization in photon-pair generation

“…The results that we have secured confirm and consolidate our preliminary results identifying a potentially significant mechanism for the nonlocal production of down-converted photon pairs, [41] now fully accounting for the multicenter sums. The unique aspect of this work extends from an advancement of the underlying theory, through a more substantial computational analysis, to results that indicate an effect that is meaningfully within the reach of experimental detection-the possibility of one photon pair in every 50 or so emerging from close but physically distinct locations.…”

“…The numerical procedure, a lattice sum calculation, follows earlier approaches for calculating quantum amplitudes associated with molecular aggregates [84,85]. Here, we expand upon a preliminary, less computationally demanding treatment of SPDC, in which results were restricted to a single element of the coupling tensor [41].…”

“…The work to be presented is concerned with further development of the quantum theory of the optically nonlinear process of SPDC [38][39][40], highlighting and quantifying an important contribution to the overall mechanism-the possibility of which arises from taking into account nonlocalized couplings [41]. Of course, an exact location for the creation of any output photon cannot be inferred by direct observation-although pump photon annihilation and down-converted photon emission are generally assumed to be colocated.…”

Quantum localization issues in nonlinear frequency conversion and harmonic generation

“…[22][23] Here, we focus on another aspect, concerned with the extent of delocalization. In a system of nanoparticles, within each of which there will generally be a system of optical centers able to play the role of one of a coupled pair, it is interesting to observe the effect of increasing particle size.…”

“…In particular, the individual photons that constitute the correlated pairs produced by SPDC can come from separate, distinct locations in the nonlinear crystal, through a delocalized mechanism. [22][23] The work presented within is V 000 0,,n9 o0 concerned with extending the physics behind this new mechanism from a specific optical process (SPDC), and applying it to another optical phenomenon, namely SHG. Identifying the variation of significance in the delocalized mechanism also leads to results that indicate an optimum size for nanoparticles, in a medium designed for frequency conversion.…”