Correlation functions with single-photon emitters under noisy resonant continuous excitation

Abstract

To characterize the statistics and indistinguishability of a source, it is common to measure the correlation functions of the emitted field using various interferometers. Here, we present a theoretical framework for the computation of the correlation functions of a two-level system that is resonantly driven by a realistic noisy cw excitation laser. Analytic expressions of the first and second-order auto-correlation functions are obtained where the various contributions of the noisy excitation source are correctly taken into account. We predict that, even in the low power regime, the noise source has a strong influence on the two-level system dynamics, which is not anticipated by simpler models. The characterization of photon indistinguishability in the pulsed excitation regime is usually done by measuring the value of the zero-delay intensity correlation obtained with a Hong-Ou-Mandel interferometer. We show that this figure is irrelevant in the cw excitation regime and we introduce the coalescence time window, a figure of merit based on a probabilistic interpretation of the notion of photon indistinguishability. We finally use the coalescence time window to quantify how noisy cw excitation influences photon indistinguishability.

Coherence in Cooperative Photon Emission from Indistinguishable Quantum Emitters

“…Notably, the 1/e width of V HOM , which gives the coherence time of the emission, for the cooperative case (≈ 1.15 ns) is comparable to the single emitter case (≈ 1.34 ns). Using the coherence time window (CTW) [45][46][47], i.e. the integrated area of V HOM , as a figure of merit, we find the CTW for the single emitter case (1.37 (1) ns) is more than twice that of the cooperative emission (0.53 (1) ns), reflecting the difference for each case in V HOM (0) and 1/e widths.…”

“…This is analogous to the interpretation of the zero-delay anti-bunching dip in the Hong-Ou-Mandel interference measurement of subsequently emitted single photons; please refer to Refs. [45][46][47] for more details. Instead, the integration over the full zero-delay peak within a large integration window (g…”

Fundamental Limits to Coherent Photon Generation with Solid-State Atomlike Transitions

“…One popular approach to mitigate these effects is to use weak coherent excitation. In the weak-excitation regime of a transform-limited optical transition, coherent scattering dominates over incoherent (spontaneous) emission due to minimal excited-state population [41][42][43][44][45][46][47][48]. Likewise, spin-flip Raman scattered photons from solid-state spin-Λ systems produce highly coherent photons; in the atomic picture such photons have coherence determined solely by the excitation source and ground (spin) state dephasing [15][16][17][18][19][20].…”

“…Therefore, we instead consider the coalescence time window CTW = V HOM (τ ) dτ , given by the shaded area in Fig. 3(A-C), which depends on the full duration of V HOM (τ ) and is thus independent of detector jitter [45,48]. A detailed analysis of CTW for atomic two-level systems and solid-state nanostruc- tures interacting with a vibrational environment is described in the SI [57].…”

“…The saturation at low-excitation power is due to the lifetime limit of the QD: the photon coherence is not solely determined by the laser coherence in this power regime. Thus, the width of the visibility dip should converge as Ω → 0, resulting in the convergence of the CTW to a finite value, as opposed to increasing indefinitely, even for an ideal continuous wave source [45,48].…”