Fundamental limit on the heralded single photons' spectral brightness

TL;DR

The paper investigates whether the spectral brightness of heralded single photons has a fundamental limit. It introduces the quality factor $Q = ESB \,\times\, SBR$ and shows $Q = C \times P$, where $P$ is the pairing probability and $C$ depends on the biphoton waveform. Experimentally, using a hot-atom double-$\Lambda$ SFWM source, it achieves $P = 0.81 \pm 0.02$ and $Q = 0.68 \pm 0.02$, with ESB = $(9.8 \pm 0.4) \times 10^{4}$ (pairs/s)\\cdot μs, SBR = $6.9 \pm 0.1$, and SB = $(7.0 \pm 0.3) \times 10^{5}$ pairs/s/MHz. This establishes a universal limit across platforms and marks a new benchmark for heralded single-photon sources, with implications for scalable quantum information processing.

Abstract

The heralded single photons' (HSPs) spectral brightness (SB) is defined as the generation rate per linewidth. As the generation rate of HSPs gets larger or the photons' linewidth becomes narrower, both of which are desirable in quantum information processing using HSPs, does the SB have a limit? We systematically studied the SB and the cross-correlation function, or equivalently, the signal-to-background ratio. The results in this study provide an answer applicable to all types of HSP sources. The answer relies on a newly defined quantity, the quality factor, which reveals how a HSP source approaches the ideal noise-free one. Furthermore, employing the HSP source based on hot atomic vapor, we achieved an SB of (7.0$\pm$0.3)$\times10^5$ pairs/s/MHz and a quality factor of 0.68$\pm$0.02 under the single-photon criterion. Both values are the highest records to date among all kinds of HSP sources.

Figures (6)

• Figure 1: The double-$\Lambda$ transition scheme for the biphoton generation used in this work. We applied the pump and coupling fields to hot atomic vapor and produced the signal and probe photons. The pump field and signal photon (the coupling field and probe photon) form the first (the second) two-photon Raman transition with a one-photon detuning of $\Delta_p$ ($\Delta_c$).
• Figure 2: The signal's and probe's heralding probabilities $h_s$ and $h_p$ are shown as functions of the pump (a) power and (b) detuning. Red (and blue) circles or squares are the experimental data with the signal (and probe) photons to herald coincidence counts. Each line represents the theoretical prediction with a proportionality matching the count rate in theory to that in measurement. The coupling power and detuning were 17 mW and 1.00 GHz in all the measurements. The pump detuning was 2.90 GHz in (a), and the pump power was 2 mW in (b). In the theoretical calculation, we used $\alpha$ (OD) = 500, $\Omega_c =$ 12$\Gamma$, $\Omega_p$ = 2.8$\Gamma$$\times$$\sqrt{\rm pump~power~in~mW}$, $b =$ 0.375, and the various values of $\gamma$, which ranged 0.0072$\Gamma$$\sim$0.020$\Gamma$ in (a) and 0.0067$\Gamma$$\sim$0.019$\Gamma$ in (b). These calculation parameters can be found in Eqs. (\ref{['eq:FWM']})-(\ref{['eq:EITm']}) and their determination methods are described in Appendix \ref{['app:theory']}.
• Figure 3: The signal's and probe's heralding probabilities $h_s$ and $h_p$ are shown as functions of the coupling (a) power and (b) detuning. Red (and blue) circles or squares are the experimental data with the signal (and probe) photons to herald coincidence counts. Each line represents the theoretical prediction with a proportionality matching the count rate in theory to that in measurement. The pump power and detuning were 2 mW and 1.90 GHz in all the measurements. The coupling detuning was 1.00 GHz in (a), and the coupling power was 35 mW in (b). In the theoretical calculation, we used $\alpha$ (OD) = 500, $\Omega_c =$ 3.0$\Gamma$$\times$$\sqrt{\rm coupling~power~in~mW}$, $\Omega_p$ = 4.0$\Gamma$, $b =$ 0.375 in (a) and 0.315 in (b), and the various values of $\gamma$, which ranged 0.0075$\Gamma$$\sim$0.045$\Gamma$ in (a) and 0.0089$\Gamma$$\sim$0.011$\Gamma$ in (b).
• Figure 4: Biphoton wave packet or two-photon correlation function, i.e., coincidence count as a function of the delay time of the probe photon upon the signal photon's heralding. Black dots are the experimental data with the highest quality factor achieved in this work, and the green line is the theoretical prediction. The pump and coupling powers (detunings) were 5.5 and 17 mW (1.90 and 1.00 GHz), respectively. The OD of the hot atomic vapor was about 500. With the same experimental condition, several measurements on different days reveal that the biphotons, collected in the polarization-maintained optical fibers, had a generation rate of (7.5$\pm$0.2)$\times$$10^5$ pairs/s, a temporal FWHM of 131$\pm$3 ns, and an SBR of 6.9$\pm$0.1. The measurements also show that the signal's and probe's heralding probabilities were 0.83$\pm$0.02 and 0.98$\pm$0.02. Thus, the above-quoted uncertainties include the day-to-day fluctuations. In the inset, the green line represents the theoretical prediction's frequency spectrum with a FWHM of 0.94$\pm$0.03 MHz, and the blue line is the best fit of a Lorentzian function with a FWHM of 1.07$\pm$0.03 MHz. We used $\alpha =$ 500, $\Omega_c =$ 12$\Gamma$, $\gamma =$ 0.012$\Gamma$, and $b$ = 0.375 in the theoretical calculation.
• Figure 5: (a) The quality factor, $Q$, and (b) the normalized quality factor, $Q/C$, as functions of the pairing probability, $P$. The definitions of $Q$, $C$, and $P$ can be found in Eqs. (\ref{['eq:relation']})-(\ref{['eq:definitionC']}). Red, blue, green, and black circles are the experimental data relating to Figs. \ref{['fig:two']}(a), \ref{['fig:two']}(b), \ref{['fig:three']}(a), and \ref{['fig:three']}(b), and purple ones are those during the search for the result in Fig. \ref{['fig:four']}, where in the measurements the pump power ranged between 1 and 11 mW, the pump detuning changed from 1.4 to 3.4 GHz, the coupling power ranged between 3 and 36 mW, and the coupling detuning changed from 0 to 3.0 GHz. The straight line in (a) [or (b)] is the best fit (or theoretical prediction) with a slope of 0.92 (or 1).