Tunable multi-photon correlations from a coherently driven quantum dot

TL;DR

The paper addresses how to shape photon statistics by mixing resonance fluorescence from a quantum dot with a coherent laser field, achieving tunable $g^{(2)}$ and higher-order coherences via a mixing factor $f_{mix}$ and phase $φ$. It develops a theory based on a mixing operator $s = σ + β$ and the quantum regression theorem to decompose correlation functions ($G^{(2)}$, $G^{(3)}$, etc.) into interference, population, and coherence contributions, and validates it with CW experiments on a neutral exciton in a microcavity. The results show controllable antibunching to bunching, including strong $g^{(2)}(0)$ and significant $g^{(3)}$ features when the signals are mixed, highlighting the role of normalization and interference in shaping photon statistics. This work provides practical tools for non-Gaussian state engineering and for shaping quantum optical fields in solid-state devices, with implications for quantum information and photonic quantum technologies.

Abstract

Mixing the fields generated by different light sources has emerged as a powerful approach for engineering non-Gaussian quantum states. Understanding and controlling the resulting photon statistics is useful for emerging quantum technologies that are underpinned by interference. In this work, we investigate intensity correlation functions arising from the interference of resonance fluorescence from a quantum emitter with a coherent laser field. We show that the observed bunching behavior results from a subtle interplay between quantum interference and the normalization of the correlation functions. We show that by adjusting the mixing ratio and phase one can achieve full tunability of the second-order correlation, ranging from anti-bunching to bunching. We further extend our analysis to third-order correlation functions, both experimentally and theoretically, to provide new insights into the interpretation of higher-order correlations and offer practical tools for shaping quantum optical fields.

Figures (6)

• Figure 1: Experimental system to study multi-photon correlations from a resonantly driven quantum dot. (a) Schematic of the experimental system. The tunable resonant laser is directed on to the unbalanced cavity containing the single quantum dot. Quarter and half- waveplates (QWP and HWP) are used to minimize laser scatter into the cross-polarized detectors whilst maximizing the visibility of the spectral features in the co-polarized detectors. (b) typical spectrum resulting from scanning the laser over the neutral exciton. (c) Rabi frequency varies linearly with the square-root of the incident laser power.
• Figure 2: Second order optical coherence $g^{(2)}(\tau)$ measured between detectors $D_1, D_2$ shown in blue, theoretical values shown in red, for Rabi frequencies of (a,b) $\Omega_0=0.56\pi\,\mathrm{ns}^{-1}$ and (c,d) $\Omega_0=3.3\pi\,\mathrm{ns}^{-1}$.
• Figure 3: Second order correlation function of the resonance fluorescence and laser mixed case. In the upper panel shows the cross-co polarized case between detectors $D_1$ and $D_3$ and lower panel the co-co polarized case between $D_3$ and $D_4$ with $\Omega_0=0.3\pi\,\text{ns}^{-1}, f_{\mathrm{mix}}=1,\phi=\pi$. Left: experimental data and right: theoretical calculations.
• Figure 4: Different parts of (a) $g^{(2)}_{\text{cross,co}}$ as defined in Eq. \ref{['eq:g2parts1']} and (b) $g^{(2)}_{\text{co,co}}$ as defined in Eq. \ref{['eq:g2parts']} for $\Omega_0=0.3\pi\,\text{ns}^{-1}, f_{\mathrm{mix}}=1,\phi=\pi$, corresponding to constant contributions as well as those of first- and second-order coherences. In panel (a), where laser photons can only be detected at one detector, the bunching at $\tau=0$ can be traced back purely to detection of laser photons at detector $D_1$. For panel (b), where laser light is mixed onto both signals, interference between dot and laser photons at both detectors can lead to additional bunching, visible by the maxima of the blue line at $\tau=0$.
• Figure 5: Controlling the correlation function Second order correlation function $g^{(2)}_{\mathrm{cross,co}}(\tau=0)$ on a logarithmic scale as a function of mixing strength $f_{\mathrm{mix}}$ and driving strength $\Omega_0$ for a phase (a) $\phi=0$ and (b) $\phi=\pi$. Blue values correspond to anti-bunching and red values to bunching. The dashed line in (b) marks $g^{(2)}(0)=1$.