Measuring the Photon Coalescence Time Window in the Continuous-Wave Regime for Resonantly Driven Semiconductor Quantum Dots

We revisit Mandel’s notion that the degree of coherence equals the degree of indistinguishability by performing Hong-Ou-Mandel- (HOM-)type interferometry with single photons elastically scattered by a cw resonantly driven excitonic transition of an InAs/GaAs epitaxial quantum dot. We present a comprehensive study of the temporal profile of the photon coalescence phenomenon which shows that photon indistinguishability can be tuned by the excitation laser source, in the same way as their coherence time. A new figure of merit, the coalescence time window, is introduced to quantify the delay below which two photons are indistinguishable. This criterion sheds new light on the interpretation of HOM experiments under cw excitation, particularly when photon coherence times are longer than the temporal resolution of the detectors. The photon indistinguishability is extended over unprecedented time scales beyond the detectors’ response time, thus opening new perspectives to conducting quantum optics with single photons and conventional detectors.

Figure 1

(a) Unbalanced Mach-Zehnder interferometer for two-photon interference measurements. The QD emission is split by a first beam splitter (${\mathrm{BS}}_A$) in two paths of different lengths and recombined at a second one (${\mathrm{BS}}_B$). Single mode polarization maintaining fibers ensure high spatial overlap at ${\mathrm{BS}}_B$ and a half–wave plate $\lambda /2$ controls the mutual polarization between the two interferometer arms. Photodetection is monitored by two avalanche photodiodes (APD) placed at the ${\mathrm{BS}}_B$ outputs, combined with spectrometers for spectral filtering and a correlator for the intensity correlation function measurements. (Inset) Orthogonal excitation-detection geometry where a QD is excited via a fiber positioned at the edge of the sample while its emission is collected by a microscope objective in an orthogonal configuration. (b) Power dependence of the RRS intensity ratio with respect to the total QD emission intensity. The power $P$ is given in units of the saturation power of the excitonic transition $P_0$, $T_1=0.30\mathrm{ns}$ and $T_2=0.50\mathrm{ns}$. (c) Intensity correlation function for $P=0.1P_0$, fitted by the intensity correlation function of a resonantly excited two-level system [19], convoluted by the HBT instrument response function (IRF).

Figure 2

(a),(b) Two-photon interference measurements for orthogonal polarization configuration ($\perp$) below saturation ($P=0.17P_0$) and above saturation ($P=1.27P_0$), respectively. (c),(d) Same as (a),(b) for parallel polarization configuration ($\parallel$). (e),(f) Two-photon interference visibility at $P=0.17P_0$ and $P=1.27P_0$, respectively. The experimental data (dots) are fitted (line) by Eq. (1) for (a),(b), Eq. (2) for (c),(d), and $V_{\mathrm{HOM}}(\tau )$ for (e),(f). All the fits are convoluted by the IRF. (g) Coalescence time window deduced from the experimental (dots) and theoretical (line) visibilities as a function of the power $P$. The laser coherence time is $T_L=16\mathrm{ns}$.

Figure 3

(a) Two-photon interference visibility for various laser coherence times $T_L$, at $P=0.3P_0$. The experimental data (dots) are shown with the fits (line) given by $V_{\mathrm{HOM}}(\tau )$, convoluted by the IRF. (b) Coalescence time window as a function of $T_L$. The shaded area depicts the reachable range of $T_L$.