Characterization of spectral diffusion by slow-light photon-correlation spectroscopy

Solid-state quantum emitters are playing a crucial role in the development of photonic quantum technologies. However, several decoherence mechanisms are known to impact the device performances and scalability. In various quantum emitter materials the fluctuation of the two-level system has been investigated by different methods to capture the evolution of coherence reduction. However, resolving the dynamics of spectral diffusion in the fundamental framework of on-demand single-photon generation remained unsolved. Hereby, the challenge is to observe with high time and energy resolution the impact of fluctuations directly in the properties of the emitted photons. In this Rapid Communication, we demonstrate the use of dispersion in a slow-light medium to map the photons frequency domain into time domain, observed as frequency-dependent time-of-flight. This allows for the measurement of the emission spectrum and the quantification of the spectral diffusion dynamics in one intensity correlation measurement. On exemplary semiconductor quantum dots, the impact of charge and spin noise on the spectral diffusion are revealed to follow an Ornstein-Uhlenbeck process. By a single measurement, broadening from the excitation repetition up to the stationary limit is resolved. This enables one to extract time-dependent two-photon interference visibilities for various timescales, which is a key performance measure for quantum emitters.

Figure 1

Experimental scheme. (a) Sketch of the experimental setup: a QD is excited by a resonant $\pi$ pulse. The emitted single photons pass through a slow-light medium (here Cs vapor). After the beamsplitter (BS) photon correlation and TCSPC is measured using single-photon counting modules (APD). (b) Illustration of the emission frequency fluctuations and the impact of dispersion $n\left(\nu \right)$ to the photons, providing a mapping ${\mathcal{M}}_{\text{disp}}$ of frequency to time domain via acquired delay and pulse distortion.

Figure 2

Mapping TCSPC to spectrum. (a) Simulation of emission frequency-dependent reshaping of initially exponentially decaying photons passing through the Cs vapor. Temporal profiles (left) and corresponding spectral profiles (right) are color coded. On the right side, the calculated transmission profile of the Cs vapor [20] at $125{}^{\circ }\mathrm{C}$ is shown (brown). (b) Measured (diamonds and dots) and simulated (line) TCSPC of QD A without (gray) and with (blue, shifted by $\approx -7\mathrm{ns}$) Cs vapor. Right: measured (dots) and predicted (line) emission spectrum of QD A that consists of two lines L and R. (c) Data and simulation for QD B.

Figure 3

Spectral diffusion in the photon-correlation measurement. (a) Normalized photon-correlation measurement for QD A without (gray) and with (blue) Cs vapor over time difference $\tau$. (b) Selected correlation peaks over several timescales. The peaks on the negative time differences are folded on top of the related positive ones to increase signal-to-noise ratio. The peaks without the vapor are shifted for the sake of clarity. Theory curves (light blue) from simulations are on top of the data. (c) Normalized correlation peak amplitude and area over the time difference. The lighter curves on top of the data represent simulation results. (d) Inferred HOM visibilities over time difference. Circles represent independent HOM measurements.

Figure 4

Millisecond charge trap dynamics. Normalized intensity correlation after the vapor with a binning of $100\mathrm{ns}$. Red curves are a fit with two exponential decays. The two regimes of correlation reduction are marked, while the dashed line indicates the time range of spectral diffusion considered in Fig. 3.