Indistinguishable photons from a two-photon cascade

Abstract

Decay of a four-level diamond scheme via a cascade is a potential source of entangled photon pairs. A solid-state implementation is the biexciton cascade in a semiconductor quantum dot. While high entanglement fidelities have been demonstrated, the two photons, XX and X, are temporally correlated, typically resulting in poor photon coherence. Here, we demonstrate a high two-photon interference visibility (a measure of the photon coherence) for both XX (V=94$\pm$2%) and X (V=82$\pm$6%) photons. This is achieved by Purcell-enhancing the biexciton transition in a low-noise device. We find that the photon coherence follows the well-known quantum optics result upon tuning the XX:X lifetime ratio over two orders of magnitude.

Figures (9)

• Figure 1: (a) Schematic of the biexciton cascade. The biexcition decays to the exciton ($\ket{\text{XX}} \rightarrow \ket{\text{X}}$) creating photon XX; the exciton decays to the ground state ($\ket{\text{X}} \rightarrow \ket{\text{0}}$) creating photon X. Only one decay pathway is shown for simplicity. (b) The XX and X photons are correlated in time limiting the indistinguishability of successive XX photons, likewise X photons. The sketch shows a simplified picture: detection of the XX results in timing jitter in the X photon. (c) Theoretical prediction of the two-photon interference visibility as a function of lifetime ratio, Eq. (\ref{['eq:HOMvsLifetime']}). Reducing $\tau_{\text{XX}}$ by Purcell enhancing $\ket{\text{XX}} \rightarrow \ket{\text{X}}$ reduces the timing jitter and improves the coherence of both XX and X photons (red shaded area). Conversely, reducing $\tau_\text{X}$ has the opposite effect (blue shaded area).
• Figure 2: Transition lifetimes detecting the X and XX photons upon scanning the cavity resonance over (a) $\ket{\text{XX}} \rightarrow \ket{\text{X}}$ and (b) $\ket{\text{X}} \rightarrow \ket{\text{0}}$. $f_\text{C}$ is the cavity resonance-frequency, $f_\text{XX}$ ($f_\text{X}$) the XX (X) resonance-frequency. Changing the cavity length $\delta_z$ allows $\tau_\text{XX}/\tau_\text{X}$ to be tuned in situ over two orders of magnitude. The asymmetry in the $\ket{\text{XX}}$ lifetime in (a) comes from enhancement of the transition by the second cavity mode at higher positive detunings. (c) Schematic of the open microcavity enhancing $\ket{\text{XX}} \rightarrow \ket{\text{X}}$, and (d) enhancing $\ket{\text{X}} \rightarrow \ket{\text{0}}$.
• Figure 3: Characterisation of the photon coherence using two-photon interference. (a) Frequency alignment of the X, XX, TPE laser and cavity for Purcell enhancement of the XX transition to reduce $\tau_{XX}$. This configuration improves the photon coherence for both XX and X photons. (b) Two-photon interference data for the XX photons, with $V_{XX}=94\pm2\%$. (c) Two-photon interference data for the X photons, with $V_{X}=82\pm6\%$. (d) Frequency alignment for Purcell enhancement of the X transition, which increases $\tau_{XX}/\tau_{X}$ and thus reduces the photon coherence for both XX (e) and X (f) photons.
• Figure 4: Photon coherence $V$ as a function of lifetime ratio $\tau_{XX}/\tau_{X}$. The solid line is Eq. (\ref{['eq:HOMvsLifetime']}). Insets: HOM visibility and lifetime ratio as a function of cavity detuning from XX (red) and X (blue) transitions.
• Figure S1: Experimental set-up.(a) A Ti:Sapphire laser produces laser pulses of 5 ps duration ($\lambda=923.238$ nm), with 90 GHz linewidth (green arrow). The spacing between laser pulses is 13.1 ns. (b) The excitation laser intensity is controlled with an acousto-optic modulator (AOM). Before the excitation of the QD, a narrow notch filter (bandwidth = 220 GHz full width at half maximum (FWHM)) ensures that any frequency components resonant with the transition being collected (here shown: XX) are removed from the excitation pulse. (c) The quantum dot, held at 4.2 K in a helium bath-cryostat, is excited to the $\ket{\text{XX}}$ via a two-photon excitation (TPE) process. The transmitted excitation laser undergoes a first filtering step using a cross-polarised microscope with a polarising beam splitter (PBS) to isolate the QD emission. In the schematic the micro-cavity is resonant with the XX (red arrows, $\lambda=924.223$ nm), and the collection of XX photons is strongly enhanced. A small fraction of the X emission (blue arrows, $\lambda=922.256$ nm) is also captured, compare Fig. \ref{['fig:spectra']}(c). By in-situ tuning of the cavity length, the reverse case can be realised, i.e., enhancing and efficient collection of the X, and a small fraction collected from the XX emission. (d) A diffraction grating (bandwidth = 30 GHz FWHM) allows light from either the XX or X transition to be transmitted for further analysis. (e) Two-photon interference measurement setup. Half-wave plate 1 (HWP 1) and a polarising beam splitter (PBS) are used to control the ratio of light going into the two arms, to account for different losses in the two optical paths. The length of one arm can be adjusted to match the time-delay between the two arms to the spacing of the laser pulses. Half-wave plate 2 (HWP 2) and fibre paddles (FP) are used to change from the co-polarised to the cross-polarised configuration. The classical interference visibility is 98.5$\pm$1%. The two paths are recombined in a fibre beam splitter (FBS), reflection:transmission = 0.525:0.475. (f) Photons are detected with superconducting nanowire single-photon detectors (SNSPDs). The combined timing jitter of the detectors and our photon counting electronics (Swabian Instruments Time Tagger Ultra) is 43 ps FWHM.