Four-Photon Interference with a High-Efficiency Quantum Dot Source

Abstract

While two-photon Hong-Ou-Mandel interference visibility has become a standard metric for single-photon sources, many optical quantum technologies require the generation and manipulation of larger photonic states. To date, efficiency limitations have prevented scaling quantum dot-based interference to the coalescence of more than two photons at a single beamsplitter. We overcome this limitation by combining a state-of-the-art quantum dot source with deterministic demultiplexing, enabling the direct observation of quantum interference fringes arising from up to four photons. We measure high mean interference contrasts of $93.0 \pm 0.1~\%$ for two photons, and $84.1 \pm 1.0~\%$ for four photons, with the complex fringe structure fully reproduced by a theoretical model. These results reveal the existence of "deep fringes" whose minima are unaffected by distinguishable photons, rendering the maximum contrast of four-photon interference highly sensitive to multi-photon emission but robust against photon distinguishability. We predict that these phenomena will extend to interference of larger numbers of photons, with relevance across a range of potential optical quantum technologies. A Fisher information analysis demonstrates that interference fringes from our source can exhibit phase sensitivity beyond the standard quantum limit, illustrating potential applications in quantum metrology.

Figures (4)

• Figure 1: (a) Schematic of the model of multi-photon interference: $a/b$ - input modes, $c/d$ - interferometer modes, $e/f$ - output modes, $g$ - photon loss mode , $\eta$ - transmission efficiency of the mode specified by the subscript, $\phi$ - phase shift. (b-d) Interference fringes produced by the input-output model for Fock state inputs up to 4 photons -- dark / pale lines correspond respectively to indistinguishable / distinguishable photon inputs ($\mathcal{I} = 1 / 0$). (e) Schematic of the experimental configuration. Single photons from the source are demultiplexed into two spatial modes $a/b$, with the first photon in $a$ delayed by the laser pulse separation $\tau_{\rm rep}$. An optional additional two-photon interference step (grey shaded box) combined with a further delay of $2\tau_{\rm rep}$ produces 2 photon inputs. The photons then pass through a displaced Sagnac interferometer (functionally equivalent to the schematic in (a)), where tilting a glass plate induces a phase shift $\phi$ between the two counter-propagating modes $c/d$. Photons at the output ports $e/f$ are detected by an array of up to 4 detectors, with correlations evaluated by time-tagging electronics. Solid lines: red - free space beam, yellow - single mode (SM) fibre, blue - polarization maintaining (PM) fibre. Acronyms: SPS - single-photon source, FPC - fibre polarization controller, Mod. - phase modulator, PBS - polarizing beam splitter, FBS - fibre beam splitter.
• Figure 2: Experimental (circles) and theoretical (solid lines) interference fringes for various $N$-photon input states as a function of the phase ($\phi$) between modes $c/d$: (a) Count rate for a single photon input. (b) Two-photon coincidence rate for single photon inputs to both ports. (c) Two-photon coincidence rate for two-photon input to a single port. (d) Four-photon coincidence rate for two-photon inputs to both ports. Parameters for the theoretical curves in (a-d) are found by fitting the experimental data (full details in supplementary material). (e-g) Theoretical four-photon interference fringes for ideal parameters with varying: (e) photon indistinguishability ($\mathcal{I}$), (f) single-photon purity $\mathrm{g^{(2)}(0)}$ and (g) interferometer mode $c$ transmission $\eta_c$ (with $\eta_d=1$). (h) Theoretical four-photon interference fringes using parameters from fit to experiment in (d).
• Figure 3: Variation of the mean two-photon interference contrast $\bar{C}_{11}$ with source parameters. (a) $\bar{C}_{11}$ as a function of $\mathrm{g^{(2)}(0)}$. Solid symbols denote experimental data: star - default configuration used in Fig. \ref{['fig:NPhotonFringes']}, triangles - reduced laser pulse area $\Theta$, diamonds - increased laser background leakage. Solid line - input/output model. (b) $\bar{C}_{11}$ as a function of photon separation. Solid circles denote experimental data, with the solid line showing an exponential fit. Inset: data from main figure (blue circles) plotted against the input-output model prediction (blue line) by converting photon separation to indistinguishability (see supplementary material for details).
• Figure 4: Calculated variation of (a,b) interference contrast $C_{ef}$ and (c,d) maximum phase sensitivity $S$ from our model as a function of source photon indistinguishability $\mathcal{I}$ (a,c) and multi-photon emission probability $\mathrm{g^{(2)}(0)}$ (b,d). Where multiple lines overlap, dashes are used. As 4 photon fringes $\ket{2_a 2_b} \rightarrow \ket{3_e 1_f}$ in general exhibit alternating deep/shallow fringes (see \ref{['fig:NPhotonFringes']}), their respective contrasts are plotted separately as bright/dark green lines respectively in (a,b). Aside from the variable under investigation, model parameters are set to ideal values: $\eta_{c,d,e,f} = 1$, (a,c) $\mathrm{g^{(2)}(0) = 0}$, (b,d) $\mathcal{I} = 1$.