Indistinguishable and efficient single photons from a quantum dot in a planar nanobeam waveguide

We demonstrate a high-purity source of indistinguishable single photons using a quantum dot embedded in a nanophotonic waveguide. The source features a near-unity internal coupling efficiency and the collected photons are efficiently coupled off chip by implementing a taper that adiabatically couples the photons to an optical fiber. By quasiresonant excitation of the quantum dot, we measure a single-photon purity larger than $99.4\%$ and a photon indistinguishability of up to $94\pm 1\%$ by using $p$-shell excitation combined with spectral filtering to reduce photon jitter. A temperature-dependent study allows pinpointing the residual decoherence processes, notably the effect of phonon broadening. Strict resonant excitation is implemented as well as another means of suppressing photon jitter, and the additional complexity of suppressing the excitation laser source is addressed. The paper opens a clear pathway towards the long-standing goal of a fully deterministic source of indistinguishable photons, which is integrated on a planar photonic chip.

Figure 1

Two-photon interference experiment on a QD embedded in a tapered nanobeam waveguide. (a) Sketch of the device. (b) Calculated $\beta$ factor for the two dipole orientations along the $x$ and $y$ axes of the nanobeam waveguide as a function of distance from the waveguide center along the $y$ axis. (c) Layer structure of the wafer used for sample fabrication, where the intrinsic layer in the middle of a p-i-n diode contains InGaAs QDs. (d) Scanning-electron micrograph of the waveguide sample with adiabatically tapered outcouplers. The emitted photons are collected by a lensed single-mode fiber. (e) Scanning-electron micrograph of the waveguide sample terminated by a circular grating outcoupler guiding the emitted photons out of plane. (f) Schematics of the experimental setup to measure the indistinguishability of single photons consecutively emitted with variable time delay $\mathrm{\Delta }t$. The photoluminescence of the QD is tuned via the applied electric field. The emitted photons are collected with a lensed fiber and sent to a HOM interferometer for correlation measurements. HWP, half-wave plate; QWP, quarter-wave plate; LP, linear polarizer; PBS, polarizing beam splitter; APDs, avalanche photodiodes.

Figure 2

Single-photon emission from an electrically controlled QD in device A under pulsed $p$-shell excitation at $4.2\mathrm{K}$. (a) Photoluminescence spectrum of the QD emitting at $907.4\mathrm{nm}$ at $0.46-\mathrm{V}$ bias [indicated by the white dashed line in (b)]. The width of the emission line is limited by the resolution of the spectrometer. (b) Photoluminescence map of the QD vs the applied voltage measured at an excitation level of $80\%$ of the saturation power. An extra line from the same QD is identified at a lower voltage and the pair most likely is the $X^0$ and $X^{+}$ transitions. The circularly polarized $X^{+}$ couples less efficiently to the nanobeam waveguide resulting in a weaker optical signature than $X^0$. (c) Intensity-correlation histogram from the QD under $p$-shell excitation on a logarithmic scale. Nearly ideal single-photon emission is demonstrated by the vanishing multiphoton probability at zero time delay $g^2\left(0\right)<0.006$. The inset shows the data in (c) on a linear scale.

Figure 3

Recorded correlation histograms in the HOM interferometer of device A for a successive time separation of emitted photons of $2.7\mathrm{ns}$ (a) and $13\mathrm{ns}$ (b), respectively, measured at $4.2\mathrm{K}$ and at $0.8P_{\mathrm{sat}}$ excitation power. The data points present the raw data without any background correction after integration over 2.5 and $1\mathrm{h}$, respectively. We note that the outcoupling and detection efficiency was not optimized in this experiment. The red line displays the modeling of the data. The visibility $V$ is extracted by fitting the data with the convolution of a single-exponential decay (QD decay) and a Voigt function (photodetector response); see Appendix pp1. (c) Measured temperature dependence of the visibility for the two time separations. The error bars are calculated by error propagation of the fitted parameter errors. The curves are obtained from the theory presented in Ref. [32], and for spherical QDs of radii 2, 3, and $4\mathrm{nm}$ [33, 34] and corresponding hole (electron) energy splitting between $s$ and $p$ shell of 15, 20, and $30\mathrm{meV}$ (30, 40, and $60\mathrm{meV}$) [35, 36] denoted by the dashed, thin solid, and thick solid lines, respectively.

Figure 4

Taper shape and properties extracted from the finite-element method simulation of a 160-nm-thick GaAs waveguide surrounded by air. (a) Taper profile (width as a function of length) obtained from the adiabatic rule with $\alpha =1$ to emphasize the shape. Inset: A fragment of a scanning-electron micrograph of a fabricated taper with $\alpha =10$. (b) Mode overlap between the waveguide mode and a Gaussian distribution of $2.5-\mu \mathrm{m}$ mode-field diameter (green dotted curve). The maximum mode overlap serves as a guideline for the optimal taper width. The effective index as a function of the waveguide width (blue points) illustrates when the optical mode is fully leaked out into air (at a width of $\lesssim 150\mathrm{nm}$).

Figure 5

Efficiency of a single-photon source with no electrical gates (device B). (a) Autocorrelation function at zero time delay $g^2\left(0\right)$ vs excitation power measured in units of the saturation power $P_{\text{sat}}$. (b) Raw count rate on an avalanche photodiode as a function of excitation power. A count rate of up to $2\mathrm{MHz}$ is observed, where about half of it stems from the QD.

Figure 6

Coincidences histogram of the HOM interference data recorded on device C under quasiresonant excitation for a successive time separation of emitted photons of $\sim 13\mathrm{ns}$, measured at $1.7\mathrm{K}$ and at $P_{\mathrm{sat}}$. The data points present the raw data without any background correction. The fit of the experimental data to theory is shown by the red line.

Figure 7

HOM correlation histograms of device C in the case of strict resonant excitation with $100-\mathrm{ps}-\mathrm{long}$ pulses at $0.8P_{\text{sat}}$ (a) and with continuous-wave excitation at $0.5P_{\text{sat}}$ (b). The operation temperature of the experiment is 1.58 K. The fit of the experimental data to theory is shown by the red line.

Figure 8

Resonance fluorescence of a quantum dot vs laser frequency detuning. The data are recorded at a power of $0.2P_{\text{sat}}$ at $1.58\mathrm{K}$. The resonance frequency $\nu =325.457\mathrm{THz}$ corresponds to a wavelength of $921.14\mathrm{nm}$. The solid line is a Lorentzian fit to the data with linewidth $\mathrm{\Gamma }=1.12\pm 0.03\mathrm{GHz}$. The weak peak on the lower-energy side stems from another QD dipole weakly coupled to the waveguide.

Figure 9

The measured instrument response function (IRF) of the Hanbury Brown and Twiss setup fitted with both a Voigt (purple) and a Gaussian (orange) function using the Poisson MLE described in the text. The Voigt function with its broader tail provides a superior fit to the line shape of the IRF evidenced by the smaller ${\chi }_{\mathrm{MLE}}^2=2.3$ vs 5.7 for the Gaussian fit.

Figure 10

Two-photon coincidence data at $4.2\mathrm{K}$ for $2.7-\mathrm{ns}$ (a) and $13-\mathrm{ns}$ (b) path delay. The peaks are fitted with either double-sided exponentials convoluted with the measured instruments response (solid purple) or a Lorentzian (dashed red) by optimizing the Poisson MLE. The corresponding reduced residues for each fit are shown below the figures.