An artificial Rb atom in a semiconductor with lifetime-limited linewidth

We report results important for the creation of a best-of-both-worlds quantum hybrid system consisting of a solid-state source of single photons and an atomic ensemble as quantum memory. We generate single photons from a GaAs quantum dot (QD) frequency matched to the Rb $D2$ transitions and then use the Rb transitions to analyze spectrally the quantum dot photons. We demonstrate lifetime-limited QD linewidths (1.42 GHz) with both resonant and nonresonant excitation. The QD resonance fluorescence in the low power regime is dominated by Rayleigh scattering, a route to match quantum dot and Rb atom linewidths and to shape the temporal wave packet of the QD photons. Noise in the solid-state environment is relatively benign: there is a blinking of the resonance fluorescence at MHz rates but negligible dephasing of the QD excitonic transition. We therefore demonstrate significant progress towards the realization of an ideal solid-state source of single photons at a key wavelength for quantum technologies.

Figure 1

Experimental setup. (a) Schematics of the resonance fluorescence setup showing orthogonally polarized excitation and detection. PBS refers to a polarizing beam splitter (PBS). The sample is glued to a piezoelectric transducer (PZT) and mounted onto an xyz-positioning stage. A solid immersion lens (SIL) on the surface of the sample increases the collection efficiency. (b) PL spectrum of a single QD under nonresonant excitation at 633 nm $(I_{\text{NR}}\sim 7$ µW/µ${\mathrm{m}}^2)$. We identify the neutral exciton (X) and a charged exciton (CX) which display narrow linewidths, limited here by the 9 GHz spectrometer resolution. (c) Sketch of the QD layer and an AFM picture of the nanoholes obtained with in situ etching [28].

Figure 2

Resonance fluorescence of the charged exciton, QD1. (a) Resonance fluorescence spectrum in the low power regime $(I_{\text{R}}=16$ nW/$\mu {\mathrm{m}}^2)$. The laser background $(\le 780$ cts/s over the 12 GHz scanning range) is indicated in green. (b) Resonance fluorescence intensity and FWHM as a function of resonant laser power. (c) Frequency tuning of CX showing a linear response to the applied voltage with very little creep over the course of several days. The $D2$ transitions of Rb are indicated as dashed lines: (i) ${}^{87}\mathrm{Rb}$ $F_g=1\to F_e^{{}^{\prime }}$, (ii) ${}^{85}\mathrm{Rb}$ $F_g=2\to F_e^{{}^{\prime }}$, (iii) ${}^{85}\mathrm{Rb}$ $F_g=3\to F_e^{{}^{\prime }}$, and (iv) ${}^{87}\mathrm{Rb}$ $F_g=2\to F_e^{{}^{\prime }}$. (d) Second order correlation of the resonance fluorescence signal. In blue, the detectors' response function (arbitrary units for the $y$ axis) measured with ultrashort laser pulses (5 ps) at the QD frequency. The red line results from a fit using Eq. (1) convoluted with the detectors' response function. All data are obtained in the presence of an additional weak, constant nonresonant laser excitation of $I_{\text{NR}}\approx 0.8$ nW/µ${\mathrm{m}}^2$. The background associated with the nonresonant excitation is smaller than the detectors' dark counts.

Figure 3

Spectroscopy of the Rb $D2$ transitions using QD photons. In (a) QD1 is excited nonresonantly and the CX resonance is swept through the Rb transitions. The solid line is a fit based on the convolution between the atomic transmission spectrum and a Lorentzian line accounting for the spectral width of the QD photons. In (b) CX is driven at resonance in the coherent Rayleigh scattering regime. The solid line is a fit where the QD is modeled as a two-level scatterer with associated resonance fluorescence spectrum (RFS).

Figure 4

Blinking statistics on QD2. Second order correlation measurement of the resonance fluorescence signal of CX as a function of increased nonresonant pump $(I_{\text{R}}=180.5$ nW/µ${\mathrm{m}}^2)$. Solid red lines are fits obtained from Eq. (3).

Figure 5

Hyperfine structure of ${}^{87}\mathrm{Rb}$ and ${}^{85}\mathrm{Rb}$ $D2$ line. (a) Sketch of the allowed hyperfine transitions. (b) Properties of the hyperfine transitions. Frequencies are given with respect to the ${}^{87}\mathrm{Rb}$ transition $F_g=2\to F_e=2$ of angular frequency ${\omega }_{\mathrm{ref}}=2\pi \times 384227848.551$ MHz. Transition strength factors $C_j^2$ are computed for linearly polarized incident light.

Figure 6

Transmission of the Rb vapor cell. The laser intensity is adjusted to the typical QD resonance fluorescence level of 5 kcts/s. The exposure time is 1 s per data point. Raw measurements are normalized using a linear baseline. The solid black line is a fit using Eqs. (A1), (A2), and (A3) with $T=24.8\pm 0.2$ °C.

Figure 7

Sensitivity on the fitting parameters. First row: computed resonant QD spectrum. Second row: absorption spectrum under resonant excitation. Third row: second order correlation function. Open circles correspond to the experimental data.

Figure 8

Decay-time measurements. (a) Nonresonant excitation scheme. (b) Histogram of the QD photons arrival time (8 ps time bins; integration time 2 min). The solid line is a fit using Eq. (C1) convoluted by the measured instrument response $(\mathrm{FWHM}=100$ ps; see inset) and scaled to the signal amplitude, with ${\mathrm{\Gamma }}_{\mathrm{sp}}=2\pi \times 1.7$ GHz and ${\mathrm{\Gamma }}_{\mathrm{c}}=2\pi \times 176$ MHz.

Figure 9

$\text{QD}1g^{\left(2\right)}\left(\tau \right)$ function at long delays. Experimental data (black), and a fit (red) using Eq. (3), with ${\tau }_c=580$ ns and $\beta =0.8$.

Figure 10

Influence of the nonresonant pump on the RF signal. Dashed lines are guides to the eyes.