Electrically-Pumped Wavelength-Tunable GaAs Quantum Dots Interfaced with Rubidium Atoms

We demonstrate the first wavelength-tunable electrically pumped source of nonclassical light that can emit photons with wavelength in resonance with the D2 transitions of 87Rb atoms. The device is fabricated by integrating a novel GaAs single-quantum-dot light-emitting diode (LED) onto a piezoelectric actuator. By feeding the emitted photons into a 75 mm long cell containing warm 87Rb vapor, we observe slow-light with a temporal delay of up to 3.4 ns. In view of the possibility of using 87Rb atomic vapors as quantum memories, this work makes an important step toward the realization of hybrid-quantum systems for future quantum networks.


Sample structure
The LED structure described in the text consists of the layer sequence shown in Figure   S1.

Figure S1
The intrinsic Al0.4Ga0.6As/GaAs quantum dot layer is sandwiched between 160 nm-n-doped and the 85 nm-p-doped GaAs layers. A 10nm GaAs capping layer is included on both the top and bottom of the structure to prevent oxidation. After selective removal of a sacrificial layer, the resulting membrane-light-emitting-diode is intergrated on a PMN-PT substrate by Au-thermocompression-bonding. Then the device is mounted onto an AlN chip carrier providing electrical contacts both to the diode nanomembranes and the piezoelectric actuator. The n-contact on top of the membrane is done by directly contacting the n-doped semiconductor layer with an Al wire via wedge bonding.

Supporting information on time delay produced by Rb cell
To support our interpretation of the delay observed in the second-order autocorrelation measurements shown in Fig.3 of the main text, we replaced the QD electroluminescence with laser pulses and recorded the arrival times of photons traversing the Rb cell at different temperatures.
A mode-locked Ti: Sapphire laser was used for this characterization. After passing the Rb cell and a monochromator (selecting a ~40 µeV-wide spectral window centered on the Rb D 2 lines), the laser pulses were sent to a single-photon detector. From the data shown in Fig. S2 we can see that the overall laser intensity decreases as the cell temperature increases.
In addition there is a second maximum appearing (marked by red vertical segments), which progressively shifts towards long delay times. The second peak is ascribed to slow light for laser frequencies between the D 2 resonances. A portion of the laser spectrum falls outside the resonances and is thus not affected by the Rb gas. Due to the possible 85 Rb impurity which we will discribe later, the D 2 transition state in our cell is even more complex. Therefore, we find the third maximum (marked by black vertical segments) on

Calibration of Rb-cell temperature from transmission spectra
The temperature of the Rb cell is controlled by a proportional-integral-derivative control loop (PID controller). Due to the imperfect heat isolation, the real temperature of the Rb gas does not coincide with the temperature measured at the heater position. To determine the real temperature of the Rb vapor, we thus measured the optical transmission spectra around the Rb D 2 absorption lines at different temperatures and fit them with the simulation calculations.

Experimental measurement
To perform such a high resolution measurement, we sent a 15-nm-broad laser beam through a pulse-shaper with a 0.2-nm-wide transmission window and a Fabry-Perot interferometer (FPI) with a free-spectral range (FSR) of 41.4 μeV (10 GHz). The laser beam comes from a pulsed Ti: Sa-Laser with a repetition rate of 80 MHz and a typical pulse width of the order of 100 fs. The combination of the pulse-shaper and FPI provides a theoretical resolution of 0.28 μeV. In practice, creep of the piezo-stack used in the FPI (which operates in DC mode) deteriorates the resolution. After the pulse shaper and the FPI, the beam passes though a double spectrometer with 1800 l/mm gratings (spectral resolution of ~20 μeV) and is recorded by a liquid-nitrogen-cooled CCD camera. A Lorentzian fit is applied to extract the wavelength and intensity information from the sharp FPI peaks when the FPI is scanned over the whole free spectral range. With this method, we extract the transmission spectra around Rb D 2 lines at 13 different cell temperatures, from 40 to 150 o C. From fig. S3 we can see, the D2 transmission spectra have not only two 2 , but three splits. The third split indicates that, there is some 85 Rb impurity, which has a bit energy shift from 87 Rb D 2 line, inside the cell. 2,3 Theoretically, 85 Rb impurity should introduce two more states, but one of it, which can be found in simulation result on Fig. S3, is merged with 87 Rb splitting in our measurement, due to the deteriorated resolution.

Simulation of the transmission spectra
Since the used cell contains not only 87 Rb but, to a smaller extent, also 85 where at n is the atomic density, λ the wavelength of the transition, τ the lifetime of the excited state V the velocity of the Rb atoms and D ∆ν the Doppler width (both normalized by λ ). The latter is defined as: where T is the vapor temperature and at m the atomic mass. Furthermore the transition strengths ( ) of the hyperfine components are calculate by where I is the nuclear spin and the       indicates the Racah 6j symbol.
The atomic density at n is derived from the vapor pressure. The vapor pressure itself shall obey the ideal gas relations and can thus be described by the Clausius-Clapeyron law.
The material specific parameter to derive the vapor pressure are taken from Refs. 2,3. Finally, the absorption ( ) κ =cκ + 1-c κ , with c as a fitting parameter. The 85 Rb concentration value should be the same for all the 13 measurements. The best strategy would be to find it by fitting all the 13 spectra. Since we noted that the temperature, which best fits the data, does not critically depend on the impurity value c and instrumental broadening Δ, we first determined these two parameters from the experimental data recorded at 70 o C (343K). The reason for choosing the set of data collected at 70 o C data is that we expect the difference between the measured and real temperature to be most pronounced at higher temperatures. Also, the transmission spectrum starts to show clear features at this temperature. Fig. S4 (a) shows the residual (sum of the square roots of the differences between measured and simulated spectra) for Δ=0.8 GHz and 85 Rb concentration 4%. We see that the minimum occurs at 343 K. The simulated spectrum at this temperature is compared to the experimental data in Fig. S4 (b), showing improved agreement compared to the results obtained without Gaussian convolution. From the fitting result, we also conclude that our Rb cell contains about 4% 85 Rb atoms. Fig. S5 shows the fitting results of all 13 measurements,

Fit of the experimental data with the simulated transmission spectra
i.e. the fitted Rb cell temperatures (a) and the corresponding residuals (b).
We see that, while the measured temperature is close to the calculated temperature up to about 80°C, pronounced deviations are apparent at higher temperatures. We attribute this observation to heat losses, which are more pronounced at higher temperatures.