Slow and fast single photons from a quantum dot interacting with the excited state hyperfine structure of the Cesium D1-line

Abstract

Hybrid interfaces between distinct quantum systems play a major role in the implementation of quantum networks. Quantum states have to be stored in memories to synchronize the photon arrival times for entanglement swapping by projective measurements in quantum repeaters or for entanglement purification. Here, we analyze the distortion of a single-photon wave packet propagating through a dispersive and absorptive medium with high spectral resolution. Single photons are generated from a single In(Ga)As quantum dot with its excitonic transition precisely set relative to the Cesium D₁ transition. The delay of spectral components of the single-photon wave packet with almost Fourier-limited width is investigated in detail with a 200 MHz narrow-band monolithic Fabry-Pérot resonator. Reflecting the excited state hyperfine structure of Cesium, "slow light" and "fast light" behavior is observed. As a step towards room-temperature alkali vapor memories, quantum dot photons are delayed for 5 ns by strong dispersion between the two 1.17 GHz hyperfine-split excited state transitions. Based on optical pumping on the hyperfine-split ground states, we propose a simple, all-optically controllable delay for synchronization of heralded narrow-band photons in a quantum network.

Figure 1

(a) Experimental setup. Single photons are generated by resonant (894 nm) or non-resonant (532 nm) excitation of an In(Ga)As QD in a liquid-Helium flow-cryostat (1). The emission frequency of the QD exciton is strain-tuned via the piezo voltage V_p. The resonant laser can be scanned over the four hyperfine-split Cs D₁ transitions. The pump laser is strongly suppressed by polarization optics: half-wave plate (HWP), linear polarizer (LiP), polarizing beam splitters (PBS), and quarter-wave plate (QWP). In case of non-resonant excitation, the single photons are further filtered from pump light and photons from other QD states with an 850 nm longpass (LP850) and a 1 nm narrow bandpass (NBP) at 894 nm, before being coupled into a fiber. From there, the QD single photons can be sent to different sections–a temperature controlled, shielded Cs cell (2), a monolithic Fabry-Pérot resonator for spectral filtering (3), and the detection part (4), consisting of a 50/50 beamsplitter (BS), two avalanche photo diodes (APD), and time-correlation electronics. (b) Energy levels of the Cs D₁ line. For most of the experiments the QD emission frequency was centered to ν₀ between the F = 4 → F′ = 3 and F = 4 → F′ = 4 transitions.

Figure 2

Overview of the QD properties. (a) Non-resonantly excited lifetime measurement of the QD exciton. A convolution of an exponential decay and the Gaussian timing instrument response (green) is fit to the data (blue). The resulting deconvoluted decay ∝ exp(−t/1.04 ns) is shown in yellow. Inset: QD spectrum with (green) and without (blue) 1 nm bandpass filter at 894.335 nm. (b) Independent scans of the 894 nm laser over the QD resonance (green) and the Cs D₁ transitions (blue). A Voigt fit (yellow) to the QD exciton spectrum reveals a FWHM linewidth of (2.4 ± 0.2) GHz. (c) The QD exciton emission under non-resonant excitation shows strong anti-bunching (blue data) of $g_{\mathrm{data}}^{\mathrm{(2)}}\mathrm{(0)}=0.19\pm 0.03$ (green), corresponding to $g_{\mathrm{d}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{v}}^{(2)}(0)=0.02\pm \begin{array}{c}0.03\\ 0.02\end{array}$ after deconvolution of the timing jitter (yellow). (d) Absorption of the non-resonantly excited QD photons in Cs vapor at ϑ_Cs = 30 °C. The QD line was scanned over the Cs D₁ spectrum. Fitting a convolution of the simulated Cs D₁ lines (green) and a Voigtian QD spectrum to the transmission data (blue) yields a QD linewidth of (3.6 ± 0.1) GHz under non-resonant excitation, which has an additional Gaussian broadening of about (2.7 ± 0.1) GHz FWHM compared to the resonant scan in (b).

Figure 3

Delay of single photons between the hyperfine-split excited Cs D₁ transitions. (a) The QD exciton emission spectrum (yellow) is tuned in the middle of the F = 4 ground state and both excited states (purple). (b) With rising temperature of the Cs vapor, the group velocity of the single photon is gradually decreased. This is demonstrated in the experiment by later detection events with increasing temperature. Simulations of the pulse transfer in the Cs cell (see Methods) are in excellent agreement with the measurements. The dashed lines are guides to the eye.

Figure 4

Spectrally resolved delay of a single photon. The photon propagates through the 40 °C Cs vapor cell at 40 mm. Only the frequency components of the QD spectrum are detected which pass the Fabry-Pérot filter around its transmission frequency ν_f. The average value for the detection time 〈τ_d〉 of a photon wave packet (green data points) is displayed as the difference to a photon traversing 40 mm of air. See text for details on corrected filter frequency ν_f (blue data points). Frequency components around ν_f = ν₀ of the QD spectrum are delayed, while others near the resonances (dashed vertical lines) at about ±0.6 GHz appear as “fast light” due to pulse distortion. Theory is calculated for Fourier-limited photons (yellow curve), photons of the filter transmission width (green curve), and photons with 384 MHz FWHM (blue curve).

Figure 5

Simulation for optical control of the single-photon delay. (a) The power of a pump laser resonant with the F = 4→F′ = 4 transition (green in inset) controls the effective optical density of the atomic vapor for a single photon of frequency ν₀ via the population of the F = 3 and F = 4 ground states. The gradient of the refractive index (b) and the temporal distribution of a delayed single photon (c) change accordingly. For high laser powers the total transmission (d) of a 192 MHz wide photon approaches 1, but the delay achieved is becoming increasingly small (e).