A. Simulations of the NARP scheme

The results of numerical simulations of quantum state dynamics illustrating the efficacy of the NARP scheme for quantum state inversion are shown in Figs. 3(a) and 3(b). These simulations were targeted at the situation of an optically driven single semiconductor QD and used a density matrix approach, taking into account deformation potential interactions with acoustic phonons.7576. Note that our sample is a simple flat wafer, which reduces collection efficiency; however, our scheme could be implemented in practice using a nanowire or other photonic structure to optimize brightness. Figures 3(a) and 3(b) show the occupation of the excited state as a function of pulse area for a range of values of positive pulse chirp for an unfiltered Gaussian spectrum [Fig. 3(a)] and a pulse subjected to spectral filtering using the mask in Eq. (1) with 2δ = 2.1 meV [Fig. 3(b)], referred to as a spectral hole pulse. The corresponding pulse characteristics are shown in Figs. 3(c) and 3(d). For the unfiltered pulse, a transition from the Rabi rotation regime to the adiabatic regime is observed as ϕ″ is increased, consistent with previous work.10,56,66–7210. Y.-J. Wei, Y.-M. He, M.-C. Chen, Y.-N. Hu, Y. He, D. Wu, C. Schneider, M. Kamp, S. Höfling, C.-Y. Lu, and J.-W. Pan, “Deterministic and robust generation of single photons from a single quantum dot with 99.5% indistinguishability using adiabatic rapid passage,” Nano Lett. 14, 6515 (2014). https://doi.org/10.1021/nl503081n56. R. Mathew, E. Dilcher, A. Gamouras, A. Ramachandran, H. Y. S. Yang, S. Freisem, D. Deppe, and K. C. Hall, “Subpicosecond adiabatic rapid passage on a single semiconductor quantum dot: Phonon-mediated dephasing in the strong-driving regime,” Phys. Rev. B 90, 035316 (2014). https://doi.org/10.1103/physrevb.90.03531666. A. Ramachandran, J. Fraser-Leach, S. O’Neal, D. G. Deppe, and K. C. Hall, “Experimental quantification of the robustness of adiabatic rapid passage for quantum state inversion in semiconductor quantum dots,” Opt. Express 29, 41766 (2021). https://doi.org/10.1364/oe.43510968. Y. Wu, I. M. Piper, M. Ediger, P. Brereton, E. R. Schmidgall, P. R. Eastham, M. Hugues, M. Hopkinson, and R. T. Phillips, “Population inversion in a single InGaAs quantum dot using the method of adiabatic rapid passage,” Phys. Rev. Lett. 106, 067401 (2011). https://doi.org/10.1103/PhysRevLett.106.06740169. A. Gamouras, R. Mathew, S. Freisem, D. G. Deppe, and K. C. Hall, “Simultaneous deterministic control of distant qubits in two semiconductor quantum dots,” Nano Lett. 13, 4666 (2013). https://doi.org/10.1021/nl401817670. T. Kaldewey, S. Luker, A. V. Kuhlmann, S. R. Valentin, A. Ludwig, A. D. Wieck, D. E. Reiter, T. Kuhn, and R. J. Warburton, “Coherent and robust high-fidelity generation of a biexciton in a quantum dot by rapid adiabatic passage,” Phys. Rev. B 95, 161302(R) (2017). https://doi.org/10.1103/physrevb.95.16130271. T. Kaldewey, S. Luker, A. V. Kuhlmann, S. R. Valentin, J.-M. Chauveau, A. Ludwig, A. D. Wieck, D. E. Reiter, T. Kuhn, and R. J. Warburton, “Demonstrating the decoupling regime of the electron-phonon interaction in a quantum dot using chirped pulse optical excitation,” Phys. Rev. B 95, 241306(R) (2017). https://doi.org/10.1103/physrevb.95.24130672. A. Ramachandran, G. R. Wilbur, S. O’Neal, D. G. Deppe, and K. C. Hall, “Suppression of decoherence tied to electron-phonon coupling in telecom-compatible quantum dots: Low-threshold reappearance regime for quantum state inversion,” Opt. Lett. 45, 6498 (2020). https://doi.org/10.1364/ol.403590 Once the adiabatic regime is reached, which occurs for ϕ″ ≳ 0.1 ps2 and θ ≳ 2π, the upper state occupation is insensitive to changes in pulse area, a key signature of adiabatic rapid passage and robust inversion. For the spectral hole pulse with ϕ″ = 0, the occupation vanishes in the absence of phonon coupling because the time-integrated Rabi frequency is zero, as discussed previously for the case of unchirped pulses.5353. Z. X. Koong, E. Scerri, M. Rambach, M. Cygorek, M. Brotons-Gisbert, R. Picard, Y. Ma, S. I. Park, J. D. Song, E. M. Gauger, and B. D. Gerardot, “Coherent dynamics in quantum emitters under dichromatic excitation,” Phys. Rev. Lett. 126, 047403 (2021). https://doi.org/10.1103/PhysRevLett.126.047403 As shown in Fig. 3(b), the inclusion of phonons leads to a small but nonzero state occupation because phonons break the spectral symmetry of the driving conditions through the introduction of incoherent dynamics.5353. Z. X. Koong, E. Scerri, M. Rambach, M. Cygorek, M. Brotons-Gisbert, R. Picard, Y. Ma, S. I. Park, J. D. Song, E. M. Gauger, and B. D. Gerardot, “Coherent dynamics in quantum emitters under dichromatic excitation,” Phys. Rev. Lett. 126, 047403 (2021). https://doi.org/10.1103/PhysRevLett.126.047403 The results in Fig. 3(b) show that the use of frequency-swept pulses also serves to break the symmetry. The state occupation increases with an increasing ϕ″. For low ϕ″, the occupation vs pulse area resembles an imperfect Rabi rotation. For ϕ″ exceeding 0.1 ps2, the adiabatic regime is reached. In this limit, for sufficiently large pulse area, the inversion process is robust to changes in pulse area for both the unfiltered pulse and the spectral hole pulse. Our simulations also indicate the robustness of NARP to laser detuning (Fig. 4), as demonstrated previously for ARP.6666. A. Ramachandran, J. Fraser-Leach, S. O’Neal, D. G. Deppe, and K. C. Hall, “Experimental quantification of the robustness of adiabatic rapid passage for quantum state inversion in semiconductor quantum dots,” Opt. Express 29, 41766 (2021). https://doi.org/10.1364/oe.435109We can gain insight into the quantum state dynamics from the energies of the dressed states of the optically driven system (E±), which are shown in Fig. 5(a). Robust inversion occurs for frequency-swept pulses with or without a spectral hole because in both cases, the adiabatic condition for quantum state transfer is satisfied. The introduction of the spectral hole leads to structure in the temporal shape of the pulse, as shown in Fig. 5(b), which has the effect of increasing the threshold pulse area for NARP. Calculations as a function of the hole width (δ) (see Fig. 6) indicate that the primary cause of this increase is the transfer of energy into the wings of the pulse, which reduces the size of the Rabi frequency at time t = 0, thereby reducing the magnitude of the dressed-state splitting at the anticrossing. The adiabatic condition |ΔdΩdt−ΩdΔdt|≪[Ω2+Δ2]32 is then recovered for larger θ, with a threshold pulse area that increases with increasing δ. Nevertheless, for a given value of δ and a sufficiently large pulse area, robust inversion occurs. The corresponding quantum state dynamics using a Bloch vector representation are shown without phonon coupling in Figs. 5(c) and 5(d). For excitation with the spectral hole pulse with ϕ″ = 0, no net excitation occurs due to the zero time-integrated Rabi frequency. For chirped pulse excitation, robust inversion of the quantum emitter is realized for either traditional ARP or NARP, with only a slight modification of the trajectory in the latter case.The results in Fig. 1(b) indicate that the fractional change in the occupation resulting from the impact of phonons diminishes as the chirp is increased. This reflects the use of positively chirped pulses, which suppress LA phonon-mediated transitions between the dressed states within the adiabatic regime at low temperatures.7475. A. J. Ramsay, T. M. Godden, S. J. Boyle, E. M. Gauger, A. Nazir, B. W. Lovett, A. V. Gopal, A. M. Fox, and M. S. Skolnick, “Effect of detuning on the phonon induced dephasing of optically driven InGaAs/GaAs quantum dots,” J. Appl. Phys. 109, 102415 (2011). https://doi.org/10.1063/1.3577963 In Fig. 3(b), the dashed and solid curves coincide for ϕ″ and θ above the threshold for ARP, indicating that phonons have no influence on quantum state dynamics in this limit. Our results therefore indicate that all of the advantages of ARP for optical inversion of quantum emitter systems, including the ability to suppress decoherence tied to phonons and the robustness of the inversion process to fluctuations in the laser source, are maintained for the NARP scheme.

B. Experimental demonstration of quantum state inversion using the NARP scheme

The results of optical control experiments on a single QD using the NARP scheme are shown in Fig. 1(e). The PL intensity vs the square root of the excitation power, which is proportional to the pulse area, is shown for an unfiltered pulse with zero chirp (Rabi, blue symbols), for an unfiltered pulse with ϕ″ = 0.15 ps2 (ARP, red symbols) and for the spectral hole pulse with ϕ″ = 0.15 ps2 (NARP, black symbols). For the unfiltered pulse with zero chirp, a damped Rabi rotation is observed. For excitation by the chirped, unfiltered pulse, the PL intensity saturates at a constant value for pulse areas above the threshold for ARP, as observed in prior experiments on similar QDs.10,66–7210. Y.-J. Wei, Y.-M. He, M.-C. Chen, Y.-N. Hu, Y. He, D. Wu, C. Schneider, M. Kamp, S. Höfling, C.-Y. Lu, and J.-W. Pan, “Deterministic and robust generation of single photons from a single quantum dot with 99.5% indistinguishability using adiabatic rapid passage,” Nano Lett. 14, 6515 (2014). https://doi.org/10.1021/nl503081n66. A. Ramachandran, J. Fraser-Leach, S. O’Neal, D. G. Deppe, and K. C. Hall, “Experimental quantification of the robustness of adiabatic rapid passage for quantum state inversion in semiconductor quantum dots,” Opt. Express 29, 41766 (2021). https://doi.org/10.1364/oe.43510968. Y. Wu, I. M. Piper, M. Ediger, P. Brereton, E. R. Schmidgall, P. R. Eastham, M. Hugues, M. Hopkinson, and R. T. Phillips, “Population inversion in a single InGaAs quantum dot using the method of adiabatic rapid passage,” Phys. Rev. Lett. 106, 067401 (2011). https://doi.org/10.1103/PhysRevLett.106.06740169. A. Gamouras, R. Mathew, S. Freisem, D. G. Deppe, and K. C. Hall, “Simultaneous deterministic control of distant qubits in two semiconductor quantum dots,” Nano Lett. 13, 4666 (2013). https://doi.org/10.1021/nl401817670. T. Kaldewey, S. Luker, A. V. Kuhlmann, S. R. Valentin, A. Ludwig, A. D. Wieck, D. E. Reiter, T. Kuhn, and R. J. Warburton, “Coherent and robust high-fidelity generation of a biexciton in a quantum dot by rapid adiabatic passage,” Phys. Rev. B 95, 161302(R) (2017). https://doi.org/10.1103/physrevb.95.16130271. T. Kaldewey, S. Luker, A. V. Kuhlmann, S. R. Valentin, J.-M. Chauveau, A. Ludwig, A. D. Wieck, D. E. Reiter, T. Kuhn, and R. J. Warburton, “Demonstrating the decoupling regime of the electron-phonon interaction in a quantum dot using chirped pulse optical excitation,” Phys. Rev. B 95, 241306(R) (2017). https://doi.org/10.1103/physrevb.95.24130672. A. Ramachandran, G. R. Wilbur, S. O’Neal, D. G. Deppe, and K. C. Hall, “Suppression of decoherence tied to electron-phonon coupling in telecom-compatible quantum dots: Low-threshold reappearance regime for quantum state inversion,” Opt. Lett. 45, 6498 (2020). https://doi.org/10.1364/ol.403590 For the chirped spectral hole pulse, the exciton inversion also exhibits a saturation behavior. For chirped pulse excitation, the pulse area required to reach full inversion is ∼30% larger for the NARP pulse than the ARP pulse. The findings in Fig. 1(e) are in qualitative agreement with the theoretical predictions in Fig. 3. The observed increase in the threshold pulse area in the experiments was smaller than in the theoretical simulations, likely reflecting the different shapes of A(ω) and associated differences in the pulse temporal structure.