SUPER Scheme in Action: Experimental Demonstration of Red-Detuned Excitation of a Quantum Emitter.

The quest for the perfect single-photon source includes finding the optimal protocol for exciting the quantum emitter. Coherent optical excitation was, up until now, achieved by tuning the laser pulses to the transition frequency of the emitter, either directly or in average. Recently, it was theoretically discovered that an excitation with two red-detuned pulses is also possible where neither of which would yield a significant upper-level population individually. We show that the so-called swing-up of quantum emitter population (SUPER) scheme can be implemented experimentally with similar properties to existing schemes by precise amplitude shaping of a broadband pulse. Because of its truly off-resonant nature, this scheme has the prospect of powering high-purity photon sources with superior photon count rate.

The future of photonic quantum technologies relies on bright, photostable, and on-demand sources of single and indistinguishable photons. To achieve the on-demand character, a deterministic state preparation of the excited state is required. The most prominent scheme for coherent optical control is the Rabi scheme, where a laser pulse tuned to the transition energy, called the π-pulse, inverts the quantum emitter population. As soon as the laser energy is detuned, the inversion fidelity drops drastically.[1] Consequently, all coherent excitation schemes to achieve a high population inversion either have a frequency component at[2−7] or are in average[8,9] resonant with the transition frequency of the quantum emitter. From this picture, a truly off-resonant excitation scheme is not desirable, even though these have the advantage of requiring only spectral filtering instead of challenging methods based on polarization filtering. Surprisingly, it was recently theoretically demonstrated that there exists a swing-up mechanism in the so-called Swing-UP of quantum EmitteR population (SUPER) scheme.[10] The SUPER scheme relies on the coherent coupling of two red-detuned lasers to coherently excite the emitter, while an individual pulse would not lead to any upper-level occupation. Up until now, this scheme existed only as a theoretical possibility. In this Letter, we show that the SUPER scheme works in a simple, yet elegant experiment to excite a quantum emitter, relying on amplitude-shaping of a broadband laser pulse.

As the quantum emitters, we choose semiconductor quantum dots because they have emerged as a promising platform for quantum communication devices with excellent performance characteristics.[11−20] Quantum dots benefit from their excellent photostability, nearly Fourier-limited emission line width and growth technologies that allow easy integration into nanoscale devices.[21−25]

Our results prove that the SUPER scheme is an efficient method to excite a quantum dot to its excited state with the same efficiency as the Rabi scheme. The off-resonant nature of this excitation bears the potential for a wide range of applications where a resonant excitation should be avoided, in particular for using quantum dots as photon sources.

We start by briefly summarizing the idea of the SUPER scheme.[10] We consider a quantum dot as a two-level system consisting of ground |g⟩ and exciton state |x⟩, separated by an energy ℏω0. This system is driven by a pulsed laser encoded in the time-dependent term Ω(t). Within the dipole and rotating wave approximations, the Hamiltonian for this system readsThe SUPER scheme requires two laser pulses that are both red-detuned (Δ1 and Δ2) from the exciton state by several millielectronvolts. In the following, we will always refer to the pulse with the smaller detuning as first pulse, that is, |Δ1| < |Δ2|. Considering a Gaussian-shaped excitation pulse, we define the generalized Rabi frequency as , where Ω is the resonant Rabi frequency of either pulse given at the maximum of the pulse temporal envelope. In the SUPER scheme, one achieves a gradual rise in the exciton population by modulating the Rabi frequency, through the beating of the two detuned pulses. If the difference between the two detunings coincides with the Rabi frequency of the first pulse, that is,, implying the condition |Δ2| > 2|Δ1|, the SUPER mechanism results in a complete population inversion of the quantum emitter.[10]

The experimental implementation of the SUPER scheme relies on frequency-domain amplitude shaping. In the calculation, instead of specifying the single laser pulse parameters explicitly, Ω(t) is obtained by an inverse Fourier transform of the laser spectrum that is multiplied by an amplitude mask to describe the pulse shaping process. Starting point is a Gaussian frequency spectrumwith a spectral full width at half maximum (fwhm) of , centered around a detuning of ℏ(ω – ω0) = −8.4 meV and an integrated resonant pulse area of α̃ = 26π. The amplitude function is approximated by two normalized Gaussian functions

This results in two contributions to the resulting spectrum at ω with variable transmission Ĩ. From this, we define the detunings as Δ = ℏ(ω – ω0). The spectral width is chosen to 0.2 meV for all calculations. To account for experimental imperfections of the pulse-shaping process, a transmission of 5% between the two peaks is added. Note that the transmission Ĩ is for the electric field in contrast to the experimental scenario where I (called transmissivity) is the intensity, that is, Ii corresponds to (Ĩi)2. A representative amplitude-shaped spectrum of the intensity is shown in Figure a. To calculate the exciton occupation, we derive the equations of motion from the Hamiltonian using the von-Neumann equation, which is then numerically integrated.[10] Because the phonon influence on the SUPER scheme has been shown to be weak,[26] we neglect phonons in the present calculations. In Figure b, we show an exemplary time dynamics at Δ1 = –4.9 meV, Δ2 = −11.12 meV and I1 = 0.5, I2 = 0.96.

Figure 1

Concept of SUPER scheme: (a) Spectrum of the broadband excitation pulse (red dashed curve) and an exemplary pulse pair (blue solid curve) after spectral shaping with transmissivities I1 = 0.5 and I2 = 0.96 at detunings Δ1 = −4.9 meV and Δ2 = −11.12 meV. Black arrow denotes the position of the targeted exciton state. (b) Calculated dynamics of the exciton population using the shaped spectrum. Inset shows the energy level scheme with detunings. |g⟩ , ground state, |x⟩, exciton state.

To experimentally obtain the two red-detuned pulses with appropriate detunings, we implement frequency-domain amplitude shaping with a folded 4f pulse shaper equipped with a programmable spatial light modulator (SLM, CRi, 128 pixels). The experimental setup is summarized in Figure . A broadband Ti:sapphire laser (MIRA 900, Coherent) produces 120 fs long, Gaussian-shaped pulses with the central wavelength of 802 nm, pulse energy of ∼4 nJ and a peak power of ∼12 kW. The collimated laser beam that enters the 4f pulse shaper is first dispersed by a blazed diffraction grating (1800 lines/mm, Newport), and then focused onto the SLM with a curved mirror (f = 500 mm), such that each pixel is assigned a narrow laser spectral window of ∼0.09 nm (0.17 meV in energy, for details see SI). The amplitude-shaped laser beam travels the same path back and leaves the pulse shaper toward the cryostat with the quantum dot. The inset in Figure shows a representative amplitude-shaped spectrum.

Figure 2

Sketch of the experimental setup: The laser beam is guided to a folded 4f pulse shaper equipped with a spatial light modulator (SLM) for amplitude-shaping the broadband spectrum (gray shade, inset). Incoming and outgoing beams are shown as separate paths for clarity. The shaped pulse-pair is directed with a beam splitter (BS) to the cryostat that holds the quantum dot at 8 K. Emitted photons from the quantum dot are sent through a bandpass filter (BPF) and a notch filter (NF) to either the spectrometer or with an additional fiber beam splitter (FBS) to the superconducting nanowire single-photon detectors (SNSPD) to record the photon coincidences. On the basis of above-band excitation, the quantum dot exciton emission line (X, green) is identified. An exemplary pulse-pair with detunings Δ1 (orange) and Δ2 (red) is also shown.

To characterize the detunings of the two pulses with respect to the exciton line, we first performed above-band gap excitation of the quantum dot. The resulting emission spectrum is shown as a green curve in Figure . A sharp exciton-emission line (X) is identified at 798.66 nm, surrounded by phonon sidebands and substrate emission. Based on this, we can choose the detunings Δ1 and Δ2. Figure also shows the unshaped laser spectrum as gray-shaded area. Its sharp edge on the high energy sideis due to a razor blade mounted behind the SLM to suppress the laser spectral tail that is resonant with the quantum dot emission line. The intensities of both pulses can be tuned individually by varying the transmissivities of the SLM pixels from 0 to 1, denoted as I1 and I2. For our experiments, the intensities of the second pulse at Δ2 = −10.6 meV range from 0.7 μW (I2 = 0) to 18.8 μW (I2 = 1) while the first pulse intensity I1 was fixed to 15.5 μW, measured at the cryostat window.

Our sample consists of GaAs/AlGaAs quantum dots obtained by the Al-droplet etching method.[27,28] The dots are embedded in the center of a λ-cavity placed between a bottom (top) distributed Bragg reflector consisting of 9(2) pairs of λ/4 thick Al0.95Ga0.05As/Al0.2Ga0.8As layers. The sample is kept in a closed-cycle cryostat with base temperature 8 K on a three-axis piezoelectric stage (ANPx101/ANPz102, attocube systems AG). The shaped pulse pair is focused onto the quantum dot with a cold aspheric lens (NA = 0.77, Edmund Optics) and the emission is collected via the same path backward, through a combination of a bandpass filter (808 nm, fwhm 3 nm, Layertec) and a notch filter (BNF-805-OD3, fwhm 0.3 nm, Optigrate) to a single-photon sensitive spectrometer (Acton SP-2750, Roper Scientific) equipped with a liquid nitrogen-cooled charge-coupled device camera (Spec10 CCD, Princeton Instruments) or superconducting nanowire single-photon detectors (SNSPD, Eos, Single Quantum). For estimating the wavelength-independent background, we integrate the photon counts on the high-energy sideband of the exciton emission peak (for a detailed discussion, see Figure S1 in SI).

To measure the SUPER scheme, we fix the detuning and the transmissivity of the first pulse to Δ1 = −4.9 meV and I1 = 0.5, respectively. We then vary the transmissivity of the second pulse (I2), and record the emitted spectra for various detunings (Δ2). The results are displayed as a two-dimensional map in Figure a, as a function of Δ2 and I2, where the color scale denotes the integrated photon counts. Every automated transmissivity scan (that is, individual columns in Figure a) records emitted spectra for 100 different I2 values, and the experiment is performed for 11 different Δ2 values. All the data shown are background-corrected as described in Figure S1 in SI. At zero intensity of the second pulse, that is, I2 = 0, only negligible photon counts are recorded, implying that no excitation occurs in the absence of the second pulse, even if the first pulse is present. By increasing I2 from 0 to 1, the exciton counts gradually increase, specifically for detunings around Δ2 = −10 to −11 meV. We find a clear region of high photon counts demonstrating that the exciton state becomes occupied by the two-pulse excitation. To validate further that the exciton state only gets populated when both pulses are switched on, we set I1 = 0, and perform the I2 – Δ2 scan, as in Figure a, which does not result in any significant exciton emission (see Figure S3a in SI).

Figure 3

Exciton population achieved by the SUPER scheme: (a) Measured photon counts at exciton emission energy as a function of the detuning Δ2 and the transmissivity I2 of the second pulse. The first pulse is fixed to Δ1 = −4.9 meV and I1 = 0.5. The scale shows the integrated exciton counts after correcting for background. The red dot indicates the parameters used in the photon quality experiment (Figure ). (b) Theoretically calculated exciton (X) population based on a two-level system. (c) Vertical line-cuts through the 2D map for Δ2 = −10.5 meV (blue), –10.6 meV (red), and −10.9 meV (green). The dashed red line indicates the parameters at which the photon quality measurements are performed.

Figure 4

Scope of SUPER scheme: (a) Measured photon counts at the exciton-emission energy (red crosses) under SUPER excitation in contrast to resonant TPE (blue circles). The x-axes values show corresponding power measured with a 1% beam sampler near the cryostat window. (b) Quantum dot emission spectra under TPE (top panel) and SUPER excitation (bottom panel). The TPE emission spectrum shows residual laser scattering and the SUPER emission spectrum shows the first detuned pulse. (c) Single photon characteristics under SUPER excitation as shown by g(2)(0) = 0.06(1). The dark green dots show the measured data, while the orange curves denote the fit.

Therefore, we conclude that under the action of two pulses below the absorption edge of the quantum dot an excitation via the SUPER scheme has taken place. The calculated dynamics of the two-level system under the red-detuned two-pulse excitation is shown in Figure b. The experimentally observed high exciton occupation at Δ2 ≈ −10.5 meV with a diagonal trend toward larger Δ2 and I2, shows excellent agreement with the theoretical results. The calculated maximum exciton occupation is ∼97% in the considered parameter window. For both experiment and theory, the condition that |Δ2| > 2|Δ1| holds.

Figure c shows line plots of the measured exciton occupation for Δ2 = −10.5, −10.6, and −10.9 meV featuring another interesting behavior: for the largest detuning Δ2 = −10.9 meV (green line), we find that the exciton counts increase monotonically with increasing I2. For Δ2 = −10.6 meV (red line), we find an increase in exciton counts up to I2 = 0.64, after which it decreases again. The most striking observation is for Δ2 = −10.5 meV (blue line), which shows close to 1.5 oscillations from I2 = 0–1 with a maximum at I2 = 0.4 and a minimum at I2 = 0.7. All these findings provide compelling evidence that the recorded exciton emission is due to the coherent excitation with two red-detuned pulses.

Following the experimental verification, here we discuss how the SUPER scheme compares to other schemes and its scope for quantum technologies. While a detailed comparison with all existing schemes goes beyond the scope of this paper, we investigate a different dot in the same sample under resonant two-photon-excitation (TPE) and SUPER excitation conditions. To perform TPE, we tune the excitation wavelength to the biexciton transition by shifting the amplitude mask in the SLM. The integrated photon counts at the exciton-emission energy obtained by the TPE (Figure a, blue circles) show coherent Rabi oscillation, as has been observed in similar works.[29] Most importantly, the maxima of both oscillations coincide, clearly demonstrating that SUPER reaches the same efficiency as TPE. Furthermore, in Figure b we show the emission spectra of the quantum dot under TPE (top panel) and SUPER excitation (bottom panel). The TPE spectrum shows the exciton and biexciton emission peaks in addition to the scattered laser energy, while the SUPER spectrum shows the exciton emission peak and the first detuned pulse. As expected, the exciton emission lines in both spectra coincide. Notably, the first detuned pulse in SUPER is clearly distant from the biexciton energy and has no chance of exciting any transition other than the targeted exciton state.

Furthermore, we verify that the SUPER scheme can be used to generate single photons. For this, we choose excitation parameters yielding maximal occupation (indicated by the red dot in Figure ), that is, we set Δ1 = −4.9 meV, I1 = 0.5, Δ2 = −10.6 meV, and I2 = 0.64. We then measure the single-photon characteristics in a Hanbury Brown and Twiss (HBT) setup. The results are displayed in Figure b. We achieve a g(2)(0) = 0.06(1), which is a very promising result toward the goal of producing high quality single photons, considering that the experiments are performed at T = 8 K. Under s-shell resonant excitation, we observed a g(2)(0) = 0.016[30] on the same quantum dot. We find that the recorded g(2)(0) under SUPER is slightly higher than under s-shell resonant excitation due to the laser scattering background, considering that the excitation power in SUPER is much higher compared to s-shell resonant excitation. We are, however, confident that scattered laser light can be suppressed better with moderate experimental effort.

It is also worthwhile to discuss SUPER in comparison to existing resonant or near-resonant excitation schemes.[7] Among those, coherent schemes include Rabi rotations,[2,3,31,32] chirped excitations exploiting the adiabatic rapid passage effect,[5,6,33−37] and dichromatic excitation.[8,9,38] Preparation of the exciton state can also be achieved by TPE to the biexciton state followed by a timed stimulation of the biexciton-to-exciton transition.[39−41] Although all of these schemes have their own advantages and disadvantages, the superiority of SUPER is that it circumvents the need for polarization filtering and is quite flexible regarding the chosen detuning values. While polarization filtering is also uncalled for in the dichromatic scheme, a clear advantage of SUPER is that both pulses are red-detuned and therefore no higher-lying states of the quantum dot will be directly addressed.

Another group of state-preparation schemes are phonon-assisted processes,[19,27,42−46] which require an additional particle, the phonon, to function. Hence, those schemes are incoherent, which might be disadvantageous when preparing superposition states. In addition, the laser pulses in phonon-assisted schemes are blue-detuned. Therefore, SUPER might also be a viable alternative to these schemes.

In conclusion, this work demonstrates that a red-detuned pulse pair can populate the exciton state in a quantum dot relying on the SUPER mechanism. This is astonishing given that a single pulse at these far detunings does not lead to a population inversion. In particular, the excitation below the absorption edge removes the stringent need of polarization filtering. Our simple yet elegant implementation of this new technique through amplitude shaping contributes toward an effortless method for generating high-purity single photons.