1. Introduction

Photo-neutralization is the name given to a technique that stabilizes a quantum dot environment using an off-resonant light source [1]. Since it is not possible to grow semiconductors without defects or impurities, a possibility to stabilize the environment is desirable. Photo-neutralization has been shown to be a necessity to achieve resonant excitation [2,3] without electrical bias and, as in our case, it can be used to increase the efficiency of the excitation. While in previous work continuous wave (CW) resonant excitation of the exciton was studied, we present a study of the effects of photo-neutralization on the efficiency and coherence using pulsed two-photon resonant excitation of the biexciton. Coherence [4] and entanglement [5] are essential for possible future quantum networks [6]. Further, resonant two-photon excitation is necessary to generate entangled photon pairs with high probability [7–9] and it improves the quality of polarization entangled photon pairs [8,10]. An additional desired feature is high extraction efficiency [11,12] to extract all of the generated photons out of the device. Not only entangled photon pairs [13–15] are of interest but also single photons, because they are a key technology for quantum information applications [16]. Therefore, a lot of studies investigated the resonant generation of single photons from quantum dots [2,8,17,18]. The resonant excitation of the quantum dot creates the possibility to coherently control the quantum dots state and to improve the indistinguishability of the emitted photons [19]. Nevertheless, in this study we do address the excitation of the biexciton state, because we are primary interested in the generation of photon pairs. In particular, we investigate the influence of photo-neutralization on the coherences of the system in a pulsed two-photon resonant scheme, which is capable of generating biexcitons inside a quantum dot with very high probability [20].

With a simple interference measurement, we demonstrate that photo-neutralization does not negatively influence the coherence of the photon. Nor does it influence the coherence of the excitation process when exciting the system resonantly to the biexciton by exploiting pulsed two-photon excitation. The latter is probed here using time-bin entanglement [21]. Usually, time-bin entanglement is used to distribute entanglement over large distances in fiber networks [22,23], but the amount of generated entanglement can also be used as a method to probe the coherence of the excitation process and the posterior free state evolution in the system [20].

2. Methods

The investigated sample contains low density (10 μm⁻²) self-assembled InAs quantum dots in GaAs, embedded in a 4 − λ planar micro-cavity. The micro-cavity is created by two distributed Bragg reflectors (DBR), where the lower DBR consists of 15.5 alternating layers of AlAs and GaAs and the upper mirror consists of 10 pairs. The sample was held at a stabilized temperature of 4.8(1) K. The unintentional background doping is likely in the 10¹⁴ cm⁻³ range. The excitation light was derived from a pulsed, tunable 82 MHz Ti:sapphire laser with a pulse length of 2 ps. Using a pulse-stretcher, the length of the pulses was adjusted to 4 ps. Thereby, the laser was spectrally narrowed. The laser wavelength was 918.7 nm, which is half the energy of the sum of biexciton and exciton emission energy (see Fig. 1(b)). For photo-neutralization we used pulsed blue light obtained from second harmonic generation of the two-photon resonant laser in a 3 mm long BBO crystal. Using a delay stage, we could time the arrival of the photo-neutralization pulse to be in between two subsequent excitation pulses. In particular, it arrived 6 ns before the resonant excitation pulse. The excitation part of the setup is schematically shown in Fig. 2.

 

Fig. 1 (a) Time-bin excitation scheme. The quantum dot is excited with two pulses |early〉 and |late〉 with a defined phase ϕ_P between them. The resulting state is given by Eq. (1) (b) Energy scheme. A two-photon process drives the system coherently from the ground state |g〉 to the biexciton state |b〉. The decay proceeds via the intermediate exciton level |x〉, resulting in a photon cascade.

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Fig. 2 Schematics of the excitation part of the setup. A pulse stretcher is used to modify the pulse length of the two-photon excitation laser to 4 ps. A part of the beam is sampled and frequency doubled with a BBO crystal. This blue light is used as photo-neutralization laser. A delay stage introduces an additional delay τ to control the relative timing between the resonant laser and the photo-neutralization laser. Please note that the time delay for the blue laser is different to the Michelson interferometer used in the analysis. The latter is part of the analysis, which is different for several measurements and is therefore not shown in this schematic.

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3. Quantum dots neutralization

Recently, Nguyen et al. performed studies [1,3] of emission quenching in quantum dots under cw resonant excitation. They showed that the origin of this phenomenon lies in the Coulomb blockade caused by a residual hole. Additionally, they demonstrated that by applying a weak off-resonant laser one can photo-neutralize the quantum dot device and enable resonant excitation.

While in our samples we do not observe as high a level of emission quenching as shown by Nguyen et al. [1,3], we observe an exponential decay in the second-order correlation function measurements (in red in Fig. 3(d)). Additionally, we observe some trion emission (Fig. 3(b)) irrespective of the method of excitation, i.e. above-band excitation and two-photon resonant excitation. Trion emission indicates the presence of a residual charge in the quantum dot. A defect in the vicinity of the quantum dot acts as a hole or electron reservoir [1,3], from where it can be captured by the quantum dot. Therefore, we believe that the observed exponential decay is mainly caused by blinking. Blinking usually denotes that the system is in some inaccessible state for some amount of time, which reduces the observed amount of signal. Another possible explanation for the exponential decay in the second-order correlation function could be an energy shift of the biexciton state caused by the electric field of the trapped charges in the vicinity of the quantum dot, through the quantum confined Stark effect [24,25], which is also known as spectral diffusion [26,27]. While spectral diffusion is also present in our system, it cannot be the most relevant effect. A detuning of the 160 GHz wide laser by 22 GHz would decrease the number of generated photons by less than 10 % [7]. In the quantum dot we studied, the inhomogeneously broadened linewidth, caused by spectral diffusion, is smaller than 5 GHz. Thus, the amount of observed missing signal cannot be described by spectral diffusion. This is contrary to cw experiments, where a small detuning can already bring the laser out of resonance. Therefore, we think that a defect close to the quantum dot causes blinking and is the origin of the exponential decay in the second-order correlation function. We want to note that an exponential decay of the second-order correlation function could be an artifact from too high count rates. This we can exclude by measuring the second-order correlation function with the same count rates in above band excitation (not shown).

 

Fig. 3 (a) Increase of biexciton-exciton coincidence counts obtained from two-photon resonant excitation as a function of off-resonant laser power. (b) Red crosses: emission spectrum under resonant two-photon excitation in the photo-neutralization regime. Green dots: emission spectrum under resonant two-photon excitation without photo-neutralization laser. Blue line: photo-luminescence caused by off-resonant laser alone. The line in red and green is only a guide for the eye. (c) Time resolved decay of the exciton photon vs. time. In green dotted: only resonant two-photon excitation. The very fast rising slope is below our time resolution and the time to the maximum is due to the biexciton decay, which is filling the exciton. In blue: excitation caused by the off-resonant laser alone. (d) Second-order correlation function measurement performed on biexciton photons. The data plotted in red dashed was obtained in photo-neutralization regime.

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4. Results

To fully describe the influence of the off-resonant laser on the system, we performed various experiments. These include measurements of the photon generation efficiency, influence on the spectrum, influence on the lifetime, influence on the multiphoton contribution, influence on the coherence of the emitted photons, and the influence on the coherence of the excitation process. Figure 3(a) shows the effect of the photo-neutralization laser on the photon generation efficiency. Here, we increased the power of off-resonant laser while keeping the two-photon resonant laser at a fixed power level. The photon generation efficiency increases dramatically up to about 20 μW of added photo-neutralization laser, where the photon generation efficiency reaches a plateau, see Fig. 3(a). Adding the photo-neutralization laser to the two-photon resonant laser increases the photon generation efficiency of the source by a factor of 1.49(1), where we defined the photon generation efficiency as the number of detected biexciton-exciton pairs. This leads to 70 · 10³ detected pairs in 10 min, compared to 47 · 10³ detected pairs without photo-neutralization. Considering our setup and detection efficiency [9], this results in a pair creation rate of 13 · 10⁶ s⁻¹ instead of 8.7 · 10⁶ s⁻¹. In contrast to previous work on the XX-X cascade [28], where the excitation parameters were optimized using an above band pump, our pump scheme does not suffer from saturation of the exciton, because the biexciton is created resonantly. Thus, with optimized excitation parameters [20], a high probability generation (up to 90 %) of the biexciton is possible.

A photoluminescence spectrum when exciting only with the off-resonant blue laser compared to the emission spectrum under two-photon resonant excitation with the off-resonant laser added can be seen in Fig. 3(b). The photoluminescence caused by the off-resonant blue laser alone is small and the biexciton-exciton pair rate created by the photo-neutralization laser alone is zero, because the blue laser does not create biexcitons at all. Nevertheless, the blue laser is sufficient to create excitons and thus also free charge carriers in the surrounding (see Fig. 3(b)). Due to the high absorbance of GaAs at the used wavelength, the above-band power is much higher than the ones reported in [1,29]. Nonetheless, the power reaching the quantum dot region is about the same. Further, a time resolved measurement of the exciton emission shows that the exciton decay, when excited with the photo-neutralization laser, is much slower (longer rise time) than the normal exciton decay (see Fig. 3(c)). The decay in resonant two-photon excitation is depicted as green dots. The decay obtained from the off-resonant blue pulse, used for the photo-neutralization, without the resonant excitation is depicted as blue solid line. For the photo-neutralization laser only, the fitted function A · (1 − e^−x/t₃) · e^−x/t₁ + c resulted in a level filling time t₃ = 4.8(2) ns and a decay time t₁ = 2.3(1)) ns, compared to t₁ = 1.0(2) ns in two-photon resonant excitation. The slow filling time is caused by the large energy difference between the blue laser and the exciton resonance so that carriers must radiatively decay through a series of states before occupying the ground state. The origin of the significant change of the lifetime (t₁) of the exciton is unclear.

To investigate the influence of photo-neutralization to the emitted photons, we measured the auto-correlation of the biexciton photon with and without the photo-neutralization laser. For this measurement, the emission of the biexciton photon is sent onto a 50:50 beamsplitter, whose outputs are detected by an avalanche photo diode each. The detection of a photon at one of the detectors defines the zero point. The time delay to a photon detected at the other detector is plotted as a histogram. The auto-correlation is shown in Fig. 3(d). The amount of signal at time zero compared to the signal at other times gives a measurement for the multi-photon contribution of the source. The measured g⁽²⁾-values are g⁽²⁾(0) = 0.038(5) for the two-photon resonant excited case and g⁽²⁾(0) = 0.035(3) for the case with blue laser added. Thus, there is no measurable increase in the multi-photon contribution caused by the photo-neutralization laser. Further, in the same figure, it can be seen that the photo-neutralization laser is reducing the blinking. The detection of the second photon in the auto-correlation measurement in Fig. 3(d) is more likely to occur within a short timescale after detection of a (start) photon, which manifests in an exponential decay of the envelope of the second-order correlation function. This can be caused by a defect in the vicinity of the quantum dot which is charging it. The additional charge prohibits the excitation of the biexciton state. Thus the system is in an inaccessible state, which is known as the blinking effect.

Most importantly, we wanted to check the influence of the photo-neutralization laser on the coherences of the system. We first investigate the influence on the emitted photon, and second investigate the influence on the coherence of the excitation process and the free evolution of the state. The latter can be probed utilizing a time-bin entanglement scheme. The observed amount of time-bin entanglement is an indirect measurement of the coherence between the ground state (the vacuum state) and the biexciton state as we will describe below. More details about the coherences in time-bin entanglement can be found in [20].

To measure the coherence time of the photons (g⁽¹⁾), we utilized an unbalanced Michelson interferometer with one variable length arm to introduce a time delay, see Fig. 2. The fixed length arm is mounted on a piezo translation stage to vary the phase of the interferometer. The visibility of the fringe contrast is plotted as a function of time delay in Fig. 4. The data shows a slight improvement of the coherences using photo-neutralization (with 20 μW blue laser), both for biexciton and exciton photon. This could come from a stabilization of the environment due to the additionally created charge carriers. The coherence length can directly be linked to the linewidth of the emission. In our case, where the coherence shows an exponential decay the line shape of the investigated line is Lorentzian. The connection between coherence time and linewidth is $t_2=\frac{1}{\pi \mathrm{\Delta }\nu }$, where Δν is the linewidth. If the coherence time would show a Gaussian shape, the line shape would also be Gaussian. Further, the connection between coherence time and linewidth would be $t_2=\sqrt{\frac{2\text{ln}(2)}{\pi }}\frac{1}{\mathrm{\Delta }\nu }$.

 

Fig. 4 (a) Coherence of the XX photon excited with two-photon resonant excitation with and without the off-resonant blue photo-neutralization laser. (b) Same as (a) for the X photon.

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To explain how time-bin entanglement was utilized to measure the coherence of the excitation process, we introduce the scheme of time-bin entanglement first. Time-bin entanglement is entanglement of photons in two temporal modes (time-bins): early and late. Such a scheme is depicted in Fig. 1(a). A laser pulse is split into two pulses early and late in an interferometer. These two pump pulses are used to create a pair of photons either in the early or in the late pulse. The early and late pulse need to have a fixed phase relation, because this phase is transfered directly onto the entangled state (see Eq. (1)). In quantum dots resonant excitation is used to coherently drive the system from ground to excited state (see Fig. 1(b)). The coherent excitation transfers the phase of the laser to the quantum dot, which is encoding the pump phase onto the entangled state. The generated entangled state is of the form

To characterize the time-bin entanglement we performed state tomography [30,31]. The fidelity of the reconstructed two-photon density matrix with the maximally entangled |Φ⁻〉 Bell state was found to be F=0.74(3) while the concurrence was C=0.51(7). The same measurement made with photo-neutralization resulted in a fidelity of F=0.76(3) while the concurrence was measured to be C=0.54(6). For both measurements the excitation probability was 6 %, where the excitation probability is defined via the Rabi oscillation of the ground to biexciton transition [7, 20]. In this model the blinking is not considered, which leads to a possible maximum probability of one, although the system might be inaccessible for finite times. 6 % excitation probability resulted in 15.9 detected pairs/s with photo-neutralization instead of 10.7 pairs/s without it. The reconstructed density matrices for the two measurements are shown in Fig. 5. Each measurement point was averaged over 10 min. The density matrix was reconstructed using the maximum-likelihood estimation method. In order to obtain the measurement errors we performed a 100 run Monte Carlo simulation of the data with a Poissonian noise model applied to the measured values.

 

Fig. 5 Reconstructed density matrices for the time-bin entangled photon pair. |e〉 is short for |early〉 and |l〉 is short for |late〉. Indices are not shown for brevity. (a) and (b) Density matrix for two-photon resonant excitation, (c) and (d) with added photo-neutralization laser.

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5. Conclusion

We investigated the method of photo-neutralization in the regime of pulsed two-photon resonant excitation of the biexciton. Thereby, we showed that optical neutralization of the quantum dot neither degrade the coherence of the photons, nor the amount of time-bin entanglement, which can be used as a measure for the coherence of the excitation process. Instead, photo-neutralization can increase the efficiency of the source.