1 Introduction

Quantum-based approaches towards secure communication technologies are currently important research areas. In the field of semiconductors, self-organized quantum dots (QDs) are thereby of specific importance [1, 2]. As fully quantized systems, they appear as artificial two-level systems with corresponding functionalities like coherent state preparation [2, 3] and Ramsey interference [4]. Appealing applications like quantum repeaters [5] or quantum relays [6] require in particular high-quality sources of entangled photons and high-fidelity quantum operations. In the past, it has been shown that some of the required criteria could be already achieved on the basis of InAs/GaAs QDs within the 900-nm emission band in terms of indistinguishable [7] and entangled photons [8]. Thereby, resonant excitation [9] and coherent state control [2, 3] played an important role for the realization of almost perfect single photon emitters. From applications point of view, it is, however, obvious that future approaches towards long-distance quantum communication require components, which are designed for the use of the low-loss optical windows in optical fibers in the telecom C- and L-bands between 1.53 and 1.625 µm. Although it is basically possible to convert the emission of existing high-quality single photon sources into the telecom bands by the use of nonlinear frequency converters [10], it seems much easier and technologically desirable to develop QD-based single photon emitter directly for the low-loss telecom bands.

Following this idea, people have already engineered and investigated GaAs-based QDs for the 1.3-µm telecom O-band. This includes first experiments on coherent state control [11] and single photon emission [12, 13]. In the 1.5-µm telecom C- and L-bands QDs and quantum dashes on the basis of InAs/InP have been reported on planar substrates [14] and pyramids [15]. The results obtained in the 1.5-µm range by non-resonant optical [16, 17] or electrical [18] pumping have to be combined now with the advanced excitation schemes demonstrated already in the 900-nm range, in order to achieve the aforementioned standards concerning indistinguishability and entanglement. Along those lines, we present here our work on single QD p–i–n photodiodes and our results on the coherent state preparation.

2 Experimental

Our approach toward 1.5-µm emitters is based on molecular beam epitaxy (MBE)-grown QDs and their integration in electric field tunable p–i–n structures, that can be also used for quantitative photocurrent (PC) readout. Optical excitation is performed by non-resonant as well as resonant optical pumping. In the latter case also ps excitation has been performed to demonstrate coherent state preparation.

2.1 MBE growth and diode fabrication

The work presented within this contribution was performed with MBE-grown self-organized InAs QDs. They are deposited on a quaternary In0.53Al0.24Ga0.23As buffer, which is lattice-matched to a (100)-oriented InP substrate. From previous work on the growth of such QDs, it is known that the emission wavelength can be adjusted within a range between 1.3 and 1.6 µm [19]. In the present case, the growth was optimized for a wavelength of 1.45 µm. In this regime a QD surface density of 1010 cm−2 could be obtained. In the low-energy tail of the inhomogeneously broadened QD photoluminescence (PL), single QD spectroscopy became routinely possible beyond 1.55 µm.

The MBE growth of p–i–n diode structures with embedded QDs was performed in the following way (see Fig. 1a): Starting from an undoped InP substrate, a 500-nm-thick n-doped InP layer (Si-doped) with a doping level of 4 × 1018 cm−3 was grown (buried n-layer). On top of this, an undoped quaternary In0.53Al0.24Ga0.23As layer with a thickness of 150 nm was grown as a lattice-matched (to InP) barrier material. The subsequent deposition of lattice-mismatched (3.2 % mismatch) InAs (nominally five monolayers) leads to the formation of self-organized QDs. The QDs are capped by a second InAlGaAs layer, which has also a thickness of 150 nm. Finally, a 500-nm-thick p-doped InP layer (Be-doped) was grown (300/2.5 × 1018 and 200 nm/1 × 1019 cm−3). As result we obtain a p–i–n diode structure with QDs in the center of the i-region. The n- and p-layers are sufficiently high doped to avoid carrier freeze out at liquid helium temperatures.

Fig. 1
figure 1

a MBE-grown layer sequence of the p–i–n diode with integrated InAs QDs. The p-layer is Be-doped with a level of 2.5 × 1018 and 1.0 × 1019 cm−3; the n-layer is Si-doped with a level of 4.0 × 1018 cm−3. b Schematic view of the processed p–i–n mesa-photodiodes with shadow masks and ohmic contact pads

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Afterward, the following technology steps have been performed to finish the sample preparation (see Fig. 1b): Mesa-type diodes with a size of 120 × 300 µm2 have been defined by optical lithography and reactive dry-etching (SiCl4). Subsequently, ohmic p-contacts have been processed by evaporation of a sequence of CrNi/Ge/Au/CrNi/Au (5/5/5/5/200 nm), which has been vacuum-annealed at a temperature of 390 °C for 30 s. After this, ohmic n-contacts have been evaporated with a layer sequence of Ge/Au/Ge/Au (40/40/40/80 nm). Final vacuum-annealing of both contacts has been performed at a temperature of 400 °C for 120 s. An Al shadow mask with a thickness of 40 nm and hole diameter of 2 µm has been placed on top of the mesa-structure to allow for the location and identification of different QDs.

With the fabricated shadow mask mesa-diodes, we obtain low dark currents and we get highly defined access to selected QDs. This allows us to perform reproducible DC photocurrent measurements on single QDs.

2.2 Spectroscopy

For our measurements, the sample was mounted in a low-temperature microscope, which was cooled to liquid helium temperatures. As objective lens we used an aspheric lens with a NA of 0.6. For the PL measurements the sample was non-resonantly excited by a cw semiconductor laser with a wavelength of 910 nm. The PL emission was collected by the same lens and analyzed in a fiber coupled spectrometer, which was equipped with an InGaAs detector. The energy resolution of the spectrometer was 60 µeV. For the case of resonant excitation, a cw single-frequency diode laser with a tuning range from 1500 to 1630 nm was used. A bias voltage (V B ) in the range of 1.5 to −5 V was applied to the diode by a high-resolution voltage source, and the electrical current was measured by a current–voltage converter with sub-pA sensitivity. For the coherent measurements, an optical parametric oscillator delivered tunable ps-pulses with a repetition frequency f of 80 MHz. The spectral full width at half maximum of the pulses was 4 nm, and the autocorrelation width was 1.2 ps. The central wavelength could be tuned from 1500 to 1610 nm.

3 Results and discussion

The experimental results presented in this paper include cw PL and PC measurements as a function of V B , including also the transition region between both regimes.

In the PC regime, we performed further highly resolved spectroscopy to analyse the V B -dependent linewidth and the fine structure splitting. In addition to this, we performed on-resonance ps experiment in order to demonstrate coherent state preparation in terms of Rabi rotations.

3.1 Quantum confined stark effect

In comparison with existing work on single photon emission from nominally undoped InP-based QD structures [17], we concentrate here on QDs, which are embedded in p–i–n structures as described before. Thereby, we can work in a bias voltage range between V B  = −5 V (strong reverse bias condition) and V B  = 1.1 V (flat-band condition). According to the geometry of the p–n junction, the internal electric field F in the intrinsic region is given by the expression:

$$\left| {\vec{F}} \right| = 37\frac{\text{kV}}{\text{cm}} - 33 \times 10^{3} \frac{ 1}{\text{cm}} \times V_{B}$$

In Fig. 2 we show PC and PL data from a single QD, which can be tuned by the quantum confined Stark effect (via V B ) between 1.567 and 1.582 µm. PL emission can be observed down to V B  = −2 V, which corresponds to an internal electric field of about 100 kV/cm. Beyond this point, the PL signal appears to be quenched by tunneling (see Fig. 2b). Between V B  = −2 V and V B  = −1 V, we observe a single emission line, which is attributed to the decay of a neutral exciton X0 in the QD. Above V B  = −1 V we observe a charging regime, in which the emission line first experiences a distinct redshift by about 2 meV and subsequently a further redshift, which is also accompanied by a line splitting. Such a behavior is known from InAs/GaAs QDs, where the formation of single and double charged excitons in tunable Schottky diodes leads to a similar scenario [20]. In the present case of a p–i–n diode, we can, however, not discriminate between electron and hole charging.

Fig. 2
figure 2

Bias voltage-dependent spectroscopic data of a single QD. a High field regime: resonantly excited PC data recorded in the range of large reverse bias. b Low field regime: PL data excited at 910 nm for the same QD at weak reverse bias

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Here we concentrate on the bias voltage regime between V B  = −4.5 V and V B  = −2 V, where PC extraction is dominant. The PC data shown in Fig. 2a show a well-resolved Stark shift with linear and quadratic components. For V B  > −2 V, the PC line extrapolates nicely toward the PL line position. Already evident in this overview data is also the trend that the PC line width clearly increases towards high negative bias voltages.

3.2 Fine structure splitting

To further analyze the fine structure of the QD ground state, we have performed highly resolved PC spectroscopy over the entire bias voltage range between V B  = −4.5 V and V B  = −1.5 V. The investigated range extends from the regime of ultra-short tunneling times to a regime where the tunneling time is larger than the spontaneous lifetime of the QD (onset of PL emission and quenching of PC extraction).

To obtain the data shown in Fig. 3, we have set the excitation wavelength of our tunable cw semiconductor laser in individual steps to the indicated wavelength (from 1592.8 to 1604.0 nm) in order to perform bias voltage sweeps across the X0 resonance. The corresponding tuning behavior, which is a result of the quantum confined Stark effect, is shown in the inset of Fig. 3. Within the displayed range we observe a total shift of about 5 meV, which can be described by a second-order polynom, as expected for a polarizable exciton. The experimentally found tuning characteristics of the resonance energy E versus V B can be parametrized as follows:

Fig. 3
figure 3

Highly resolved PC data (without background correction) of a single QD with fully resolved fine structure splitting. With increasing reverse bias V B , an increasing tunneling rate leads to a pronounced lifetime broadening. The inset shows the tuning characteristics of the QD as a result of the quantum confined Stark effect

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$$E = 780.7 {\text{meV}} + 0.74\frac{\text{meV}}{\text{V}}V_{B} - 0.23\frac{\text{meV}}{{{\text{V}}^{ 2} }}V_{B}^{2}$$

The spectroscopic data shown in Fig. 3 clearly show that the X0 line is split in a doublet with 85-µeV line separation. To avoid excessive power broadening of the transitions, we have performed those measurements at fairly low excitation powers. Under those conditions, we get negligible background signal (not subtracted here), but a finite noise contribution. In some of the shown doublets, a third line may be detectable, whose origin is so far not clear. We tentatively attribute the appearance of such lines to interactions with remote charge fluctuations or to noise. In the regime, where the resonance appears at low reverse bias voltages (V B  = −1.5 V to V B  = −2.5 V), we observe linewidths of the fine structure split components down to 10 µeV. With decreasing bias voltages (V B  = −2.5 V to V B  = −4.5 V), we find a pronounced line broadening, which finally leads to a merging of the fine structure split lines.

To further confirm the interpretation in terms of a fine structure splitting of the ground state, we performed polarization-dependent PC spectroscopy, as shown in Fig. 4. The fine structure splitting of a QD ground state in an asymmetric confinement potential is caused by electron–hole exchange interaction [21], which leads to a splitting (E FSS) of the ground state of the neutral exciton into linear polarized (and orthogonal oriented) |X >and |Y >components (see inset in Fig. 4).

Fig. 4
figure 4

Polarization analysis of the fine structure split doublet. π x , π y , and 45° polarizations have been applied for selective excitation of the low energy line, high energy line, or both lines. The resonance lines have been fitted by Lorentzians

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Experimentally, we find a doublet of Lorentzian-shaped lines (splitting 85 µeV), which show orthogonal linear polarizations (see Fig. 4). This clearly demonstrates that the observed splitting can be in fact interpreted as the fine structure splitting of the neutral exciton ground state. It should be further remarked, that the alignment of the found π x and π y polarization directions coincides with the [0–11] and [011] crystal axis.

3.3 Linewidth and dephasing time

On the basis of our interpretations with regard to a fine structure split ground state and Lorentzian-shaped resonances, we are further able to extract the spectral width of the observed resonances over almost the entire bias voltage range shown in Fig. 3. Fitting the experimentally observed resonances by Lorentzians, we obtained the data for the bias-dependent linewidth Γ shown in Fig. 5a. With decreasing bias voltage, the linewidth increases from about 10 µeV to more than 250 µeV. This roughly exponential increase is caused by the aforementioned increase in the tunneling rate with increasing internal electric fields, which finally causes severe lifetime broadening.

Fig. 5
figure 5

a Bias voltage-dependent linewidths as extracted from the data shown in Fig. 3 by Lorentzian fits. b Corresponding dephasing times (see text)

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From the linewidth data shown in Fig. 5a, we have also calculated respective dephasing times, which are important in particular for coherent manipulations in terms of Rabi rotations, as shown later on. For a diode structure with PC extraction as used here, the decay of population can either appear by spontaneous emission (rate γ R ) or by the field-induced ionization of an exciton (followed by charge tunneling, rate γ T ). The inverse of the total rate of population loss γ total is given by the sum of the inverse rates of those two processes:

$$\frac{1}{{\gamma_{\text{total}} \left( F \right)}} = \frac{1}{{\gamma_{R} }} + \frac{1}{{\gamma_{T} \left( F \right)}} = T_{1} \left( F \right)$$

Our experimental data for the linewidth Γ and its electric field dependence is dominated by this combined mechanism of population decay, which is given by the T 1 time. From the measured linewidth we calculate the dephasing time T 2 according to \(T_{2} \left( F \right) = 2T_{1} \left( F \right) = \frac{2\hbar }{{\varGamma \left( {\text{F}} \right)}}\).

For an assessment of the available dephasing times as shown in Fig. 5b, one has to compare those values with the pulse width of the ps excitation source used for coherent state control. It appears that our 1.2-ps-wide pulses are below the dephasing time of the QD in the entire V B -regime.

3.4 Rabi rotation

From earlier work on InAs/GaAs QDs, it is well known that a resonantly driven single exciton system can be successfully described as a two-level system. For resonant cw excitation, the basic effects of nonlinear saturation and power broadening have been observed [22]. For ps excitation also Rabi rotations have been demonstrated [3]. The special case of π-pulse excitation has been recently also used very successfully as excitation scheme for high-quality single photon sources and sources for indistinguishable photons [7, 8]. It is expected that future single photon sources for the telecom bands will also benefit from π-pulse excitation.

As a first step towards this goal, we have performed Rabi flopping experiments on single QD in photodiodes. Thereby we take advantage from PC detection, which can provide a truly quantitative measurement of the obtained occupancy. As shown schematically in Fig. 6a, ps π-pulse excitation will result in the ideal case in a creation of a one-exciton occupancy. For sufficiently high bias voltage V B , the exciton will be ionized and can be hence detected as discrete charge flow in an external circuit. For a π-pulse repetition frequency f, we obtain a deterministic PC of \(I = f \times e\), where e is the elementary charge [3]. A comparison of this ideally obtainable current with experimentally obtained values provides therefore an absolute measure of the success rate of the coherent state preparation.

Fig. 6
figure 6

a Schematic view of the QD photodiode under π-pulse excitation with repetition frequency f. Each π-pulse is creating an exciton, which contributes to the PC after ionization. The PC in the external circuit is given by I = f × e. b Measured Rabi rotations as a function of pulse area (see also text). An incoherent background signal (blue solid line) has been subtracted from the measured data points (black crosses). The red dashed line shows ideal Rabi rotations

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To obtain this information, we have performed resonant ps PC experiments with the aforementioned optical parametric oscillator. The measurements have been performed in a bias voltage range between V B  = −2.6 V and V B  = −3.6 V, which extends from a low field regime with still incomplete tunneling to a high field regime with increased dephasing (see Fig. 5b). The best conditions for PC extraction have been found in a region around V B  = =−3.1 V, where the QD resonance appears at a wavelength of 1594.1 nm. For this condition we observe well-developed Rabi rotations with increasing pulse area. We find a pronounced PC maximum for a pulse area of π, followed by clear minimum at 2π. The dashed red line in Fig. 6b indicates the PC, which we would expect for an ideal two-level system. The solid blue line represents the incoherent background contribution of the PC, which has been subtracted from the original data (linear in power, quadratic in pulse area, caused by stray light absorption within the whole mesa-structure). Compared to the maximum possible PC for π-pulse excitation (\(I = f \times e = 12.8 {\text{pA}}\)), we observe a peak value of about 12 pA in our experiment. This means, that the sequence of coherent state preparation followed by charge extraction via tunneling could be performed with a success rate of more than 93 %. The small deviation from the ideal case could be caused either by an incomplete state preparation, which may be caused by the finite dephasing rate, or by radiative (or even non-radiative) recombination, which competes with PC extraction.

4 Conclusion

We have fabricated InP-based p–i–n photodiodes containing self-organized InAs QDs with emission wavelength in the telecom C- and L-bands. In bias voltage-dependent experiment we have been able to investigate relevant system parameters like the fine structure of the ground state, the tuning behavior, and the linewidth on the single QD level. In ps measurements we have further demonstrated efficient coherent state preparation via Rabi rotations.