1. Introduction

Quantum information processing [1] such as quantum communication [2] and quantum computation [3] holds promise for the solution of many intractable problems in information technology. One of the promising candidates for the implementation of the quantum information processing devices is a coherent, optically driven, semiconductor quantum dot (QD) system since the system enables very fast operation of the elementary unit of quantum information — a qubit [4–10]. Here we propose and demonstrate a coherent optically driven QD system operating at a telecommunication wavelength. The telecom-band photons have attracted much attention as a prominent candidate for various quantum-information-processing applications [11]. It allows using low-loss optical fibers and various fiber optic devices, which helps in creating a sophisticated high-power optical pulse system required for driving multiple quantum gate operations in the coherent two level system. We show coherent manipulation of a telecom-band exciton-qubit as a key step toward practical optical implementation of quantum information processing devices.

An exciton in a self-assembled quantum dot (QD) has been a promising candidate for qubits. Single exciton-qubit gates have been achieved in QDs via coherent manipulation of two-level systems through Rabi oscillations [12]. The Rabi oscillations are the sinusoidal time evolution of the population difference in a two-level system that occurs at the Rabi frequency, before the system decoheres. Dephasing times for excitons in self-assembled QDs have been shown to exceed several hundred picoseconds [13], allowing sufficiently high numbers of coherent manipulations with picosecond pulses. Rabi oscillations have been observed in photoluminescence (PL) [4], absorption [5,6], and photocurrent (PC) measurements [7–10]. However, the driving optical pulses have been in the near-infrared range shorter than 1 µm.

One obstacle in creating a quantum computer, particularly for operating multi-quantum gates, is to obtain precise coherent control of the system isolated from the decohering effects of the environment. In the case of exciton-based qubits, qubit control is performed by ultrafast optical pulses, whose time scale is much faster than the decoherence time limited by the exciton lifetime. However, the preparation of such optical pulses becomes more difficult and complicated as the number of qubits increases. In this paper, we propose the use of optical pulses at telecommunication wavelengths for quantum gate operation. The optical pulses are prepared by taking advantage of standard optical fibers, which are currently the most widespread medium for information transfer, and many types of fiber optic devices. Such optical fiber systems provide spatial flexibility, high stability, and easy optical alignment. The fiber optic devices enable flexible beam-splitting and -combining of optical pulses with different wavelengths and controlled time-delays. The system that incorporates such functionalities is highly advantageous, particularly for multi-qubit operations and quantum error corrections. Inevitable attenuation during the pulse controls can be compensated repeatedly for, using fiber amplifiers. Thus, the system can be made more compact, and has high flexibility in the placement of components associated with the building units of qubits. These are important steps towards high-performance quantum networks.

 

Fig. 1. Schematic illustration of the PC measurements. When the excitation laser is resonant with the transition energy, an exciton is created and measured as a PC signal.

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To demonstrate exciton qubit operation using a telecommunication wavelength light, we employ a PC measurement technique. The principle of the PC measurement is shown schematically in Fig. 1. Under resonant excitation, a photon can be absorbed, creating an exciton in the QD. Under appropriate bias voltage conditions, the carriers can tunnel out from the QD, and be detected as a photocurrent. This allows a very sensitive and direct measurement of QD occupancy at resonant excitation of the excitonic ground-state. In other words, the exciton qubit state is monitored via the photocurrent. Another advantage of PC techniques is that photodetectors are not required for the measurement. At present, viable detectors operating at telecommunication wavelengths have much lower quantum efficiency and much higher dark count probability than detectors for visible and near-infrared lights.

 

Fig. 2. (a) Macro-PL spectrum of our QD. The emission range extends over 1.3 µm. (b) PC spectra of a single QD in the region of the excitonic ground state energy. The background has been subtracted. In this CW-experiment, the laser energy is fixed for each spectrum, whereas the transition energy is tuned by gate voltage via the QCSE. A number of different laser energies have been recorded sequentially, each leading to a resonance at a specific voltage on the photodiode. With increasing gate voltage, the resonant PC intensity increases due to a faster tunneling rate.

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2. Experiments

2.1. Sample preparation

Our samples were grown by molecular beam epitaxy on an n-doped GaAs substrate. A 110-nm-thick undoped GaAs buffer layer was deposited on the 300-nm-thick n-doped GaAs buffer layer. Following this, an InAs QD layer with 5 periods of an InAs/GaAs strain-relaxation-layer (SRL) [14] and 110-nm-thick undoped-GaAs cap layer were formed. A macro-PL spectrum of the sample measured at 4 K is shown in Fig. 2(a). The transition wavelength of our QD is longer than 1300 nm, which enables the low-temperature measurements of telecomband excitons.

2.2. Device structure

We fabricated an n-i Schottky photodiode structure with QDs. An ohmic contact was established on the back. A 5-nm-thick titanium layer was deposited on the top surface as a semitransparent Schottky contact. Optical selection of a single QD was performed using shadow masks composed of an 80-nm-thick aluminum layer and a 20-nm-thick gold layer with apertures of 700 nm in diameter. This structure allowed a voltage-control of the QD exciton energy as a consequence of the quantum-confined Stark effect (QCSE).

2.3. Measurements

All the measurements were conducted using a micro-PL system at 4.2 K. We used a continuous-wave (CW) tunable semiconductor laser for CW excitation. The excited electron-hole pair is detected as PC. The PC spectrum is obtained by sweeping the exciton energy through the laser line via the QCSE. The narrow bandwidth of the laser (<1 MHz) allows to measure the exciton homogeneous linewidth. The polarization of the laser is set parallel to the splitting axis to excite one of the exciton states split due to QD asymmetry.

To study the coherent properties of our single QD photodiode, we performed pulse-excited PC measurements. The optical setup is shown in Fig. 3. The excitation light source is an optical parametric oscillator pumped by a mode-locked Ti: Sapphire laser with 100 fs pulses at 80 MHz repetition rate. The output pulses pass through a pulse-shaping system [17], which reshapes the pulse to the linewidth of 0.4 nm (7 ps). The long pulse duration helps to suppress nonlinear effects in the optical fibers. Using a Pr-doped fluoride fiber amplifier, polarization-controlled pulses are amplified by 14 dB without spectral and temporal broadening. The amplified pulses pass through a power controller. An objective lens is used to focus the excitation pulse onto the sample.

 

Fig. 3. Optical setup for pulse-excited PC measurements. Spectral pulse shapes of input and output from/to the Pr-doped fluoride fiber amplifier are shown in insets. The output pulse is amplified by approximately 14 dB. No spectral broadening is observed in the amplification process. Temporal pulsewidth of the output pulse is 7 ps which is close to the Fourier-transform limit.

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3. Results and discussion

Figure 2(b) displays PC resonances obtained successively for several excitation wavelengths ranging from 1291 to 1303 nm. The scanning range is in the low-energy tail of the spectral distribution of our QDs. The spatial density of 1×10¹⁰/cm² and the high spectral inhomogeneity allow for the observation of a single dot. Each PC peak reflects the resonance condition E _exciton(V _B)=E _Laser, when the QCSE shifts the exciton energy into resonance with the laser [15,16]. The voltage axis can be transformed into an energy axis via the QCSE. The excitonic photocurrent resonance exhibits a typical linewidth of approximately 4 mV, which corresponds to a spectral linewidth of approximately 30 µeV. The PC peaks appear at higher gate voltage as compared to typical 1 µm QDs [6,7]. This is due to a deeper confinement of the 1.3 µm QDs than 1 µm QDs.

For the discussion of the coherent properties of our single QD photodiode, we compare the relevant timescales in this system. The lifetime of a coherent polarization is given by the decoherence or dephasing time. Only within this characteristic time it is possible to perform coherent manipulations in the system. Recent experiments on self-assembled InGaAs QDs have shown low-temperature dephasing times in excess of 500 ps [13]. In the PC measurement, if the tunneling time of the confined carriers is less than the dephasing time, it also limits the time range for coherent interactions. The tunneling should be faster than the repetition rate of our excitation, whereas it should be slower than single-pulse passing time, because the carrier should remain in the dot during the single-pulse excitation. For our entire gate voltage range, the PC peak increases with increasing the gate voltage, as shown in Fig. 2(b), indicating that the tunneling time decreases with increasing gate voltage. At approximately 3.2 V, the linewidth of the PC peak becomes ~40 µeV which is directly related to the tunneling time of several tens of ps. Therefore, we have performed the pulse measurements at gate voltages between 3.2 and 3.3 V, where the tunneling time is less than the dephasing time, yet it is sufficiently long for 7 ps pulse excitation.

 

Fig. 4. Power dependence of the PC intensity. (a) Rabi oscillation of the PC at resonance for increasing excitation pulse area. The photocurrents are obtained for different accumulation times to obtain sufficient S/N ratio. The oscillation is fitted by an exponentially-damped sine function (red line). The green dashed line shows the theoretical maximum of the PC. A value of pulse area of 1 corresponds to an average CW excitation intensity of ~250 µW on the QD sample. (b) I-V properties at excitation of π/2 and π pulses centered at 1300.55 nm. The upper axis shows the energy shift of the exciton energy from the central wavelength of the excitation pulse converted from the gate voltage via the QCSE.

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The resulting pulse-area dependent PC intensity and the spectra for π/2 and π pulses obtained by the pulse-excited PC measurement are shown in Fig. 4(a) and (b), respectively. We observe more than one period of a damped Rabi oscillation in the PC, which reflects directly and quantitatively the resulting occupancy in the two-level system. The first maximum of the Rabi oscillations corresponds to an excitation with a π-pulse, which appears at the pulse area of 1. The conversion factor between excitation power P and pulse area θ is represented by θ=1.9 µW^-1/2 P ^1/2. The value is close to that of a 1 µm dot [10]. Applied to a two-level system with an initial occupancy of 0, a single π-pulse leads to a complete inversion of the system, namely, to occupancy 1.

Exciting exactly one electron-hole pair leads to the delivery of one elementary charge e to an outer circuit, per laser pulse. With a pulse repetition frequency f=80 MHz, we expect a time-integrated net current I=f e, which is equal to 12.8 pA [shown in Fig. 4(a) by a green dashed line]. We nearly reach the theoretical maximum for the PC. Reaching the theoretical maximum is due to all of the excited excitons contributing to the photocurrent signal, and is a quantitative proof for Rabi flopping. The dephasing time of our telecom-band exciton is expected to be comparable or larger than the that of the 1 µm dots because a similar 1.5 periods of Rabi oscillation is observed even by using an excitation laser of 40 ps pulse-width.

We observe a damped Rabi oscillation in the PC. The reason for the damping of the Rabi oscillations has been studied by several groups [18–20]. In our case, the number of oscillations is still limited by the maximum power of the output pulse. However, in principle, we can easily increase the excitation power by splitting the pulses and using more fiber amplifiers to operate more quantum gates because our single QD photodiode is operated at a telecommunication wavelength.

In conclusion, we have successfully observed exciton Rabi oscillations with picosecond pulses at 1.3 µm, and have shown that the fiber system including a fiber amplifier is very useful for driving the coherent system for quantum gate operations. This suggests that we can operate the optical quantum gate many times without limiting the input laser pulse power. The advantage, high flexibility and stability of the fiber system make the telecom-band exciton qubit a promising candidate for implementations of future quantum information devices and high performance quantum networks.