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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 18 — Sep. 1, 2008
  • pp: 13949–13954
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Coherently driven semiconductor quantum dot at a telecommunication wavelength

Hiroyuki Takagi, Toshihiro Nakaoka, Katsuyuki Watanabe, Naoto Kumagai, and Yasuhiko Arakawa  »View Author Affiliations


Optics Express, Vol. 16, Issue 18, pp. 13949-13954 (2008)
http://dx.doi.org/10.1364/OE.16.013949


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Abstract

We proposed and demonstrate use of optical driving pulses at a telecommunication wavelength for exciton-based quantum gate operation. The exciton in a self-assembled quantum dot is coherently manipulated at 1.3 µm through Rabi oscillation. The telecom-band exciton-qubit system incorporates standard optical fibers and fiber optic devices. The coherent manipulation of the two-level system compatible with flexible and stable fiber network paves the way toward practical optical implementation of quantum information processing devices.

© 2008 Optical Society of America

1. Introduction

Quantum information processing [1

1. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge Univ. Press, Cambridge, 2000).

] such as quantum communication [2

2. D. P. DiVicenzo, “Quantum computation,” Science 270, 255–261 (2000). [CrossRef]

] and quantum computation [3

3. N. Gisin, R. Thew, and Quantum communication,” Nature Photon. 1, 165–171 (2007). [CrossRef]

] 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

4. H. Htoon et al., “Interplay of Rabi oscillations and quantum interference in semiconductor quantum dots,” Phys. Rev. Lett. 88, 087401 (2002). [CrossRef]

10

10. S. Stufler, P. Machnikowski, P. Ester, M. Bichler, V. M. Axt, T. Kuhn, and A. Zrenner, “Two-photon Rabi oscillations in a single InxGa1-xAs/GaAs quantum dot,” Phys. Rev. B 73, 125304 (2006).

]. 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

11. J. Chen, J. B. Altepeter, M. Medic, K. F. Lee, B. Gokden, R. H. Hadfield, S. W. Nam, and P. Kumar, “Demonstration of a quantum controlled-NOT gate in the telecommunications band,” Phys. Rev. Lett. 100, 133603 (2008). [CrossRef] [PubMed]

]. 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

12. L. Allen and J. H. Eberly, Optical Resonance and Two Level Atoms (Wiley, New York, 1975).

]. 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

13. P. Borri, W. Langbein, S. Schneider, and U. Woggon, “Ultralong dephasing time in InGaAs quantum dots,” Phys. Rev. Lett. 87, 157401 (2001). [CrossRef] [PubMed]

], allowing sufficiently high numbers of coherent manipulations with picosecond pulses. Rabi oscillations have been observed in photoluminescence (PL) [4

4. H. Htoon et al., “Interplay of Rabi oscillations and quantum interference in semiconductor quantum dots,” Phys. Rev. Lett. 88, 087401 (2002). [CrossRef]

], absorption [5

5. T. H. Stievater, X. Li, D. G. Steel, D. Gammon, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “Rabi Oscillations of Excitons in Single Quantum Dots,” Phys. Rev. Lett. 87, 133603 (2001). [CrossRef] [PubMed]

,6

6. X. Li, Y. Wu, D. Steel, D. Gammon, T. H. Stievater, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “An all-optical quantum gate in a semiconductor quantum dot,” Science 301, 809–811 (2003). [CrossRef] [PubMed]

], and photocurrent (PC) measurements [7

7. A. Zrenner, E. Beham, S. Stuffer, F. Findeis, M. Bichler, and G. Abstreiter, “Coherent properties of a two-level system based on a quantum dot photodiode,” Nature 418, 612–614 (2002). [CrossRef] [PubMed]

10

10. S. Stufler, P. Machnikowski, P. Ester, M. Bichler, V. M. Axt, T. Kuhn, and A. Zrenner, “Two-photon Rabi oscillations in a single InxGa1-xAs/GaAs quantum dot,” Phys. Rev. B 73, 125304 (2006).

]. 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.

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.

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

14. J. Tatebayashi, M. Nishioka, and Y. Arakawa, “Over 1.5 µm light emission from InAs quantum dots embedded in InGaAs strain-reducing layer grown by metalorganic chemical vapor deposition,” Appl. Phys. Lett. 78, 3469–3471 (2001). [CrossRef]

] 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

17. A. M. Weiner, J. P. Heritage, and E. M. Kirschner, “High-resolution femtosecond pulse shaping,” J. Opt. Sot. Am. B 5, 1563–1572 (1988). [CrossRef]

], 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.

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

6. X. Li, Y. Wu, D. Steel, D. Gammon, T. H. Stievater, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “An all-optical quantum gate in a semiconductor quantum dot,” Science 301, 809–811 (2003). [CrossRef] [PubMed]

,7

7. A. Zrenner, E. Beham, S. Stuffer, F. Findeis, M. Bichler, and G. Abstreiter, “Coherent properties of a two-level system based on a quantum dot photodiode,” Nature 418, 612–614 (2002). [CrossRef] [PubMed]

]. This is due to a deeper confinement of the 1.3 µm QDs than 1 µm QDs.

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.

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

10. S. Stufler, P. Machnikowski, P. Ester, M. Bichler, V. M. Axt, T. Kuhn, and A. Zrenner, “Two-photon Rabi oscillations in a single InxGa1-xAs/GaAs quantum dot,” Phys. Rev. B 73, 125304 (2006).

]. 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

18. Q. Q. Wang, A. Muller, P. Bianucci, E. Rossi, Q. K. Xue, T. Takagahara, C. Piermarocchi, A. H. MacDonald, and C. K. Shih, “Decoherence processes during optical manipulation of excitonic qubits in semiconductor quantum dots,” Phys. Rev. B 72, 035306 (2005).

20

20. J. M. Villas-Bôas, A. O. Govorov, and S. E. Ulloa, “Decoherence of Rabi oscillations in a single quantum dot,” Phys. Rev. Lett. 94, 057404 (2005). [CrossRef] [PubMed]

]. 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.

Acknowledgments

This study was supported in part by Special Coordination Funds for Promoting Science and Technology.

Present address: System Platforms Research Laboratories, NEC Corporation, 1753, Shimonumabe, Nakahara-Ku, Kawasaki, Kanagawa 211-8666, Japan.

References and links

1.

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge Univ. Press, Cambridge, 2000).

2.

D. P. DiVicenzo, “Quantum computation,” Science 270, 255–261 (2000). [CrossRef]

3.

N. Gisin, R. Thew, and Quantum communication,” Nature Photon. 1, 165–171 (2007). [CrossRef]

4.

H. Htoon et al., “Interplay of Rabi oscillations and quantum interference in semiconductor quantum dots,” Phys. Rev. Lett. 88, 087401 (2002). [CrossRef]

5.

T. H. Stievater, X. Li, D. G. Steel, D. Gammon, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “Rabi Oscillations of Excitons in Single Quantum Dots,” Phys. Rev. Lett. 87, 133603 (2001). [CrossRef] [PubMed]

6.

X. Li, Y. Wu, D. Steel, D. Gammon, T. H. Stievater, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “An all-optical quantum gate in a semiconductor quantum dot,” Science 301, 809–811 (2003). [CrossRef] [PubMed]

7.

A. Zrenner, E. Beham, S. Stuffer, F. Findeis, M. Bichler, and G. Abstreiter, “Coherent properties of a two-level system based on a quantum dot photodiode,” Nature 418, 612–614 (2002). [CrossRef] [PubMed]

8.

R. S. Kolodka, A. J. Ramsay, J. Skiba-Szymanska, P. W. Fry, H. Y. Liu, A. M. Fox, and M. S. Skolnick, “Inversion recovery of single quantum-dot exciton based qubit,” Phys. Rev. B 75, 193306 (2007).

9.

A. Zrenner, S. Stuffer, P. Ester, and M. Bichler, “Manipulations of a Qubit in a Semiconductor Quantum Dot,” Adv. Solid State Phys. 45, 173–184 (2005). [CrossRef]

10.

S. Stufler, P. Machnikowski, P. Ester, M. Bichler, V. M. Axt, T. Kuhn, and A. Zrenner, “Two-photon Rabi oscillations in a single InxGa1-xAs/GaAs quantum dot,” Phys. Rev. B 73, 125304 (2006).

11.

J. Chen, J. B. Altepeter, M. Medic, K. F. Lee, B. Gokden, R. H. Hadfield, S. W. Nam, and P. Kumar, “Demonstration of a quantum controlled-NOT gate in the telecommunications band,” Phys. Rev. Lett. 100, 133603 (2008). [CrossRef] [PubMed]

12.

L. Allen and J. H. Eberly, Optical Resonance and Two Level Atoms (Wiley, New York, 1975).

13.

P. Borri, W. Langbein, S. Schneider, and U. Woggon, “Ultralong dephasing time in InGaAs quantum dots,” Phys. Rev. Lett. 87, 157401 (2001). [CrossRef] [PubMed]

14.

J. Tatebayashi, M. Nishioka, and Y. Arakawa, “Over 1.5 µm light emission from InAs quantum dots embedded in InGaAs strain-reducing layer grown by metalorganic chemical vapor deposition,” Appl. Phys. Lett. 78, 3469–3471 (2001). [CrossRef]

15.

F. Findeis, M. Baier, E. Beham, A. Zrenner, and G. Abstreiter, “Photocurrent and photoluminescence of a single self-assembled quantum dot in electric fields,” Appl. Phys. Lett. 78, 2958–2960 (2001). [CrossRef]

16.

R. Oulton, J. J. Finley, A. D. Ashmore, I. D. Gregory, I. D. Mowbray, M. S. Skolnick, M. J. Steer, M. A. San-Lin Liew, A. J. Migliorato, and Cullis, “Manipulation of the homogeneous linewidth of an individual In(Ga)As quantum dot,” Phys. Rev. B 66, 45313 (2002).

17.

A. M. Weiner, J. P. Heritage, and E. M. Kirschner, “High-resolution femtosecond pulse shaping,” J. Opt. Sot. Am. B 5, 1563–1572 (1988). [CrossRef]

18.

Q. Q. Wang, A. Muller, P. Bianucci, E. Rossi, Q. K. Xue, T. Takagahara, C. Piermarocchi, A. H. MacDonald, and C. K. Shih, “Decoherence processes during optical manipulation of excitonic qubits in semiconductor quantum dots,” Phys. Rev. B 72, 035306 (2005).

19.

J. Förstner, C. Weber, J. Danckwerts, and A. Knorr, “Phonon-assisted damping of Rabi oscillations in semiconductor quantum dots,” Phys. Rev Lett. 91, 127401 (2003). [CrossRef] [PubMed]

20.

J. M. Villas-Bôas, A. O. Govorov, and S. E. Ulloa, “Decoherence of Rabi oscillations in a single quantum dot,” Phys. Rev. Lett. 94, 057404 (2005). [CrossRef] [PubMed]

OCIS Codes
(060.0060) Fiber optics and optical communications : Fiber optics and optical communications
(190.5970) Nonlinear optics : Semiconductor nonlinear optics including MQW
(270.0270) Quantum optics : Quantum optics
(300.6470) Spectroscopy : Spectroscopy, semiconductors

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: May 30, 2008
Revised Manuscript: July 23, 2008
Manuscript Accepted: August 20, 2008
Published: August 25, 2008

Citation
Hiroyuki Takagi, Toshihiro Nakaoka, Katsuyuki Watanabe, Naoto Kumagai, and Yasuhiko Arakawa, "Coherently driven semiconductor quantum dot at a telecommunication wavelength," Opt. Express 16, 13949-13954 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-18-13949


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References

  1. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge Univ. Press, Cambridge, 2000).
  2. D. P. DiVicenzo, "Quantum computation," Science 270, 255-261 (2000). [CrossRef]
  3. N. Gisin and R. Thew, "Quantum communication," Nature Photon. 1, 165-171 (2007). [CrossRef]
  4. H. Htoon et al., "Interplay of Rabi oscillations and quantum interference in semiconductor quantum dots," Phys. Rev. Lett. 88, 087401 (2002). [CrossRef]
  5. T. H. Stievater, X. Li, D. G. Steel, D. Gammon, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, "Rabi Oscillations of Excitons in Single Quantum Dots," Phys. Rev. Lett. 87, 133603 (2001). [CrossRef] [PubMed]
  6. X. Li, Y. Wu, D. Steel, D. Gammon, T. H. Stievater, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, "An all-optical quantum gate in a semiconductor quantum dot," Science 301, 809--811 (2003). [CrossRef] [PubMed]
  7. A. Zrenner, E. Beham, S. Stuffer, F. Findeis, M. Bichler, and G. Abstreiter, "Coherent properties of a two-level system based on a quantum dot photodiode," Nature 418, 612-614 (2002). [CrossRef] [PubMed]
  8. R. S. Kolodka, A. J. Ramsay, J. Skiba-Szymanska, P. W. Fry, H. Y. Liu, A. M. Fox, and M. S. Skolnick, "Inversion recovery of single quantum-dot exciton based qubit," Phys. Rev. B 75, 193306 (2007).
  9. A. Zrenner, S. Stuffer, P. Ester, and M. Bichler, "Manipulations of a Qubit in a Semiconductor Quantum Dot," Adv. Solid State Phys. 45, 173-184 (2005). [CrossRef]
  10. S. Stufler, P. Machnikowski, P. Ester, M. Bichler, V. M. Axt, T. Kuhn, and A. Zrenner, "Two-photon Rabi oscillations in a single InxGa1-xAs/GaAs quantum dot," Phys. Rev. B 73, 125304 (2006).
  11. J. Chen, J. B. Altepeter, M. Medic, K. F. Lee, B. Gokden, R. H. Hadfield, S. W. Nam, and P. Kumar, "Demonstration of a quantum controlled-NOT gate in the telecommunications band," Phys. Rev. Lett. 100,133603 (2008). [CrossRef] [PubMed]
  12. L. Allen and J. H. Eberly, Optical Resonance and Two Level Atoms (Wiley, New York, 1975).
  13. P. Borri, W. Langbein, S. Schneider, and U. Woggon, "Ultralong dephasing time in InGaAs quantum dots," Phys. Rev. Lett. 87, 157401 (2001). [CrossRef] [PubMed]
  14. J. Tatebayashi, M. Nishioka, and Y. Arakawa, "Over 1.5 µm light emission from InAs quantum dots embedded in InGaAs strain-reducing layer grown by metalorganic chemical vapor deposition," Appl. Phys. Lett. 78, 3469-3471 (2001). [CrossRef]
  15. F. Findeis, M. Baier, E. Beham, A. Zrenner, and G. Abstreiter, "Photocurrent and photoluminescence of a single self-assembled quantum dot in electric fields," Appl. Phys. Lett. 78, 2958-2960 (2001). [CrossRef]
  16. R. Oulton, J. J. Finley, A. D. Ashmore, I. D. Gregory, I. D., Mowbray, M. S. Skolnick, M. J. Steer, M. A. San-Lin Liew, Migliorato, and A. J. Cullis, "Manipulation of the homogeneous linewidth of an individual In(Ga)As quantum dot," Phys. Rev. B 66, 45313 (2002).
  17. A. M. Weiner, J. P. Heritage, and E. M. Kirschner, "High-resolution femtosecond pulse shaping," J. Opt. Sot. Am. B 5, 1563-1572 (1988). [CrossRef]
  18. Q. Q. Wang, A. Muller, P. Bianucci, E. Rossi, Q. K. Xue, T. Takagahara, C. Piermarocchi, A. H. MacDonald, and C. K. Shih, "Decoherence processes during optical manipulation of excitonic qubits in semiconductor quantum dots," Phys. Rev. B 72, 035306 (2005).
  19. J. Förstner, C. Weber, J. Danckwerts, and A. Knorr, "Phonon-assisted damping of Rabi oscillations in semiconductor quantum dots," Phys. Rev Lett. 91, 127401 (2003). [CrossRef] [PubMed]
  20. J. M. Villas-Bôas, A. O. Govorov, and S. E. Ulloa, "Decoherence of Rabi oscillations in a single quantum dot," Phys. Rev. Lett. 94, 057404 (2005). [CrossRef] [PubMed]

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