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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 5 — Feb. 28, 2011
  • pp: 4182–4187
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Photon antibunching from a single lithographically defined InGaAs/GaAs quantum dot

V. B. Verma, Martin J. Stevens, K. L. Silverman, N. L. Dias, A. Garg, J. J. Coleman, and R. P. Mirin  »View Author Affiliations


Optics Express, Vol. 19, Issue 5, pp. 4182-4187 (2011)
http://dx.doi.org/10.1364/OE.19.004182


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Abstract

We demonstrate photon antibunching from a single lithographically defined quantum dot fabricated by electron beam lithography, wet chemical etching, and overgrowth of the barrier layers by metalorganic chemical vapor deposition. Measurement of the second-order autocorrelation function indicates g(2)(0) = 0.395 ± 0.030, below the 0.5 limit necessary for classification as a single photon source.

© 2011 OSA

Single photon emitters are important for quantum key distribution (QKD) [1

1. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002). [CrossRef]

,2

2. E. Waks, K. Inoue, C. Santori, D. Fattal, J. Vuckovic, G. S. Solomon, and Y. Yamamoto, “Secure communication: quantum cryptography with a photon turnstile,” Nature 420(6917), 762 (2002). [CrossRef] [PubMed]

], quantum metrology, and quantum information processing applications [3

3. A. Imamoğlu, “Are quantum dots useful for quantum computation?” Physica E 16(1), 47–50 (2003). [CrossRef]

,4

4. A. Kiraz, M. Atatüre, and A. Imamoğlu, “Quantum-dot single-photon sources: Prospects for applications in linear optics quantum-information processing,” Phys. Rev. A 69(3), 032305 (2004). [CrossRef]

]. Sources of single photons include epitaxial self-assembled quantum dots (SAQDs) [5

5. R. P. Mirin, “Photon antibunching at high temperature from a single InGaAs/GaAs quantum dot,” Appl. Phys. Lett. 84(8), 1260 (2004). [CrossRef]

7

7. P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoğlu, “A quantum dot single-photon turnstile device,” Science 290(5500), 2282–2285 (2000). [CrossRef] [PubMed]

], colloidal quantum dots [8

8. X. Brokmann, G. Messin, P. Desbiolles, E. Giacobino, M. Dahan, and J. P. Hermier, “Colloidal CdSe/ZnS quantum dots as single-photon sources,” N. J. Phys. 6, 99 (2004). [CrossRef]

], single molecules [9

9. B. Lounis and W. E. Moerner, “Single photons on demand from a single molecule at room temperature,” Nature 407(6803), 491–493 (2000). [CrossRef] [PubMed]

], and color centers in diamond [10

10. C. Kurtsiefer, S. Mayer, P. Zarda, and H. Weinfurter, “Stable solid-state source of single photons,” Phys. Rev. Lett. 85(2), 290–293 (2000). [CrossRef] [PubMed]

,11

11. T. M. Babinec, B. J. M. Hausmann, M. Khan, Y. Zhang, J. R. Maze, P. R. Hemmer, and M. Lončar, “A diamond nanowire single-photon source,” Nat. Nanotechnol. 5(3), 195–199 (2010). [CrossRef] [PubMed]

]. Of these sources, epitaxial SAQDs are attractive due to their ease of fabrication and incorporation within other photonic structures such as optical cavities. While it has been demonstrated that an optical cavity can be positioned and fabricated around a single SAQD with a high degree of accuracy [12

12. K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 (2007). [CrossRef] [PubMed]

14

14. A. Dousse, L. Lanco, J. Suffczyński, E. Semenova, A. Miard, A. Lemaître, I. Sagnes, C. Roblin, J. Bloch, and P. Senellart, “Controlled light-matter coupling for a single quantum dot embedded in a pillar microcavity using far-field optical lithography,” Phys. Rev. Lett. 101(26), 267404 (2008). [CrossRef]

], the random nature of the SAQD nucleation process limits the scalability of this approach.

As a result, numerous techniques have been investigated for deterministically positioning a QD such as growth in etched nanoholes [15

15. C. Schneider, A. Huggenberger, T. Sünner, T. Heindel, M. Strauß, S. Göpfert, P. Weinmann, S. Reitzenstein, L. Worschech, M. Kamp, S. Höfling, and A. Forchel, “Single site-controlled In(Ga)As/GaAs quantum dots: growth, properties and device integration,” Nanotechnology 20(43), 434012 (2009). [CrossRef] [PubMed]

,16

16. P. Atkinson, M. B. Ward, S. P. Bremner, D. Anderson, T. Farrow, G. A. C. Jones, A. J. Shields, and D. A. Ritchie, “Site-Control of InAs Quantum Dots using Ex-Situ Electron-Beam Lithographic Patterning of GaAs Substrates,” Jpn. J. Appl. Phys. 45(No. 4A), 2519–2521 (2006). [CrossRef]

], atomic force microscopy [17

17. H. Z. Song, T. Usuki, T. Ohshima, Y. Sakuma, M. Kawabe, Y. Okada, K. Takemoto, T. Miyazawa, S. Hirose, Y. Nakata, M. Takatsu, and N. Yokoyama, “Site-controlled quantum dots fabricated using an atomic-force microscope assisted technique,” Nanoscale Res. Lett. 1(2), 160–166 (2006). [CrossRef]

], and growth in inverted pyramidal recesses [18

18. A. Mohan, M. Felici, P. Gallo, B. Dwir, A. Rudra, J. Faist, and E. Kapon, “Polarization-entangled photons produced with high-symmetry site-controlled quantum dots,” Nat. Photonics 4(5), 302–306 (2010). [CrossRef]

]. While these approaches have been shown to produce high optical quality site-controlled QDs, the bottom-up approach to fabrication implies that the QD properties depend critically on growth parameters and the properties of the prepatterned substrate such as the separation between QDs in the array and the individual pattern dimensions.

The fabrication process begins with a base structure grown by molecular beam epitaxy (MBE) on an undoped (100) GaAs substrate and consists of a 20-period GaAs/AlAs distributed Bragg reflector (DBR) stack to increase the extraction efficiency of light produced by the quantum dots, a 130 nm GaAs lower core, an 8 nm In0.2Ga0.8As quantum well, and a 10 nm GaAs cap. The DBR was designed to provide a peak reflectivity of ~99.6% at 910 nm. Including more DBR periods would in principle increase the reflectivity to be closer to the ideal value of 100%. However, we felt that the value of 99.6% was sufficiently close to the ideal value for the purposes of this experiment. In addition, the QD emission wavelength depends on the size of the QD as well as strain effects, which makes the exact alignment of the QD emission with the reflectivity peak of the DBR difficult in practice.

Electron beam lithography was performed with a scanning electron microscope with an acceleration voltage of 30 kV and beam current of 20 pA. Polymethyl methacrylate (PMMA) was used as the electron beam resist. Regular arrays of dots were patterned in square lattices with various pitches ranging from 500 nm to 5 µm. The dot diameters were also varied between approximately 60 nm and 130 nm_by modifying the electron beam dose. After development, 20 nm of titanium metal was evaporated on the sample, followed by liftoff in acetone. The metal dot patterns were then transferred into the underlying quantum well layer by use of a phosphoric acid-based etchant. The etch was timed to provide an etch depth of 25 nm, resulting in QDs with diameters ranging between approximately 10 nm and 80 nm. Note that the diameters of the QDs are smaller than the diameters of the titanium etch masks due to undercutting during the wet etching process. After etching, the titanium was stripped in buffered hydrofluoric acid. Figure 1
Fig. 1 An array of 30 nm diameter etched QDs on a pitch of 1 µm. The inset shows a magnified image of a single QD.
shows an array of 30 nm diameter QDs on a 1 µm pitch after stripping the etch mask. Following the etching step, the barrier layers were regrown in a low pressure MOCVD reactor and consist of a 130 nm GaAs upper core, an 80 nm AlAs confinement layer, and a 10 nm GaAs cap.

Figure 3
Fig. 3 Emission spectrum of a 35 nm QD in a 2.5 µm pitch array. The inset shows the integrated intensity of the exciton line at 888.6 nm as a function of pump power. The solid line is a linear fit to the data below 200 nW.
shows the emission spectrum of a low density QD array consisting of 35 nm diameter QDs on a 2.5 µm pitch at a time-average pump power of 100 nW. Since the diameter of the pump spot is approximately 4 µm, the pump laser primarily excites a single QD in this array. The primary peak at 888.6 nm has a full width at half maximum of 0.16 nm or 260 µeV, significantly larger than the linewidths of typical self-assembled QDs [21

21. K. Leosson, J. R. Jensen, J. M. Hvam, and W. Langbein, “Linewidth Statistics of Single InGaAs Quantum Dot Photoluminescence Lines,” Phys. Status Solidi B 221(1), 49–53 (2000). [CrossRef]

]. The resolution of the spectrometer used for this measurement was ~0.02 nm. While the origin of the larger linewidth requires further investigation, we suggest that it may be due to spectral diffusion caused by trapped charges near the etched interfaces of the QD and within the regrown barrier layer [22

22. J. Seufert, R. Weigand, G. Bacher, T. Kümmell, A. Forchel, K. Leonardi, and D. Hommel, “Spectral diffusion of the exciton transition in a single self-organized quantum dot,” Appl. Phys. Lett. 76(14), 1872 (2000). [CrossRef]

]. As shown in the inset, the linear dependence of the integrated intensity on pump power below 200 nW suggests that this spectral line is due to emission from a single exciton state. The smaller peaks on the long-wavelength side of the primary peak are likely due to emission from adjacent QDs in the array that are at the edge of the pump beam. This was verified by moving the sample stage and observing the simultaneous decay of the primary peak and increase in the intensity of the adjacent peaks. In addition, the intensity of the adjacent peaks has a much weaker correlation with pump power than the single exciton line, making it unlikely that these peaks correspond to emission from biexciton or charged exciton states from the same QD. Although we fabricated lower density arrays of QDs with 5µm pitch, the emission linewidths of the QDs were found to vary across the sample between approximately 250 µeV and 800 µeV. The QD in this particular 2.5 µm pitch array was selected for measurement of the second order correlation function because it demonstrated one of the narrowest linewidths measured.

Figure 4
Fig. 4 Second order correlation function g2(τ) measured on the exciton line at 888.6 nm in the emission spectrum of Fig. 3.
shows the second-order correlation function measured on the single-exciton line at 888.6 nm in Fig. 3. The measurement was performed at a pump power of 175 nW. The monochromator was set to pass 888.6 nm with a spectral bandwidth of ~0.1 nm to the HBTI. The theoretical DBR reflectivity at the wavelength of the exciton emission is ~98.4%, slightly lower than the reflectivity at the DBR design wavelength of 910 nm. The count rate on each SPAD was approximately 700 Hz for the duration of the measurement. Although the timing electronics allow us to collect data for time separations τ up to 16 µs, we show only the first few peaks around τ = 0 for clarity. The value of g(2)(0) was computed by taking the area of the peak at zero time delay and dividing by the average area of all other peaks. Performing this calculation without subtracting the background due to dark counts on the SPADs yields g(2)(0) = 0.395 ± 0.030. This value is below the 0.5 limit necessary for classification as a single photon source [23

23. R. Loudon, The Quantum Theory of Light (Oxford University Press, 1983).

]. The background in the g(2)(0) measurement was estimated by averaging the coincidence counts between pump pulses over a 1.5 ns time window. Measurement of the decay time of the QD luminescence at a pump power of 200 nW indicated a biexponential decay with a fast component of 470 ps and a slow component of 2.1 ns as shown in Fig. 5
Fig. 5 Time resolved trace of the QD luminescence at a pump power of 200 nW. The solid red curve is a biexponential fit to the data.
. Thus we can safely assume that the majority of coincidence counts between pump pulses are due to dark counts and not long-lived QD emission. After subtracting the contribution due to dark counts we obtain g(2)(0) = 0.314 ± 0.029. The remaining counts at zero time delay may be due to the weak background emission around the single exciton line, as shown in Fig. 3, and imperfect spectral filtering of the two longer wavelength peaks caused by emission from adjacent QDs in the array. The slow component of the QD time resolved decay also suggests the presence of carrier traps in the barrier layer which may supply carriers to the QD over long time scales and result in the emission of additional photons after the production of the first photon within the same pump pulse.

Acknowledgments

The authors thank Todd Harvey for assistance with the MBE growth. The work at Illinois was supported by the U.S. Department of Energy, Office of Basic Energy Sciences as part of an Energy Frontier Research Center and the National Science Foundation (ECCS 08-21979).

References and links

1.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002). [CrossRef]

2.

E. Waks, K. Inoue, C. Santori, D. Fattal, J. Vuckovic, G. S. Solomon, and Y. Yamamoto, “Secure communication: quantum cryptography with a photon turnstile,” Nature 420(6917), 762 (2002). [CrossRef] [PubMed]

3.

A. Imamoğlu, “Are quantum dots useful for quantum computation?” Physica E 16(1), 47–50 (2003). [CrossRef]

4.

A. Kiraz, M. Atatüre, and A. Imamoğlu, “Quantum-dot single-photon sources: Prospects for applications in linear optics quantum-information processing,” Phys. Rev. A 69(3), 032305 (2004). [CrossRef]

5.

R. P. Mirin, “Photon antibunching at high temperature from a single InGaAs/GaAs quantum dot,” Appl. Phys. Lett. 84(8), 1260 (2004). [CrossRef]

6.

C. Santori, D. Fattal, J. Vuckovic, G. S. Solomon, and Y. Yamamoto, “Single-photon generation with InAs quantum dots,” N. J. Phys. 6, 89 (2004). [CrossRef]

7.

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoğlu, “A quantum dot single-photon turnstile device,” Science 290(5500), 2282–2285 (2000). [CrossRef] [PubMed]

8.

X. Brokmann, G. Messin, P. Desbiolles, E. Giacobino, M. Dahan, and J. P. Hermier, “Colloidal CdSe/ZnS quantum dots as single-photon sources,” N. J. Phys. 6, 99 (2004). [CrossRef]

9.

B. Lounis and W. E. Moerner, “Single photons on demand from a single molecule at room temperature,” Nature 407(6803), 491–493 (2000). [CrossRef] [PubMed]

10.

C. Kurtsiefer, S. Mayer, P. Zarda, and H. Weinfurter, “Stable solid-state source of single photons,” Phys. Rev. Lett. 85(2), 290–293 (2000). [CrossRef] [PubMed]

11.

T. M. Babinec, B. J. M. Hausmann, M. Khan, Y. Zhang, J. R. Maze, P. R. Hemmer, and M. Lončar, “A diamond nanowire single-photon source,” Nat. Nanotechnol. 5(3), 195–199 (2010). [CrossRef] [PubMed]

12.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 (2007). [CrossRef] [PubMed]

13.

A. Badolato, K. Hennessy, M. Atatüre, J. Dreiser, E. Hu, P. M. Petroff, and A. Imamoglu, “Deterministic coupling of single quantum dots to single nanocavity modes,” Science 308(5725), 1158–1161 (2005). [CrossRef] [PubMed]

14.

A. Dousse, L. Lanco, J. Suffczyński, E. Semenova, A. Miard, A. Lemaître, I. Sagnes, C. Roblin, J. Bloch, and P. Senellart, “Controlled light-matter coupling for a single quantum dot embedded in a pillar microcavity using far-field optical lithography,” Phys. Rev. Lett. 101(26), 267404 (2008). [CrossRef]

15.

C. Schneider, A. Huggenberger, T. Sünner, T. Heindel, M. Strauß, S. Göpfert, P. Weinmann, S. Reitzenstein, L. Worschech, M. Kamp, S. Höfling, and A. Forchel, “Single site-controlled In(Ga)As/GaAs quantum dots: growth, properties and device integration,” Nanotechnology 20(43), 434012 (2009). [CrossRef] [PubMed]

16.

P. Atkinson, M. B. Ward, S. P. Bremner, D. Anderson, T. Farrow, G. A. C. Jones, A. J. Shields, and D. A. Ritchie, “Site-Control of InAs Quantum Dots using Ex-Situ Electron-Beam Lithographic Patterning of GaAs Substrates,” Jpn. J. Appl. Phys. 45(No. 4A), 2519–2521 (2006). [CrossRef]

17.

H. Z. Song, T. Usuki, T. Ohshima, Y. Sakuma, M. Kawabe, Y. Okada, K. Takemoto, T. Miyazawa, S. Hirose, Y. Nakata, M. Takatsu, and N. Yokoyama, “Site-controlled quantum dots fabricated using an atomic-force microscope assisted technique,” Nanoscale Res. Lett. 1(2), 160–166 (2006). [CrossRef]

18.

A. Mohan, M. Felici, P. Gallo, B. Dwir, A. Rudra, J. Faist, and E. Kapon, “Polarization-entangled photons produced with high-symmetry site-controlled quantum dots,” Nat. Photonics 4(5), 302–306 (2010). [CrossRef]

19.

V. B. Verma and J. J. Coleman, “High density patterned quantum dot arrays fabricated by electron beam lithography and wet chemical etching,” Appl. Phys. Lett. 93(11), 111117 (2008). [CrossRef]

20.

V. B. Verma, U. Reddy, N. L. Dias, K. P. Bassett, X. Li, and J. J. Coleman, “Patterned Quantum Dot Molecule Laser Fabricated by Electron Beam Lithography and Wet Chemical Etching,” IEEE J. Quantum Electron. (to be published).

21.

K. Leosson, J. R. Jensen, J. M. Hvam, and W. Langbein, “Linewidth Statistics of Single InGaAs Quantum Dot Photoluminescence Lines,” Phys. Status Solidi B 221(1), 49–53 (2000). [CrossRef]

22.

J. Seufert, R. Weigand, G. Bacher, T. Kümmell, A. Forchel, K. Leonardi, and D. Hommel, “Spectral diffusion of the exciton transition in a single self-organized quantum dot,” Appl. Phys. Lett. 76(14), 1872 (2000). [CrossRef]

23.

R. Loudon, The Quantum Theory of Light (Oxford University Press, 1983).

OCIS Codes
(250.0250) Optoelectronics : Optoelectronics
(270.0270) Quantum optics : Quantum optics
(270.5290) Quantum optics : Photon statistics
(250.5590) Optoelectronics : Quantum-well, -wire and -dot devices

ToC Category:
Quantum Optics

History
Original Manuscript: October 29, 2010
Revised Manuscript: December 29, 2010
Manuscript Accepted: January 16, 2011
Published: February 17, 2011

Citation
V. B. Verma, Martin J. Stevens, K. L. Silverman, N. L. Dias, A. Garg, J. J. Coleman, and R. P. Mirin, "Photon antibunching from a single lithographically defined InGaAs/GaAs quantum dot," Opt. Express 19, 4182-4187 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-5-4182


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References

  1. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002). [CrossRef]
  2. E. Waks, K. Inoue, C. Santori, D. Fattal, J. Vuckovic, G. S. Solomon, and Y. Yamamoto, “Secure communication: quantum cryptography with a photon turnstile,” Nature 420(6917), 762 (2002). [CrossRef] [PubMed]
  3. A. Imamoğlu, “Are quantum dots useful for quantum computation?” Physica E 16(1), 47–50 (2003). [CrossRef]
  4. A. Kiraz, M. Atatüre, and A. Imamoğlu, “Quantum-dot single-photon sources: Prospects for applications in linear optics quantum-information processing,” Phys. Rev. A 69(3), 032305 (2004). [CrossRef]
  5. R. P. Mirin, “Photon antibunching at high temperature from a single InGaAs/GaAs quantum dot,” Appl. Phys. Lett. 84(8), 1260 (2004). [CrossRef]
  6. C. Santori, D. Fattal, J. Vuckovic, G. S. Solomon, and Y. Yamamoto, “Single-photon generation with InAs quantum dots,” N. J. Phys. 6, 89 (2004). [CrossRef]
  7. P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoğlu, “A quantum dot single-photon turnstile device,” Science 290(5500), 2282–2285 (2000). [CrossRef] [PubMed]
  8. X. Brokmann, G. Messin, P. Desbiolles, E. Giacobino, M. Dahan, and J. P. Hermier, “Colloidal CdSe/ZnS quantum dots as single-photon sources,” N. J. Phys. 6, 99 (2004). [CrossRef]
  9. B. Lounis and W. E. Moerner, “Single photons on demand from a single molecule at room temperature,” Nature 407(6803), 491–493 (2000). [CrossRef] [PubMed]
  10. C. Kurtsiefer, S. Mayer, P. Zarda, and H. Weinfurter, “Stable solid-state source of single photons,” Phys. Rev. Lett. 85(2), 290–293 (2000). [CrossRef] [PubMed]
  11. T. M. Babinec, B. J. M. Hausmann, M. Khan, Y. Zhang, J. R. Maze, P. R. Hemmer, and M. Lončar, “A diamond nanowire single-photon source,” Nat. Nanotechnol. 5(3), 195–199 (2010). [CrossRef] [PubMed]
  12. K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 (2007). [CrossRef] [PubMed]
  13. A. Badolato, K. Hennessy, M. Atatüre, J. Dreiser, E. Hu, P. M. Petroff, and A. Imamoglu, “Deterministic coupling of single quantum dots to single nanocavity modes,” Science 308(5725), 1158–1161 (2005). [CrossRef] [PubMed]
  14. A. Dousse, L. Lanco, J. Suffczyński, E. Semenova, A. Miard, A. Lemaître, I. Sagnes, C. Roblin, J. Bloch, and P. Senellart, “Controlled light-matter coupling for a single quantum dot embedded in a pillar microcavity using far-field optical lithography,” Phys. Rev. Lett. 101(26), 267404 (2008). [CrossRef]
  15. C. Schneider, A. Huggenberger, T. Sünner, T. Heindel, M. Strauß, S. Göpfert, P. Weinmann, S. Reitzenstein, L. Worschech, M. Kamp, S. Höfling, and A. Forchel, “Single site-controlled In(Ga)As/GaAs quantum dots: growth, properties and device integration,” Nanotechnology 20(43), 434012 (2009). [CrossRef] [PubMed]
  16. P. Atkinson, M. B. Ward, S. P. Bremner, D. Anderson, T. Farrow, G. A. C. Jones, A. J. Shields, and D. A. Ritchie, “Site-Control of InAs Quantum Dots using Ex-Situ Electron-Beam Lithographic Patterning of GaAs Substrates,” Jpn. J. Appl. Phys. 45(No. 4A), 2519–2521 (2006). [CrossRef]
  17. H. Z. Song, T. Usuki, T. Ohshima, Y. Sakuma, M. Kawabe, Y. Okada, K. Takemoto, T. Miyazawa, S. Hirose, Y. Nakata, M. Takatsu, and N. Yokoyama, “Site-controlled quantum dots fabricated using an atomic-force microscope assisted technique,” Nanoscale Res. Lett. 1(2), 160–166 (2006). [CrossRef]
  18. A. Mohan, M. Felici, P. Gallo, B. Dwir, A. Rudra, J. Faist, and E. Kapon, “Polarization-entangled photons produced with high-symmetry site-controlled quantum dots,” Nat. Photonics 4(5), 302–306 (2010). [CrossRef]
  19. V. B. Verma and J. J. Coleman, “High density patterned quantum dot arrays fabricated by electron beam lithography and wet chemical etching,” Appl. Phys. Lett. 93(11), 111117 (2008). [CrossRef]
  20. V. B. Verma, U. Reddy, N. L. Dias, K. P. Bassett, X. Li, and J. J. Coleman, “Patterned Quantum Dot Molecule Laser Fabricated by Electron Beam Lithography and Wet Chemical Etching,” IEEE J. Quantum Electron. (to be published).
  21. K. Leosson, J. R. Jensen, J. M. Hvam, and W. Langbein, “Linewidth Statistics of Single InGaAs Quantum Dot Photoluminescence Lines,” Phys. Status Solidi B 221(1), 49–53 (2000). [CrossRef]
  22. J. Seufert, R. Weigand, G. Bacher, T. Kümmell, A. Forchel, K. Leonardi, and D. Hommel, “Spectral diffusion of the exciton transition in a single self-organized quantum dot,” Appl. Phys. Lett. 76(14), 1872 (2000). [CrossRef]
  23. R. Loudon, The Quantum Theory of Light (Oxford University Press, 1983).

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