Abstract

Kerr-nonlinearity induced self-focusing or self-defocusing effect provides the opportunity for exploring fundamental phenomena related to the light-matter interactions. Here we show that the linear and nonlinear dispersion responses are significantly sensitive to both the detunings and the tunneling strengths of the indirect-excitonic (IX) states in an asymmetric triple quantum dot system. In particular, the nonlinear dispersion properties are dominated by the tunnel-enhanced cross-Kerr nonlinearity from one of the IX states. Meanwhile, by varying the detunings of other IX states, we reveal that the tunnel-enhanced cross-Kerr nonlinearity gives rise to the realization of the self-focusing and self-defocusing effects. Moreover, by taking into account the effect of the longitudinal-acoustic-phonon induced dephasing of the IX states, it is possible to modulate the height and position of the peak of the self-focusing or self-defocusing effect. Our results may have potential applications in nonlinear-optics and quantum-optics devices based on the tunnel-enhanced nonlinearities in this solid-state system.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (1)

X. Q. Luo, Z. Z. Li, J. Jing, W. Xiong, T. F. Li, and T. Yu, “Spectral features of the tunneling-induced transparency and the Autler-Townes doublet and triplet in a triple quantum dot,” Sci. Rep. 8, 3107 (2018).
[Crossref] [PubMed]

2017 (3)

J. Y. Wang, S. Y. Huang, G. Y. Huang, D. Pan, J. H. Zhao, and H. Q. Xu, “Coherent transport in a linear triple quantum dot made from a pure-phase InAs nanowire,” Nano. Lett. 17, 4158–4164 (2017).
[Crossref] [PubMed]

S. Hughes and G. S. Agarwal, “Anisotropy-induced quantum interference and population trapping between orthogonal quantum dot exciton states in semiconductor cavity systems,” Phys. Rev. Lett. 118, 063601 (2017).
[Crossref] [PubMed]

Y. H. Xu, W. X. Wang, Y. Q. Ge, H. Y. Guo, X. J. Zhang, S. Chen, Y. H. Deng, Z. G. Lu, and H. Zhang, “Stabilization of black phosphorous quantum dots in PMMA nanofiber film and broadband nonlinear optics and ultrafast photonics application,” Adv. Funct. Mater. 27, 1702437 (2017).
[Crossref]

2016 (2)

P. L. Ardelt, M. Koller, T. Simmet, L. Hanschke, A. Bechtold, A. Regler, J. Wierzbowski, H. Riedl, J. J. Finley, and K. Müller, “Optical control of nonlinearly dressed states in an individual quantum dot,” Phys. Rev. B 93, 165305 (2016).
[Crossref]

Q. C. Liu, T. F. Li, X. Q. Luo, H. Zhao, W. Xiong, Y. S. Zhang, Z. Chen, J. S. Liu, W. Chen, F. Nori, J. S. Tsai, and J. Q. You, “Method for identifying electromagnetically induced transparency in a tunable circuit quantum electrodynamics system,” Phys. Rev. A 93, 053838 (2016).
[Crossref]

2015 (2)

D. Mogilevtsev, E. R. Gómez, S. B. Cavalcanti, and L. E. Oliveira, “Slow light in semiconductor quantum dots: effects of non-Markovianity and correlation of dephasing reservoirs,” Phys. Rev. B 92, 235446 (2015).
[Crossref]

P. Lodahl, S. Mahmoodian, and S. Stobbe, “Interfacing single photons and single quantum dots with photonic nanostructures,” Rev. Mod. Phys. 87, 347–400 (2015).
[Crossref]

2014 (2)

H. S. Borges and A. Alcalde, and S. E, Ulloa, “Exchange interaction and tunneling-induced transparency in coupled quantum dots,” Phys. Rev. B 90, 205311 (2014).
[Crossref]

M. Sahrai, M. R. Mehmannavaz, and H. Sattari, “Optically controllable switch for light propagation based on triple coupled quantum dots,” Appl. Opt. 53, 2375–2383 (2014).
[Crossref] [PubMed]

2013 (3)

Z. L. Xiang, S. Ashhab, J. Q. You, and F. Nori, “Hybrid quantum circuits: superconducting circuits interacting with other quantum systems,” Rev. Mod. Phys. 85, 623–653 (2013).
[Crossref]

G. Gligorić, A. Maluckov, L. Hadžievski, G. Y. Slepyan, and B. A. Malomed, “Discrete solitons in an array of quantum dots,” Phys. Rev. B 88, 155329 (2013).
[Crossref]

H. S. Borges, L. Sanz, J. M. Villas-Bôas, and A. M. Alcalde, “Quantum interference and control of the optical response in quantum dot molecules,” Appl. Phys. Lett. 103, 222101 (2013).
[Crossref]

2012 (4)

H. S. Borges, L. Sanz, J. M. Villas-Bôas, O. O. Diniz-Neto, and A. M. Alcalde, “Tunneling induced transparency and slow light in quantum dot molecules,” Phys. Rev. B 85, 115425 (2012).
[Crossref]

C. Y. Hsieh, Y. P. Shim, M. Korkusinski, and P. Hawrylak, “Physics of lateral triple quantumdot molecules with controlled electron numbers,” Rep. Prog. Phys. 75, 114501 (2012).
[Crossref]

L. Gaudreau, G. Granger, A. Kam, G. C. Aers, S. A. Studenikin, P. Zawadzki, M. P. Ladrière, Z. R. Wasilewski, and A. S. Sachrajda, “Coherent control of three-spin states in a triple quantum dot,” Nat. Phys. 8, 54–58 (2012).
[Crossref]

Z. G. Chen, M. Segev, and D. N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75, 086401 (2012).
[Crossref] [PubMed]

2011 (2)

X. Q. Luo, D. L. Wang, Z. Q. Zhang, J. W. Ding, and W. M. Liu, “Nonlinear optical behavior of a four-level quantum well with coupled relaxation of optical and longitudinal phonons,” Phys. Rev. A 84, 033803 (2011).
[Crossref]

W. X. Yang, A. X. Chen, R. K. Lee, and Y. Wu, “Matched slow optical soliton pairs via biexciton coherence in quantum dots,” Phys. Rev. A 84, 013835 (2011).
[Crossref]

2010 (1)

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82, 2257–2298 (2010).
[Crossref]

2009 (1)

B. D. Gerardot, D. Brunner, P. A. Dalgarno, K. Karrai, A. Badolato, P. M. Petroff, and R. J. Warburton, “Dressed excitonic states and quantum interference in a three-level quantum dot ladder system,” New J. Phys. 11, 013028 (2009).
[Crossref]

2008 (2)

J. Berney, M. T. Portella-Oberli, and B. Deveaud, “Dressed excitons within an incoherent electron gas: observation of a Mollow triplet and an Autler-Townes doublet,” Phys. Rev. B 77, 121301 (2008).
[Crossref]

K. G. Rasmussen, H. I. Jørgensen, T. Hayashi, P. E. Lindelof, and T. A. Fujisawa, “A triple quantum dot in a single-wall carbon nanotube,” Nano. Lett. 8, 1055–1060 (2008).
[Crossref]

2007 (2)

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47–189 (2007).
[Crossref]

G. T. Adamashvili, C. Weber, A. Knorr, and N. T. Adamashvili, “Optical nonlinear waves in semiconductor quantum dots: solitons and breathers,” Phys. Rev. A 75, 063808 (2007).
[Crossref]

2006 (6)

A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, “Self-compression of ultrashort laser pulses down to one optical cycle by filamentation,” J. Mod. Opt. 53, 75–85 (2006).
[Crossref]

G. Stibenz, N. Zhavoronkov, and G. Steinmeyer, “Self-compression of millijoule pulses to 7.8 fs duration in a white-light filament,” Opt. Lett. 31, 274–276 (2006).
[Crossref] [PubMed]

C. H. Yuan and K. D. Zhu, “Voltage-controlled slow light in asymmetry double quantum dots,” Appl. Phys. Lett. 89, 052115 (2006).
[Crossref]

G. A. Mourou, T. Tajima, and S. V. Bulanov, “Optics in the relativistic regime,” Rev. Mod. Phys. 78, 309–371 (2006).
[Crossref]

G. J. Beirne, C. Hermannstädter, L. Wang, A. Rastelli, O. G. Schmidt, and P. Michler, “Quantum light emission of two lateral tunnel-coupled (In, Ga)As/GaAs quantum dots controlled by a tunable static electric field,” Phys. Rev. Lett. 96, 137401 (2006).
[Crossref]

A. S. Bracker, M. Scheibner, M. F. Doty, E. A. Stinaff, I. V. Ponomarev, J. C. Kim, L. J. Whitman, T. L. Reinecke, and D. Gammon, “Engineering electron and hole tunneling with asymmetric InAs quantum dot molecules,” Appl. Phys. Lett. 89, 233110 (2006).
[Crossref]

2005 (3)

B. Krause, T. H. Metzger, A. Rastelli, R. Songmuang, S. Kiravittaya, and O. G. Schmidt, “Shape, strain, and ordering of lateral InAs quantum dot molecules,” Phys. Rev. B 72, 085339 (2005).
[Crossref]

H. J. Krenner, S. Stufler, M. Sabathil, E. C. Clark, P. Ester, M. Bichler, G. Abstreiter, J. J. Finley, and A. Zrenner, “Recent advances in exciton-based quantum information processing in quantum dot nanostructures,” New J. Phys. 7, 184 (2005).
[Crossref]

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, J. Majer, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Approaching unit visibility for control of a superconducting qubit with dispersive readout,” Phys. Rev. Lett. 95, 060501 (2005).
[Crossref] [PubMed]

2004 (2)

J. M. Villas-Bôas, A. O. Govorov, and S. E. Ulloa, “Coherent control of tunneling in a quantum dot molecule,” Phys. Rev. B 69, 125342 (2004).
[Crossref]

J. Kim, S. L. Chuang, P. C. Ku, and C. J. Chang-Hasnian, “Slow light using semiconductor quantum dots,” J. Phys: Condens. Matter 16, S3727–S3735 (2004).

2003 (4)

P. Borri, W. Langbein, U. Woggon, M. Schwab, M. Bayer, S. Fafard, Z. Wasilewski, and P. Hawrylak, “Exciton dephasing in quantum dot molecules,” Phys. Rev. Lett. 91, 267401 (2003).
[Crossref]

D. S. Saraga and D. Loss, “Spin-entangled currents created by a triple quantum dot,” Phys. Rev. Lett. 90, 166803 (2003).
[Crossref] [PubMed]

X. Q. 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]

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[Crossref] [PubMed]

2000 (1)

A. Tackeuchi, T. Kuroda, and K. Mase, “Dynamics of carrier tunneling between vertically aligned double quantum dots,” Phys. Rev. B 62, 1568–1571 (2000).
[Crossref]

1996 (2)

B. Ohnesorge, M. Albrecht, J. Oshinowo, A. Forchel, and Y. Arakawa, “Rapid carrier relaxation in self-assembled InxGa1−xAs/GaAs quantum dots,” Phys. Rev. B 54, 11532–11538 (1996).
[Crossref]

H. Schmidt and A. Imamoglu, “Giant Kerr nonlinearities obtained by electromagnetically induced transparency,” Opt. Lett. 21, 1936–1938 (1996).
[Crossref] [PubMed]

1994 (1)

1990 (1)

U. Bockelmann and G. Bastard, “Phonon scattering and energy relaxation in two-, one-, and zero-dimensional electron gases,” Phys. Rev. B 42, 8947–8951 (1990).
[Crossref]

1966 (1)

E. Garmire, R. Y. Chiao, and C. H. Townes, “Dynamics and characteristics of the self-trapping of intense light beams,” Phys. Rev. Lett. 16, 347–349 (1966).
[Crossref]

1965 (3)

N. F. Pilipetskii and A. R. Rustamov, “Observation of self-focusing of light in liquids,” JETP Lett. 2, 55 (1965).

P. Lallemand and N. Bloembergen, “Self-focusing of laser beams and stimulated Raman gain in liquids,” Phys. Rev. Lett. 15, 1010–1012 (1965).
[Crossref]

P. L. Kelley, “Self-focusing of optical beams,” Phys. Rev. Lett. 15, 1005–1008 (1965).
[Crossref]

1964 (1)

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13, 479–482 (1964).
[Crossref]

Abstreiter, G.

H. J. Krenner, S. Stufler, M. Sabathil, E. C. Clark, P. Ester, M. Bichler, G. Abstreiter, J. J. Finley, and A. Zrenner, “Recent advances in exciton-based quantum information processing in quantum dot nanostructures,” New J. Phys. 7, 184 (2005).
[Crossref]

Adamashvili, G. T.

G. T. Adamashvili, C. Weber, A. Knorr, and N. T. Adamashvili, “Optical nonlinear waves in semiconductor quantum dots: solitons and breathers,” Phys. Rev. A 75, 063808 (2007).
[Crossref]

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X. Q. 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]

Other (4)

P. Michler, Single Semiconductor Quantum Dots(Springer, 2009).
[Crossref]

R. W. Boyd, Nonlinear Optics (Academic, 2008).

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2013).

R. W. Boyd, S. G. Lukishova, and Y. R. Shen, Self-Focusing: Past and Present(Springer, 2010).

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Figures (6)

Fig. 1
Fig. 1 (a) Schematic diagram of the energy levels of a tunnel-coupled asymmetric triple QD system, which consists of the left, central and right dots, but with a different size for each dot. (b) The asymmetric triple QD is suitably designed, so that the conduction-band levels can all become resonant when applying a gate voltage on the triple QD system. (c) When considering the excitation scheme of the triple QD system, there are four excitonic states: |0〉 is the exciton vacuum state where there is no exciton inside the triple QD due to the absence of optical excitation, |1〉 represents a direct excitonic state created in the central dot, while |2〉 and |3〉 are the indirect excitonic states, which are formed from the left and right dots, respectively. ω01 and ω12(ω13) are the frequency differences between states |0〉↔|1〉 and |1〉↔|2〉(|3〉), respectively. Γ j 0 (j = 1, 2, 3) are the energy relaxation rates between states | j〉 and |0〉. T12(3) describes the tunneling coupling between the left (right) and central dots, which can be controlled by modulating the external electric field. The red and blue parts of state |3〉 denote this state working in the red-and blue-detuned cases, respectively.
Fig. 2
Fig. 2 The linear dispersion properties as a function of the probe detuning Δ1 with different tunneling strengths: (a) T12 = Γ1/5, T13 = Γ1/8; (b) T12 = Γ1/8, T13 = Γ1/5; (c) T12 = Γ1, T13 = Γ1/2; and (d) T12 = Γ1/2, T13 = Γ1. All the given parameters are normalized with respect to Γ1: ω12 = 0, Γ2 = Γ3 = 10−3Γ1, Ω p = 10−2Γ1, and Γ1 = 10µeV. The inset in (a) or (b) is a zoomed view of the given range.
Fig. 3
Fig. 3 The real parts of the cross-Kerr nonlinearities (a) χCK−LD and (b) χCK−RD as a function of the probe detuning Δ1 with different tunneling strengths in the weak-tunneling regime: T12 = Γ1/5, T13 = Γ1/8 (solid curves); T12 = Γ1/8, T13 = Γ1/5 (dashed curves). The inset is a zoomed view of the given range in (a) or (b). Other parameters used are the same as in Fig. 2.
Fig. 4
Fig. 4 The real parts of the cross-Kerr nonlinearities (a) χCK−LD and (b) χCK−RD as a function of the probe detuning Δ1 with different tunneling strengths in the strong-tunneling regime: T12 = Γ1, T13 = Γ1/2 (solid curves); T12 = Γ1/2, T13 = Γ1 (dashed curves). The inset is a zoomed view of the given range in (a) or (b). Other parameters used are the same as in Fig. 2.
Fig. 5
Fig. 5 (a) The real part of the cross-Kerr nonlinearity χCK−LD as a function of the detuning parameters Δ1 and ω13 for the tunneling strengths T12 = Γ1/2 and T13 = Γ1. (b), (c), (d) and (e) are the cross sections of (a) with varying frequency difference ω13. Other parameters used are the same as in Fig. 2.
Fig. 6
Fig. 6 The real part of the cross-Kerr nonlinearity χCK−LD as a function of the probe field detuning Δ1 with different decoherence rates for self-focusing effect (a) and self-defocusing effect (b): Γ2 = 10−3Γ1, Γ3 = 10−3Γ1 [black dashed (solid)]; Γ2 = 10−2Γ1, Γ3 = 10−3Γ1 [red dashed (solid)]; Γ2 = 10−3Γ1, Γ3 = 10−2Γ1 [green dashed (solid)]; Γ2 = 10−3Γ1, Γ3 = 10−1Γ1 [blue dashed (solid)]. The tunneling strengths are T12 = Γ1/2 and T13 = Γ1 = 10 µeV. The inset in (a) or (b) is a zoomed view of the given range. Other parameters used are the same as in Fig. 2.

Equations (13)

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= ω 10 σ 11 + ω 20 σ 22 + ω 30 σ 33 ( Ω p e i ω p t σ 10 + T 12 σ 12 + T 13 σ 13 + H . c . ) ,
1 = j = 1 3 Δ j σ j j ( Ω p σ 10 + T 12 σ 12 + T 13 σ 13 + H . c . ) ,
ρ t = i [ 1 , ρ ] + j = 1 3 ( Γ j 0 D [ σ 0 j ] ρ + γ j ϕ 2 D [ σ j j ] ρ ) ,
ρ 01 = ϒ 2 ϒ 3 Ω p ϒ 1 ϒ 2 ϒ 3 T 12 2 ϒ 3 T 13 2 ϒ 2 ,
χ ( Δ 1 ) = U 01 Ω p ρ 01 ,
χ ( Δ 1 ) U 01 ( χ p ( 1 ) ( Δ 1 ) + χ p ( 3 , CK LD ) ( Δ 1 ) T 12 2 + χ p ( 3 , CK RD ) ( Δ 1 ) T 13 2 ) , = U 01 ( χ ( 1 ) + χ CK LD + χ CK RD ) ,
χ ( 1 ) = ϒ 2 ϒ 1 ϒ 2 T 12 2 + ϒ 3 ϒ 1 ϒ 3 T 13 2 ,
χ CK LD = T 12 2 ϒ 3 2 ϒ 2 ( ϒ 1 ϒ 3 T 13 2 ) 2 ,
χ CK RD = T 13 2 ϒ 2 2 ϒ 3 ( ϒ 1 ϒ 2 T 12 2 ) 2 .
t ρ 00 = Γ 10 ρ 11 + Γ 20 ρ 22 + Γ 30 ρ 33 + i Ω p ρ 10 i Ω p * ρ 01 , t ρ 11 = Γ 10 ρ 11 i Ω p ρ 10 + i T 12 ( ρ 21 ρ 12 ) + i Ω p * ρ 01 + i T 13 ( ρ 31 ρ 13 ) , t ρ 22 = Γ 20 ρ 22 i T 12 ( ρ 21 ρ 12 ) , t ρ 33 = Γ 30 ρ 33 i T 13 ( ρ 31 ρ 13 ) , t ρ 01 = i ( Δ 1 + i Γ 1 ) ρ 01 i T 12 ρ 02 i T 13 ρ 03 + i Ω p ( ρ 11 ρ 00 ) , t ρ 02 = i ( Δ 2 + i Γ 2 ) ρ 02 i T 12 ρ 01 + i Ω p ρ 12 , t ρ 03 = i ( Δ 3 + i Γ 3 ) ρ 03 i T 13 ρ 01 + i Ω p ρ 13 , t ρ 12 = i ( Δ 12 + i Γ 12 ) ρ 12 + i Ω p * ρ 02 + i T 13 ρ 32 + i T 12 ( ρ 22 ρ 11 ) , t ρ 13 = i ( Δ 13 + i Γ 13 ) ρ 13 + i Ω p * ρ 03 + i T 12 ρ 23 + i T 13 ( ρ 33 ρ 11 ) , t ρ 23 = i ( Δ 23 + i Γ 23 ) ρ 23 i T 13 ρ 21 + i T 12 ρ 13 ,
t ρ 01 ( t ) = i ( Δ 1 + i Γ 1 ) ρ 01 ( t ) i T 12 ρ 02 ( t ) i T 13 ρ 03 ( t ) + i Ω p [ ρ 11 ( t ) ρ 00 ( t ) ] , t ρ 02 ( t ) = i ( Δ 2 + i Γ 2 ) ρ 02 ( t ) i T 12 ρ 01 ( t ) + i Ω p ρ 12 ( t ) , t ρ 03 ( t ) = i ( Δ 3 + i Γ 3 ) ρ 03 ( t ) i T 13 ρ 01 ( t ) + i Ω p ρ 13 ( t ) .
t ρ 01 = i ( Δ 1 + i Γ 1 ) ρ 01 i T 12 ρ 02 i T 13 ρ 03 + i Ω p , t ρ 02 = i ( Δ 2 + i Γ 2 ) ρ 02 i T 12 ρ 01 , t ρ 03 = i ( Δ 3 + i Γ 3 ) ρ 03 i T 13 ρ 01 .
ρ 01 = ( Δ 2 + i Γ 2 ) ( Δ 3 + i Γ 3 ) Ω p ( Δ 1 + i Γ 1 ) ( Δ 2 + i Γ 2 ) ( Δ 3 + i Γ 3 ) T 12 2 ( Δ 3 + i Γ 3 ) T 13 2 ( Δ 2 + i Γ 2 ) .

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