Abstract

Tunneling-induced large fifth-order nonlinearity is theoretically demonstrated in a double-quantum-dot system. The resonant tunneling induces constructive interference for the third- and fifth-order nonlinear effects. The competition between the linearity and nonlinearity leads to a transparency window at some frequency detunings, where the fifth-order nonlinear refractive index could be increased to be more than one order of magnitude larger than that on resonance. An analytical expression shows that the resonant tunneling mainly contributes to the dramatic enhancement of the fifth-order nonlinear response.

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  36. T. Frey, P. J. Leek, M. Beck, A. Blais, T. Ihn, K. Ensslin, and A. Wallraff, “Dipole coupling of a double quantum dot to a microwave resonator,” Phys. Rev. Lett. 108, 046807 (2012).
    [CrossRef]
  37. J. Villas-Boâs, A. Govorov, and S. Ulloa, “Coherent control of tunneling in a quantum dot molecule,” Phys. Rev. B 69, 125342 (2004).
    [CrossRef]
  38. E. Paspalakis, Z. Kis, E. Voutsinas, and A. Terzis, “Controlled rotation in a double quantum dot structure,” Phys. Rev. B 69, 155316 (2004).
    [CrossRef]
  39. Y. Peng, Y. Niu, Y. Qi, H. Yao, and S. Gong, “Optical precursors with tunneling-induced transparency in asymmetric quantum wells,” Phys. Rev. A 83, 013812 (2011).
    [CrossRef]
  40. Y. Peng, Y. Niu, N. Cui, and S. Gong, “Cavity linewidth narrowing by voltage-controlled induced transparency in asymmetry quantum dot molecules,” Opt. Commun. 284, 824–827 (2011).
    [CrossRef]
  41. S. Marcinkevičius, A. Gushterov, and J. Reithmaier, “Transient electromagnetically induced transparency in self-assembled quantum dots,” Appl. Phys. Lett. 92, 041113 (2008).
    [CrossRef]
  42. J. Li, R. Yu, L. Si, and X. Yang, “Voltage-controlled storage and retrieval of an infrared-light pulse in a quantum-dot molecule,” Opt. Commun. 282, 2437–2441 (2009).
    [CrossRef]
  43. J. Kim, S. Chuang, P. Ku, and C. Chang-Hasnain, “Slow light using semiconductor quantum dots,” J. Phys.: Condens. Matter 16, S3727–S3735 (2004).
    [CrossRef]
  44. Y. Zhang, M. Belic, Z. Wu, C. Yuan, R. wang, K. Lu, and Y. Zhang, “Multicharged optical vortices induced in a dissipative atomic vapor system,” Phys. Rev. A 88, 013847 (2013).
    [CrossRef]
  45. M. Saha and A. Sarma, “Modulation instability in nonlinear metamaterials induced by cubic–quintic nonlinearities and higher order dispersive effects,” Opt. Commun. 291, 321–325 (2013).
    [CrossRef]
  46. C. Ottaviani, S. Rebic, D. Vitali, and P. Tombesi, “Cross phase modulation in a five-level atomic medium semiclassical theory,” Eur. Phys. J. D 40, 281–296 (2006).
    [CrossRef]
  47. B. Luo, Y. Liu, and H. Guo, “Magnetically induced simultaneous slow and fast light,” Opt. Lett. 35, 64–66 (2010).
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  48. S. Sagona-Stophel, J. Weatherall, and C. Search, “Index of refraction engineering in five-level dressed interacting ground states atoms,” Opt. Lett. 36, 3130–3132 (2011).
    [CrossRef]

2014

A. Reiserer, N. Kalb, G. Rempe, and S. Ritter, “A quantum gate between a flying optical photon and a single trapped atom,” Nature 508, 237–240 (2014).
[CrossRef]

H. Zheng, N. Li, Z. Zhang, Z. Wu, C. Lei, Y. Zhang, and Y. Zhang, “Power quantum control of odd-order multiwave mixing in an electromagnetically induced transparency window,” J. Opt. Soc. Am. B 31, 1263–1272 (2014).
[CrossRef]

W. Chen, M. Shen, Q. Kong, J. Shi, Q. Wang, and W. Krolikowski, “Interactions of nonlocal dark solitons under competing cubic–quintic nonlinearities,” Opt. Lett. 39, 1764–1767 (2014).
[CrossRef]

C. Hang and G. Huang, “Guiding ultraslow weak-light bullets with Airy beams in a coherent atomic system,” Phys. Rev. A 89, 013821 (2014).
[CrossRef]

A. Paredes, D. Feijoo, and H. Michinel, “Coherent cavitation in the liquid of light,” Phys. Rev. Lett. 112, 173901 (2014).
[CrossRef]

F. Boitier, A. Orieux, C. Autebert, A. Lemaitre, E. Galopin, C. Manquest, C. Sirtori, I. Favero, G. Leo, and S. Ducci, “Electrically injected photon-pair source at room temperature,” Phys. Rev. Lett. 112, 183901 (2014).
[CrossRef]

2013

H. Sun, S. Fan, H. Zhang, and S. Gong, “Tunneling-induced high-efficiency four-wave mixing in asymmetric quantum wells,” Phys. Rev. B 87, 235310 (2013).
[CrossRef]

F. Zhou, Y. Qi, H. Sun, D. Chen, J. Yang, Y. Niu, and S. Gong, “Electromagnetically induced grating in asymmetric quantum wells via Fano interference,” Opt. Express 21, 12249–12259 (2013).
[CrossRef]

N. Sköld, A. Giroday, A. Bennett, I. Farrer, D. Ritchie, and A. Shields, “Electrical control of the exciton fine structure of a quantum dot molecule,” Phys. Rev. Lett. 110, 016804 (2013).
[CrossRef]

Z. Chen and G. Huang, “Stern–Gerlach effect of multi-component ultraslow optical solitons via electromagnetically induced transparency,” J. Opt. Soc. Am. B 30, 2248–2256 (2013).
[CrossRef]

Y. Qi, F. Zhou, J. Yang, Y. Niu, and S. Gong, “Controllable twin laser pulse propagation and dual-optical switching in a four-level quantum dot nanostructure,” J. Opt. Soc. Am. B 30, 1928–1936 (2013).
[CrossRef]

J. Colless, A. Mahoney, J. Hornibrook, A. Doherty, H. Lu, A. Gossard, and D. Reilly, “Dispersive readout of a few-electron double quantum dot with fast RF gate sensors,” Phys. Rev. Lett. 110, 046805 (2013).
[CrossRef]

E. Falcão-Filho, C. Araújo, G. Boudebs, H. Leblond, and V. Skarka, “Robust two-dimensional spatial solitons in liquid carbon disulfide,” Phys. Rev. Lett. 110, 013901 (2013).
[CrossRef]

O. Firstenberg, T. Peyronel, Q. Liang, A. Gorshkov, M. Lukin, and V. Vuletić, “Attractive photons in a quantum nonlinear medium,” Nature 502, 71–75 (2013).
[CrossRef]

W. Liu, A. Bracker, D. Gammon, and M. Doty, “Dynamic hole trapping in InAs/AlGaAs/InAs quantum dot molecules,” Phys. Rev. B 87, 195308 (2013).
[CrossRef]

Y. Zhang, M. Belic, Z. Wu, C. Yuan, R. wang, K. Lu, and Y. Zhang, “Multicharged optical vortices induced in a dissipative atomic vapor system,” Phys. Rev. A 88, 013847 (2013).
[CrossRef]

M. Saha and A. Sarma, “Modulation instability in nonlinear metamaterials induced by cubic–quintic nonlinearities and higher order dispersive effects,” Opt. Commun. 291, 321–325 (2013).
[CrossRef]

2012

K. Müller, A. Bechtold, C. Ruppert, M. Zecherle, G. Reithmaier, M. Bichler, H. Krenner, G. Abstreiter, A. Holleitner, J. Villas-Boâs, M. Betz, and J. Finley, “Electrical control of interdot electron tunneling in a double InGaAs quantum-dot nanostructure,” Phys. Rev. Lett. 108, 197402 (2012).
[CrossRef]

T. Frey, P. J. Leek, M. Beck, A. Blais, T. Ihn, K. Ensslin, and A. Wallraff, “Dipole coupling of a double quantum dot to a microwave resonator,” Phys. Rev. Lett. 108, 046807 (2012).
[CrossRef]

X. Zhang, H. Wang, C. Liu, X. Han, C. Fan, J. Wu, and J. Gao, “Direct conversion of slow light into a stationary light pulse,” Phys. Rev. A 86, 023821 (2012).
[CrossRef]

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

2011

X. Lü, J. Wu, L. Zheng, and Z. Zhan, “Voltage-controlled entanglement and quantum-information transfer between spatially separated quantum-dot molecules,” Phys. Rev. A 83, 042302 (2011).
[CrossRef]

Y. Peng, Y. Niu, Y. Qi, H. Yao, and S. Gong, “Optical precursors with tunneling-induced transparency in asymmetric quantum wells,” Phys. Rev. A 83, 013812 (2011).
[CrossRef]

Y. Peng, Y. Niu, N. Cui, and S. Gong, “Cavity linewidth narrowing by voltage-controlled induced transparency in asymmetry quantum dot molecules,” Opt. Commun. 284, 824–827 (2011).
[CrossRef]

S. Sagona-Stophel, J. Weatherall, and C. Search, “Index of refraction engineering in five-level dressed interacting ground states atoms,” Opt. Lett. 36, 3130–3132 (2011).
[CrossRef]

2010

2009

K. Dolgaleva, H. Shin, and R. Boyd, “Observation of a microscopic cascaded contribution to the fifth-order nonlinear susceptibility,” Phys. Rev. Lett. 103, 113902 (2009).
[CrossRef]

Y. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four-wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102, 013601 (2009).
[CrossRef]

P. Lunnemann and J. Mørky, “Reducing the impact of inhomogeneous broadening on quantum dot based electromagnetically induced transparency,” Appl. Phys. Lett. 94, 071108 (2009).
[CrossRef]

L. Wang, A. Rastelli, S. Kiravittaya, M. Benyoucef, and O. Schmidt, “Self-assembled quantum dot molecules,” Adv. Mater. 21, 2601–2618 (2009).
[CrossRef]

J. Li, R. Yu, L. Si, and X. Yang, “Voltage-controlled storage and retrieval of an infrared-light pulse in a quantum-dot molecule,” Opt. Commun. 282, 2437–2441 (2009).
[CrossRef]

2008

S. Marcinkevičius, A. Gushterov, and J. Reithmaier, “Transient electromagnetically induced transparency in self-assembled quantum dots,” Appl. Phys. Lett. 92, 041113 (2008).
[CrossRef]

2007

2006

C. Ottaviani, S. Rebic, D. Vitali, and P. Tombesi, “Cross phase modulation in a five-level atomic medium semiclassical theory,” Eur. Phys. J. D 40, 281–296 (2006).
[CrossRef]

2005

J. Wu, J. Gao, J. Xu, L. Silvestri, M. Artoni, G. La Rocca, and F. Bassani, “Ultrafast all optical switching via tunable Fano interference,” Phys. Rev. Lett. 95, 057401 (2005).
[CrossRef]

Y. Niu, R. Li, and S. Gong, “High efficiency four-wave mixing induced by double-dark resonances in a five-level tripod system,” Phys. Rev. A 71, 043819 (2005).
[CrossRef]

2004

Y. Wu and L. Deng, “Ultraslow optical solitons in a cold four-state medium,” Phys. Rev. Lett. 93, 143904 (2004).
[CrossRef]

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

E. Paspalakis, Z. Kis, E. Voutsinas, and A. Terzis, “Controlled rotation in a double quantum dot structure,” Phys. Rev. B 69, 155316 (2004).
[CrossRef]

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

2003

H. Kang and Y. Zhu, “Observation of large Kerr nonlinearity at low light intensities,” Phys. Rev. Lett. 91, 093601 (2003).
[CrossRef]

2001

H. Wang, D. Goorskey, and M. Xiao, “Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system,” Phys. Rev. Lett. 87, 073601 (2001).
[CrossRef]

2000

T. Brabec and F. Krausz, “Intense few-cycle laser fields: frontiers of nonlinear optics,” Rev. Mod. Phys. 72, 545–591 (2000).
[CrossRef]

1999

S. Harris and L. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611–4614 (1999).
[CrossRef]

1997

J. Faist, F. Capasso, C. Sirtori, K. West, and L. Pfeiffer, “Controlling the sign of quantum interference by tunnelling from quantum wells,” Nature 390, 589–591 (1997).
[CrossRef]

Abstreiter, G.

K. Müller, A. Bechtold, C. Ruppert, M. Zecherle, G. Reithmaier, M. Bichler, H. Krenner, G. Abstreiter, A. Holleitner, J. Villas-Boâs, M. Betz, and J. Finley, “Electrical control of interdot electron tunneling in a double InGaAs quantum-dot nanostructure,” Phys. Rev. Lett. 108, 197402 (2012).
[CrossRef]

Alcalde, A.

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

Anderson, B.

Y. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four-wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102, 013601 (2009).
[CrossRef]

Araújo, C.

E. Falcão-Filho, C. Araújo, G. Boudebs, H. Leblond, and V. Skarka, “Robust two-dimensional spatial solitons in liquid carbon disulfide,” Phys. Rev. Lett. 110, 013901 (2013).
[CrossRef]

Artoni, M.

J. Wu, J. Gao, J. Xu, L. Silvestri, M. Artoni, G. La Rocca, and F. Bassani, “Ultrafast all optical switching via tunable Fano interference,” Phys. Rev. Lett. 95, 057401 (2005).
[CrossRef]

Autebert, C.

F. Boitier, A. Orieux, C. Autebert, A. Lemaitre, E. Galopin, C. Manquest, C. Sirtori, I. Favero, G. Leo, and S. Ducci, “Electrically injected photon-pair source at room temperature,” Phys. Rev. Lett. 112, 183901 (2014).
[CrossRef]

Bassani, F.

J. Wu, J. Gao, J. Xu, L. Silvestri, M. Artoni, G. La Rocca, and F. Bassani, “Ultrafast all optical switching via tunable Fano interference,” Phys. Rev. Lett. 95, 057401 (2005).
[CrossRef]

Bechtold, A.

K. Müller, A. Bechtold, C. Ruppert, M. Zecherle, G. Reithmaier, M. Bichler, H. Krenner, G. Abstreiter, A. Holleitner, J. Villas-Boâs, M. Betz, and J. Finley, “Electrical control of interdot electron tunneling in a double InGaAs quantum-dot nanostructure,” Phys. Rev. Lett. 108, 197402 (2012).
[CrossRef]

Beck, M.

T. Frey, P. J. Leek, M. Beck, A. Blais, T. Ihn, K. Ensslin, and A. Wallraff, “Dipole coupling of a double quantum dot to a microwave resonator,” Phys. Rev. Lett. 108, 046807 (2012).
[CrossRef]

Belic, M.

Y. Zhang, M. Belic, Z. Wu, C. Yuan, R. wang, K. Lu, and Y. Zhang, “Multicharged optical vortices induced in a dissipative atomic vapor system,” Phys. Rev. A 88, 013847 (2013).
[CrossRef]

Bennett, A.

N. Sköld, A. Giroday, A. Bennett, I. Farrer, D. Ritchie, and A. Shields, “Electrical control of the exciton fine structure of a quantum dot molecule,” Phys. Rev. Lett. 110, 016804 (2013).
[CrossRef]

Benyoucef, M.

L. Wang, A. Rastelli, S. Kiravittaya, M. Benyoucef, and O. Schmidt, “Self-assembled quantum dot molecules,” Adv. Mater. 21, 2601–2618 (2009).
[CrossRef]

Betz, M.

K. Müller, A. Bechtold, C. Ruppert, M. Zecherle, G. Reithmaier, M. Bichler, H. Krenner, G. Abstreiter, A. Holleitner, J. Villas-Boâs, M. Betz, and J. Finley, “Electrical control of interdot electron tunneling in a double InGaAs quantum-dot nanostructure,” Phys. Rev. Lett. 108, 197402 (2012).
[CrossRef]

Bichler, M.

K. Müller, A. Bechtold, C. Ruppert, M. Zecherle, G. Reithmaier, M. Bichler, H. Krenner, G. Abstreiter, A. Holleitner, J. Villas-Boâs, M. Betz, and J. Finley, “Electrical control of interdot electron tunneling in a double InGaAs quantum-dot nanostructure,” Phys. Rev. Lett. 108, 197402 (2012).
[CrossRef]

Blais, A.

T. Frey, P. J. Leek, M. Beck, A. Blais, T. Ihn, K. Ensslin, and A. Wallraff, “Dipole coupling of a double quantum dot to a microwave resonator,” Phys. Rev. Lett. 108, 046807 (2012).
[CrossRef]

Boitier, F.

F. Boitier, A. Orieux, C. Autebert, A. Lemaitre, E. Galopin, C. Manquest, C. Sirtori, I. Favero, G. Leo, and S. Ducci, “Electrically injected photon-pair source at room temperature,” Phys. Rev. Lett. 112, 183901 (2014).
[CrossRef]

Borges, H.

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

Boudebs, G.

E. Falcão-Filho, C. Araújo, G. Boudebs, H. Leblond, and V. Skarka, “Robust two-dimensional spatial solitons in liquid carbon disulfide,” Phys. Rev. Lett. 110, 013901 (2013).
[CrossRef]

Boyd, R.

K. Dolgaleva, H. Shin, and R. Boyd, “Observation of a microscopic cascaded contribution to the fifth-order nonlinear susceptibility,” Phys. Rev. Lett. 103, 113902 (2009).
[CrossRef]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).

Brabec, T.

T. Brabec and F. Krausz, “Intense few-cycle laser fields: frontiers of nonlinear optics,” Rev. Mod. Phys. 72, 545–591 (2000).
[CrossRef]

Bracker, A.

W. Liu, A. Bracker, D. Gammon, and M. Doty, “Dynamic hole trapping in InAs/AlGaAs/InAs quantum dot molecules,” Phys. Rev. B 87, 195308 (2013).
[CrossRef]

Capasso, F.

J. Faist, F. Capasso, C. Sirtori, K. West, and L. Pfeiffer, “Controlling the sign of quantum interference by tunnelling from quantum wells,” Nature 390, 589–591 (1997).
[CrossRef]

Chang-Hasnain, C.

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

Chen, D.

Chen, W.

Chen, Z.

Chuang, S.

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

Colless, J.

J. Colless, A. Mahoney, J. Hornibrook, A. Doherty, H. Lu, A. Gossard, and D. Reilly, “Dispersive readout of a few-electron double quantum dot with fast RF gate sensors,” Phys. Rev. Lett. 110, 046805 (2013).
[CrossRef]

Cui, N.

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N. Sköld, A. Giroday, A. Bennett, I. Farrer, D. Ritchie, and A. Shields, “Electrical control of the exciton fine structure of a quantum dot molecule,” Phys. Rev. Lett. 110, 016804 (2013).
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Zheng, H.

Zheng, L.

X. Lü, J. Wu, L. Zheng, and Z. Zhan, “Voltage-controlled entanglement and quantum-information transfer between spatially separated quantum-dot molecules,” Phys. Rev. A 83, 042302 (2011).
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J. Opt. Soc. Am. B

J. Phys. B

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[CrossRef]

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Opt. Commun.

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Phys. Rev. A

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Phys. Rev. B

J. Villas-Boâs, A. Govorov, and S. Ulloa, “Coherent control of tunneling in a quantum dot molecule,” Phys. Rev. B 69, 125342 (2004).
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H. Sun, S. Fan, H. Zhang, and S. Gong, “Tunneling-induced high-efficiency four-wave mixing in asymmetric quantum wells,” Phys. Rev. B 87, 235310 (2013).
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Figures (5)

Fig. 1.
Fig. 1.

(a) Three-level QDM model with coupling scheme and (b) its dressed-state picture.

Fig. 2.
Fig. 2.

Real parts of fifth-order nonlinearities χ(5) on resonance (δ2=0) and with frequency detunings (δ2=Γ1). Ωp=0.2Γ1, Te=2Γ1, Γ1=0.01meV, and Γ2=103Γ1.

Fig. 3.
Fig. 3.

Linear χ(1), third-order χ(3), and fifth-order χ(5) susceptibilities on resonance (δ2=0, left column) and with frequency detuning (δ2=Γ1, right column). Other parameters as Fig. 2.

Fig. 4.
Fig. 4.

Imaginary part of total susceptibility Im[χ] and real part of fifth-order susceptibility Re[χ(5)] vary with different probe field strength. (a) Ωp=0.13Γ1 and δ2=0; (b) Ωp=0.1Γ1 and δ2=Γ1; (c) as (b) but Ωp=0.13Γ1; (d) as (b) but Ωp=0.18Γ1. Other parameters as Fig. 2.

Fig. 5.
Fig. 5.

Real parts of T(Te), T(O), and χ(5) at (a) δ2=0 and (b) δ2=Γ1. Other parameters as Fig. 2.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

ρ˙00=Γ10ρ11+Γ20ρ22+iΩp(ρ01ρ10),ρ˙11=Γ10ρ11+iTe(ρ12ρ21)+iΩp(ρ10ρ01),ρ˙22=Γ20ρ22+iTe(ρ21ρ12),ρ˙10=(iδ1+Γ1)ρ10iΩp(ρ00ρ11)iTeρ20,ρ˙20=[i(δ1+δ2)+Γ2]ρ20+iΩpρ21iTeρ10,ρ˙21=(iω12+Γ1+Γ2)ρ12iTe(ρ22ρ11)iΩpρ02,
P=ε0χE,
χ=χ(1)+χ(3)|Ep|2+χ(5)|Ep|4.
χ(1)=ΓoptV|μ10|2ε0Ωpρ10(1)=C1δ1+δ2+2iΓ2(iδ1Γ1)[i(δ1+δ2)2Γ2]+2Te2,
χ(3)=ΓoptV|μ10|4ε0Ωpρ10(3)=C2Γ2(δ1+δ2)2{Te2(3δ1δ2)[(δ1+δ2)(3δ1δ2)+Te2]A1(A2+A3+A4)+(δ1δ2)3(7δ12+δ22)+Γ12(δ13δ2)A1(A2+A3+A4)},
C2=C1|μ10|2,A1=(δ1+δ2)2[Te2+i(Γ1+2iδ1)(δ1+δ2)],A2=2Te6(Γ1Γ2)Γ2(Γ12+4δ12)[Γ12+(δ1δ2)2](δ1+δ2)2,A3=2Te2(δ1+δ2)[Γ12Γ2(δ1δ2)+Γ13(δ1+δ2)+4Γ1δ12(δ1+δ2)2Γ2δ1(δ12+4δ1δ2,δ22)],A4=Te4[3Γ12Γ28Γ1δ1(δ1+δ2)+Γ2(7δ12+10δ1δ2δ22)].
χ(5)=ΓoptV|μ10|6ε0Ωpρ10(5)=C3Te2Γ13Γ2(T1T2+T3T4T5)OB12(B2B3+B4)3,
C3=C1|μ10|4,T1=4Te8Γ1(3Γ1δ14Γ2δ1Γ1δ2),T2=2Γ2δ17[53Γ13+4Γ2δ2(77δ216δ1)+4Γ1(23δ12+25δ1δ25522)],T3=Te4[Γ1Γ2(227iΓ2428δ1)δ14+4Γ14(11δ1δ2)(δ1+δ2)2+2Γ22δ14(197δ1+36δ2)+4Γ12δ1(10iΓ2δ13+23δ14+31δ13δ2+2δ12δ22+2δ1δ23+7δ24)],T4=2Te2[95Γ13Γ2δ15+4Γ16(δ1+δ2)3+2Γ22δ15(117δ12+47δ1δ2305δ22)2Γ1Γ2δ15(121δ12+104δ1δ2163δ22)+8Γ14δ1(3δ14+9δ13δ2+10δ12δ22+6δ1δ23+3δ24)+Γ12δ13(15iΓ2δ13+26δ14+62δ13δ2+50δ12δ22+38δ1δ23+46δ24)],T5=2Te6{75Γ1Γ2δ13+Γ22δ12(79δ111δ2)+4Γ14(δ1+δ2)+Γ12[7iΓ2δ12+4(δ1+δ2)(7δ124δ1δ2+δ22)]},O=16Γ13Γ23δ18[3Γ12(δ1δ2)+δ1(δ12δ1δ25δ25)],B1=Te2+(Γ12iδ1)[Γ2i(δ1+δ2)],B2=2Te4(Γ12Γ1Γ22Γ22),B3=iΓ1Γ2{(δ1+δ2)(Γ13+2iΓ12δ1)+(Γ1+2iδ1)[δ13δ12δ2+δ22(δ2iΓ2)]2δ12(2Γ2+iδ2)Γ1δ1δ22},B4=Te2Γ1{Γ2(3δ12+6δ1δ2δ22)+Γ12[Γ2+2i(δ1+δ2)]+2iΓ1[Γ2(δ1δ2)+2iδ1(δ1+δ2)]}.

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