Abstract

We perform a theoretical study of the bistable four-wave mixing (FWM) response in a coupled system comprised of a semiconductor quantum dot (SQD) and a photonic crystal (PC) nanocavity in which the SQD is embedded. It is shown that the shape of the FWM spectrum can switch among single-peaked, double-peaked, triple-peaked, and four-peaked arising from the vacuum Rabi splitting and the exciton-nanocavity coupling. Especially, we map out bistability phase diagrams within a parameter subspace of the system, and find that it is easy to turn on or off the bistable FWM response by only adjusting the excitation frequency or the pumping intensity. Our results offer a feasible means for measuring the SQD-PC nanocavity coupling strength and open a new avenue to design optical switches and memories.

© 2017 Optical Society of America

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2017 (5)

S. Dutta and S. A. Rangwala, “All-optical switching in a continuously operated and strongly coupled atom-cavity system,” Appl. Phys. Lett. 110(12), 121107 (2017).

A. Dalafi and M. H. Naderi, “Intrinsic cross-Kerr nonlinearity in an optical cavity containing an interacting Bose-Einstein condensate,” Phys. Rev. A 95(4), 043601 (2017).

T. K. Mavrogordatos, G. Tancredi, M. Elliott, M. J. Peterer, A. Patterson, J. Rahamim, P. J. Leek, E. Ginossar, and M. H. Szymańska, “Simultaneous bistability of a qubit and resonator in circuit quantum electrodynamics,” Phys. Rev. Lett. 118(4), 040402 (2017).
[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(6), 063601 (2017).
[PubMed]

B. S. Nugroho, A. A. Iskandar, V. A. Malyshev, and J. Knoester, “Instabilities in the optical response of a semiconductor quantum dot-metal nanoparticle heterodimer: self-oscillations and chaos,” J. Opt. 19, 015004 (2017).

2016 (8)

S. H. Asadpour and H. R. Soleimani, “Phase dependence of optical bistability and multistability in a four-level quantum system near a plasmonic nanostructure,” J. Appl. Phys. 119(2), 023102 (2016).

K. H. Madsen, T. B. Lehmann, and P. Lodahl, “Role of multilevel states on quantum-dot emission in photonic-crystal cavities,” Phys. Rev. B 94(23), 235301 (2016).

J. B. Li, S. Liang, S. Xiao, M. D. He, N. C. Kim, L. Q. Chen, G. H. Wu, Y. X. Peng, X. Y. Luo, and Z. P. Guo, “Four-wave mixing signal enhancement and optical bistability of a hybrid metal nanoparticle-quantum dot molecule in a nanomechanical resonator,” Opt. Express 24(3), 2360–2369 (2016).
[PubMed]

Q. Mermillod, D. Wigger, V. Delmonte, D. E. Reiter, C. Schneider, M. Kamp, S. Hofling, W. Langbein, T. Kuhn, G. Nogues, and J. Kasprzak, “Dynamics of excitons in individual InAs quantum dots revealed in four-wave mixing spectroscopy,” Optica 3(4), 377–384 (2016).

B. Sarma and A. K. Sarma, “Controllable optical bistability in a hybrid optomechanical system,” J. Opt. Soc. Am. B 33(7), 1335–1340 (2016).

F. Wang, X. Feng, and C. H. Oh, “Optical bistability and multistability via quantum coherence in chiral molecules,” Opt. Express 24(13), 13702–13713 (2016).
[PubMed]

A. M. Barth, S. Lüker, A. Vagov, D. E. Reiter, T. Kuhn, and V. M. Axt, “Fast and selective phonon-assisted state preparation of a quantum dot by adiabatic undressing,” Phys. Rev. B 94(4), 045306 (2016).

S. H. Kazemi, S. Ghanbari, and M. Mahmoudi, “Controllable optical bistability in a cavity optomechanical system with a Bose-Einstein condensate,” Laser Phys. 26, 055502 (2016).

2015 (2)

Z. P. Wang, S. Zhen, and B. Yu, “Controlling optical bistability of acceptor and donor quantum dots embedded in a nonlinear photonic crystal,” Laser Phys. Lett. 12(4), 046004 (2015).

P. Lodahl, S. Mahmoodian, and S. Stobbe, “Interfacing single photons and single quantum dots with photonic nanostructures,” Rev. Mod. Phys. 87(2), 347–400 (2015).

2014 (4)

J. Li, R. Yu, C. Ding, and Y. Wu, “Optical bistability and four-wave mixing with a single nitrogen-vacancy center coupled to a photonic crystal nanocavity in the weak-coupling regime,” Opt. Express 22(12), 15024–15038 (2014).
[PubMed]

S. H. Asadpour and H. R. Soleimani, “Optical bistability in a three-level lambda molecule with permanent dipole moments,” J. Opt. Soc. Am. B 31(12), 3123–3130 (2014).

X. Xia, J. Xu, and Y. Yang, “Controllable optical bistability of an asymmetric cavity containing a single two-level atom,” Phys. Rev. A 90(4), 043857 (2014).

D. E. Reiter, T. Kuhn, M. Glässl, and V. M. Axt, “The role of phonons for exciton and biexciton generation in an optically driven quantum dot,” J. Phys. Condens. Matter 26(42), 423203 (2014).
[PubMed]

2013 (8)

J. M. Daniels, P. Machnikowski, and T. Kuhn, “Excitons in quantum dot molecules: Coulomb coupling, spin-orbit effects, and phonon-induced line broadening,” Phys. Rev. B 88(20), 205307 (2013).

M. Glässl, A. M. Barth, and V. M. Axt, “Proposed robust and high-fidelity preparation of excitons and biexcitons in semiconductor quantum dots making active use of phonons,” Phys. Rev. Lett. 110(14), 147401 (2013).
[PubMed]

S. Safaei, Ö. E. Müstecaplıoğlu, and B. Tanatar, “Bistable behavior of a two-mode Bose-Einstein condensate in an optical cavity,” Laser Phys. 23(3), 035501 (2013).

Y. C. Yu, J. F. Liu, X. L. Zhuo, G. Chen, C. J. Jin, and X. H. Wang, “Vacuum Rabi splitting in a coupled system of single quantum dot and photonic crystal cavity: effect of local and propagation Green’s functions,” Opt. Express 21(20), 23486–23497 (2013).
[PubMed]

Z. Wang and B. Yu, “Switching from optical bistability to multistability in a coupled semiconductor double-quantum-dot nanostructure,” J. Opt. Soc. Am. B 30(11), 2915–2920 (2013).

J. Liu, S. Ates, M. Lorke, J. Mørk, P. Lodahl, and S. Stobbe, “A comparison between experiment and theory on few-quantum-dot nanolasing in a photonic-crystal cavity,” Opt. Express 21(23), 28507–28512 (2013).
[PubMed]

P. Lodahl and S. Stobbe, “Solid-state quantum optics with quantum dots in photonic nanostructures,” Nanophotonics 2(1), 39–55 (2013).

B. S. Nugroho, A. A. Iskandar, V. A. Malyshev, and J. Knoester, “Bistable optical response of a nanoparticle heterodimer: Mechanism, phase diagram, and switching time,” J. Chem. Phys. 139(1), 014303 (2013).
[PubMed]

2012 (5)

M. R. Singh, C. Racknor, and D. Schindel, “Controlling the photoluminescence of acceptor and donor quantum dots embedded in a nonlinear photonic crystal,” Appl. Phys. Lett. 101(5), 051115 (2012).

J. B. Li, N. C. Kim, M. T. Cheng, L. Zhou, Z. H. Hao, and Q. Q. Wang, “Optical bistability and nonlinearity of coherently coupled exciton-plasmon systems,” Opt. Express 20(2), 1856–1861 (2012).
[PubMed]

A. V. Malyshev, “Condition for resonant optical bistability,” Phys. Rev. A 86(6), 065804 (2012).

J. Yuan, W. Feng, P. Li, X. Zhang, Y. Zhang, H. Zheng, and Y. Zhang, “Controllable vacuum Rabi splitting and optical bistability of multi-wave-mixing signal inside a ring cavity,” Phys. Rev. A 86(6), 063820 (2012).

Y. Dumeige, A. M. Yacomotti, P. Grinberg, K. Bencheikh, E. L. Cren, and J. A. Levenson, “Microcavity-quality-factor enhancement using nonlinear effects close to the bistability threshold and coherent population oscillations,” Phys. Rev. A 85(6), 063824 (2012).

2011 (3)

J. J. Li and K. D. Zhu, “A quantum optical transistor with a single quantum dot in a photonic crystal nanocavity,” Nanotechnology 22(5), 055202 (2011).
[PubMed]

S. Yang, M. Alamri, J. Evers, and M. S. Zubairy, “Controllable optical switch using a Bose-Einstein condensate in an optical cavity,” Phys. Rev. A 83(5), 053821 (2011).

A. Rundquist, A. Majumdar, and J. Vučković, “Off-resonant coupling between a single quantum dot and a nanobeam photonic crystal cavity,” Appl. Phys. Lett. 99(25), 251907 (2011).

2010 (2)

J. Kasprzak, S. Reitzenstein, E. A. Muljarov, C. Kistner, C. Schneider, M. Strauss, S. Höfling, A. Forchel, and W. Langbein, “Up on the Jaynes-Cummings ladder of a quantum-dot/microcavity system,” Nat. Mater. 9(4), 304–308 (2010).
[PubMed]

A. Mitra and R. Vyas, “Entanglement and bistability in coupled quantum dots inside a driven cavity,” Phys. Rev. A 81(1), 012329 (2010).

2009 (2)

X. Guo and S. Lü, “Controllable optical bistability in photonic-crystal one-atom laser,” Phys. Rev. A 80(4), 043826 (2009).

J. Kasprzak and W. Langbein, “Four-wave mixing from individual excitons: Intensity dependence and imaging,” Phys. Status Solidi, B Basic Res. 246(4), 820–823 (2009).

2008 (3)

B. Gu, W. Ji, P. S. Patil, and S. M. Dharmaprakash, “Ultrafast optical nonlinearities and figures of merit in acceptor-substituted 3,4,5-trimethoxy chalcone derivatives: Structure-property relationships,” J. Appl. Phys. 103(10), 103511 (2008).

R. D. Artuso and G. W. Bryant, “Optical response of strongly coupled quantum dot-metal nanoparticle systems: double peaked Fano structure and bistability,” Nano Lett. 8(7), 2106–2111 (2008).
[PubMed]

S. Reitzenstein, C. Böckler, A. Bazhenov, A. Gorbunov, A. Löffler, M. Kamp, V. D. Kulakovskii, and A. Forchel, “Single quantum dot controlled lasing effects in high-Q micropillar cavities,” Opt. Express 16(7), 4848–4857 (2008).
[PubMed]

2007 (3)

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).
[PubMed]

S. Gupta, K. L. Moore, K. W. Murch, and D. M. Stamper-Kurn, “Cavity nonlinear optics at low photon numbers from collective atomic motion,” Phys. Rev. Lett. 99(21), 213601 (2007).
[PubMed]

V. S. C. Manga Rao and S. Hughes, “Single quantum-dot Purcell factor and factor in a photonic crystal waveguide,” Phys. Rev. B 75(20), 205437 (2007).

2005 (2)

2004 (4)

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432(7014), 200–203 (2004).
[PubMed]

L. M. Duan and H. J. Kimble, “Scalable photonic quantum computation through cavity-assisted interactions,” Phys. Rev. Lett. 92(12), 127902 (2004).
[PubMed]

H. Chang, H. Wu, C. Xie, and H. Wang, “Controlled Shift of optical bistability hysteresis curve and storage of optical signals in a four-level atomic system,” Phys. Rev. Lett. 93(21), 213901 (2004).
[PubMed]

Th. Elsässer, B. Nagorny, and A. Hemmerich, “Optical bistability and collective behavior of atoms trapped in a high-Q ring cavity,” Phys. Rev. A 69(3), 033403 (2004).

2003 (1)

B. Nagorny, T. Elsässer, and A. Hemmerich, “Collective atomic motion in an optical lattice formed inside a high finesse cavity,” Phys. Rev. Lett. 91(15), 153003 (2003).
[PubMed]

2001 (1)

H. Wang, D. J. Goorskey, and M. Xiao, “Bistability and instability of three-level atoms inside an optical cavity,” Phys. Rev. A 65(1), 011801 (2001).

1988 (1)

C. M. Savage and H. J. Carmichael, “Single-atom optical bistability,” IEEE J. Quantum Electron. 24(8), 1495–1498 (1988).

1987 (1)

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987).
[PubMed]

1982 (1)

1981 (1)

R. W. Boyd, M. G. Raymer, P. Narum, and D. J. Harter, “Four-wave parametric interactions in a strongly driven two-level system,” Phys. Rev. A 24(1), 411–423 (1981).

1976 (1)

H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, “Differential gain and bistability using a sodium-filled Fabry-Perot interferometer,” Phys. Rev. Lett. 36(19), 1135–1138 (1976).

Agarwal, G. S.

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(6), 063601 (2017).
[PubMed]

Alamri, M.

S. Yang, M. Alamri, J. Evers, and M. S. Zubairy, “Controllable optical switch using a Bose-Einstein condensate in an optical cavity,” Phys. Rev. A 83(5), 053821 (2011).

Artuso, R. D.

R. D. Artuso and G. W. Bryant, “Optical response of strongly coupled quantum dot-metal nanoparticle systems: double peaked Fano structure and bistability,” Nano Lett. 8(7), 2106–2111 (2008).
[PubMed]

Asadpour, S. H.

S. H. Asadpour and H. R. Soleimani, “Phase dependence of optical bistability and multistability in a four-level quantum system near a plasmonic nanostructure,” J. Appl. Phys. 119(2), 023102 (2016).

S. H. Asadpour and H. R. Soleimani, “Optical bistability in a three-level lambda molecule with permanent dipole moments,” J. Opt. Soc. Am. B 31(12), 3123–3130 (2014).

Atatüre, M.

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).
[PubMed]

Ates, S.

Axt, V. M.

A. M. Barth, S. Lüker, A. Vagov, D. E. Reiter, T. Kuhn, and V. M. Axt, “Fast and selective phonon-assisted state preparation of a quantum dot by adiabatic undressing,” Phys. Rev. B 94(4), 045306 (2016).

D. E. Reiter, T. Kuhn, M. Glässl, and V. M. Axt, “The role of phonons for exciton and biexciton generation in an optically driven quantum dot,” J. Phys. Condens. Matter 26(42), 423203 (2014).
[PubMed]

M. Glässl, A. M. Barth, and V. M. Axt, “Proposed robust and high-fidelity preparation of excitons and biexcitons in semiconductor quantum dots making active use of phonons,” Phys. Rev. Lett. 110(14), 147401 (2013).
[PubMed]

Badolato, A.

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).
[PubMed]

Barth, A. M.

A. M. Barth, S. Lüker, A. Vagov, D. E. Reiter, T. Kuhn, and V. M. Axt, “Fast and selective phonon-assisted state preparation of a quantum dot by adiabatic undressing,” Phys. Rev. B 94(4), 045306 (2016).

M. Glässl, A. M. Barth, and V. M. Axt, “Proposed robust and high-fidelity preparation of excitons and biexcitons in semiconductor quantum dots making active use of phonons,” Phys. Rev. Lett. 110(14), 147401 (2013).
[PubMed]

Bazhenov, A.

Bencheikh, K.

Y. Dumeige, A. M. Yacomotti, P. Grinberg, K. Bencheikh, E. L. Cren, and J. A. Levenson, “Microcavity-quality-factor enhancement using nonlinear effects close to the bistability threshold and coherent population oscillations,” Phys. Rev. A 85(6), 063824 (2012).

Böckler, C.

Boyd, R. W.

R. W. Boyd, M. G. Raymer, P. Narum, and D. J. Harter, “Four-wave parametric interactions in a strongly driven two-level system,” Phys. Rev. A 24(1), 411–423 (1981).

Bryant, G. W.

R. D. Artuso and G. W. Bryant, “Optical response of strongly coupled quantum dot-metal nanoparticle systems: double peaked Fano structure and bistability,” Nano Lett. 8(7), 2106–2111 (2008).
[PubMed]

Carmichael, H. J.

C. M. Savage and H. J. Carmichael, “Single-atom optical bistability,” IEEE J. Quantum Electron. 24(8), 1495–1498 (1988).

Chang, H.

H. Chang, H. Wu, C. Xie, and H. Wang, “Controlled Shift of optical bistability hysteresis curve and storage of optical signals in a four-level atomic system,” Phys. Rev. Lett. 93(21), 213901 (2004).
[PubMed]

Chen, G.

Chen, L. Q.

Cheng, M. T.

Cren, E. L.

Y. Dumeige, A. M. Yacomotti, P. Grinberg, K. Bencheikh, E. L. Cren, and J. A. Levenson, “Microcavity-quality-factor enhancement using nonlinear effects close to the bistability threshold and coherent population oscillations,” Phys. Rev. A 85(6), 063824 (2012).

Dalafi, A.

A. Dalafi and M. H. Naderi, “Intrinsic cross-Kerr nonlinearity in an optical cavity containing an interacting Bose-Einstein condensate,” Phys. Rev. A 95(4), 043601 (2017).

Daniels, J. M.

J. M. Daniels, P. Machnikowski, and T. Kuhn, “Excitons in quantum dot molecules: Coulomb coupling, spin-orbit effects, and phonon-induced line broadening,” Phys. Rev. B 88(20), 205307 (2013).

Delmonte, V.

Deppe, D. G.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432(7014), 200–203 (2004).
[PubMed]

Dharmaprakash, S. M.

B. Gu, W. Ji, P. S. Patil, and S. M. Dharmaprakash, “Ultrafast optical nonlinearities and figures of merit in acceptor-substituted 3,4,5-trimethoxy chalcone derivatives: Structure-property relationships,” J. Appl. Phys. 103(10), 103511 (2008).

Ding, C.

Duan, L. M.

L. M. Duan and H. J. Kimble, “Scalable photonic quantum computation through cavity-assisted interactions,” Phys. Rev. Lett. 92(12), 127902 (2004).
[PubMed]

Dumeige, Y.

Y. Dumeige, A. M. Yacomotti, P. Grinberg, K. Bencheikh, E. L. Cren, and J. A. Levenson, “Microcavity-quality-factor enhancement using nonlinear effects close to the bistability threshold and coherent population oscillations,” Phys. Rev. A 85(6), 063824 (2012).

Dutta, S.

S. Dutta and S. A. Rangwala, “All-optical switching in a continuously operated and strongly coupled atom-cavity system,” Appl. Phys. Lett. 110(12), 121107 (2017).

Ell, C.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432(7014), 200–203 (2004).
[PubMed]

Elliott, M.

T. K. Mavrogordatos, G. Tancredi, M. Elliott, M. J. Peterer, A. Patterson, J. Rahamim, P. J. Leek, E. Ginossar, and M. H. Szymańska, “Simultaneous bistability of a qubit and resonator in circuit quantum electrodynamics,” Phys. Rev. Lett. 118(4), 040402 (2017).
[PubMed]

Elsässer, T.

B. Nagorny, T. Elsässer, and A. Hemmerich, “Collective atomic motion in an optical lattice formed inside a high finesse cavity,” Phys. Rev. Lett. 91(15), 153003 (2003).
[PubMed]

Elsässer, Th.

Th. Elsässer, B. Nagorny, and A. Hemmerich, “Optical bistability and collective behavior of atoms trapped in a high-Q ring cavity,” Phys. Rev. A 69(3), 033403 (2004).

Evers, J.

S. Yang, M. Alamri, J. Evers, and M. S. Zubairy, “Controllable optical switch using a Bose-Einstein condensate in an optical cavity,” Phys. Rev. A 83(5), 053821 (2011).

Fält, S.

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).
[PubMed]

Feng, W.

J. Yuan, W. Feng, P. Li, X. Zhang, Y. Zhang, H. Zheng, and Y. Zhang, “Controllable vacuum Rabi splitting and optical bistability of multi-wave-mixing signal inside a ring cavity,” Phys. Rev. A 86(6), 063820 (2012).

Feng, X.

Forchel, A.

J. Kasprzak, S. Reitzenstein, E. A. Muljarov, C. Kistner, C. Schneider, M. Strauss, S. Höfling, A. Forchel, and W. Langbein, “Up on the Jaynes-Cummings ladder of a quantum-dot/microcavity system,” Nat. Mater. 9(4), 304–308 (2010).
[PubMed]

S. Reitzenstein, C. Böckler, A. Bazhenov, A. Gorbunov, A. Löffler, M. Kamp, V. D. Kulakovskii, and A. Forchel, “Single quantum dot controlled lasing effects in high-Q micropillar cavities,” Opt. Express 16(7), 4848–4857 (2008).
[PubMed]

Gerace, D.

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).
[PubMed]

Ghanbari, S.

S. H. Kazemi, S. Ghanbari, and M. Mahmoudi, “Controllable optical bistability in a cavity optomechanical system with a Bose-Einstein condensate,” Laser Phys. 26, 055502 (2016).

Gibbs, H. M.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432(7014), 200–203 (2004).
[PubMed]

H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, “Differential gain and bistability using a sodium-filled Fabry-Perot interferometer,” Phys. Rev. Lett. 36(19), 1135–1138 (1976).

Ginossar, E.

T. K. Mavrogordatos, G. Tancredi, M. Elliott, M. J. Peterer, A. Patterson, J. Rahamim, P. J. Leek, E. Ginossar, and M. H. Szymańska, “Simultaneous bistability of a qubit and resonator in circuit quantum electrodynamics,” Phys. Rev. Lett. 118(4), 040402 (2017).
[PubMed]

Glässl, M.

D. E. Reiter, T. Kuhn, M. Glässl, and V. M. Axt, “The role of phonons for exciton and biexciton generation in an optically driven quantum dot,” J. Phys. Condens. Matter 26(42), 423203 (2014).
[PubMed]

M. Glässl, A. M. Barth, and V. M. Axt, “Proposed robust and high-fidelity preparation of excitons and biexcitons in semiconductor quantum dots making active use of phonons,” Phys. Rev. Lett. 110(14), 147401 (2013).
[PubMed]

Goorskey, D. J.

H. Wang, D. J. Goorskey, and M. Xiao, “Bistability and instability of three-level atoms inside an optical cavity,” Phys. Rev. A 65(1), 011801 (2001).

Gorbunov, A.

Grant, D. E.

Grinberg, P.

Y. Dumeige, A. M. Yacomotti, P. Grinberg, K. Bencheikh, E. L. Cren, and J. A. Levenson, “Microcavity-quality-factor enhancement using nonlinear effects close to the bistability threshold and coherent population oscillations,” Phys. Rev. A 85(6), 063824 (2012).

Gu, B.

B. Gu, W. Ji, P. S. Patil, and S. M. Dharmaprakash, “Ultrafast optical nonlinearities and figures of merit in acceptor-substituted 3,4,5-trimethoxy chalcone derivatives: Structure-property relationships,” J. Appl. Phys. 103(10), 103511 (2008).

Gulde, S.

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).
[PubMed]

Guo, X.

X. Guo and S. Lü, “Controllable optical bistability in photonic-crystal one-atom laser,” Phys. Rev. A 80(4), 043826 (2009).

Guo, Z. P.

Gupta, S.

S. Gupta, K. L. Moore, K. W. Murch, and D. M. Stamper-Kurn, “Cavity nonlinear optics at low photon numbers from collective atomic motion,” Phys. Rev. Lett. 99(21), 213601 (2007).
[PubMed]

Hao, Z. H.

Harter, D. J.

R. W. Boyd, M. G. Raymer, P. Narum, and D. J. Harter, “Four-wave parametric interactions in a strongly driven two-level system,” Phys. Rev. A 24(1), 411–423 (1981).

He, M. D.

Hemmerich, A.

Th. Elsässer, B. Nagorny, and A. Hemmerich, “Optical bistability and collective behavior of atoms trapped in a high-Q ring cavity,” Phys. Rev. A 69(3), 033403 (2004).

B. Nagorny, T. Elsässer, and A. Hemmerich, “Collective atomic motion in an optical lattice formed inside a high finesse cavity,” Phys. Rev. Lett. 91(15), 153003 (2003).
[PubMed]

Hendrickson, J.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432(7014), 200–203 (2004).
[PubMed]

Hennessy, K.

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).
[PubMed]

Hofling, S.

Höfling, S.

J. Kasprzak, S. Reitzenstein, E. A. Muljarov, C. Kistner, C. Schneider, M. Strauss, S. Höfling, A. Forchel, and W. Langbein, “Up on the Jaynes-Cummings ladder of a quantum-dot/microcavity system,” Nat. Mater. 9(4), 304–308 (2010).
[PubMed]

Hu, E. L.

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).
[PubMed]

Hughes, S.

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(6), 063601 (2017).
[PubMed]

V. S. C. Manga Rao and S. Hughes, “Single quantum-dot Purcell factor and factor in a photonic crystal waveguide,” Phys. Rev. B 75(20), 205437 (2007).

Imamoglu, A.

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).
[PubMed]

Iskandar, A. A.

B. S. Nugroho, A. A. Iskandar, V. A. Malyshev, and J. Knoester, “Instabilities in the optical response of a semiconductor quantum dot-metal nanoparticle heterodimer: self-oscillations and chaos,” J. Opt. 19, 015004 (2017).

B. S. Nugroho, A. A. Iskandar, V. A. Malyshev, and J. Knoester, “Bistable optical response of a nanoparticle heterodimer: Mechanism, phase diagram, and switching time,” J. Chem. Phys. 139(1), 014303 (2013).
[PubMed]

Ji, W.

B. Gu, W. Ji, P. S. Patil, and S. M. Dharmaprakash, “Ultrafast optical nonlinearities and figures of merit in acceptor-substituted 3,4,5-trimethoxy chalcone derivatives: Structure-property relationships,” J. Appl. Phys. 103(10), 103511 (2008).

Jin, C. J.

John, S.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987).
[PubMed]

Joshi, A.

Kamp, M.

Kasprzak, J.

Q. Mermillod, D. Wigger, V. Delmonte, D. E. Reiter, C. Schneider, M. Kamp, S. Hofling, W. Langbein, T. Kuhn, G. Nogues, and J. Kasprzak, “Dynamics of excitons in individual InAs quantum dots revealed in four-wave mixing spectroscopy,” Optica 3(4), 377–384 (2016).

J. Kasprzak, S. Reitzenstein, E. A. Muljarov, C. Kistner, C. Schneider, M. Strauss, S. Höfling, A. Forchel, and W. Langbein, “Up on the Jaynes-Cummings ladder of a quantum-dot/microcavity system,” Nat. Mater. 9(4), 304–308 (2010).
[PubMed]

J. Kasprzak and W. Langbein, “Four-wave mixing from individual excitons: Intensity dependence and imaging,” Phys. Status Solidi, B Basic Res. 246(4), 820–823 (2009).

Kazemi, S. H.

S. H. Kazemi, S. Ghanbari, and M. Mahmoudi, “Controllable optical bistability in a cavity optomechanical system with a Bose-Einstein condensate,” Laser Phys. 26, 055502 (2016).

Khitrova, G.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432(7014), 200–203 (2004).
[PubMed]

Kim, N. C.

Kimble, H. J.

L. M. Duan and H. J. Kimble, “Scalable photonic quantum computation through cavity-assisted interactions,” Phys. Rev. Lett. 92(12), 127902 (2004).
[PubMed]

D. E. Grant and H. J. Kimble, “Optical bistability for two-level atoms in a standing-wave cavity,” Opt. Lett. 7(8), 353–355 (1982).
[PubMed]

Kistner, C.

J. Kasprzak, S. Reitzenstein, E. A. Muljarov, C. Kistner, C. Schneider, M. Strauss, S. Höfling, A. Forchel, and W. Langbein, “Up on the Jaynes-Cummings ladder of a quantum-dot/microcavity system,” Nat. Mater. 9(4), 304–308 (2010).
[PubMed]

Knoester, J.

B. S. Nugroho, A. A. Iskandar, V. A. Malyshev, and J. Knoester, “Instabilities in the optical response of a semiconductor quantum dot-metal nanoparticle heterodimer: self-oscillations and chaos,” J. Opt. 19, 015004 (2017).

B. S. Nugroho, A. A. Iskandar, V. A. Malyshev, and J. Knoester, “Bistable optical response of a nanoparticle heterodimer: Mechanism, phase diagram, and switching time,” J. Chem. Phys. 139(1), 014303 (2013).
[PubMed]

Kuhn, T.

A. M. Barth, S. Lüker, A. Vagov, D. E. Reiter, T. Kuhn, and V. M. Axt, “Fast and selective phonon-assisted state preparation of a quantum dot by adiabatic undressing,” Phys. Rev. B 94(4), 045306 (2016).

Q. Mermillod, D. Wigger, V. Delmonte, D. E. Reiter, C. Schneider, M. Kamp, S. Hofling, W. Langbein, T. Kuhn, G. Nogues, and J. Kasprzak, “Dynamics of excitons in individual InAs quantum dots revealed in four-wave mixing spectroscopy,” Optica 3(4), 377–384 (2016).

D. E. Reiter, T. Kuhn, M. Glässl, and V. M. Axt, “The role of phonons for exciton and biexciton generation in an optically driven quantum dot,” J. Phys. Condens. Matter 26(42), 423203 (2014).
[PubMed]

J. M. Daniels, P. Machnikowski, and T. Kuhn, “Excitons in quantum dot molecules: Coulomb coupling, spin-orbit effects, and phonon-induced line broadening,” Phys. Rev. B 88(20), 205307 (2013).

Kulakovskii, V. D.

Langbein, W.

Q. Mermillod, D. Wigger, V. Delmonte, D. E. Reiter, C. Schneider, M. Kamp, S. Hofling, W. Langbein, T. Kuhn, G. Nogues, and J. Kasprzak, “Dynamics of excitons in individual InAs quantum dots revealed in four-wave mixing spectroscopy,” Optica 3(4), 377–384 (2016).

J. Kasprzak, S. Reitzenstein, E. A. Muljarov, C. Kistner, C. Schneider, M. Strauss, S. Höfling, A. Forchel, and W. Langbein, “Up on the Jaynes-Cummings ladder of a quantum-dot/microcavity system,” Nat. Mater. 9(4), 304–308 (2010).
[PubMed]

J. Kasprzak and W. Langbein, “Four-wave mixing from individual excitons: Intensity dependence and imaging,” Phys. Status Solidi, B Basic Res. 246(4), 820–823 (2009).

Leek, P. J.

T. K. Mavrogordatos, G. Tancredi, M. Elliott, M. J. Peterer, A. Patterson, J. Rahamim, P. J. Leek, E. Ginossar, and M. H. Szymańska, “Simultaneous bistability of a qubit and resonator in circuit quantum electrodynamics,” Phys. Rev. Lett. 118(4), 040402 (2017).
[PubMed]

Lehmann, T. B.

K. H. Madsen, T. B. Lehmann, and P. Lodahl, “Role of multilevel states on quantum-dot emission in photonic-crystal cavities,” Phys. Rev. B 94(23), 235301 (2016).

Levenson, J. A.

Y. Dumeige, A. M. Yacomotti, P. Grinberg, K. Bencheikh, E. L. Cren, and J. A. Levenson, “Microcavity-quality-factor enhancement using nonlinear effects close to the bistability threshold and coherent population oscillations,” Phys. Rev. A 85(6), 063824 (2012).

Li, J.

Li, J. B.

Li, J. J.

J. J. Li and K. D. Zhu, “A quantum optical transistor with a single quantum dot in a photonic crystal nanocavity,” Nanotechnology 22(5), 055202 (2011).
[PubMed]

Li, P.

J. Yuan, W. Feng, P. Li, X. Zhang, Y. Zhang, H. Zheng, and Y. Zhang, “Controllable vacuum Rabi splitting and optical bistability of multi-wave-mixing signal inside a ring cavity,” Phys. Rev. A 86(6), 063820 (2012).

Liang, S.

Liu, J.

Liu, J. F.

Lodahl, P.

K. H. Madsen, T. B. Lehmann, and P. Lodahl, “Role of multilevel states on quantum-dot emission in photonic-crystal cavities,” Phys. Rev. B 94(23), 235301 (2016).

P. Lodahl, S. Mahmoodian, and S. Stobbe, “Interfacing single photons and single quantum dots with photonic nanostructures,” Rev. Mod. Phys. 87(2), 347–400 (2015).

P. Lodahl and S. Stobbe, “Solid-state quantum optics with quantum dots in photonic nanostructures,” Nanophotonics 2(1), 39–55 (2013).

J. Liu, S. Ates, M. Lorke, J. Mørk, P. Lodahl, and S. Stobbe, “A comparison between experiment and theory on few-quantum-dot nanolasing in a photonic-crystal cavity,” Opt. Express 21(23), 28507–28512 (2013).
[PubMed]

Löffler, A.

Lorke, M.

Lü, S.

X. Guo and S. Lü, “Controllable optical bistability in photonic-crystal one-atom laser,” Phys. Rev. A 80(4), 043826 (2009).

Lüker, S.

A. M. Barth, S. Lüker, A. Vagov, D. E. Reiter, T. Kuhn, and V. M. Axt, “Fast and selective phonon-assisted state preparation of a quantum dot by adiabatic undressing,” Phys. Rev. B 94(4), 045306 (2016).

Luo, X. Y.

Machnikowski, P.

J. M. Daniels, P. Machnikowski, and T. Kuhn, “Excitons in quantum dot molecules: Coulomb coupling, spin-orbit effects, and phonon-induced line broadening,” Phys. Rev. B 88(20), 205307 (2013).

Madsen, K. H.

K. H. Madsen, T. B. Lehmann, and P. Lodahl, “Role of multilevel states on quantum-dot emission in photonic-crystal cavities,” Phys. Rev. B 94(23), 235301 (2016).

Mahmoodian, S.

P. Lodahl, S. Mahmoodian, and S. Stobbe, “Interfacing single photons and single quantum dots with photonic nanostructures,” Rev. Mod. Phys. 87(2), 347–400 (2015).

Mahmoudi, M.

S. H. Kazemi, S. Ghanbari, and M. Mahmoudi, “Controllable optical bistability in a cavity optomechanical system with a Bose-Einstein condensate,” Laser Phys. 26, 055502 (2016).

Majumdar, A.

A. Rundquist, A. Majumdar, and J. Vučković, “Off-resonant coupling between a single quantum dot and a nanobeam photonic crystal cavity,” Appl. Phys. Lett. 99(25), 251907 (2011).

Malyshev, A. V.

A. V. Malyshev, “Condition for resonant optical bistability,” Phys. Rev. A 86(6), 065804 (2012).

Malyshev, V. A.

B. S. Nugroho, A. A. Iskandar, V. A. Malyshev, and J. Knoester, “Instabilities in the optical response of a semiconductor quantum dot-metal nanoparticle heterodimer: self-oscillations and chaos,” J. Opt. 19, 015004 (2017).

B. S. Nugroho, A. A. Iskandar, V. A. Malyshev, and J. Knoester, “Bistable optical response of a nanoparticle heterodimer: Mechanism, phase diagram, and switching time,” J. Chem. Phys. 139(1), 014303 (2013).
[PubMed]

Manga Rao, V. S. C.

V. S. C. Manga Rao and S. Hughes, “Single quantum-dot Purcell factor and factor in a photonic crystal waveguide,” Phys. Rev. B 75(20), 205437 (2007).

Mavrogordatos, T. K.

T. K. Mavrogordatos, G. Tancredi, M. Elliott, M. J. Peterer, A. Patterson, J. Rahamim, P. J. Leek, E. Ginossar, and M. H. Szymańska, “Simultaneous bistability of a qubit and resonator in circuit quantum electrodynamics,” Phys. Rev. Lett. 118(4), 040402 (2017).
[PubMed]

McCall, S. L.

H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, “Differential gain and bistability using a sodium-filled Fabry-Perot interferometer,” Phys. Rev. Lett. 36(19), 1135–1138 (1976).

Mermillod, Q.

Mitra, A.

A. Mitra and R. Vyas, “Entanglement and bistability in coupled quantum dots inside a driven cavity,” Phys. Rev. A 81(1), 012329 (2010).

Moore, K. L.

S. Gupta, K. L. Moore, K. W. Murch, and D. M. Stamper-Kurn, “Cavity nonlinear optics at low photon numbers from collective atomic motion,” Phys. Rev. Lett. 99(21), 213601 (2007).
[PubMed]

Mørk, J.

Muljarov, E. A.

J. Kasprzak, S. Reitzenstein, E. A. Muljarov, C. Kistner, C. Schneider, M. Strauss, S. Höfling, A. Forchel, and W. Langbein, “Up on the Jaynes-Cummings ladder of a quantum-dot/microcavity system,” Nat. Mater. 9(4), 304–308 (2010).
[PubMed]

Murch, K. W.

S. Gupta, K. L. Moore, K. W. Murch, and D. M. Stamper-Kurn, “Cavity nonlinear optics at low photon numbers from collective atomic motion,” Phys. Rev. Lett. 99(21), 213601 (2007).
[PubMed]

Müstecaplioglu, Ö. E.

S. Safaei, Ö. E. Müstecaplıoğlu, and B. Tanatar, “Bistable behavior of a two-mode Bose-Einstein condensate in an optical cavity,” Laser Phys. 23(3), 035501 (2013).

Naderi, M. H.

A. Dalafi and M. H. Naderi, “Intrinsic cross-Kerr nonlinearity in an optical cavity containing an interacting Bose-Einstein condensate,” Phys. Rev. A 95(4), 043601 (2017).

Nagorny, B.

Th. Elsässer, B. Nagorny, and A. Hemmerich, “Optical bistability and collective behavior of atoms trapped in a high-Q ring cavity,” Phys. Rev. A 69(3), 033403 (2004).

B. Nagorny, T. Elsässer, and A. Hemmerich, “Collective atomic motion in an optical lattice formed inside a high finesse cavity,” Phys. Rev. Lett. 91(15), 153003 (2003).
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Narum, P.

R. W. Boyd, M. G. Raymer, P. Narum, and D. J. Harter, “Four-wave parametric interactions in a strongly driven two-level system,” Phys. Rev. A 24(1), 411–423 (1981).

Nogues, G.

Nugroho, B. S.

B. S. Nugroho, A. A. Iskandar, V. A. Malyshev, and J. Knoester, “Instabilities in the optical response of a semiconductor quantum dot-metal nanoparticle heterodimer: self-oscillations and chaos,” J. Opt. 19, 015004 (2017).

B. S. Nugroho, A. A. Iskandar, V. A. Malyshev, and J. Knoester, “Bistable optical response of a nanoparticle heterodimer: Mechanism, phase diagram, and switching time,” J. Chem. Phys. 139(1), 014303 (2013).
[PubMed]

Oh, C. H.

Patil, P. S.

B. Gu, W. Ji, P. S. Patil, and S. M. Dharmaprakash, “Ultrafast optical nonlinearities and figures of merit in acceptor-substituted 3,4,5-trimethoxy chalcone derivatives: Structure-property relationships,” J. Appl. Phys. 103(10), 103511 (2008).

Patterson, A.

T. K. Mavrogordatos, G. Tancredi, M. Elliott, M. J. Peterer, A. Patterson, J. Rahamim, P. J. Leek, E. Ginossar, and M. H. Szymańska, “Simultaneous bistability of a qubit and resonator in circuit quantum electrodynamics,” Phys. Rev. Lett. 118(4), 040402 (2017).
[PubMed]

Peng, Y. X.

Peterer, M. J.

T. K. Mavrogordatos, G. Tancredi, M. Elliott, M. J. Peterer, A. Patterson, J. Rahamim, P. J. Leek, E. Ginossar, and M. H. Szymańska, “Simultaneous bistability of a qubit and resonator in circuit quantum electrodynamics,” Phys. Rev. Lett. 118(4), 040402 (2017).
[PubMed]

Racknor, C.

M. R. Singh, C. Racknor, and D. Schindel, “Controlling the photoluminescence of acceptor and donor quantum dots embedded in a nonlinear photonic crystal,” Appl. Phys. Lett. 101(5), 051115 (2012).

Rahamim, J.

T. K. Mavrogordatos, G. Tancredi, M. Elliott, M. J. Peterer, A. Patterson, J. Rahamim, P. J. Leek, E. Ginossar, and M. H. Szymańska, “Simultaneous bistability of a qubit and resonator in circuit quantum electrodynamics,” Phys. Rev. Lett. 118(4), 040402 (2017).
[PubMed]

Rangwala, S. A.

S. Dutta and S. A. Rangwala, “All-optical switching in a continuously operated and strongly coupled atom-cavity system,” Appl. Phys. Lett. 110(12), 121107 (2017).

Raymer, M. G.

R. W. Boyd, M. G. Raymer, P. Narum, and D. J. Harter, “Four-wave parametric interactions in a strongly driven two-level system,” Phys. Rev. A 24(1), 411–423 (1981).

Reiter, D. E.

A. M. Barth, S. Lüker, A. Vagov, D. E. Reiter, T. Kuhn, and V. M. Axt, “Fast and selective phonon-assisted state preparation of a quantum dot by adiabatic undressing,” Phys. Rev. B 94(4), 045306 (2016).

Q. Mermillod, D. Wigger, V. Delmonte, D. E. Reiter, C. Schneider, M. Kamp, S. Hofling, W. Langbein, T. Kuhn, G. Nogues, and J. Kasprzak, “Dynamics of excitons in individual InAs quantum dots revealed in four-wave mixing spectroscopy,” Optica 3(4), 377–384 (2016).

D. E. Reiter, T. Kuhn, M. Glässl, and V. M. Axt, “The role of phonons for exciton and biexciton generation in an optically driven quantum dot,” J. Phys. Condens. Matter 26(42), 423203 (2014).
[PubMed]

Reitzenstein, S.

J. Kasprzak, S. Reitzenstein, E. A. Muljarov, C. Kistner, C. Schneider, M. Strauss, S. Höfling, A. Forchel, and W. Langbein, “Up on the Jaynes-Cummings ladder of a quantum-dot/microcavity system,” Nat. Mater. 9(4), 304–308 (2010).
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S. Reitzenstein, C. Böckler, A. Bazhenov, A. Gorbunov, A. Löffler, M. Kamp, V. D. Kulakovskii, and A. Forchel, “Single quantum dot controlled lasing effects in high-Q micropillar cavities,” Opt. Express 16(7), 4848–4857 (2008).
[PubMed]

Rundquist, A.

A. Rundquist, A. Majumdar, and J. Vučković, “Off-resonant coupling between a single quantum dot and a nanobeam photonic crystal cavity,” Appl. Phys. Lett. 99(25), 251907 (2011).

Rupper, G.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432(7014), 200–203 (2004).
[PubMed]

Safaei, S.

S. Safaei, Ö. E. Müstecaplıoğlu, and B. Tanatar, “Bistable behavior of a two-mode Bose-Einstein condensate in an optical cavity,” Laser Phys. 23(3), 035501 (2013).

Sarma, A. K.

Sarma, B.

Savage, C. M.

C. M. Savage and H. J. Carmichael, “Single-atom optical bistability,” IEEE J. Quantum Electron. 24(8), 1495–1498 (1988).

Scherer, A.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432(7014), 200–203 (2004).
[PubMed]

Schindel, D.

M. R. Singh, C. Racknor, and D. Schindel, “Controlling the photoluminescence of acceptor and donor quantum dots embedded in a nonlinear photonic crystal,” Appl. Phys. Lett. 101(5), 051115 (2012).

Schneider, C.

Q. Mermillod, D. Wigger, V. Delmonte, D. E. Reiter, C. Schneider, M. Kamp, S. Hofling, W. Langbein, T. Kuhn, G. Nogues, and J. Kasprzak, “Dynamics of excitons in individual InAs quantum dots revealed in four-wave mixing spectroscopy,” Optica 3(4), 377–384 (2016).

J. Kasprzak, S. Reitzenstein, E. A. Muljarov, C. Kistner, C. Schneider, M. Strauss, S. Höfling, A. Forchel, and W. Langbein, “Up on the Jaynes-Cummings ladder of a quantum-dot/microcavity system,” Nat. Mater. 9(4), 304–308 (2010).
[PubMed]

Shchekin, O. B.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432(7014), 200–203 (2004).
[PubMed]

Singh, M. R.

M. R. Singh, C. Racknor, and D. Schindel, “Controlling the photoluminescence of acceptor and donor quantum dots embedded in a nonlinear photonic crystal,” Appl. Phys. Lett. 101(5), 051115 (2012).

Soleimani, H. R.

S. H. Asadpour and H. R. Soleimani, “Phase dependence of optical bistability and multistability in a four-level quantum system near a plasmonic nanostructure,” J. Appl. Phys. 119(2), 023102 (2016).

S. H. Asadpour and H. R. Soleimani, “Optical bistability in a three-level lambda molecule with permanent dipole moments,” J. Opt. Soc. Am. B 31(12), 3123–3130 (2014).

Stamper-Kurn, D. M.

S. Gupta, K. L. Moore, K. W. Murch, and D. M. Stamper-Kurn, “Cavity nonlinear optics at low photon numbers from collective atomic motion,” Phys. Rev. Lett. 99(21), 213601 (2007).
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Stobbe, S.

P. Lodahl, S. Mahmoodian, and S. Stobbe, “Interfacing single photons and single quantum dots with photonic nanostructures,” Rev. Mod. Phys. 87(2), 347–400 (2015).

P. Lodahl and S. Stobbe, “Solid-state quantum optics with quantum dots in photonic nanostructures,” Nanophotonics 2(1), 39–55 (2013).

J. Liu, S. Ates, M. Lorke, J. Mørk, P. Lodahl, and S. Stobbe, “A comparison between experiment and theory on few-quantum-dot nanolasing in a photonic-crystal cavity,” Opt. Express 21(23), 28507–28512 (2013).
[PubMed]

Strauss, M.

J. Kasprzak, S. Reitzenstein, E. A. Muljarov, C. Kistner, C. Schneider, M. Strauss, S. Höfling, A. Forchel, and W. Langbein, “Up on the Jaynes-Cummings ladder of a quantum-dot/microcavity system,” Nat. Mater. 9(4), 304–308 (2010).
[PubMed]

Szymanska, M. H.

T. K. Mavrogordatos, G. Tancredi, M. Elliott, M. J. Peterer, A. Patterson, J. Rahamim, P. J. Leek, E. Ginossar, and M. H. Szymańska, “Simultaneous bistability of a qubit and resonator in circuit quantum electrodynamics,” Phys. Rev. Lett. 118(4), 040402 (2017).
[PubMed]

Tanatar, B.

S. Safaei, Ö. E. Müstecaplıoğlu, and B. Tanatar, “Bistable behavior of a two-mode Bose-Einstein condensate in an optical cavity,” Laser Phys. 23(3), 035501 (2013).

Tancredi, G.

T. K. Mavrogordatos, G. Tancredi, M. Elliott, M. J. Peterer, A. Patterson, J. Rahamim, P. J. Leek, E. Ginossar, and M. H. Szymańska, “Simultaneous bistability of a qubit and resonator in circuit quantum electrodynamics,” Phys. Rev. Lett. 118(4), 040402 (2017).
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Vagov, A.

A. M. Barth, S. Lüker, A. Vagov, D. E. Reiter, T. Kuhn, and V. M. Axt, “Fast and selective phonon-assisted state preparation of a quantum dot by adiabatic undressing,” Phys. Rev. B 94(4), 045306 (2016).

Venkatesan, T. N. C.

H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, “Differential gain and bistability using a sodium-filled Fabry-Perot interferometer,” Phys. Rev. Lett. 36(19), 1135–1138 (1976).

Vuckovic, J.

A. Rundquist, A. Majumdar, and J. Vučković, “Off-resonant coupling between a single quantum dot and a nanobeam photonic crystal cavity,” Appl. Phys. Lett. 99(25), 251907 (2011).

Vyas, R.

A. Mitra and R. Vyas, “Entanglement and bistability in coupled quantum dots inside a driven cavity,” Phys. Rev. A 81(1), 012329 (2010).

Wang, F.

Wang, H.

H. Chang, H. Wu, C. Xie, and H. Wang, “Controlled Shift of optical bistability hysteresis curve and storage of optical signals in a four-level atomic system,” Phys. Rev. Lett. 93(21), 213901 (2004).
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Wang, X. H.

Wang, Z.

Wang, Z. P.

Z. P. Wang, S. Zhen, and B. Yu, “Controlling optical bistability of acceptor and donor quantum dots embedded in a nonlinear photonic crystal,” Laser Phys. Lett. 12(4), 046004 (2015).

Wigger, D.

Winger, M.

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).
[PubMed]

Wu, G. H.

Wu, H.

H. Chang, H. Wu, C. Xie, and H. Wang, “Controlled Shift of optical bistability hysteresis curve and storage of optical signals in a four-level atomic system,” Phys. Rev. Lett. 93(21), 213901 (2004).
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Wu, Y.

Xia, X.

X. Xia, J. Xu, and Y. Yang, “Controllable optical bistability of an asymmetric cavity containing a single two-level atom,” Phys. Rev. A 90(4), 043857 (2014).

Xiao, M.

Xiao, S.

Xie, C.

H. Chang, H. Wu, C. Xie, and H. Wang, “Controlled Shift of optical bistability hysteresis curve and storage of optical signals in a four-level atomic system,” Phys. Rev. Lett. 93(21), 213901 (2004).
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Xu, J.

X. Xia, J. Xu, and Y. Yang, “Controllable optical bistability of an asymmetric cavity containing a single two-level atom,” Phys. Rev. A 90(4), 043857 (2014).

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Y. Dumeige, A. M. Yacomotti, P. Grinberg, K. Bencheikh, E. L. Cren, and J. A. Levenson, “Microcavity-quality-factor enhancement using nonlinear effects close to the bistability threshold and coherent population oscillations,” Phys. Rev. A 85(6), 063824 (2012).

Yang, S.

S. Yang, M. Alamri, J. Evers, and M. S. Zubairy, “Controllable optical switch using a Bose-Einstein condensate in an optical cavity,” Phys. Rev. A 83(5), 053821 (2011).

Yang, W.

Yang, Y.

X. Xia, J. Xu, and Y. Yang, “Controllable optical bistability of an asymmetric cavity containing a single two-level atom,” Phys. Rev. A 90(4), 043857 (2014).

Yoshie, T.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432(7014), 200–203 (2004).
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Yu, B.

Z. P. Wang, S. Zhen, and B. Yu, “Controlling optical bistability of acceptor and donor quantum dots embedded in a nonlinear photonic crystal,” Laser Phys. Lett. 12(4), 046004 (2015).

Z. Wang and B. Yu, “Switching from optical bistability to multistability in a coupled semiconductor double-quantum-dot nanostructure,” J. Opt. Soc. Am. B 30(11), 2915–2920 (2013).

Yu, R.

Yu, Y. C.

Yuan, J.

J. Yuan, W. Feng, P. Li, X. Zhang, Y. Zhang, H. Zheng, and Y. Zhang, “Controllable vacuum Rabi splitting and optical bistability of multi-wave-mixing signal inside a ring cavity,” Phys. Rev. A 86(6), 063820 (2012).

Zhang, X.

J. Yuan, W. Feng, P. Li, X. Zhang, Y. Zhang, H. Zheng, and Y. Zhang, “Controllable vacuum Rabi splitting and optical bistability of multi-wave-mixing signal inside a ring cavity,” Phys. Rev. A 86(6), 063820 (2012).

Zhang, Y.

J. Yuan, W. Feng, P. Li, X. Zhang, Y. Zhang, H. Zheng, and Y. Zhang, “Controllable vacuum Rabi splitting and optical bistability of multi-wave-mixing signal inside a ring cavity,” Phys. Rev. A 86(6), 063820 (2012).

J. Yuan, W. Feng, P. Li, X. Zhang, Y. Zhang, H. Zheng, and Y. Zhang, “Controllable vacuum Rabi splitting and optical bistability of multi-wave-mixing signal inside a ring cavity,” Phys. Rev. A 86(6), 063820 (2012).

Zhen, S.

Z. P. Wang, S. Zhen, and B. Yu, “Controlling optical bistability of acceptor and donor quantum dots embedded in a nonlinear photonic crystal,” Laser Phys. Lett. 12(4), 046004 (2015).

Zheng, H.

J. Yuan, W. Feng, P. Li, X. Zhang, Y. Zhang, H. Zheng, and Y. Zhang, “Controllable vacuum Rabi splitting and optical bistability of multi-wave-mixing signal inside a ring cavity,” Phys. Rev. A 86(6), 063820 (2012).

Zhou, L.

Zhu, K. D.

J. J. Li and K. D. Zhu, “A quantum optical transistor with a single quantum dot in a photonic crystal nanocavity,” Nanotechnology 22(5), 055202 (2011).
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Zhuo, X. L.

Zubairy, M. S.

S. Yang, M. Alamri, J. Evers, and M. S. Zubairy, “Controllable optical switch using a Bose-Einstein condensate in an optical cavity,” Phys. Rev. A 83(5), 053821 (2011).

Appl. Phys. Lett. (3)

S. Dutta and S. A. Rangwala, “All-optical switching in a continuously operated and strongly coupled atom-cavity system,” Appl. Phys. Lett. 110(12), 121107 (2017).

A. Rundquist, A. Majumdar, and J. Vučković, “Off-resonant coupling between a single quantum dot and a nanobeam photonic crystal cavity,” Appl. Phys. Lett. 99(25), 251907 (2011).

M. R. Singh, C. Racknor, and D. Schindel, “Controlling the photoluminescence of acceptor and donor quantum dots embedded in a nonlinear photonic crystal,” Appl. Phys. Lett. 101(5), 051115 (2012).

IEEE J. Quantum Electron. (1)

C. M. Savage and H. J. Carmichael, “Single-atom optical bistability,” IEEE J. Quantum Electron. 24(8), 1495–1498 (1988).

J. Appl. Phys. (2)

B. Gu, W. Ji, P. S. Patil, and S. M. Dharmaprakash, “Ultrafast optical nonlinearities and figures of merit in acceptor-substituted 3,4,5-trimethoxy chalcone derivatives: Structure-property relationships,” J. Appl. Phys. 103(10), 103511 (2008).

S. H. Asadpour and H. R. Soleimani, “Phase dependence of optical bistability and multistability in a four-level quantum system near a plasmonic nanostructure,” J. Appl. Phys. 119(2), 023102 (2016).

J. Chem. Phys. (1)

B. S. Nugroho, A. A. Iskandar, V. A. Malyshev, and J. Knoester, “Bistable optical response of a nanoparticle heterodimer: Mechanism, phase diagram, and switching time,” J. Chem. Phys. 139(1), 014303 (2013).
[PubMed]

J. Opt. (1)

B. S. Nugroho, A. A. Iskandar, V. A. Malyshev, and J. Knoester, “Instabilities in the optical response of a semiconductor quantum dot-metal nanoparticle heterodimer: self-oscillations and chaos,” J. Opt. 19, 015004 (2017).

J. Opt. Soc. Am. B (3)

J. Phys. Condens. Matter (1)

D. E. Reiter, T. Kuhn, M. Glässl, and V. M. Axt, “The role of phonons for exciton and biexciton generation in an optically driven quantum dot,” J. Phys. Condens. Matter 26(42), 423203 (2014).
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Laser Phys. (2)

S. H. Kazemi, S. Ghanbari, and M. Mahmoudi, “Controllable optical bistability in a cavity optomechanical system with a Bose-Einstein condensate,” Laser Phys. 26, 055502 (2016).

S. Safaei, Ö. E. Müstecaplıoğlu, and B. Tanatar, “Bistable behavior of a two-mode Bose-Einstein condensate in an optical cavity,” Laser Phys. 23(3), 035501 (2013).

Laser Phys. Lett. (1)

Z. P. Wang, S. Zhen, and B. Yu, “Controlling optical bistability of acceptor and donor quantum dots embedded in a nonlinear photonic crystal,” Laser Phys. Lett. 12(4), 046004 (2015).

Nano Lett. (1)

R. D. Artuso and G. W. Bryant, “Optical response of strongly coupled quantum dot-metal nanoparticle systems: double peaked Fano structure and bistability,” Nano Lett. 8(7), 2106–2111 (2008).
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Nanophotonics (1)

P. Lodahl and S. Stobbe, “Solid-state quantum optics with quantum dots in photonic nanostructures,” Nanophotonics 2(1), 39–55 (2013).

Nanotechnology (1)

J. J. Li and K. D. Zhu, “A quantum optical transistor with a single quantum dot in a photonic crystal nanocavity,” Nanotechnology 22(5), 055202 (2011).
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Nat. Mater. (1)

J. Kasprzak, S. Reitzenstein, E. A. Muljarov, C. Kistner, C. Schneider, M. Strauss, S. Höfling, A. Forchel, and W. Langbein, “Up on the Jaynes-Cummings ladder of a quantum-dot/microcavity system,” Nat. Mater. 9(4), 304–308 (2010).
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Nature (2)

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).
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T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432(7014), 200–203 (2004).
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Opt. Express (7)

J. B. Li, S. Liang, S. Xiao, M. D. He, N. C. Kim, L. Q. Chen, G. H. Wu, Y. X. Peng, X. Y. Luo, and Z. P. Guo, “Four-wave mixing signal enhancement and optical bistability of a hybrid metal nanoparticle-quantum dot molecule in a nanomechanical resonator,” Opt. Express 24(3), 2360–2369 (2016).
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J. Liu, S. Ates, M. Lorke, J. Mørk, P. Lodahl, and S. Stobbe, “A comparison between experiment and theory on few-quantum-dot nanolasing in a photonic-crystal cavity,” Opt. Express 21(23), 28507–28512 (2013).
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J. Li, R. Yu, C. Ding, and Y. Wu, “Optical bistability and four-wave mixing with a single nitrogen-vacancy center coupled to a photonic crystal nanocavity in the weak-coupling regime,” Opt. Express 22(12), 15024–15038 (2014).
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S. Reitzenstein, C. Böckler, A. Bazhenov, A. Gorbunov, A. Löffler, M. Kamp, V. D. Kulakovskii, and A. Forchel, “Single quantum dot controlled lasing effects in high-Q micropillar cavities,” Opt. Express 16(7), 4848–4857 (2008).
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J. B. Li, N. C. Kim, M. T. Cheng, L. Zhou, Z. H. Hao, and Q. Q. Wang, “Optical bistability and nonlinearity of coherently coupled exciton-plasmon systems,” Opt. Express 20(2), 1856–1861 (2012).
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Y. C. Yu, J. F. Liu, X. L. Zhuo, G. Chen, C. J. Jin, and X. H. Wang, “Vacuum Rabi splitting in a coupled system of single quantum dot and photonic crystal cavity: effect of local and propagation Green’s functions,” Opt. Express 21(20), 23486–23497 (2013).
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F. Wang, X. Feng, and C. H. Oh, “Optical bistability and multistability via quantum coherence in chiral molecules,” Opt. Express 24(13), 13702–13713 (2016).
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Opt. Lett. (3)

Optica (1)

Phys. Rev. A (11)

R. W. Boyd, M. G. Raymer, P. Narum, and D. J. Harter, “Four-wave parametric interactions in a strongly driven two-level system,” Phys. Rev. A 24(1), 411–423 (1981).

A. V. Malyshev, “Condition for resonant optical bistability,” Phys. Rev. A 86(6), 065804 (2012).

X. Guo and S. Lü, “Controllable optical bistability in photonic-crystal one-atom laser,” Phys. Rev. A 80(4), 043826 (2009).

Y. Dumeige, A. M. Yacomotti, P. Grinberg, K. Bencheikh, E. L. Cren, and J. A. Levenson, “Microcavity-quality-factor enhancement using nonlinear effects close to the bistability threshold and coherent population oscillations,” Phys. Rev. A 85(6), 063824 (2012).

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A. Dalafi and M. H. Naderi, “Intrinsic cross-Kerr nonlinearity in an optical cavity containing an interacting Bose-Einstein condensate,” Phys. Rev. A 95(4), 043601 (2017).

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Figures (6)

Fig. 1
Fig. 1 (a) Schematic diagram of a SQD embedded in a PC nanocavity. The system is driven by a strong pump laser and detected by a weak probe laser [37]. (b) The energy level scheme of an exciton in the SQD interacting with the photons in the PC nanocavity.
Fig. 2
Fig. 2 (a) The FWM signal |p−1/μEpr*h−1Γ2−1| as a function of the probe-pump detuning δ for Ipu = 1 MHz2 with and without the exciton-nanocavity coupling. Dependence of the FWM signal |p−1/μEpr*h−1Γ2−1| on the pumping intensity Ipu when g = 2 MHz (b), g = 6 MHz (c) and g = 30 MHz (d). Here Δ pu = 0.
Fig. 3
Fig. 3 The FWM signal |p−1/μEpr*h−1Γ2−1| as a function of the probe-pump detuning δ when the exciton-pump field detuning Δ pu is 0, 15 MHz, 30 MHz and −30 MHz. The parameters used here are g = 30 MHz and Ipu = 1000 MHz2.
Fig. 4
Fig. 4 The FWM signal |p−1/μEpr*h−1Γ2−1| (a) and the population inversion w0 (b) as a function of the pumping intensity Ipu in the no, weak, and intermediate coupling regimes. The simulations are performed for Δ pu = 0 and g = 0, 2, 6, and 30 MHz. (c) Dependence of OB on the excitation frequency (i.e. Δ pu ) in the strong coupling regime. The simulations are performed for g = 30 MHz and Δ pu = 0, 15, and 30 MHz. (d) Optical hysteresis loop of the population difference w0 with the pumping intensity Ipu. Here Δ pu = 0 and g = 30 MHz.
Fig. 5
Fig. 5 Bistability phase diagrams of the FWM response of the SQD-nanocavity system in the parameter subspace (Ipu; g). (a) Δ pu = 0; (b) Δ pu = 30 MHz. The colored areas represent the subspace where the bistability exists. (c) Comparison of the results obtained in the above two bistability phase diagrams.
Fig. 6
Fig. 6 Bistability phase diagram of the FWM response of the SQD-nanocavity system in the parameter subspace (Ipu; Δ pu ; g = 30 MHz). The colored area represents the subspace where the bistability exists.

Equations (7)

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H = Δ p u σ z + Δ p c b + b + g ( σ 10 b + σ 01 b + ) Ω ( σ 10 + σ 01 ) μ E p r ( σ 10 e i δ t + σ 01 e i δ t ) ,
p ˙ = ( i Δ p u + Γ 2 ) p + i g w Λ i Ω w i μ E p r w e i δ t ,
w ˙ = Γ 1 ( w + 1 ) 2 i g ( p * Λ p Λ + ) + 2 i Ω ( p * p ) + 2 i μ E p r ( p * e i δ t p e i δ t ) ,
Λ ˙ = ( i Δ p c + κ 2 ) Λ i g p ,
| F W M | = | p 1 1 Γ 2 1 μ E p r * | = | C 8 p 0 + C 5 w 0 Γ 2 1 [ C 9 ( C 6 C 4 ) + C 7 ] | .
p 0 = i Ω w 0 / [ Γ 2 + i ( C 1 g w 0 Δ p u ) ] , b 0 = i C 1 Ω w 0 / [ Γ 2 + i ( C 1 g w 0 Δ p u ) ] , C 1 = i g / ( κ 2 + i Δ p c ) , C 2 = i g / ( κ 2 + i ( Δ p c δ ) ) , C 3 = i g / [ κ 2 + i ( Δ p c + δ ) ] , C 4 = i ( Ω g b 0 * ) / [ Γ 2 i ( Δ p u δ C 2 * g w 0 ) ] , C 5 = i / [ Γ 2 i ( Δ p u δ C 2 * g w 0 ) ] , C 6 = ( i δ + Γ 1 ) / [ 2 i ( g b 0 + g C 2 * p 0 + Ω ) ] , C 7 = ( g C 3 p 0 * g b 0 * + Ω ) / ( g b 0 + g C 2 * p 0 + Ω ) , C 8 = 1 / ( g b 0 + g C 2 * p 0 + Ω ) , C 9 = [ Γ 2 + i ( δ + Δ p u C 3 g w 0 ) ] / i ( g b 0 Ω ) .
Γ 1 ( w 0 + 1 ) [ Γ 2 + i ( C 1 * g w 0 Δ p u ) ] [ Γ 2 i ( C 1 g w 0 Δ p u ) ] + 4 Γ 2 Ω 2 w 0 = 0.

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