Abstract

The coherent light-matter interaction has drawn an enormous amount of attention for its fundamental importance in the cavity quantum-electrodynamics (C-QED) field and great potential in quantum information applications. Here, we design a hybrid C-QED system consisting of a quantum dot (QD) driven by two-tone fields implanted in a photonic crystal (PhC) cavity coupled to an auxiliary cavity with a single-mode waveguide and investigate the hybrid system operating in the weak, intermediate, and strong coupling regimes of the light-matter interaction via comparing the QD-photon interaction with the dipole decay rate and the cavity field decay rate. The results indicate that the auxiliary cavity plays a key role in the hybrid system, which affords a quantum channel to influence the absorption of the probe field. By controlling the coupling strength between the auxiliary cavity and the PhC cavity, the phenomenon of the Mollow triplet can appear in the intermediate coupling regime, and even in the weak coupling regime. We further study the strong coupling interaction manifested by vacuum Rabi splitting in the absorption with manipulating the cavity-cavity coupling under different parameter regimes. This study provides a promising platform for understanding the dynamics of QD-C-QED systems and paving the way toward on-chip QD-based nanophotonic devices.

© 2018 Chinese Laser Press

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2014 (5)

Y. C. Liu, X. Luan, H. K. Li, Q. Gong, C. W. Wong, and Y. F. Xiao, “Coherent polariton dynamics in coupled highly dissipative cavities,” Phys. Rev. Lett. 112, 213602 (2014).
[Crossref]

J. Q. Liao, Q. Q. Wu, and F. Nori, “Entangling two macroscopic mechanical mirrors in a two-cavity optomechanical system,” Phys. Rev. A 89, 014302 (2014).
[Crossref]

B. Peng, S. K. Ozdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

H. Jing, S. K. Ozdemir, X. Y. Lu, J. Zhang, L. Yang, and F. Nori, “PT-symmetric phonon laser,” Phys. Rev. Lett. 113, 053604 (2014).
[Crossref]

L. Chang, X. Jiang, S. Hua, C. Yang, J. Wen, L. Jiang, G. Li, G. Wang, and M. Xiao, “Parity-time symmetry and variable optical isolation in active-passive-coupled microresonators,” Nat. Photonics 8, 524–529 (2014).
[Crossref]

2013 (3)

H. Toida, T. Nakajima, and S. Komiyama, “Vacuum Rabi splitting in a semiconductor circuit QED system,” Phys. Rev. Lett. 110, 066802 (2013).
[Crossref]

H. Kim, R. Bose, T. C. Shen, G. S. Solomon, and E. Waks, “A quantum logic gate between a solid-state quantum bit and a photon,” Nat. Photonics 7, 373–377 (2013).
[Crossref]

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, 23486–23497 (2013).
[Crossref]

2012 (4)

A. Majumdar, M. Bajcsy, and J. Vuckovic, “Design and analysis of photonic crystal coupled cavity arrays for quantum simulation,” Phys. Rev. A 85, 041801 (2012).
[Crossref]

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoglu, “Ultrafast all-optical switching by single photons,” Nat. Photonics 6, 605–609 (2012).
[Crossref]

R. Bose, D. Sridharan, H. Kim, G. S. Solomon, and E. Waks, “Low-photon-number optical switching with a single quantum dot coupled to a photonic crystal cavity,” Phys. Rev. Lett. 108, 227402 (2012).
[Crossref]

A. Reinhard, T. Volz, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoglu, “Strongly correlated photons on a chip,” Nat. Photonics 6, 93–96 (2012).
[Crossref]

2011 (3)

Y.-C. Liu, Y.-F. Xiao, B.-B. Li, X.-F. Jiang, Y. Li, and Q. Gong, “Coupling of a single diamond nanocrystal to a whispering-gallery microcavity: photon transportation benefitting from Rayleigh scattering,” Phys. Rev. A 84, 011805 (2011).
[Crossref]

Y.-F. Xiao, M. Li, Y.-C. Liu, Y. Li, X. Sun, and Q. Gong, “Asymmetric Fano resonance analysis in indirectly coupled microresonators,” Phys. Rev. A 83, 019902 (2011).
[Crossref]

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

2010 (2)

E. del Valle and F. P. Laussy, “Mollow triplet under incoherent pumping,” Phys. Rev. Lett. 105, 233601 (2010).
[Crossref]

M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, “Laser oscillation in a strongly coupled single quantum-dot-nanocavity system,” Nat. Phys. 6, 279–283 (2010).
[Crossref]

2009 (1)

J. L. O’Brien, A. Furusawa, and J. Vuckovic, “Photonic quantum technologies,” Nat. Photonics 3, 687–695 (2009).
[Crossref]

2008 (2)

R. Johne, N. A. Gippius, G. Pavlovic, D. D. Solnyshkov, I. A. Shelykh, and G. Malpuech, “Entangled photon pairs produced by a quantum dot strongly coupled to a microcavity,” Phys. Rev. Lett. 100, 240404 (2008).
[Crossref]

A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuckovic, “Coherent generation of non-classical light on a chip via photon-induced tunnelling and blockade,” Nat. Phys. 4, 859–863 (2008).
[Crossref]

2007 (5)

D. Englund, A. Faraon, I. Fushman, N. Stoltz, P. Petroff, and J. Vuckovic, “Controlling cavity reflectivity with a single quantum dot,” Nature 450, 857–861 (2007).
[Crossref]

X. Xu, B. Sun, P. R. Berman, D. G. Steel, A. S. Bracker, D. Gammon, and L. J. Sham, “Coherent optical spectroscopy of a strongly driven quantum dot,” Science 317, 929–932 (2007).
[Crossref]

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

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics 1, 449–458 (2007).
[Crossref]

C. Guerlin, J. Bernu, S. Deleglise, C. Sayrin, S. Gleyzes, S. Kuhr, M. Brune, J.-M. Raimond, and S. Haroche, “Progressive field-state collapse and quantum non-demolition photon counting,” Nature 448, 889–893 (2007).
[Crossref]

2006 (1)

W.-H. Chang, W.-Y. Chen, H.-S. Chang, T.-P. Hsieh, J.-I. Chyi, and T.-M. Hsu, “Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,” Phys. Rev. Lett. 96, 117401 (2006).
[Crossref]

2005 (2)

E. Peter, P. Senellart, D. Martrou, A. Lemaitre, J. Hours, J. M. Gerard, and J. Bloch, “Exciton-photon strong-coupling regime for a single quantum dot embedded in a microcavity,” Phys. Rev. Lett. 95, 067401 (2005).
[Crossref]

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

2004 (3)

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

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, 200–203 (2004).
[Crossref]

J. P. Reithmaier, G. Sek, A. Loffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432, 197–200 (2004).
[Crossref]

2003 (1)

K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
[Crossref]

2002 (3)

C. Monroe, “Quantum information processing with atoms and photons,” Nature 416, 238–246 (2002).
[Crossref]

H. Mabuchi and A. C. Doherty, “Cavity quantum electrodynamics: coherence in context,” Science 298, 1372–1377 (2002).
[Crossref]

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

1946 (1)

E. M. Purcell, H. C. Torrey, and R. V. Pound, “Resonance absorption by nuclear magnetic moments in a solid,” Phys. Rev. 69, 37–38 (1946).
[Crossref]

Abstreiter, G.

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

Andrade, I. C.

S. Lichtmannecker, M. Kaniber, S. Echeverri-Arteaga, I. C. Andrade, J. Ruiz-Rivas, T. Reichert, M. Becker, M. Blauth, G. Reithmaier, P. L. Ardelt, M. Bichler, E. A. Gomez, H. Vinck-Posada, E. del Valle, and J. J. Finley, “Coexistence of weak and strong coupling with a quantum dot in a photonic molecule,” arXiv:1806.10160v1 (2018).

Arakawa, Y.

M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, “Laser oscillation in a strongly coupled single quantum-dot-nanocavity system,” Nat. Phys. 6, 279–283 (2010).
[Crossref]

Ardelt, P. L.

S. Lichtmannecker, M. Kaniber, S. Echeverri-Arteaga, I. C. Andrade, J. Ruiz-Rivas, T. Reichert, M. Becker, M. Blauth, G. Reithmaier, P. L. Ardelt, M. Bichler, E. A. Gomez, H. Vinck-Posada, E. del Valle, and J. J. Finley, “Coexistence of weak and strong coupling with a quantum dot in a photonic molecule,” arXiv:1806.10160v1 (2018).

Asano, T.

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics 1, 449–458 (2007).
[Crossref]

Atature, M.

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

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

Badolato, A.

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoglu, “Ultrafast all-optical switching by single photons,” Nat. Photonics 6, 605–609 (2012).
[Crossref]

A. Reinhard, T. Volz, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoglu, “Strongly correlated photons on a chip,” Nat. Photonics 6, 93–96 (2012).
[Crossref]

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

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

Bajcsy, M.

A. Majumdar, M. Bajcsy, and J. Vuckovic, “Design and analysis of photonic crystal coupled cavity arrays for quantum simulation,” Phys. Rev. A 85, 041801 (2012).
[Crossref]

Becker, M.

S. Lichtmannecker, M. Kaniber, S. Echeverri-Arteaga, I. C. Andrade, J. Ruiz-Rivas, T. Reichert, M. Becker, M. Blauth, G. Reithmaier, P. L. Ardelt, M. Bichler, E. A. Gomez, H. Vinck-Posada, E. del Valle, and J. J. Finley, “Coexistence of weak and strong coupling with a quantum dot in a photonic molecule,” arXiv:1806.10160v1 (2018).

Beham, E.

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

Bender, C. M.

B. Peng, S. K. Ozdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

Berman, P. R.

X. Xu, B. Sun, P. R. Berman, D. G. Steel, A. S. Bracker, D. Gammon, and L. J. Sham, “Coherent optical spectroscopy of a strongly driven quantum dot,” Science 317, 929–932 (2007).
[Crossref]

Bernu, J.

C. Guerlin, J. Bernu, S. Deleglise, C. Sayrin, S. Gleyzes, S. Kuhr, M. Brune, J.-M. Raimond, and S. Haroche, “Progressive field-state collapse and quantum non-demolition photon counting,” Nature 448, 889–893 (2007).
[Crossref]

Bichler, M.

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

S. Lichtmannecker, M. Kaniber, S. Echeverri-Arteaga, I. C. Andrade, J. Ruiz-Rivas, T. Reichert, M. Becker, M. Blauth, G. Reithmaier, P. L. Ardelt, M. Bichler, E. A. Gomez, H. Vinck-Posada, E. del Valle, and J. J. Finley, “Coexistence of weak and strong coupling with a quantum dot in a photonic molecule,” arXiv:1806.10160v1 (2018).

Blauth, M.

S. Lichtmannecker, M. Kaniber, S. Echeverri-Arteaga, I. C. Andrade, J. Ruiz-Rivas, T. Reichert, M. Becker, M. Blauth, G. Reithmaier, P. L. Ardelt, M. Bichler, E. A. Gomez, H. Vinck-Posada, E. del Valle, and J. J. Finley, “Coexistence of weak and strong coupling with a quantum dot in a photonic molecule,” arXiv:1806.10160v1 (2018).

Bloch, J.

E. Peter, P. Senellart, D. Martrou, A. Lemaitre, J. Hours, J. M. Gerard, and J. Bloch, “Exciton-photon strong-coupling regime for a single quantum dot embedded in a microcavity,” Phys. Rev. Lett. 95, 067401 (2005).
[Crossref]

Bose, R.

H. Kim, R. Bose, T. C. Shen, G. S. Solomon, and E. Waks, “A quantum logic gate between a solid-state quantum bit and a photon,” Nat. Photonics 7, 373–377 (2013).
[Crossref]

R. Bose, D. Sridharan, H. Kim, G. S. Solomon, and E. Waks, “Low-photon-number optical switching with a single quantum dot coupled to a photonic crystal cavity,” Phys. Rev. Lett. 108, 227402 (2012).
[Crossref]

Boyd, R. W.

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

Bracker, A. S.

X. Xu, B. Sun, P. R. Berman, D. G. Steel, A. S. Bracker, D. Gammon, and L. J. Sham, “Coherent optical spectroscopy of a strongly driven quantum dot,” Science 317, 929–932 (2007).
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Nat. Photonics (6)

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Nat. Phys. (3)

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Nature (8)

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Figures (6)

Fig. 1.
Fig. 1. (a) Schematic of the C-QED system coupled to an auxiliary cavity, and the two cavities coupled to each other via the photon-hopping interaction; (b) two energy levels of a QD coupled to a single-cavity mode and two optical fields; (c) and (d) are the energy level transitions with an entangled state |ntot (na and nc represent the number state of the photon mode of cavity a and cavity c; ntot=na+nc is the total photon number of the two cavities).
Fig. 2.
Fig. 2. (a)–(c) Probe absorption spectra of the probe field as a function of probe detuning Δs at Δp=0 under three conditions, i.e., weak coupling, intermediate coupling, and strong coupling regimes. The parameters used are Γ1=5.2  MHz, κa=κc=8.0  MHz, Ωpu2=1.0(MHz)2, Δa=0, Δc=0.
Fig. 3.
Fig. 3. Probe absorption spectra as a function of cavity-cavity coupling strength J in the weak coupling regime (g=2.0  MHz). The other parameters are the same as in Fig. 2.
Fig. 4.
Fig. 4. Probe absorption spectra as a function of cavity-cavity coupling strength J in the intermediate coupling regime (g=6.0  MHz). The other parameters are the same as in Fig. 2.
Fig. 5.
Fig. 5. Probe absorption spectra as a function of cavity-cavity coupling strength J in the strong coupling regime (g=30  MHz). The other parameters are the same as in Fig. 2.
Fig. 6.
Fig. 6. Probe absorption spectra as a function of the pump frequency detuning Δp in the strong coupling regime (g=30  MHz). J=2.0κa, Ωp2=20(MHz)2, and the other parameters are the same as in Fig. 2.

Equations (8)

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H=Δpσz+Δaa+a+Δcc+c+g(σ+a+σa+)+J(a+c+ac+)Ωp(σ+σ)μEs(σ+eiδt+σeiδt),
tσz=Γ1(σz+1)ig(σ+aσa+)+iΩp(σ+σ)+iμEs(σ+eiδtσeiδt),
tσ=(iΔp+Γ2)σ+2igaσz2iΩpσz2iμEsσzeiδt+τin(t),
ta=(iΔa+κa/2)aigσiJc+ain(t),
tc=(iΔc+κc/2)ciJa+cin(t),
Γ1(w0+1){4g2w02(Δc2+κc2/4)2g2w0[2J2(ΔpΔc+Γ2κc)+Δc2(Γ2κa2ΔpΔa)+κc2(Γ2κa/2ΔpΔa)]+(Δp2+Γ22)Ξ}+4w0Γ2Ωp2Ξ=0,
Ξ=(Δa2+κa2/4)(Δc2+κc2/4)+J2(κaκc/22ΔaΔc)+J4.
χ(1)(ωs)=[ϵ7Π1(Λ4+ϵ6Π2)2iw0Λ4]Γ2Λ1Λ4+ϵ5ϵ6Π1Π2,