Cavity QED analysis of an exciton-plasmon hybrid molecule via the generalized nonlocal optical response method

Harini Hapuarachchi, Malin Premaratne, Qiaoliang Bao, Wenlong Cheng, Sarath D. Gunapala, and Govind P. Agrawal

Phys. Rev. B 95, 245419 – Published 19 June 2017

Abstract

A metal nanoparticle coupled to a semiconductor quantum dot forms a tunable hybrid system which exhibits remarkable optical phenomena. Small metal nanoparticles possess nanocavitylike optical concentration capabilities due to the presence of strong dipolar excitation modes in the form of localized surface plasmons. Semiconductor quantum dots have strong luminescent capabilities widely used in many applications such as biosensing. When a quantum dot is kept in the vicinity of a metal nanoparticle, a dipole-dipole coupling occurs between the two nanoparticles giving rise to various optical signatures in the scattered spectra. This coupling makes the two nanoparticles behave like a single hybrid molecule. Hybrid molecules made of metal nanoparticles (MNPs) and quantum dots (QDs) under the influence of an external driving field have been extensively studied in literature, using the local response approximation (LRA). However, such previous work in this area was not adequate to explain some experimental observations such as the size-dependent resonance shift of metal nanoparticles which becomes quite significant with decreasing diameter. The nonlocal response of metallic nanostructures which is hitherto disregarded by such studies is a main reason for such nonclassical effects. The generalized nonlocal optical response (GNOR) model provides a computationally less-demanding path to incorporate such properties into the theoretical models. It allows unified theoretical explanation of observed experimental phenomena which previously seemed to require ab initio microscopic theory. In this paper, we analyze the hybrid molecule in an external driving field as an open quantum system using a cavity-QED approach. In the process, we quantum mechanically model the dipole moment operator and the dipole response field of the metal nanoparticle taking the nonlocal effects into account. We observe that the spectra resulting from the GNOR based model effectively demonstrate the experimentally observed size dependent amplitude scaling, linewidth broadening, and resonance shift phenomena compared to the respective LRA counterparts. Then, we provide a comparison between our suggested GNOR based cavity-QED model and the conventional LRA model, where it becomes evident that our analytical model provides a close match to the experimentally suggested behavior. Furthermore, we show that the Rayleigh scattering spectra of the MNP-QD hybrid molecule possess an asymmetric Fano interference pattern that is tunable to suit various applications.

Received 30 January 2017
Revised 14 May 2017

DOI:https://doi.org/10.1103/PhysRevB.95.245419

Physics Subject Headings (PhySH)

Cavity quantum electrodynamics Permittivity Rayleigh scattering Surface plasmons

Nanoparticles Quantum dots

Rotating wave approximation

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Harini Hapuarachchi^* and Malin Premaratne^†

Advanced Computing and Simulation Laboratory (AχL), Department of Electrical and Computer Systems Engineering, Monash University, Clayton, Victoria 3800, Australia

Qiaoliang Bao

Department of Materials Science and Engineering, Monash University, Clayton, Victoria 3800, Australia

Wenlong Cheng

Department of Chemical Engineering, Faculty of Engineering, Monash University, Clayton 3800, Victoria, Australia and The Melbourne Centre for Nanofabrication, 151 Wellington Road, Clayton 3168, Victoria, Australia

Sarath D. Gunapala

Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109, USA

Govind P. Agrawal

The Institute of Optics, University of Rochester, Rochester, New York 14627, USA

^*harini.hapuarachchi@monash.edu
^†malin.premaratne@monash.edu

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Vol. 95, Iss. 24 — 15 June 2017

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Images

Figure 1
The schematic diagram of the MNP-QD hybrid molecule in the external driving field. The right insert shows an example Rayleigh scattering spectrum of the hybrid molecule discussed in detail in Secs. 2f and 3.
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Figure 2
Comparison of the near-resonant behavior of the GNOR based modified Clausius Mossotti factor presented by Raza et al. [28], with its complex Lorentzian approximated form presented in this paper for different MNP radii at $ε_{b} = 5$ . (a) Absolute value of the unapproximated nonlocal Clausius Mossotti factor of Raza et al. given by (38). (b) Absolute value of the approximated nonlocal Clausius Mossotti factor $β_{cm_a}^{NL}$ given by (45). (c) The percentage error between the absolute values of the unapproximated and approximated (GNOR based) Clausius Mossotti factors given in the previous two subfigures. Percentage errors at resonance are marked on the respective curves in subfigure (c).
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Figure 3
Variation of coherent Rayleigh scattering spectra of the hybrid molecule with varying $r_{m}$ and $ε_{b}$ in the local and nonlocal (GNOR) models. Curves are normalized by the largest peak in the respective subfigure. Subfigures (a) and (b) capture the variation of the scattered intensity for different radii at $ε_{b} = 5$ , whereas (c) and (d) capture the scattering intensity variation with the environment permittivity $ε_{b}$ at $r_{m} = 8 nm$ . For all four panels $Δ = 20 meV$ and $R = 14 nm$ are used. All figures clearly indicate an asymmetric Fano interference pattern near the resonance frequency of the QD. It can be observed that this asymmetry is tunable using $r_{m}$ and $ε_{b}$ .
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Figure 4
(a) LRA and GNOR based coherent Rayleigh scattering spectra for $s_{α} = 2$ . (b) Coherent Rayleigh scattering spectra for $s_{α} = - 1$ . Other parameters used include $ε_{b} = 5, r_{m} = 8 nm, R = 15 nm$ , and $Δ = 20 meV$ . All curves are normalized by the peak intensity of the respective LRA based spectrum for the purpose of amplitude comparison. It can be observed that the Fano interference pattern near the resonance of the QD is influenced by the orientation of the external field.
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Figure 5
Subfigures (a)–(f) depict two-dimensional plots for the coherent scattered intensity of the hybrid molecule, normalized by the maximum intensity of each subfigure for $ε_{b} = 5$ and $r_{m} = 8 nm$ . (a) Shows the scattered intensity variation against $Δ$ and $ω$ when $R = 15 nm$ in the LRA. (b) Shows the scattered intensity against $Δ$ and $ω$ for the same set of parameters as in (a) in the nonlocal GNOR model. The subfigures (c) and (d) show, respectively, the local and nonlocal (GNOR) scattering intensities against $μ_{q d}$ and $ω$ . The local and nonlocal (GNOR) scattering intensities against $R$ and $ω$ are shown in (e) and (f), respectively. The subfigures (c)– (f) use $Δ = 20 meV$ and $R = 15 nm$ . Subfigure (g) shows the variation of $ω_{m}$ against $r_{m}$ and $ε_{b}$ predicted by the LRA, whereas (f) shows the same variation as predicted by the nonlocal GNOR model. From figures (a)– (f) it can be observed that model parameters such as MNP-QD detuning, dipole moment, and distance dramatically affect the Fano lineshape resulting from the interference of the MNP and QD spectra.
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Figure 6
(a) $P_{1}$ calculated using (51a) for silver at the respective resonance frequencies for different MNP radii and environment permittivities. Approximation of $(1 + δ_{NL})$ by $R e (1 + δ_{NL})$ in all the nonlocal (GNOR) equations is justified when $P_{1}$ is small and positive. (b) $P_{2}$ calculated using (51b) for silver at the respective resonance frequencies for different MNP radii and environment permittivities. $P_{2}$ represents the de-facto tolerance level for the MNP dipole moment element $μ_{m}^{NL}$ given by (46b). Thus, $P_{2}$ can be used to assess tolerance levels of the dipole moment elements given in Table 1.
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