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Color online Diagrams illustrating schematically the geometry of the three structures discussed in the paper: a the / 2 BMC, b the / 2 half BMC, and c the / 4 BMC.
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We present a theoretical analysis of the consequence of coupling between higher photonic modes and intersubband excitations in microcavities with embedded multiple quantum wells (MQWs). The polariton dispersion relations and angle-resolved absorption spectra are calculated numerically using a semiclassical approach based on a transfer-matrix formul...
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... numerical calculations reported in this paper are per- formed for the three systems see Fig. 1. The first one is the / 2 BMC presented in Fig. 1a. To facilitate the comparison with results presented in the literature we assume that this structure is similar to those studied experimentally by Du- pont et al. 2 and theoretically in our previous paper. 6 It is grown on a GaAs semi-insulating substrate GaAs and con- sists of a ...
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... numerical calculations reported in this paper are per- formed for the three systems see Fig. 1. The first one is the / 2 BMC presented in Fig. 1a. To facilitate the comparison with results presented in the literature we assume that this structure is similar to those studied experimentally by Du- pont et al. 2 and theoretically in our previous paper. 6 It is grown on a GaAs semi-insulating substrate GaAs and con- sists of a 140-repeat N QW = 140 MQW embedded between a 0.4-m-thick ...
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... the intersubband cavity polaritons we also discuss a system which differs from the above- mentioned one only by i the smaller value of the Al 0.21 Ga 0.79 As barrier thickness not 290 Å but 115 Å and ii the presence between the MQW and the coupling mir- ror of the additional Al 0.21 Ga 0.79 As spacing layer with thick- ness d spac = L MC / 2 see Fig. 1b. We call it the / 2 "half" ...
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... giant mode splitting was also observed in the / 4 BMC where the confinement of the radiation is realized by sandwiching the optically active material between a bottom dielectric mirror and a top metallic mirror. 5,9 For this reason we have also performed appropriate simulations for a / 4 BMC see Fig. 1c. It differs from the previously described / 2 BMC see Fig. 1a by i the reduction in the N QW from 140 to 70 and ii replacement of the upper dielectric- metallic mirror by the purely metallic Au mirror. Now we briefly discuss the main properties of the un- coupled photonic modes in the systems shown schematically in Fig. 1. The photonic ...
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... splitting was also observed in the / 4 BMC where the confinement of the radiation is realized by sandwiching the optically active material between a bottom dielectric mirror and a top metallic mirror. 5,9 For this reason we have also performed appropriate simulations for a / 4 BMC see Fig. 1c. It differs from the previously described / 2 BMC see Fig. 1a by i the reduction in the N QW from 140 to 70 and ii replacement of the upper dielectric- metallic mirror by the purely metallic Au mirror. Now we briefly discuss the main properties of the un- coupled photonic modes in the systems shown schematically in Fig. 1. The photonic modes supported by the / 2 BMC and the half / 2 BMC can ...
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... for a / 4 BMC see Fig. 1c. It differs from the previously described / 2 BMC see Fig. 1a by i the reduction in the N QW from 140 to 70 and ii replacement of the upper dielectric- metallic mirror by the purely metallic Au mirror. Now we briefly discuss the main properties of the un- coupled photonic modes in the systems shown schematically in Fig. 1. The photonic modes supported by the / 2 BMC and the half / 2 BMC can modeled, in the first approxima- tion, by the Fabry-Perot MC with nearly perfect dielectric mirrors. It implies that the photonic modes in these systems can be divided into even n =1,3,... and odd n =2,4,... parity in E z with respect to the center of the cavity ...
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... photonic modes supported by the / 2 BMC and the half / 2 BMC can modeled, in the first approxima- tion, by the Fabry-Perot MC with nearly perfect dielectric mirrors. It implies that the photonic modes in these systems can be divided into even n =1,3,... and odd n =2,4,... parity in E z with respect to the center of the cavity photonic modes see Fig. 1 in Ref. 14. In the case of the / 4 BMC see Fig. 1c the simplified model with the metallic back mirror and the dielectric coupling mirror can be used. Em- ploying this fact, one finds that the photonic modes sup- ported by the above-mentioned system practically coincide with even-parity photonic modes supported by the / 2 BMC. Due to ...
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... half / 2 BMC can modeled, in the first approxima- tion, by the Fabry-Perot MC with nearly perfect dielectric mirrors. It implies that the photonic modes in these systems can be divided into even n =1,3,... and odd n =2,4,... parity in E z with respect to the center of the cavity photonic modes see Fig. 1 in Ref. 14. In the case of the / 4 BMC see Fig. 1c the simplified model with the metallic back mirror and the dielectric coupling mirror can be used. Em- ploying this fact, one finds that the photonic modes sup- ported by the above-mentioned system practically coincide with even-parity photonic modes supported by the / 2 BMC. Due to that, the photonic modes in the / 4 BMC will be ...
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... into account in the correct interpretation of the angle-resolved absorption spectra at 1 res . Numerical simulations pre- sented in the next section fully support the above suggestion. Figure 3 displays the dependence of the polariton modes obtained solving numerically the dispersion Eq. 12 see also Eq. 13 for the systems schematically shown in Fig. 1. Figure 4 displays the k x dependence of the polariton modes extracted from Fig. 3 with the help of Eq. 31. Only a few upper and lower branches n 3, which are mainly responsible for the features observed in the angle-resolved absorption spectra, are ...
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Citations
... To reduce the numerical complexity of modeling the dielectric environment composed of several QWs and corresponding barriers, we employ an effective medium approach describing the full QW stack as a layer of a total thickness of d QW = 210 nm and total surface density N 2DEG [53]. The CR of the 2DEG is implemented as a gyrotropic medium, where the dielectric tensor of a plasma of charge carriers magnetically biased along the z direction describes the two-dimensional polarization response of the CR in the plane perpendicular to the magnetic field: ...
The achievement of large values of the light–matter coupling in nanoengineered photonic structures can lead to multiple photonic resonances contributing to the final properties of the same hybrid polariton mode. We develop a general theory describing multi-mode light–matter coupling in systems of reduced dimensionality, and we explore their phenomenology, validating our theory’s predictions against numerical electromagnetic simulations. On one hand, we characterize the spectral features linked with the multi-mode nature of the polaritons. On the other hand, we show how the interference between different photonic resonances can modify the real-space shape of the electromagnetic field associated with each polariton mode. We argue that the possibility of engineering nanophotonic resonators to maximize multi-mode mixing, and to alter the polariton modes via applied external fields, could allow for the dynamical real-space tailoring of subwavelength electromagnetic fields.
... In the z direction we only employ the background dielectric constant, as the confinement inhibits a plasma response. Additionally, to reduce numerical complexity of modelling several quantum wells and corresponding barriers between them with finite thickness, we employ an effective medium for the complete quantum well stack with an effective dielectric tensor [43]. In the xy-direction, we employ periodic boundary conditions to reflect the array character of our structure and solve Maxwell's equations numerically. ...
The achievement of large values of the light-matter coupling in nanoengineered photonic structures can lead to multiple photonic resonances contributing to the final properties of the same hybrid polariton mode. We develop a general theory describing multi-mode light-matter coupling in systems of reduced dimensionality and we explore their novel phenomenology, validating the predictions of our theory against numerical electromagnetic simulations. On the one hand, we characterise the spectral features linked with the multi-mode nature of the polaritons. On the other hand, we show how the interference between different photonic resonances can modify the real-space shape of the electromagnetic field associated with each polariton mode. We argue that the possibility of engineering nanophotonic resonators to maximise the multi-mode mixing, and to alter the polariton modes via applied external fields, could allow for the dynamical real-space tailoring of subwavelength electromagnetic fields.
... At the end of our theoretical study, we test its accuracy and provide an experimentally suitable observable, by calculating the reflectivity of the same heterostructure coupled to a planar metallic resonator via transfer matrix approach in effective medium approximation including local field effects, that has been treated in several theoretical works [105,109,110,111]. Results are shown in Fig.5.12, which recover pretty well the eigenmodes spectrum of Fig. 5.11 (a). ...
When in a quantum optical system the coupling between matter and cavity mode becomes comparable to the bare excitation frequency, we enter a non-perturbative coupling regime, as perturbation theory fails describing the system’s dynamics. While recent advances in Cavity Quantum Electrodynamics allowed to achieve very high values of the coupling strength, thanks to the resonators properties optimization and the employment of solid-state devices, an ever growing interest has been shown about the possibility of significantly modify materials’ properties. It has been demonstrated that the chemical structure of molecules strongly coupled to a photon mode can be altered, which opens the possibility to manipulate and control chemical reactions.
The aim of this thesis is to explore non-perturbative regimes on several quantum systems, and to investigate the effects of the coupling upon their properties, such as internal degrees of freedom or electronic states structure. I first developed a novel theory to determine the polariton spectrum of a dipolar ensamble in which a Ising-like dipole-dipole interaction in the 2 non-perturbative regime is considered. A further important focus is the investigation of the saturation effects due to the inclusion of the inter-dipole interaction, and the interplay between the latter and light-matter coupling strength. I also explored specifically the influence of the coupling on the rotational degrees of freedom of an ensemble of two-dimensional freely rotating dipoles, all coupled to a single cavity mode, finding that they are driven by the collective light-matter coupling to undergo a crossover between an isotropic and an aligned phase. I then investigated the case of cavity-embedded doped quantum wells, demonstrating that not only it is possible to couple a discrete cavity mode and bound-to-continuum transitions, but also that a novel bound exciton state appears, induced by the coupling strength. This results shows how light–matter coupling can be used to tune both optical and electronic properties of semiconductor heterostructures beyond those permitted by mere crystal properties. Finally, I explored the physics of an array of THz metamaterial resonators coupled to cyclotron resonances of a two-dimensional electron gas, developing a multiple-mode theory that takes in account the interaction between multiple photon modes mediated by the electrons. My results show that this cross-interaction, due to the strong two-dimensional geometry of the optically active medium, leads to the hybridization of different uncoupled photon modes, and manifests as a visible change of the distribution of the coupled electromagnetic field.
... On the other hand, in the systems studied experimentally by Dupont et al. [8,9], the n-doped semiconductor layers (with ω p,mirr ω IT ) play the role of the mirrors. Consequently, intersubband excitation couples resonantly not with the plasmonic-type modes but only with the photonictype modes located far above ω p,mirr [37,38]. Nevertheless, it is reasonable to expect that the systems with n + -doped semiconductor mirrors can be designed so as to achieve an interesting situation when ω IT = ω surf p,mirr ≈ ω cutoff A . ...
... We want to stress that in contrast with the earlier papers discussing the resonant coupling between electronic excitation and surface plasmon polariton modes (see, e.g., [18,34]), we do not restrict our discussion to the simplest three-layer geometry, where (cubic) optically active material occupies the whole space between the mirrors. To demonstrate an important role of the symmetry of the resonators in the formation of the multimode ISPP branches (i.e., the branches containing more than one resonator mode [38]), the case of the (asymmetric) four-layer structure shown in Fig. 1(b) is additionally discussed. In this structure, only half of the space between the mirrors is occupied by an active material. ...
... As in our previous papers [37,38], the semiclassical approach based on the transfer matrix formalism and the effective-medium approximation will be employed. The claddings are described by the Drude model. ...
We theoretically discuss properties of intersubband surface plasmon polaritons (ISPPs) supported by the system consisting of a multiple quantum well (MQW) slab embedded into planar resonator with highly doped semiconducting claddings playing the role of cavity mirrors. Symmetric structures,where theMQWslab occupies the whole space between the claddings and asymmetric structures, where the MQW occupy only half of the space etween mirrors, are considered. We focus mainly on the nearly degenerate structures where intersubband frequency is close to frequency of the surface plasmon of the mirrors. The ISPP characteristics are calculated numerically using a semiclassical approach based on the transfer matrix formalism and the effective-medium approximation. The claddings are described by the lossless Drude model. The possibility of engineering the dispersion of the ISPP branches is demonstrated. In particular, for certain parameters of the asymmetric structures we observe the formation of the multimode ISPP branches with two zero group velocity points. We show that the properties of the ISPP branches are reasonably well interpreted employing quasiparticle picture provided that the concept of the mode overlap factor is generalized, taking into account the dispersive character of the mirrors.
In addition to this, we demonstrate that the lossless dispersion characteristics of the ISPP branches obtained in the paper are consistent with the angle-resolved reflection-absorption spectra of the GaAlAs-based realistic plasmonic resonators.
... The influence of the cavity has been studied, confirming its importance to reach the strong coupling regime [70]: when missing, the electroluminscent signal is the one of the bare intersubband transition (figure 1.11b); when present, its main contribution comes from the polaritonic states (figure 1.11a). The secondary feature in figure (1.11a) comes from the coupling between intersubband excitations and higher photonic modes [71,72]. ...
Intersubband polaritons are light-matter excitations originating from the strong coupling between an intersubband quantum well electronic transition and a microcavity photon mode. In the low density limit, \textit{i.e.}, when only a tiny fraction of the Fermi sea is excited, these excitations are well described by a quadratic effective bosonic Hamiltonian. However, when the number of excitations in the system increases, deviations from this behavior occur. In this thesis we study how the Coulomb electron-electron interaction and the Pauli saturation of the electronic transitions affect the physics of intersubband polaritons by adapting a commutator technique for composite bosons. We develop a microscopic theory to derive the polariton-polariton interactions and explain how it can be encoded in effective quartic bosonic Hamiltonian. Using realistic set of parameters we predict that polariton-polariton interactions can be signicant, especially in the THz range. This work paves the way to promising future studies in nonlinear optics with intersubband polaritons. The main results of this work are published in Ref. [1].
... Where cav is the dielectric constant of the cavity, f 12 is the oscillator strength,L eff cav is the effective thickness of the cavity, N QW is the QW number. Since the overlap of the optical mode with the quantum wells is not constant due to the different z-position, we introduce a normalized effective cavity lengthL eff cav (k) to take into account this factor, similarly to what has already been proposed by [16] : ...
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... The strong-coupling-regime ͑SCR͒, in which the dipole coupling between intersubband excitation and the cavity photon gives rise to coherent mixed modes ͑intersubband cavity polaritons͒ has recently received a lot of attention from both experimentalists and theoreticians. [1][2][3][4][5] In view of applications for optoelectronic devices, the analysis of the nonlinear intersubband properties is a fundamental and intriguing field of MC physics. ...
... Note that when is very close to res then the lower polariton branches, associated with higher photonic modes ͑n Ͼ 1͒, are closely spaced slightly below IT . 5 The above mentioned modes are responsible for the appearance of the small central peak in the angle-resolved absorption spectra reported by Dupont et al. 1,2 ͓The spatial distribution profile of ͉H y ͉ arising from an incident field with Х −n Ј and = res ͑not presented here͒ supports the above statement ͑see also Ref. 5͒.͔ It is interesting to note that in the presence of the inhomogeneous broadening, the formation of the additional central peak is possible also in the single cavity mode approximation. ...
... It is interesting to note that in the presence of the inhomogeneous broadening, the formation of the additional central peak is possible also in the single cavity mode approximation. 5,21 It is obvious that we can expect a substantial deviation from the linear absorption spectra in the limit of strong in-tensities of the incident light. A detailed inspection of the equations predicted by the FPM ͑see also Figs. 1 and 3͒ suggests that as long as condition ⍀ R 2ء 1 ӷ ␥ IT 2 , ␥ c 1 2 is fulfilled, the two main absorption peaks are located far from the resonance ͉͑ Ϯ1 Ј − IT ͉ 2 ӷ ␥ c 1 2 , ␥ IT 2 ͒. ...
We theoretically discuss the nonlinear intersubband response of multiple-quantum-well structures
embedded in microcavities with plane-wave approximation. We employ a semiclassical approach
based on the transfer matrix formalism and the so-called sheet model. The linear absorptive losses
are taken into account. It is shown that in the strong-coupling-regime the saturation effect leads to
the evolution of the absorption spectra from a pair of simple harmonic oscillators to highly
anharmonic ones. The usefulness of the simplified analytical approach, based on a standard
multibeam interference analysis and the “mean-field” approximation is also demonstrated.
The central theme of cavity quantum electrodynamics is the coupling of a single optical mode with a single matter excitation, leading to a doublet of cavity polaritons which govern the optical properties of the coupled structure. Especially in the ultrastrong coupling regime, where the ratio of the vacuum Rabi frequency and the quasi-resonant carrier frequency of light, ΩR/ω c, approaches unity, the polariton doublet bridges a large spectral bandwidth 2ΩR, and further interactions with off-resonant light and matter modes may occur. The resulting multi-mode coupling has recently attracted attention owing to the additional degrees of freedom for designing light–matter coupled resonances, despite added complexity. Here, we experimentally implement a novel strategy to sculpt ultrastrong multi-mode coupling by tailoring the spatial overlap of multiple modes of planar metallic THz resonators and the cyclotron resonances of Landau-quantized two-dimensional electrons, on subwavelength scales. We show that similarly to the selection rules of classical optics, this allows us to suppress or enhance certain coupling pathways and to control the number of light–matter coupled modes, their octave-spanning frequency spectra, and their response to magnetic tuning. This offers novel pathways for controlling dissipation, tailoring quantum light sources, nonlinearities, correlations as well as entanglement in quantum information processing.
Similarly to a previouswork on the homogeneous electron gas [Y. Todorov, Phys.Rev.B89, 075115 (2014)], we
apply the Power-Zienau-Wooley (PZW) formulation of the quantum electrodynamics to the case of an electron gas quantum confined by one-dimensional potential. We provide a microscopic description of all collective plasmon modes of the gas, oscillating both along and perpendicular to the direction of quantum confinement. Furthermore, we study the interaction of the collective modes with a photonic structure, planar metallic waveguide, by using the full expansion of the electromagnetic field into normal modes. We show how the boundary conditions for the electromagnetic field influence both the transverse light-matter coupling and the longitudinal particle- particle interactions. The PZW descriptions appear thus as a convenient tool to study semiconductor quantum optics in geometries where quantum-confined particles interact with strongly confined electromagnetic fields inmicroresonators, such as the ones used to achieve the ultrastrong light-matter coupling regime.
We theoretically discuss the properties of intersubband polaritons supported by a multiple-quantum-well structure embedded in the planar microcavity with dielectric and plasmonic mirrors. A semiclassical approach based on the transfer matrix formalism supplemented by the sheet model and the "microscopic" implementation of the effective medium approximation is employed. The presence of the intrasubband transition is taken into account. The obtained results show that in the case of realistic systems exhibiting superstrong coupling regime, radiative coupling between cavity modes can lead to the violation of a commonly used single-mode cavity approximation. It manifests itself as a formation of hybrid polariton modes having a non-negligible admixture of higher photonic modes and/or surface plasmonic modes. The comparison with results predicted by a microscopic quantum approach recently developed is also presented. Performing the above mentioned comparison we pay special attention to the role of intra-and interwell Coulomb couplings.
