Cavity-induced exciton localization and polariton blockade in two-dimensional semiconductors coupled to an electromagnetic resonator

Letter
Open Access

Cavity-induced exciton localization and polariton blockade in two-dimensional semiconductors coupled to an electromagnetic resonator

Emil V. Denning, Martijn Wubs, Nicolas Stenger, Jesper Mørk, and Philip Trøst Kristensen

Phys. Rev. Research 4, L012020 – Published 17 February 2022

Abstract

Recent experiments have demonstrated strong light–matter coupling between electromagnetic nanoresonators and pristine sheets of two-dimensional semiconductors, and it has been speculated whether these systems can enter the quantum regime operating at the few-polariton level. To address this question, we present a microscopic quantum theory for the interaction between excitons in a sheet of two-dimensional material and a localized electromagnetic resonator. We find that the light–matter interaction breaks the symmetry of the otherwise translation-invariant system and thereby effectively generates a localized exciton mode, which is coupled to an environment of residual exciton modes. This dissipative coupling increases with tighter lateral confinement, and our analysis reveals this to be a potential challenge in realizing nonlinear exciton-exciton interaction. Nonetheless, we predict that polariton blockade due to nonlinear exciton-exciton interactions is well within reach for nanoresonators coupled to transition-metal dichalcogenides, provided that the lateral confinement can be sufficiently tight to make the nonlinearity overcome the polariton dephasing caused by phonon interactions.

Received 26 March 2021
Revised 13 January 2022
Accepted 14 January 2022

DOI:https://doi.org/10.1103/PhysRevResearch.4.L012020

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Cavity quantum electrodynamics Exciton polariton Excitons Open quantum systems Open quantum systems & decoherence Plasmonics Quantum states of light Quasiparticles & collective excitations

Condensed Matter, Materials & Applied PhysicsAtomic, Molecular & Optical

Authors & Affiliations

Emil V. Denning ^1,2,3,*, Martijn Wubs ^1,2,4, Nicolas Stenger^1,2,4, Jesper Mørk ^1,2, and Philip Trøst Kristensen ^1,2

¹Department of Photonics Engineering, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark
²NanoPhoton - Center for Nanophotonics, Technical University of Denmark, Ørsteds Plads 345A, DK-2800 Kgs. Lyngby, Denmark
³Nichtlineare Optik und Quantenelektronik, Institut für Theoretische Physik, Technische Universität Berlin, 10623 Berlin, Germany
⁴Center for Nanostructured Graphene, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark

^*[email protected]

Quantum theory of two-dimensional materials coupled to electromagnetic resonators

Emil V. Denning, Martijn Wubs, Nicolas Stenger, Jesper Mørk, and Philip Trøst Kristensen

Phys. Rev. B 105, 085306 (2022)

Article Text

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Issue

Vol. 4, Iss. 1 — February - April 2022

Subject Areas

Condensed Matter Physics

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Images

Figure 1
(a) Illustration of an electromagnetic resonator coupled to a sheet of 2D material. (b) Exciton–resonator coupling $G_{0}$ , nonlinear exciton-exciton interaction $W_{0}^{'}$ and decay rate into residual exciton modes $Γ_{res}$ as a function of the lateral confinement $L$ of the electromagnetic field, as well as the exciton dephasing from phonon scattering, $γ_{x}^{'}$ , in ${WS}_{2}$ at a temperature of 300 K. Yellow shading marks the regime where $L$ is large enough that the residual excitons can be ignored and small enough that $W_{0}^{'}$ exceeds the polariton dephasing, such that polariton blockade is possible. Blue shading marks the regime where the residual excitons have a non-negligible impact on the dynamics.
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Figure 2
(a) The localized resonant field ( ${\hat{a}}_{c}$ , orange dot) is coupled to a continuum of exciton modes with momentum $k$ . (b) Through a linear transformation, the light–matter interaction can be described as a coupling between the resonant field and a single, collective exciton reaction coordinate ( ${\hat{B}}_{0}$ ) which, in turn, is coupled to an environment of residual exciton modes ( ${\hat{\tilde{B}}}_{i}$ ). (c) Exciton spectral density (blue) and residual spectral density (green) for an electromagnetic field with lateral Gaussian confinement corresponding to Eq. (4). The exciton reaction coordinate frequency, $Ω_{0}$ , is indicated with a dashed black line. The inset shows the Gaussian lateral field profile.
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Figure 3
(a) Exact time evolution of resonator excitation number, $〈 {\hat{a}}_{c}^{†} {\hat{a}}_{c} 〉$ (black solid lines), compared with the Markovian theory (orange dashed lines) and with the residual excitons ignored (red dotted lines) for a separable field profile with Gaussian in-plane distributions and different lateral confinement lengths, $L$ . The 2D material was taken to be ${WS}_{2}$ , and $L_{z} = 150 nm, ω_{c} = Ω_{0}, ℏ γ_{c} = 5 meV$ , and $| n \cdot p_{cv} | / p_{cv} = 0.5$ . The light–matter coupling with these parameters is $ℏ G_{0} = 22 meV$ .
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Figure 4
(a) Optimal antibunching vs lateral confinement, $L$ , for monolayer ${WS}_{2}$ coupled to a resonant field with Gaussian in-plane distribution at temperatures of 4 and 300 K and resonator linewidths $ℏ γ_{c}$ of 25 and $50 meV$ . Parameters: $L_{z} = 50 nm, F = 1.5 meV, | p_{cv} \cdot n | / p_{cv} = 0.75$ , corresponding to $ℏ G_{0} = 57.5 meV$ . (b) Nonlinear interaction strength $W_{0}^{'}$ vs $L$ , compared to exciton linewidth, $Γ_{x} = γ_{x} + γ_{x}^{'}$ , and exciton dephasing, $γ_{x}^{'}$ . The thin vertical lines in panels a and b mark the value of $L$ where $g^{(2)} (0)$ drops below 1 for $T = 300 K$ . (c) Delay-time dependence of steady-state second-order correlation function for optimized parameters as in panel a, at a lateral confinement length of $L = 6.9 nm$ . Plot signatures correspond to those in panel a.
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