Direct Polariton-To-Electron Tunneling in Quantum Cascade Detectors Operating in the Strong Light-Matter Coupling Regime

M. Lagrée, M. Jeannin, G. Quinchard, O. Ouznali, A. Evirgen, V. Trinité, R. Colombelli, and A. Delga

Phys. Rev. Applied 17, 044021 – Published 12 April 2022

Abstract

Modern optoelectronic devices rely on cavity electrodynamics concepts for improved performances, embedding the active medium in an optical cavity to enhance the light-matter coupling. This coupling rate is usually small compared to the electronic and photon energies. Despite several demonstrations, devices operating with much larger light-matter coupling strength, in the so-called strong light-matter coupling regime, are yet to be demonstrated as viable, practical candidates. One of the main technological obstacles that hamper their dissemination is the comprehension of the carrier current extraction and injection from and into strongly coupled light-matter states. Here, we study this fundamental phenomenon in midinfrared quantum cascade detectors (QCDs) operating in the moderate to strong light-matter coupling regime. They operate around $λ = 10 μ m$ with a minimum Rabi splitting of 9.3 meV. A simple model based on the usual description of transport in QCDs does not reproduce the polaritonic features in the photocurrent spectra. On the contrary, a more refined approach, based on the semiclassical coupled modes theory, is capable of reproducing both optical and electrical spectra with excellent agreement. By correlating absorption and photoresponse with the simulations, we demonstrate that—in this system—resonant tunneling from the polaritonic states appears to be the predominant extraction mechanism. The dark intersubband states do not have a significant role in the process, contrary to what happens in electrically injected polaritonic emitters.

Received 27 October 2021
Revised 11 March 2022
Accepted 28 March 2022

DOI:https://doi.org/10.1103/PhysRevApplied.17.044021

Physics Subject Headings (PhySH)

Intersubband polariton Light-matter interaction Optoelectronics Semiconductor quantum optics

III-V semiconductors Optical sources & detectors Quantum wells Semiconductor microcavities

Condensed Matter, Materials & Applied PhysicsAtomic, Molecular & Optical

Authors & Affiliations

M. Lagrée ^1,*, M. Jeannin ^2,§, G. Quinchard^1,§, O. Ouznali², A. Evirgen¹, V. Trinité ^1,†, R. Colombelli^2,‡, and A. Delga¹

¹III-V Lab, Campus Polytechnique, 1, Avenue Augustin Fresnel, RD 128, Palaiseau cedex 91767, France
²Centre de Nanosciences et de Nanotechnologies (C2N), CNRS UMR, 9001, Université Paris-Saclay, Palaiseau 91120, France

^*mathurin.lagree@3-5lab.fr
^†virginie.trinite@3-5lab.fr
^‡raffaele.colombelli@u-psud.fr
^§These authors contributed equally.

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 17, Iss. 4 — April 2022

Subject Areas

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) SEM image of a patch cavity-embedded QCD detector. $S$ is the patch lateral size and $P$ is the array period. Patches are electrically connected using gold wires deposited on a dielectric bridge layer. The active layers, the QCDs, are embedded between gold layers ( $Au$ ). (b) Band structure of the QCD [11.0/3.6/4.2/3.8/4.6/2.8/5.3/2.5 nm, starting with the doped quantum well $n_{2D} = 5 e 11 {cm}^{- 2}$ , $(In, Ga) As$ in bold, $(Al, In) As$ normal], represented on one period ( $T = 295 K$ ). (c) Schematic representation of the system: the incoming light excitation ( $ω)$ couples to the optical cavity ( $ω_{c}$ ), which is coupled to the intersubband transition ( ${\tilde{ω}}_{ISB}$ ). The ISB mode is itself coupled to an extractor mode ( $ω_{E}$ ), representing the electronic cascade. The different dissipation channels are represented ( $γ_{c}$ , $Γ_{c}$ , $γ_{ISB}$ , and $γ_{E}$ ).
Reuse & Permissions
Figure 2
Reflectivity measurements (continuous lines) and CMT global fit (dashed lines), represented in the form of absorption $A = 1 - R$ , for different patch sizes $S$ and fixed period $P = 5 μ m$ . The scale used is the same for all spectra and offsets are added for visibility. (a) Empty cavities (undoped active layers). Cavity dispersion (blue crosses) is computed using Eq. (3) ( $n_{eff} = 3.28$ ) (b) Doped QCDs ( $n_{2D} = 5 e 11 {cm}^{- 2}$ ) embedded inside the patch cavities. Polaritonic dispersion is computed using the Hamiltonian $H$ in Eq. (2) ( $n_{eff} = 3.33$ , $ω_{ISB} = 115 meV$ , $ω_{P} = 25 meV$ ). See Fig. S1 within the Supplemental Material [35] for additional reflectivity measurements and fits. Although extremely low, propagated errors from the fit are represented on the spectra with the thickness of the gray curves.
Reuse & Permissions
Figure 3
(a) Normalized photocurrent measurements (continuous lines) and three-resonator CMT global fit (dashed lines), for devices with period $P = 7 μ m$ and different patch sizes $S$ . Offsets are added for visibility. The gray areas represent the fit errors propagated on the spectra (see Sec. 1 within the Supplemental Material [35] for the detailed computations of the errors). The polaritonic dispersion (blue crosses) is computed considering only the cavity-ISB interaction in the Hamiltonian $H$ of Eq. (11), unperturbed by the QCD extractor ( $n_{eff} = 3.23$ , $ω_{ISB} = 115 meV$ , $ω_{P} = 29 meV$ ). (b) Computed transfer function between the extracted power ( $A_{E}$ ) and the total power dissipated inside the QCD ( $A_{E} + A_{ISB}$ ). Lower panels: possible extraction schemes for a QCD in the strong light-matter coupling regime. (c) Dark-state mediated extraction: polaritonic excitations ( $ω_{\pm})$ relax into the dark states ( $ω_{ISB})$ , and they are subsequently extracted through the electronic cascade. (d) Resonant tunneling through the polaritonic states: polaritonic excitations directly tunnel from the polaritonic reservoir into the electronic cascade. In this case the dark states are not involved in the process.
Reuse & Permissions

Physical Review Applied