Intersubband Polariton-Polariton Scattering in a Dispersive Microcavity

M. Knorr, J. M. Manceau, J. Mornhinweg, J. Nespolo, G. Biasiol, N. L. Tran, M. Malerba, P. Goulain, X. Lafosse, M. Jeannin, M. Stefinger, I. Carusotto, C. Lange, R. Colombelli, and R. Huber

Phys. Rev. Lett. 128, 247401 – Published 16 June 2022

Abstract

The ultrafast scattering dynamics of intersubband polaritons in dispersive cavities embedding $GaAs / AlGaAs$ quantum wells are studied directly within their band structure using a noncollinear pump-probe geometry with phase-stable midinfrared pulses. Selective excitation of the lower polariton at a frequency of $\sim 25 THz$ and at a finite in-plane momentum $k_{‖}$ leads to the emergence of a narrowband maximum in the probe reflectivity at $k_{‖} = 0$ . A quantum mechanical model identifies the underlying microscopic process as stimulated coherent polariton-polariton scattering. These results mark an important milestone toward quantum control and bosonic lasing in custom-tailored polaritonic systems in the mid and far infrared.

Received 22 December 2021
Revised 10 March 2022
Accepted 15 April 2022

DOI:https://doi.org/10.1103/PhysRevLett.128.247401

Physics Subject Headings (PhySH)

Intersubband polariton Nonlinear optics Quantum description of light-matter interaction Ultrafast optics Ultrafast phenomena

Ultrafast pump-probe spectroscopy

Condensed Matter, Materials & Applied PhysicsAtomic, Molecular & Optical

Authors & Affiliations

M. Knorr ¹, J. M. Manceau ^2,*, J. Mornhinweg ¹, J. Nespolo³, G. Biasiol ⁴, N. L. Tran², M. Malerba², P. Goulain ², X. Lafosse², M. Jeannin², M. Stefinger¹, I. Carusotto ³, C. Lange ^5,†, R. Colombelli ², and R. Huber ¹

¹Department of Physics, University of Regensburg, 93040 Regensburg, Germany
²Centre de Nanosciences et de Nanotechnologies (C2N), CNRS UMR 9001, Université Paris Saclay, 91120 Palaiseau, France
³INO-CNR BEC Center and Dipartimento di Fisica, Universita di Trento, I-38123 Povo, Italy
⁴Laboratorio TASC, CNR-IOM, Area Science Park, 34149 Basovizza, Trieste, Italy
⁵Department of Physics, TU Dortmund University, 44227 Dortmund, Germany

^*jean-michel.manceau@c2n.upsaclay.fr
^†christoph.lange@tu-dortmund.de

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Vol. 128, Iss. 24 — 17 June 2022

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Images

Figure 1
(a) Sample scheme and spatial distribution of the out-of plane electric field component $| E_{z} |$ . $Λ$ : metal grating periodicity. (b) Conduction band structure (gray line) and wave function squared moduli for first ( $Ψ_{1}$ ) and second ( $Ψ_{2}$ ) subbands inside an 8.3 nm $GaAs / {Al}_{0.3 3} {Ga}_{0.6 7} As$ QW with growth direction $z$ . ISB: intersubband transition. (c) Calculated reflectance (RCWA) of the sample. The strong coupling of ISB (black dashed) and cavity resonance (black dotted) leads to the emergence of polariton states (LP and UP). Measured data (blue dots) is shown for comparison. The red line marks the pump angle of incidence $θ = 21 °$ . (d) Spectra of narrowband (red solid line) and broadband (red dashed line) pump pulses and calculated reflectance at $θ = 21 °$ (blue line) at a lattice temperature of 10 K. (e) Sketch of parametric polariton-polariton scattering: the pump pulse creates polaritons at finite $k_{‖}$ . Scattering of two pump polaritons leads to amplification of the probe pulse through one of the polaritons, while excess momentum is carried away by the other polariton.
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Figure 2
(a) Schematic geometry of the angle-resolved ultrafast pump-probe experiment. The sample is probed at normal incidence with varying pump-probe delay time $Δ t$ . The angle of incidence $θ$ of the pump pulses can be adjusted without changing $Δ t$ or the spatial overlap of the pump and probe foci. Inset: measured waveforms as incident onto the sample (left) and reflected from it (right). (b) Measured reflectance spectra as a function of pump-probe delay time $Δ t$ for a broadband pump pulse with a bandwidth of 3.9 THz (peak intensity $350 MW / {cm}^{2}$ , $θ = 21 °$ ). (c) Theoretical calculation of the excited polariton population $ρ_{2}$ . (d) Spectra before the arrival of the pump pulse (gray) and at $Δ t = 0$ (blue), and calculated reflectance of the uncoupled cavity resonance (red).
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Figure 3
(a) Measured reflectance spectra in dependence of pump-probe delay time $Δ t$ for a narrowband pump pulse with a bandwidth of 0.6 THz (peak intensity $70 MW / {cm}^{2}$ , $θ = 21 °$ ). (b) Simulated reflectance including scattering terms between pump and probe pulses. (c) Experimental pump spectrum (red) as well as measured (blue line) and simulated (shaded area) reflectance at $Δ t = 0$ . A narrowband feature emerges with slightly lower center frequency (blue dashed line, 24.8 THz) than the pump center frequency (red dashed line, 25 THz). (d) Simulated reflectance excluding scattering terms between pump and probe pulses.
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Figure 4
(a)–(c) Measured reflectance spectra for pump peak intensities of $40 MW / {cm}^{2}$ (a), $57 MW / {cm}^{2}$ (b), and $80 MW / {cm}^{2}$ (c) as a function of $Δ t$ . (d) Reflectance for different pump intensities ranging from $10 MW / {cm}^{2}$ to $80 MW / {cm}^{2}$ at $Δ t = 0$ (solid lines) and for $Δ t < 0$ (dashed). (e) Black curve: reflectance at the spectral maximum of the signature at $Δ t = 0$ as a function of pump peak intensity $I_{peak}$ . Black dots: discrete values extracted from measurements shown in panels (a)–(c). Blue line: linear fit to the data for pump intensities between $180 kW / {cm}^{2}$ and $4 MW / {cm}^{2}$ . (f) Measured spectral fluence $Φ_{ν}^{out}$ in dependence of probe input $Φ_{ν}^{probe}$ at the spectral maximum of the signature at $Δ t = 0$ (black dots) and linear fit (blue line). The linear dependence signifies stimulation. (g) Simulated reflectance for $Δ t = 0$ at the spectral maximum of polariton-polariton scattering in dependence of the pump intensity.
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