Enhanced Cavity Optomechanics with Quantum-Well Exciton Polaritons

N. Carlon Zambon, Z. Denis, R. De Oliveira, S. Ravets, C. Ciuti, I. Favero, and J. Bloch

Phys. Rev. Lett. 129, 093603 – Published 25 August 2022

Abstract

Semiconductor microresonators embedding quantum wells can host tightly confined and mutually interacting excitonic, optical, and mechanical modes at once. We theoretically investigate the case where the system operates in the strong exciton-photon coupling regime, while the optical and excitonic resonances are parametrically modulated by the interaction with a mechanical mode. Owing to the large exciton-phonon coupling at play in semiconductors, we predict an enhancement of polariton-phonon interactions by 2 orders of magnitude with respect to mere optomechanical coupling: a near-unity single-polariton quantum cooperativity is within reach for current semiconductor resonator platforms. We further analyze how polariton nonlinearities affect dynamical backaction, modifying the capability to cool or amplify the mechanical motion.

Received 24 February 2022
Accepted 18 July 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.093603

Physics Subject Headings (PhySH)

Exciton polariton Optomechanics Semiconductor quantum optics

Semiconductor microcavities

Atomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

Authors & Affiliations

N. Carlon Zambon ^1,*,†,∥, Z. Denis ^2,*,‡, R. De Oliveira², S. Ravets ¹, C. Ciuti², I. Favero², and J. Bloch¹

¹Centre de Nanosciences et de Nanotechnologies (C2N), CNRS-Université Paris-Saclay, 91120 Palaiseau, France
²Université Paris Cité, CNRS, Matériaux et Phénomènes Quantiques, F-75013 Paris, France

^*These authors contributed equally to this work.
^†Corresponding author. carlonn@ethz.ch
^‡Corresponding author. zakari.denis@univ-paris-diderot.fr
^∥Present address: Photonics Laboratory, ETH Zürich, 8093 Zürich, Switzerland.

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Vol. 129, Iss. 9 — 26 August 2022

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Images

Figure 1
(a) A resonator supports optical and mechanical modes with respective frequencies $ω_{c}$ and $Ω_{m}$ . It also embeds a quantum well (QW) with excitonic resonance at $ω_{x} \approx ω_{c}$ . The cavity is driven by a laser with frequency $ω$ . We denote $g_{i j}$ the pairwise couplings among the modes. (b) Energy level diagram. Strong exciton-photon coupling results in a Rabi splitting $Ω_{R} \approx 2 g_{c x}$ between the upper ( $U$ ) and lower ( $L$ ) polariton normal modes. The mechanical mode modulates the polariton resonances through the effective couplings $g_{l m}$ and $g_{u m}$ , producing Stokes (s) and anti-Stokes (as) sidebands.
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Figure 2
Sketch of a disk (a), ring (b), and pillar (c) microresonator. Here, (a), (b) are $0.2 μ m$ thick with an outer radius $R_{d} = 2 μ m$ ; in (b) the inner radius is $1.5 μ m$ . (c) is $2.6 μ m$ in diameter and defined by two GaAs/AlAs distributed Bragg reflectors (DBRs) and $λ / 2$ GaAs spacer. All structures are adjusted to yield optical resonances near $E_{x} = 1.463 eV$ (for a 8 nm thick ${In}_{0.05} {Ga}_{0.95} As$ QW [57]). Normalized intensity profiles of a cavity mode ( $| E |^{2}$ ) and strain field ( $| Σ |$ ) are shown for in-plane and orthogonal cuts. The QW positions are highlighted with solid lines: in (a), (b) two QWs are displaced by $\pm 15 nm$ from the cavity field antinode ( $η_{S} \approx 1$ ), whereas in (c) 4 QWs displaced by $\pm (15, 39) nm$ from the center of the spacer $η_{S} = (0.93, 0.62)$ . The calculated $M$ frequency ( $Ω_{m} / 2 π$ ) and coupling rates ( $g_{i j} / 2 π$ ) are listed for the selected modes. We list $g_{c m} / 2 π$ for a cavity mode detuning of 40–10 nm from the GaAs band gap. Information on the optical and mechanical decay rates can be found in [57].
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Figure 3
(a) Single-polariton cooperativity versus exciton fraction and pillar radius ( $R_{p}$ ). (b) Cut through panel (a) for $R_{p} = 0.7 μ m$ showing the effect of inhomogeneous $X$ broadening (Gaussian linewidth indicated in the inset). (c) Polariton inhomogeneous-broadening $Γ_{inh}$ , relative to the mechanical damping $Γ$ .
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Figure 4
(a) Optomechanical damping rate $Γ_{opt}$ versus detuning ( $\tilde{δ}$ ), and photon occupation ( $\tilde{n}$ ) for repulsive interactions ( $χ > 0$ ). Dashed black (red) lines trace the sideband detuning ${\tilde{δ}}_{\pm}$ (the mechanical-oscillation threshold, OMO); unstable regions are shaded in gray. (b) Enhancement of $Γ_{opt}^{\pm}$ at the sidebands ${\tilde{δ}}_{\pm}$ relative to its value for $χ = 0$ as a function of the cavity occupation. (c) Mean phonon occupation $n_{eff}$ versus detuning for $\tilde{n} = 50$ . Dashed lines indicate the thermal population and the lowest $n_{eff}$ for $χ = 0$ . (d) Minimal $n_{eff}$ versus the cavity occupation. In (b)–(d) markers denote numerical solutions while lines show the analytical results [57].
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