Theory of coherent optical nonlinearities of intersubband transitions in semiconductor quantum wells

Abstract

We theoretically study the coherent nonlinear response of electrons confined in semiconductor quantum wells under the effect of an electromagnetic radiation close to resonance with an intersubband transition. Our approach is based on the time-dependent Schrödinger-Poisson equation stemming from a Hartree description of Coulomb-interacting electrons. This equation is solved by standard numerical tools and the results are interpreted in terms of approximated analytical formulas. For growing intensity, we observe a red-shift of the effective resonance frequency due to the reduction of the electric dipole moment and the corresponding suppression of the depolarization shift. The competition between coherent nonlinearities and incoherent saturation effects is discussed. The strength of the resulting optical nonlinearity is estimated across different frequency ranges from Mid-IR to THz with an eye to on-going experiments on intersubband polariton condensation and speculative quantum optical applications such as single-photon emission.

Magnetic-field-induced cavity protection for intersubband polaritons

“…In combination with higher-Q cavity configurations, our proposal has the potential to lead to polariton devices with unprecedented performances. Based on available experimental evidence, we anticipate that a narrower polariton linewidth will be a game-changing step in view of technological applications of intersubband polaritons, including nonlinear polariton devices [33] and polariton lasing [10,16]. On a longer perspective, our proposal highlights intersubband polariton physics in the presence of magnetic fields as a novel arena where to study the interplay between light-matter interaction with quantum Hall physics [51][52][53][54][55][56][57].…”

“…In spite of this, it must be kept in mind that the effect of electron-electron interactions is still present in the presence of magnetic field [31,32] and, in particular, the effect of Coulomb interactions onto the electron motion along the z-axis is completely unaffected by the magnetic field along z. As such, it keeps giving an important contribution to the nonlinearity of the ISB response to strong electromagnetic fields [33]. This implies that our results are directly applicable to the on-going quest of developing ISB polaritonic devices with strong optical non-linearities and polariton lasers, where a reduced polariton linewidth can be a game-changing improvement [10].…”

Intersubband Polariton-Polariton Scattering in a Dispersive Microcavity

“…The mode mixing originates from light scattering on the spatially modulated population difference ΠðxÞ via the nonlinear saturation of the ISB transition and the nonlinear suppression of the depolarization shift stemming from Coulomb interactions included as η [53]. The coupled differential equations are numerically solved for a set of parameters of ω cav ; ω ISB ; Ω R ; Γ coh ¼ 18 THz, and Γ cav ¼ 10 THz retrieved from the steady-state characterization of the sample, while excitation-induced dephasing Γ EID ¼ 20 THz and η ¼ −2π × 4.8 THz are chosen for optimum agreement with the experiment (Supplemental Material [46]).…”