Generalized Gross-Pitaevskii model for intersubband polariton lasing

Abstract

We develop a generalized Gross-Pitaevskii approach to the driven-dissipative dynamics of intersubband polaritons in patterned planar microcavities where the cavity mode is strongly coupled to an intersubband transition in doped quantum wells. Substantial differences with respect to the case of interband excitonic polaritons are highlighted, in particular the non-Markovian features of the radiative decay. The accuracy of the method is validated on the linear reflection properties of the cavity, that quantitatively reproduce experimental observations. The theoretical framework is then applied in the nonlinear regime to study optical parametric oscillation processes for intersubband polaritons. Our findings open interesting perspectives in view of novel coherent laser sources operating in the mid and far infrared.Planar semiconductor microcavities have emerged as a versatile tool to address fundamental questions in the physics of light-matter interaction, and realize a new generation of optoelectronic devices, with applications that are still largely unexplored [1]. In particular, a rich variety of optical phenomena are observed when a quantum well element is embedded in the cavity layer and an electronic transition is resonantly coupled to the cavity mode. Depending on the structure and the doping level of the quantum well, the transition can be of either inter-band [2] or inter-subband nature [3]: in the former case, it involves some electrons being promoted from the valence to the conduction band and is typically located in the near-infrared or visible domain. In the latter case, electrons (or holes) are promoted from a filled subband of the conduction (or valence) band to another, initially empty subband. For a strong enough light-matter coupling, photons can undergo several absorption-emission cycles before being lost. In this so-called strong lightmatter coupling regime, the eigenmodes are superpositions of photonic and matter excitations: depending on the nature of the electronic transition involved, we usually speak of interband polaritons or intersubband polaritons.As a few decades of intense theoretical and experimental research have shown, interband (IB) polaritons combine the extremely low mass of cavity photons (orders of magnitude lower than the excitonic one) with sizable interactions stemming from their excitonic component. These remarkable properties have been at the heart of the celebrated observations of Bose-Einstein condensation [4] and superfluidity effects [5,6] in a polariton gas and are still being widely exploited in a number of exciting directions, as reviewed in [1,7,8].Since with the early observations [9, 10], the research on intersubband (ISB) polaritons has also made impressive steps. In addition to their operation at much longer wavelengths in the mid or far infrared spectively), ISB polaritons display a few other remarkable differences compared to IB ones. Since a large number of electrons are involved in the optical transition, the Rabi splitting can be pushed to extremely high val...

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

“…These two effects are in competition on the lower polariton branch, but add up to reinforce the effective nonlinearity experienced by the upper polariton. These predictions are of great importance in the context of intersubband polariton physics with potential application to ISB polariton condensation and lasing 24,25 . As a final, more speculative topic, in Sec.…”

“…As a concrete benchmark of the strength of our ISB nonlinearities, we will consider the light intensity value that is needed to have a frequency shift comparable to the linewidth. This is the typical condition under which important nonlinear effects such as optical bistability 37 or optical parametric oscillation start occurring 25 . The discussion that follows will mostly concentrate on the latter effect, which is a promising strategy to achieve lasing and Bose-Einstein condensation effects in novel wavelength regions 24,38 .…”

“…Note that this effective interaction term has an opposite sign compared to the exciton-polariton case 37 . In analogy to this exciton-polariton case, a positive interaction coefficient between ISB polaritons g > 0 was erroneously assumed by two of us for the calculations in 25 , with no major prejudice for the overall conclusions of that work.…”

Intersubband Polariton-Polariton Scattering in a Dispersive Microcavity

“…Ultrafast modulation of the coupling strength [28,[37][38][39] opens intriguing possibilities for tailored subcycle dynamics [40]. Moreover, it has been predicted that ISB polaritons, like their excitonic counterpart, can undergo nonequilibrium condensation, enabling inversionless lasing, and thus on-chip coherent terahertz and midinfrared light sources [41][42][43]. Yet up to now, a key ingredient given by a stimulated scattering mechanism toward the final state has been missing.…”

Observation of Intersubband Polaritons in a Single Nanoantenna Using Nano-FTIR Spectroscopy

“…22 . However, these effects, have not been reported yet for ISB polaritons, and theoretical frameworks 22,23 still require experimental verifications.…”