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Halide perovskites, such as methylammonium lead bromide (MAPbBr$_3$), host tightly bound three-dimensional excitons which are robust at room temperature. Excellent optical properties of MAPbBr$_3$ allow for designing of optical single-mode waveguides and cavities in the frequency range close to the excitonic transitions. Taken together, this turns MAPbBr$_3$ into an excellent platform for probing exciton-polariton nonlinear phenomena at room temperature. Here we investigate ultrafast non-equilibrium dynamics of polaritons under pulsed fs non-resonant excitation. We demonstrate the presence of the stimulated acoustic phonon-assisted scattering regime above threshold pump fluence, characterized by the explosive growth of emission intensity, a redshift of the emission spectral maximum, spectral narrowing, and sub-picosecond emission dynamics. Our theoretical findings are well confirmed by the results of experimental measurements.

Integration of 2D semiconductors with photonic crystal slabs provides an attractive approach to achieve strong light--matter coupling and exciton-polariton formation in a planar chip-compatible geometry. However, for the development of practical devices, it is crucial that the polariton excitations in the structure are easily tunable and exhibit strong nonlinear response. Here we study neutral and charged exciton-polaritons in an electrostatically gated planar photonic crystal slab with an embedded monolayer semiconductor MoSe$_2$ and experimentally demonstrate strong polariton nonlinearity, which can be tuned via gate voltage. We find that modulation of dielectric environment within the photonic crystal results in the formation of two distinct resonances with significantly different nonlinear response, which enables optical switching with ultrashort laser pulses. Our results open new avenues towards development of active polaritonic devices in a compact chip-compatible implementation.

Noncentrosymmetric nature of single-layer transition metal dichalcogenides manifest itself in the finite piezoelectricity and valley-Zeeman coupling. We microscopically model nonlinear exciton transport in nano-bubble of single-layers of transition metal dichalcogenide. Thanks to the giant piezoelectric effect, we obtain an enormous internal electric field, $E_{\rm piezo}\sim 10^7$V/m, resulting in a built-in dipole moment of excitons. We demonstrate that the piezo-induced dipole-dipole interaction provides a novel channel for the nonlinear exciton transport distinct from the conventional isotropic funneling of excitons and leading to the formation of hexagon-shaped exciton droplet on top of a circularly symmetric nano-bubble. The effect is tunable via the bubble size dependence of the piezo-electric field $E_{\rm piezo} \sim h^2_{\rm max}/R^3$ with $h_{\rm max}$ and $R$ being the bubble height and radius, respectively.

We demonstrate the controlled coherent transfer of topological domain walls in a one-dimensional non-Hermitian chain of interacting Bose-Einstein condensates. The topological protection stems from a spatially patterned pump in an open-dissipative system. As a testbed setup of the proposed phenomenon, we consider a chain of coupled micropillars with embedded quantum wells, possessing exciton-polariton resonances. The transfer of a domain wall is driven by spatially localised, adiabatic pump modulation in the vicinity of the domain wall. The stochastic calculations prove the coherent nature of the domain wall transfer. For appropriate system parameters the coherence degree is preserved after multiple transitions, paving the way towards long-range transfer of a coherent quantum state., Comment: 8 pages, 6 figures

We predict the existence of non-Hermitian topologically protected end states in a one-dimensional exciton-polariton condensate lattice, where topological transitions are driven by the laser pump pattern. We show that the number of end states can be described by a Chern number and a topological invariant based on the Wilson loop. We find that such transitions arise due to {\it enforced exceptional points} which can be predicted directly from the bulk Bloch wave functions. This allows us to establish a new type of bulk-boundary correspondence for non-Hermitian systems and to compute the phase diagram of an open chain analytically. Finally, we demonstrate topological lasing of a single end-mode in a realistic model of a microcavity lattice., Comment: Main text (6 pages) and Supplementary Material (4 pages)

We show that strong light-matter coupling can be used to overcome a long standing problem that has prevented efficient optical emission from carbon nanotubes. The luminescence from the nominally bright exciton states of carbon nanotubes is quenched due to the fast nonradiative scattering to the dark exciton state having a lower energy. We present a theoretical analysis to show that by placing carbon nanotubes in an optical microcavity the bright exctonic state may be split into two hybrid exciton-polariton states, while the dark state remains unaltered. For sufficiently strong coupling between the bright exciton and the cavity, we show that the energy of the lower polariton may be pushed below that of the dark exciton. This overturning of the relative energies of the bright and dark excitons prevents the dark exciton from quenching the emission. Our resutls pave the way for a new approach to band-engineering the properties of the nanoscale optoelectronic devices., Comment: 35 pages, 5 figures, 6 pages of supplementary materials, 1 supplementary figure

The exactly solvable model of quasi-conical quantum dot, having a form of spherical sector is proposed. Due to the specific symmetry of the problem the separation of variables in spherical coordinates is possible in the one-electron Schrodinger equation. Analytical expressions for wave function and energy spectrum are obtained. It is shown that at small values of the stretch angle of spherical sector the problem reduced to the conical QD problem. The comparison with previously performed works showed good agreement of results. As an application of the obtained results, the quantum transitions in the system are considered.

An analytical solution of the quantum problem of an electron on a spherical segment with angular confinement potential of the form of rectangular impenetrable walls is presented. It is shown that the problem is reduced to finding solution of hypergeometric equation. As an application of the obtained results the quantum transitions in this system are discussed, and it is shown that the selection rule for quantum number l is removed due to the violation of spherical symmetry of the problem.