Exciton-polaritons in lattices: A non-linear photonic simulator

Microcavity polaritons are mixed light–matter quasiparticles with extraordinary nonlinear properties, which can be easily accessed in photoluminescence experiments. Thanks to the possibility of designing the potential landscape of polaritons, this system provides a versatile photonic platform to emulate 1D and 2D Hamiltonians. Polaritons allow transposing to the photonic world some of the properties of electrons in solid-state systems, and to engineer Hamiltonians for photons with novel transport properties. Here we review some experimental implementations of polariton Hamiltonians using lattice geometries.     

Dynamics of polaritons resonantly created at the upper polariton branch

We have studied the polariton relaxation dynamics in a CdTe microcavity at low temperatures after resonant excitation into the upper polariton branch (UPB). Initially, we have set a negative exciton–cavity detuning, such that the energy difference between the two polariton branches coincides with that of an LO phonon. Our experimental results reveal a sublinear dependence of the integrated emission from the lower polariton branch (LPB) with excitation power. This evidences not only an inefficient LO phonon mediated relaxation from the UPB to the LPB but also a substantial inhibition of polariton relaxation along the LPB. After that, we have progressively reduced the negative detuning, approaching the exciton–cavity resonance. Under these conditions it is possible to observe a nonlinear emission arising from K0 LPB-states similar to that observed after nonresonant excitation. Marked oscillations are present in the time evolution traces, with a period that does not depend on excitation power or detuning.     

Renormalized dispersion of elementary excitations in spinor polariton condensates

We analyse the polarization of spinor polariton condensates and corresponding dispersions of elementary excitations. We have considered the effects of magnetic field induced splitting in circular polarizations and residual splitting in linear polarizations in the ground state provided by the cavity asymmetry. We show that anisotropic polariton–polariton interactions fully compensate the Zeeman splitting in circular polarizations below the critical magnetic field, thus leading to the spin-Meissner effect for the polariton condensates. We also analyzed the effect of polariton–polariton interactions on the stability of the gap in linear polarizations characteristic for anisotropic microcavities. It was shown that in realistic systems this gap increases with concentration of the particles, thus contributing to the stability of the pinning of linear polarization of photoemission in semiconductor microcavities for pump intensities above the stimulation threshold.     

Equivalence of the Abraham momentum and the Minkowski momentum of photons in media

The century-long debate on the momentum of light in a medium involves two rival forms of momentum, namely those of Abraham and Minkowksi. In this Letter, we analyze this dilemma from the view of the quantum theory of light, the result of which can be easily extended to the classical level. It is found that the Abraham momentum of one polariton mode in linear and dispersive dielectrics differs from its Minkowski momentum, by a considerable factor. However, after taking all branches into consideration, we find the two lead to the same end, which unifies the two rival forms of momentum. The sum rule is traditional, but our conclusion provides a new perspective on the Abraham-Minkowski dilemma, and is consistent with existing experiments including a recent measurement of recoil momentum of atoms using an atom interferometer with Bose-Einstein Condensates [G. K. Campbell et al. Phys. Rev. Lett. 94, 170403 (2005).], the Cerenkov effect, the Doppler effect and the phase matching conditions in nonlinear optical processes.     

Coherent response of a semiconductor microcavity in the strong coupling regime

We have studied the coherent dynamics of a semiconductor microcavity by means of interferometric correlation measurements with subpicosecond time resolution in a backscattering geometry. Evidence is brought of the resolution of a homogeneous polariton line in an inhomogeneously broadened exciton system. Surprisingly, photon-like polaritons exhibit an inhomogeneous dephasing. Moreover, we observe an unexpected stationary coherence up to 8 ps for the lower polariton branch close to resonance. All these experimental results are well reproduced within the framework of a linear dispersion theory assuming a coherent superposition of the reflectivity and resonant Rayleigh scattering signals with a well-defined relative phase.     

Artificial graphenes: Dirac matter beyond condensed matter

After the discovery of graphene and of its many fascinating properties, there has been a growing interest for the study of “artificial graphenes”. These are totally different and novel systems that bear exciting similarities with graphene. Among them are lattices of ultracold atoms, microwave or photonic lattices, “molecular graphene” or new compounds like phosphorene. The advantage of these structures is that they serve as new playgrounds for measuring and testing physical phenomena that may not be reachable in graphene, in particular the possibility of controlling the existence of Dirac points (or Dirac cones) existing in the electronic spectrum of graphene, of performing interference experiments in reciprocal space, of probing geometrical properties of the wave functions, of manipulating edge states, etc. These cones, which describe the band structure in the vicinity of the two connected energy bands, are characterized by a topological “charge”. They can be moved in the reciprocal space by appropriate modification of external parameters (pressure, twist, sliding, stress, etc.). They can be manipulated, created or suppressed under the condition that the total topological charge be conserved. In this short review, I discuss several aspects of the scenarios of merging or emergence of Dirac points as well as the experimental investigations of these scenarios in condensed matter and beyond.     

Quantum theory of polaritons with spatial dispersion: Exact solutions

Summary We give the exact solution of the quantum polariton problem with spatial dispersion. The exact polariton eigenstates are obtained in terms of photon and polariton states. For all values ofk a nonlinear contribution of the photon and polarization states is present in the polariton wave function. Two- and three-photon components are explicitly singled out.

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Riassunto Si presentano le soluzioni esatte del problema quantistico del polaritone con dispersione spaziale. Gli autostati polaritonici esatti sono ottenuti come combinazioni di stati fotonici e di stati di polarizzazione. Contributi non lineari di fotoni e di quanti di polarizzazione sono presenti a tutti i valori dik. Componenti a due fotoni e a tre fotoni sono date in forma esplicita.

     

Quantum wire polaritons

Summary Using a nonlocal susceptibility with cilindrical symmetry as computed from the microscopic theory, we obtain the exciton-polariton modes in quantum wires, where the translational symmetry is preserved in one direction only. Resonant polaritons, with a finite radiative lifetime, result for , while wire polaritons with infinite radiative lifetime result fork _‖>k ₀. Dispersion laws and lifetimes are given for all values ofk _‖, and the separation between the longitudinal and the nonlongitudinal mode is obtained. Numerical examples are given for GaAs/Ga_1−x Al _x As quantum wires.     

Strong-coupling regime at room temperature in one-dimensional microcavities containing ultraviolet-emitting perovskites

We have realized several one-dimensional (1D) microcavities, containing self-assembled perovskite layers, emitting in the ultraviolet (UV) range (around 3.5 eV), working in the strong-coupling regime at room temperature. Procedures to increase the quality factor of the microcavities have been explored. Two different technologies have to be combined: the soft technologies related to the organic materials and polymers and the technologies which are more specific to inorganic materials, such as electron-beam evaporation and sputtering, used in particular to deposit dielectric mirrors.     

Bragg quantum wells in weak confinement regime

The optical properties of Bragg quantum wells are studied for exciton confinement under center-of-mass quantization. A variational model of Wannier exciton envelope function, that embodies the correct boundary conditions for center-of-mass, is adopted for calculation. The present non-adiabatic exciton model is compared with adiabatic results and with heuristic “hard sphere” model. The radiative self-energy of a single-quantum well (SQW) and multi-quantum wells (MQWs) are computed in the semiclassical framework, and in effective mass approximation, by self-consistent solution of Schroedinger and Maxwell equations. This microscopic solution is free from “fitting” parameter values, except for the non-radiative broadening, and also the exciton dead-layer and the additional boundary condition are not taken ad hoc, but come coherently from the variational principle and self-consistent Schroedinger-Maxwell solution. Dispersion curves of exciton-polariton propagating in a MQW, under Bragg condition, are studied by selected numerical examples. The case of optical gap in correspondence of higher excited states is studied, and, moreover, the interesting effect of gap enhancement or inhibition, in correspondence of non-resonant Bragg energy, will be addressed.