Exciton-polariton solitons are strongly nonlinear quasiparticles composed of coupled exciton-photon states due to the interaction of light with matter. In semiconductor microcavity systems such as semiconductor micro and nanowires, polaritons are characterized by a negative mass which when combined with the repulsive nonlinear exciton-exciton interaction, leads to the generation of bright polariton solitons. In this work we investigate the dynamics of bright exciton-polariton solitons in a finite-size microcavity waveguide, for which radiative losses are assumed balanced by the external pumping. An exact bright-soliton solution to the model equations of motion, consisting of a periodic train of polariton pulses, is obtained in terms of Jacobi elliptic functions. Exact analytical expressions corresponding to the energies of both photonic and excitonic components of the pulse train are found. Results suggest that the size (i.e. the length) of a microwire waveguide plays a relevant role in obtaining a quantitative estimate of the energy that could be conveyed by polariton solitons propagating in the medium.
A cavity-polariton, formed due to the strong coupling between exciton and cavity mode, is one of the most promising composite bosons for realizing macroscopic spontaneous coherence at high temperature. Up to date, most of polariton quantum degeneracy experiments were conducted in the complicated two-dimensional (2D) planar microcavities. The role of dimensionality in coherent quantum degeneracy of a composite bosonic system of exciton polaritons remains mysterious. Here we report the first experimental observation of a one-dimensional (1D) polariton condensate in a ZnO microwire at room temper…
We report on the experimental investigation of the polarization-dependent energy splitting in the lower exciton-polariton branches of a 1D microcavity. The splitting observed for the lowest branch can reach up to 1 meV. It does not result from low temperature thermal constraints but from anisotropic mechanical internal strains induced by etching. Those strains remove the degeneracy both in the photonic ($δE_{\mathrm{ph}}$) and excitonic ($δE_{\mathrm{exc}}$) components of the polariton but also in the photon-exciton coupling ($δΩ$). Those three contributions are accurately infered from experim…
We consider the excitation of polariton wakefields due to a propagating source in a semiconductor micro cavity. We show that two kinds of wakes are possible, depending on the constituents fraction (either exciton or photon) of the polariton wavefunction. The nature of the wakefields (pure excitonic or polaritonic) can be controled by changing the speed of propagation of the external pump. This process could be used as a diagnostic for the internal parameters of the microcavity.
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 two orders of magnitude with respect to mere optomechanical coupling: a near-unity single…
The Andreev-Bashkin effect, or superfluid drag, is predicted in a system of Bose-condensed excitonic polaritons in optical microcavity coupled by electron-exciton interaction with a superconducting layer. Two possible setups with spatially indirect dipole excitons or direct excitons are considered. The drag density characterizing a magnitude of this effect is found by many-body calculations with taking into account dynamical screening of electron-exciton interaction. For the superconducting electronic layer, we assume the recently proposed polaritonic mechanism of Cooper pairing, although the …
Recent experiments have demonstrated strong light-matter coupling between electromagnetic nanoresonators and pristine sheets of two-dimensional semiconductors, and it has been speculated whether these systems can enter the quantum regime operating at the few-polariton level. To address this question, we present a first-principles microscopic quantum theory for the interaction between excitons in an infinite sheet of two-dimensional material and a localised electromagnetic resonator. We find that the light-matter interaction breaks the symmetry of the otherwise translation-invariant system and …
We present a microscopic semi-analytical theory for the description of organic molecules interacting strongly with a cavity mode. Exciton-vibration coupling within the molecule and exciton-cavity interaction are treated on an equal footing by employing a temperature-dependent variational approach. The interplay between strong exciton-vibration coupling and strong exciton-cavity coupling gives rise to a hybrid ground state, which we refer to as the lower polaron polariton. Explicit expressions for the ground-state wave function, the zero-temperature quasiparticle weight of the lower polaron pol…
We model a dye-doped polymeric nanosphere as an ensemble of quantum emitters and use it to investigate the localized exciton-polaritons supported by such a nanosphere. By determining the time evolution of the density matrix of the collective system, we explore how an incident laser field may cause transient optical field enhancement close to the surface of such nanoparticles. Our results provide further evidence that excitonic materials can be used to good effect in nanophotonics.
We propose a continuous variable analog of quantum controlled-NOT gates based on a system of exciton-polaritons in semiconductor microcavities. This can be realized by the engineering of parametric interaction between control and target polariton modes, which can be varied in time. As an explicit setup we use a system of dipolaritons, which allows for enhancement of parametric interaction by auxiliary classical fields and scalable multigate system realization. The calculated fidelity is shown to exceed 99% for realistic system parameters.
Exciton-polaritons are mixed light-matter quasiparticles. We have developed a statistical model describing stochastic exciton-photon transitions within a condensate of exciton polaritons. We show that the exciton-photon correlator depends on the "hidden variable" which characterizes the rate of exciton-photon transformations in the condensate. We discuss implications of this effect for the quantum statistics of photons emitted by polariton lasers.
We examine the photoluminescence of highly-excited exciton-polariton condensates in semiconductor microcavities. Under strong pumping, exciton-polariton condensates have been observed to undergo a lasing transition where strong coupling between the excitons and photons is lost. We discuss an alternative high-density scenario, where the strong coupling is maintained. We find that the photoluminescence smoothly transitions between the lower polariton energy to the cavity photon energy. An intuitive understanding of the change in spectral characteristics is given, as well as differences to the ph…
We develop a theory of spin fluctuations of exciton-polaritons in a semiconductor microcavity under the non-resonant unpolarized pumping. It is shown that the corresponding spin noise is sensitive to the scattering rates in the system, occupation of the ground state, statistics of polaritons, and interactions. The spin noise spectrum drastically narrows in the polariton lasing regime due to formation of a polariton condensate, while its shape can become non-Lorentzian owing to interaction-induced spin decoherence.
We develop a many-body theory for the properties of exciton-polaritons interacting strongly with a Bose-Einstein condensate (BEC) of exciton-polaritons in another spin state. Interactions lead to the presence of a two-body bound state, the bi-exciton, giving rise to a Feshbach resonance in the polariton spectrum when its energy is equal to that of two free polaritons. Using the minimal set of terms to describe this resonance, our theory recovers the main findings of two experiments probing interaction effects for upper and lower polaritons in a BEC. This strongly supports that Feshbach physics…
We present a mechanism to endow the polariton gas with attractive interactions. The scheme relies on an exciton reservoir, which can be formed even if excitons lie outside of the light-cone. Such an attractive interaction should open new routes in the physics of quantum fluids, that we illustrate with a simple but nontrivial application whereby the polariton condensate enters the self-oscillation regime powered by the attraction from the reservoir. This results in pulsed emission in the GhZ regime.
Boosting self hybridized exciton polaritons with metal clad WS2 waveguides
Institute of Experimental and Applied Physics, Kiel University（基尔大学实验与应用物理研究所）；Ruprecht Haensel Laboratory, Deutsches Elektronen-Synchrotron DESY（德国电子同步加速器研究所鲁普雷希特·亨塞尔实验室）
We have developed a model in order to account for electron-vibrational effects on absorption, luminescence of molecular aggregates and exciton-polaritons in nanofibers. The model generalizes the mean-field electron-vibrational theory developed by us earlier to the systems with spatial symmetry, exciton luminescence and the exciton-polaritons with spatial dispersion. The correspondence between manifestation of electron-vibrational interaction in monomers, molecular aggregates and exciton-polariton dispersion in nanofibers is obtained by introducing the aggregate line-shape functions in terms of…
We present a quantitative microscopic analysis of the formation of exciton-polaritons, the composite particles possessing light and material components, polariton-polariton interactions, and resonant pumping dynamics in cylindrical semiconductor micropillars. We discuss how the redistribution effect can be used in devices generating photons with non zero orbital angular momenta.
We present a many-body theory for exciton-trion-polaritons in doped two-dimensional materials. Exciton-trion-polaritons are robust coherent hybrid excitations involving excitons, trions, and photons. Signatures of these polaritons have been recently seen in experiments. In these polaritons, the 2-body exciton states are coupled to the material ground state via exciton-photon interaction and the 4-body trion states are coupled to the exciton states via Coulomb interaction. The trion states are not directly optically coupled to the material ground state. The energy-momentum dispersion of these p…
Until now, the generation of an excitonic reservoir in a cavity polariton system under quasi-resonant pumping has always been neglected. We show that in microcavities having a small Rabi splitting (typically GaAs cavities with a single quantum well), this reservoir can be efficiently populated by polariton-phonon scattering. We consider the influence of the exciton reservoir on the energy shifts of the resonantly pumped polariton modes. We show that the presence of this reservoir effectively reduces the spin anisotropy of the polariton-polariton interaction, in agreement with recent experiment…
We explore nonlinear transitions of polariton wavepackets, first, to a soliton and then to a standing wave polariton condensate in a multi-mode microwire system. At low polariton density we observe ballistic propagation of the multi-mode polariton wavepackets arising from the interference between different transverse modes. With increasing polariton density, the wavepackets transform into single mode bright solitons due to effects of both inter-modal and intra-modal polariton-polariton scattering. Further increase of the excitation density increases thermalisation speed leading to relaxation o…
Macroscopic wave packets of spin-polarized exciton-polaritons in two-dimensional microcavities experience the zitterbewegung, the effect manifested by the appearance of the oscillatory motion of polaritons in the direction normal to the initial propagation direction. The oscillating trajectories of exciton-polaritons are adjustable by the control parameters: the splitting of the longitudinal and transverse exciton-polariton modes, the wave vector and the width of the resonant cw pump. Our theoretical analysis supported by the numerical calculations allowed to optimize values of the control par…
Analysis of exciton-polariton condensation under different pumping schemes for 1D and 2D microcavities including the effect of strong correlation between polaritons
Integrated circuits of photonic components are the goal of applied polaritonics. Here, we propose a compact clock generator based on an exciton-polariton micropillar, providing optical signal with modulation frequency up to 100 GHz. This generator can be used for driving polariton devices. The clock frequency can be controlled by the driving laser frequency. The device also features low power consumption (1 pJ/pulse).
We develop the theoretical formalism to calculate second-order correlations in dissipative exciton-polariton system and we propose intensity-intensity correlation experiments to reveal the physics of exciton-light coupling in semiconductor microcavities in the Rabi oscillation regime. We predict a counter intuitive behaviour of the correlator between upper and lower polariton branches: due to the decoherence caused by stochastic exciton-photon conversions this correlator is expected to decrease below 1, while the individual second-order coherence of upper and lower polaritons exhibits non-mono…
We photo-excite slab polymer waveguides doped with J-aggregating dye molecules and measure the leaky emission from strongly coupled waveguide exciton polariton modes at room temperature. We show that the momentum of the waveguide exciton polaritons can be controlled by modifying the thickness of the excitonic waveguide. Non-resonantly pumped excitons in the slab excitonic waveguide decay into transverse electric and transverse magnetic strongly coupled exciton waveguide modes with radial symmetry. These leak to cones of light with radial and azimuthal polarizations.
We detail the influence of a magnetic field on exciton-polaritons inside a semiconductor microcavity. Magnetic field can be used as a tuning parameter for exciton and photon resonances. We discuss the change of the exciton energy, the oscillator strength and redistribution of the polariton density along the dispersion curves due to the magnetically-induced detuning. We have observed that field-induced shrinkage of the exciton wave function has a direct influence not only on the exciton oscillator strength, which is observed to increase with the magnetic field, but also on the polariton linewid…
We consider exciton-polaritons in a honeycomb lattice of micropillars subjected to circularly polarized (${σ_\pm}$) incoherent pumps, which are arranged to form two domains in the lattice. We predict that the nonlinear interaction between the polaritons and the reservoir excitons gives rise to the topological valley Hall effect where in each valley two counterpropagating helical edge modes appear. Under a resonant pump, ${σ_\pm}$ polaritons propagate in different directions without being reflected around bends. The polaritons propagating along the interface have extremely high effective lifeti…
We analyse the interaction of exciton and exciton-polariton condensates in semiconductor microcavity with a coherent acoustic wave. An analytical solution for the dispersion of excitations of coupled condensate-phonon system is found in the approximation of k-independent interactions. Accounting for k-dependence results in a stronger modification of the dispersion, and even in the appearance of the "roton instability" region.
We introduce and model spin-Rabi oscillations based on exciton-polaritons in semiconductor microcavities. The phase and polarization of oscillations can be controlled by resonant coherent pulses and the propagation of oscillating domains gives rise to phase-dependent interference patterns in real space. We show that interbranch polariton-polariton scattering controls the propagation of oscillating domains, which can be used to realize logic gates based on an analogue variable phase.
Monolayer transition metal dichalcogenides, known for exhibiting strong excitonic resonances, constitute a very interesting and versatile platform for investigation of light-matter interactions. In this work we report on a strong coupling regime between excitons in monolayer WSe2 and photons confined in an open, voltage-tunable dielectric microcavity. The tunability of our system allows us to extend the exciton-polariton state over a wide energy range and, in particular, to bring the excitonic component of the lower polariton mode into resonance with other excitonic transitions in monolayer WS…
We demonstrate the potential of quantum operation using lattices of exciton-polaritons in patterned semiconductor microcavities. By introducing an inverse four-wave mixing scheme acting on localized modes, we show that it is possible to develop non-classical correlations between individual condensates. This allows a concept of quantum exciton-polariton networks, characterized by the appearance of multimode entanglement even in the presence of realistic levels of dissipation.
We propose a way to directly excite compact localized condensates in a nearly flat band of the exciton-polariton Lieb lattice by short Laguerre-Gaussian pulses and investigate the dynamics of these condensates in the presence of repulsive polariton-polariton interaction and distributed losses in the lattice. The evolution of a low-density compact polariton condensate shows fast Rabi oscillations between its excitonic and photonic components, with slow beatings of the Rabi oscillation amplitude. Both oscillations and beatings are suppressed at higher condensate densities due to polariton-polari…
We propose a scheme for calculation of optical functions of a semiconductor with Rydberg excitons, for a wide interval of dimensions. We start with 2-dimensional structure, then going to thin films and ending on 3-dimensional bulk crystals. The calculations including the polaritons are performed, the case of large number of polariton branches is discussed and obtained theoretical absorption spectra show good agreement with experimental data.
We analyze the interaction of exciton-polariton condensates in a one-dimensional semiconductor microcavity with acoustic phonons. We consider the case of a coherently pumped condensate and demonstrate that upon passing of a certain threshold the parametric instability in the system leads to the generation of a coherent acoustic wave and additional polariton harmonics. The process is strongly affected by exciton-exciton interactions which lead to the appearance of the effects of the bistability and hysteresis in the system.
A simple model, describing the dynamics of the non-equilibrium pseudospin of a homogeneous Bose-Einstein condensate of exciton polaritons, has been formulated. It explains the suppression of spin splitting of a non-equilibrium polariton condensate in an external magnetic field, the optical alignment, and the conversion of alignment into orientation of polaritons. It has been shown that inverse effects are possible, to wit, the spontaneous circular polarization and the enhancement of spin splitting of a non-equilibrium condensate of polaritons in the absence of external field.
Embedding a monolayer of a transition metal dichalcogenide in a high-Q optical cavity results in the formation of distinct exciton polariton modes. The polaritons are affected by the strong exciton-phonon interaction in the monolayer. We use a time convolutionless master equation to calculate the phonon influence on the spectra of the polaritons. We discuss the non-trivial dependence of the line shapes of both branches on temperature and detuning. The peculiar polariton dispersion relation results in a linewidth of the lower polariton being largely independent of the coupling to acoustic phono…
We investigate the interaction of excitons in a two dimensional lattice and photons in a planar cavity in the presence of disorder. The strong exciton-photon coupling is described in terms of polariton quasi-particles, which are scattered by a disorder potential. We consider three kinds of disorder: (a) inhomogeneous exciton energy, (b) inhomogeneous exciton-photon coupling and (c) deviations from an ideal lattice. These three types of disorder are characteristic of different physical systems, and their separate analysis gives insight on the competition between randomness and light-matter coup…
We study photocurrent of exciton polaritons in inversion broken systems. We use an effective Hamiltonian and Green's function approaches to deduce the formula for polariton photocurrent. The obtained formula shows the polariton photocurrent is proportional to the polariton density and shows opposite signs for the upper and lower branches. Nonvanishing polariton photocurrent requires time reversal symmetry breaking in addition to inversion symmetry breaking. We show that exciton states in transition metal dichalcogenides such as MoS$_2$ support polariton photocurrent once we break time reversal…
We investigate the process of condensation of exciton-polaritons in a one-dimensional nanowire, predicting spontaneous formation of domains of uncondensed excitons and condensed polaritons. We demonstrate a universal scaling law for the density of domains, which results from the competition between characteristic timescales present in the system. However, we find that the system does not follow the standard Kibble-Żurek scenario of a nonequilibrium phase transition.
We present indications, that the wave function-stiffness condition during energy-relaxation as observed in single-phase state quantum systems manifests also in a single particle ensemble. This is demonstrated for exciton-polaritons in the strong coupling regime in a ZnO-based microcavity at T = 10 K for non-resonant excitation. It is well known that the pump-induced spatially inhomogeneous background potential leads to nearly equally spaced energy levels in the k-space distribution for propagating polariton Bose-Einstein condensates. Surprisingly this particular pattern is also observable for …
We study nonlinear dynamics of exciton-polaritons in an incoherently pumped semiconductor microcavity with embedded weak-contrast lattice and coupled to an exciton reservoir. We elucidate fundamental features of non-equilibrium exciton-polariton condensate trapped in one-dimensional periodical potential close to zero momentum (so-called "Zero-state") and to the state at the boundary of Brillouin zone ("$π$-state"). Within the framework of the mean-field theory, we identify different regimes of both relaxation and oscillatory dynamics of coherent exciton-polaritons governed by superpositions of…
Coupled states of semiconductor quantum well (QW) excitons and photons in a two dimensional (2D) periodic lattice of microcavities are analyzed theoretically, revealing allowed bands and forbidden gaps in the energy spectrum of exciton polaritons. Photonic crystal exciton polaritons have spatially uniform excitonic constituent set by flat QWs, but exhibit periodic Bloch oscillations in the plane of QWs due to their photonic component. The envelope functions of photonic crystal exciton polaritons can be tailored via effective potential of a photonic crystal heterostructure, by using quasi-perio…
We show that recent paper by Flayac et al. [Phys. Rev. B 81, 045318 (2010) and arXiv:0911.1650] is misleading. We demonstrate the existence of static half-quantum vortices in exciton-polariton condensates and calculate the warping of their polarization texture produced by TE-TM splitting of polariton band.
We study the polarization optical properties of microcavities with embedded (110)-oriented quantum wells. The spin dynamics of exciton polaritons in such structures is governed by the interplay of the spin-orbit splitting of exciton states, which is odd in the in-plane momentum, and the longitudinal-transverse splitting of cavity modes, which is even in the momentum. We demonstrate the generation of polariton spin currents by linearly polarized optical pump and analyze the arising polariton spin textures in the cavity plane. Tuning the excitation spot size, which controls the polariton distrib…
We derive the closure relation for $N$ polaritons made of three different types of excitons: bosonized excitons, Frenkel or Wannier excitons. In the case of polaritons made of Wannier excitons, we show how this closure relation, which appears as non-diagonal, may reduce to the one of $N$ elementary bosons, the photons, with its $1/N!$ prefactor, or to the one of $N$ Wannier excitons, with its $(1/N!)^2$ prefactor. Widely different forms of closure relations are thus found depending on the composite bosons at hand. Comparison with closure relations of excitons, either bosonized or kept composit…
We present a generic model for the description of non-equilibrium Bose-Einstein condensates, suited for the modelling of non-resonantly pumped polariton condensates in a semiconductor microcavity. The excitation spectrum and scattering of the non-equilibrium condensate with a defect are discussed.
We study the momentum distribution and relaxation dynamics of semiconductor microcavity polaritons by angle-resolved and time-resolved spectroscopy. Above a critical pump level, the thermalization time of polaritons at positive detunings becomes shorter than their lifetime, and the polaritons form a quantum degenerate Bose-Einstein distribution in thermal equilibrium with the lattice.
In this work we study theoretically the axial spectral asymmetry of a 1D periodic multilayer systems composed by hybrid two-layers (isotropic/anisotropic) and for photon energies close to the electronic energy gaps of semiconductors (excitons). The non-normal optical properties of these resonant non-magnetic photonic crystals, where linear and quadratic spatial dispersion effects are both present, will be computed in the framework of exciton-polariton by self-consistent Maxwell-Schroedinger equation solutions in the effective mass approximation. The tailoring of hybrid crystal, where exciton-p…
Exciton-photon beats known as polariton Rabi oscillations in semiconductor microcavities are usually excited by short pulses of light. We consider a different pumping scheme, assuming a cw pumping of the Rabi oscillator from an exciton reservoir. We account for the initial pulse of light setting the phase, exciton decay due to exciton-phonon and exciton-exciton scattering, photon leakage, and blueshift of the exciton resonance due to interactions. We find non-trivial stationary solutions reminiscent of Kapitza pendulum, where polaritons are accumulated at the upper branch while the lower branc…
Realizing nonlinear optical response in the low photon density limit in solid-state systems has been a long-standing challenge. Semiconductor microcavities in the strong coupling regime hosting exciton-polaritons have emerged as attractive candidates in this context. However, the weak interaction between these quasiparticles has been a hurdle in this quest. Dipolar excitons provide an attractive strategy to overcome this limitation but are often hindered by their weak oscillator strength. The interlayer dipolar excitons in naturally occurring homobilayer MoS$_2$ alleviates this issue owing to …
Twisted atomically thin semiconductors are characterized by moiré excitons. Their optical signatures and selection rules are well understood. However, their hybridization with photons in the strong coupling regime for heterostructures integrated in an optical cavity has not been in the focus of research yet. Here, we combine an excitonic density matrix formalism with a Hopfield approach to provide microscopic insights into moiré exciton polaritons. In particular, we show that exciton-light coupling, polariton energy, and even the number of polariton branches can be controlled via the twist ang…
We theoretically study the transport of exciton polaritons under different applied photon potentials. The relation between the photon potentials and the thickness of the cavity layer is calculated by the finite element simulation. The theoretical analysis and numerical calculation indicate that the cavity photon potential is proportional to the thickness of the cavity layer with the coefficient being about $1.8$ meV/nm. Further, the periodic and linear photon potentials are considered to control the transport of the exciton polaritons in weak- and strong-field pump situations. In both situatio…
