Unstable and stable regimes of polariton condensation
F. Baboux, D. De Bernardis, V. Goblot, V. N. Gladilin, C. Gomez, E. Galopin, L. Le Gratiet, A. Lemaître, I. Sagnes, I. Carusotto, M. Wouters, A. Amo, J. Bloch
Modulational instabilities play a key role in a wide range of nonlinear optical phenomena, leading e.g. to the formation of spatial and temporal solitons, rogue waves and chaotic dynamics. Here we experimentally demonstrate the existence of a modulational instability in condensates of cavity polaritons, arising from the strong coupling of cavity photons with quantum well excitons. For this purpose we investigate the spatiotemporal coherence properties of polariton condensates in GaAs-based microcavities under continuous-wave pumping. The chaotic behavior of the instability results in a strongly reduced spatial and temporal coherence and a significantly inhomogeneous density. Additionally we show how the instability can be tamed by introducing a periodic potential so that condensation occurs into negative mass states, leading to largely improved coherence and homogeneity. These results pave the way to the exploration of long-range order in dissipative quantum fluids of light within a controlled platform.
We demonstrate condensation of microcavity polaritons with a very sharp threshold occuring at two orders of magnitude lower pump intensity than previous demonstrations of condensation. The long cavity-lifetime and trapping and pumping geometries are crucial to the realization of this low threshold. Polariton condensation, or "polariton lasing" has long been proposed as a promising source of coherent light at lower threshold than traditional lasing, and these results suggest methods to bring this threshold even lower.
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 examine the Bose-Einstein condensation of exciton-polaritons in a semiconductor microcavity via an electrical current. We propose that by embedding a quantum dot p-i-n junction inside the cavity, the tunneling current through the device can reveal features of condensation due to a one-to-one correspondence of the photons to the condensate polaritons. Such a device can also be used to observe the phase interference of the order parameters from two condensates.
Exciton-polaritons resulting from the strong exciton-photon interaction stimulate the development of novel coherent light sources with low threshold, long range spatial, and temporal coherence to circumvent the ever increasing energy demands of optical communications. Polaritons from bound states in the continuum (BICs) are promising for Bose-Einstein condensation owing to their infinite quality factors that enlarge photon lifetimes and benefit polariton accumulations. However, BIC polariton condensation remains limited to cryogenic temperatures ascribed to the small exciton binding energies o…
Polariton lattice condensates provide a platform for on chip quantum emulations. Interactions in extended polariton lattices are currently limited by the intrinsic photonic disorder of microcavities. Here, we fabricate a strain compensated planar GaAs/AlAs microcavity with embedded InGaAs quantum wells and report on polariton condensation under non-resonant optical excitation. Evidence of polariton condensation is supported spectroscopically both in reflection and transmission geometry, whilst the observation of a second threshold to photon lasing allows us to conclusively distinguish between …
We study theoretically the Bose-Einstein condensation in periodic polariton lattices in presence of a localized reservoir. Using the Schrödinger and Boltzmann equations, we find analytically the parameters determining the choice of the bandgap for condensation on the defect states.
Bose-Einstein condensation in strongly correlated lattices provides the possibility to coherently generate macroscopic quantum states, which have attracted tremendous attention as ideal platforms for quantum simulation. Ultracold atoms in optical lattices are one of such promising systems, where their realizations of different phases of matter exhibit promising applications in condensed matter physics, chemistry, and cosmology. Nevertheless, this is only accessible with ultralow temperatures in the nano to micro Kelvin scale set by the typical inverse mass of an atom. Alternative systems such …
We present a microcavity structure with a shifted photonic stop-band to enable efficient non-resonant injection of a polariton condensate with spectrally broad femtosecond pulses. The concept is demonstrated theoretically and confirmed experimentally for a planar GaAs/AlGaAs multilayer heterostructure pumped with ultrashort near-infrared pulses while photoluminescence is collected to monitor the optically injected polariton density. As the excitation wavelength is scanned, a regime of polariton condensation can be reached in our structure at a consistently lower fluence threshold than in a sta…
Polaritons, mixed light-matter quasiparticles, undergo a transition to a condensed, macroscopically coherent state at low temperatures or high densities. Recent experiments show that coupling light to organic molecules inside a microcavity allows condensation at room temperature. The molecules act as saturable absorbers with transitions dressed by molecular vibrational modes. Motivated by this we calculate the phase diagram and spectrum of a modified Tavis-Cummings model, describing vibrationally dressed two-level systems, coupled to a cavity mode. Coupling to vibrational modes can induce re-e…
Two-photon absorption (TPA) allows accessing dark states of matter otherwise inaccessible to light, which serve as important building blocks for quantum information processing. In a semiconductor microcavity, TPA driven condensation of strongly-coupled light-matter exciton-polaritons can enable new solid-state quantum simulations of dark state-condensate interactions, and was predicted to stimulate THz emission. Here, we report the first observation of two-photon pumped polariton condensation, demonstrated by angle-resolved photoluminescence in a GaAs-based microcavity. TPA is evidenced in the…
We study Frenkel exciton-polariton Bose-Einstein condensation in a two-dimensional defect-free triangular photonic crystal with an organic semiconductor active medium containing bound excitons with dipole moments oriented perpendicular to the layers. We find photonic Bloch modes of the structure and consider their strong coupling regime with the excitonic component. Using the Gross- Pitaevskii equation for exciton polaritons and the Boltzmann equation for the external exciton reservoir, we demonstrate the formation of condensate at the points in reciprocal space where photon group velocity equ…
We present a numerical study of exciton-polariton (polariton) condensation in a staggered polariton graphene showing a gapped s-band at the $K$ and $K'$ valleys. The condensation occurs at $K$ or $K'$, at the kinetically-favorable negative mass extrema of the valence band. Considering attractive polariton-polariton interaction allows to generate a spatially extended condensate. Spontaneous symmetry breaking occurring during the condensate build-up leads to the formation of valley-polarized domains following the Kibble-Zurek scenario. The selection of a single valley breaks time-reversal symmet…
Analysis of exciton-polariton condensation under different pumping schemes for 1D and 2D microcavities including the effect of strong correlation between polaritons
We study the condensation of exciton-polaritons in a two-dimensional Lieb lattice of micropillars. We show selective polariton condensation into the flatbands formed by S and P$_{x;y}$ orbital modes of the micropillars under non-resonant laser excitation. The real space mode patterns of these condensates are accurately reproduced by the calculation of related Bloch modes of S- and P-flatbands. Our work emphasizes the potential of exciton-polariton lattices to emulate Hamiltonians of advanced potential landscapes. Furthermore, the obtained results provide a deeper inside into the physics of fla…
We develop a kinetic theory of microcavity polaritons in presence of both Coulomb and polariton-phonon interaction, obeying particle number conservation. We study the growth of a macroscopic population of condensed particles in the lowest polariton state, under steady-state incoherent excitation of higher energy states. The collective excitation spectrum, resulting from the Coulomb Hamiltonian treated within the Hartree-Fock-Bogolubov framework, strongly influences the polariton condensation kinetics. In particular, for values of the excitation intensity above the condensation threshold, scatt…
The first realization of a polariton condensate was recently achieved in a CdTe microcavity [Kasprzak et al., Nature 443, 409 (2006)]. We compare the experimental phase boundaries, for various detunings and cryostat temperatures, with those found theoretically from a model which accounts for features of microcavity polaritons such as reduced dimensionality, internal composite structure, disorder in the quantum wells, polariton-polariton interactions, and finite lifetime.
Bose Einstein condensation of exciton-polaritons has recently been reported in homogeneous structures only affected by random in-plane fluctuations. We have taken advantage of the ubiquitous defects in semiconductor microcavities to reveal the spontaneous dynamical condensation of polaritons in the quantised levels of a trap. We observe condensation in several quantized states, taking their snapshots in real and reciprocal space. We show also the effect of particle interactions for high occupations numbers, revealed by a change in the confined wave function toward the Thomas Fermi profile.
The dynamics of spatial coherence and momentum distribution of polaritons in the regime of Bose-Einstein condensation are investigated in a GaAs microcavity with embedded quantum wells under nonresonant excitation with picosecond laser pulses. It is shown that the onset of the condensate first order sparial coherence is accompanied by narrowing of the polariton momentum distribution. At the same time, at sufficiently high excitation densities, there is significant qualitative discrepancy between the dynamic behavior of the width of the polariton momentum distribution determined from direct mea…
We report the mean field model of nonequilibrium polariton condensation in annular effective non-Hermitian potential traps, stemming from incoherent optically induced excitonic reservoirs of annular shape. We solve the linearized extended Gross-Pitaevskii equation in the approximation of two delta-function effective shell potentials for complex spectra of trapped polariton modes and calculate corresponding condensation threshold optical pumping powers. The exhaustive map of condensate quantum number transitions in the multi-dimensional space of trap parameters, including a cascade of topologic…
Two dimensional (2D) perovskites are promising materials for photonic applications, given their outstanding nonlinear optical properties, ease of fabrication and versatility. In particular, exploiting their high oscillator strength, the crystalline form of 2D perovskites can be used as excitonic medium in optical microcavities, allowing for the study of their optical properties in the strong light-matter coupling regime. While polariton condensation has been observed in different materials at room temperature, here we observe for the first time two distinct threshold processes in a 2D perovski…
Bose-Einstein condensate of exciton polaritons in a semiconductor microcavity is a macroscopically populated coherent quantum state subject to concurrent pumping and decay. Debates about the fundamental nature of the condensed phase in this open quantum system still persist. Here, we gain a new insight into the spontaneous condensation process by imaging long-lifetime exciton polaritons in a high-quality inorganic microcavity in the single-shot optical excitation regime, without averaging over multiple condensate realisations. In this highly non-stationary regime, a condensate is strongly infl…
We investigate the statistics of microcavity polariton Bose-Einstein condensation by measuring photoluminescence dynamics from a GaAs microcavity excited by single laser excitation pulses. We directly observe fluctuations (jitter) of the polariton condensation onset time and model them using a master equation for the occupancy probabilities. The jitter of the condensation onset time is an inherent property of the condensate formation and its magnitude is approximately equal to the rise time of the condensate density. We investigate temporal correlations between the emission of condensate in op…
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…
Recent experiments have shown that it is possible to create an in-plane harmonic potential trap for a two-dimensional (2D) gas of exciton-polaritons in a microcavity structure, and evidence has been reported of Bose-Einstein condensation of polaritons accumulated in this type of trap. We present here the theory of Bose-Einstein condensation (BEC) and superfluidity of the exciton polaritons in a harmonic potential trap. Along the way, we determine a general method for defining the superfluid fraction in a 2D trap, in terms of angular momentum representation. We show that in the continuum limit,…
We develop a theory for the dynamics of the density matrix describing a multimode polariton condensate. In such a condensate several single-particle orbitals become highly occupied, due to stimulated scattering from reservoirs of high-energy excitons. A generic few-parameter model for the system leads to a Lindblad equation which includes saturable pumping, decay, and condensate interactions. We show how this theory can be used to obtain the population distributions, and the time-dependent first- and second-order coherence functions, in such a multimode condensate. As a specific application, w…
We create exciton-polaritons in a zero-dimensional (0D) microcavity filled with organic ladder-type conjugated polymer in the strong light-matter interaction regime. Photonic confinement at wavelength scale is realized in the longitudinal direction by two dielectric Bragg mirrors and laterally by a sub-micron Gaussian-shaped defect. The cavity is separated into two parts allowing nanometer position control and enabling tuning of exciton and photon fractions of the polariton wavefunction. Polariton condensation is achieved with non-resonant, picosecond optical excitation at ambient conditions a…
We adopt a kinetic theory of polariton non-equilibrium Bose-Einstein condensation, to describe the formation of off-diagonal long-range order. The theory accounts properly for the dominant role of quantum fluctuations in the condensate. In realistic situations with optical excitation at high energy, it predicts a significant depletion of the condensate caused by long-wavelength fluctuations. As a consequence, the one-body density matrix in space displays a partially suppressed long-range order and a pronounced dependence on the finite size of the system.
Condensation of microcavity polaritons and the substantial influence of pair-breaking disorder and decoherence leading to a laser regime has been recently considered using two different models: a model for direct two band excitons in a disordered quantum well coupled to light and a model where the cavity mode couples instead to a medium of localised excitons, represented by two-level oscillators in the presence of dephasing processes. Even if complementary from the point of view of assumptions, the models share most of the main conclusions and show similar phase diagrams. The issue whether exc…
We investigate exciton-polariton condensation under magnetic field in a single high-quality semiconductor micropillar cavity. We observe successive polariton condensation of each spin component for two distinct threshold powers. Pronounced and non-monotonous variations of both the Zeeman splitting and the circular polarization of the emission are measured across these two condensation thresholds. This unexpected behavior deeply deviates from the so-called spin Meissner effect predicted for a fully thermalized system. Our measurements can be understood in a kinetic approach taking into account …
The Bose-Einstein condensation (BEC) of magnetoexcitonic polaritons in a graphene layer embedded in a optical microcavity in a high magnetic field $B$ is predicted. The essential property of this system (in contrast, e.g., to a quantum well embedded in a cavity) is stronger influence of magnetic field and weaker influence of disorder. A two-dimensional (2D) magnetoexcitonic polaritons gas is considered in a planar harmonic electric field potential applied to excitons or a parabolic shape of the optical cavity causing the trapping of microcavity photons. It is shown that the effective polariton…
We describe photonic crystal microcavities with very strong light-matter interaction to realize room-temperature, equilibrium, exciton-polariton Bose-Einstein condensation (BEC). This is achieved through a careful balance between strong light-trapping in a photonic band gap (PBG) and large exciton density enabled by a multiple quantum-well (QW) structure with moderate dielectric constant. This enables the formation of long-lived, dense 10~$μ$m - 1~cm scale cloud of exciton-polaritons with vacuum Rabi splitting (VRS) that is roughly 7\% of the bare exciton recombination energy. We introduce a w…
Exciton-polaritons can condense to a macroscopic quantum state through a non-equilibrium process of pumping and decay. In recent experiments, polariton condensates are used to observe, for a short time, nonlinear Josephson phenomena by coupling two condensates. However, it is still not clear how these phenomena are affected by the pumping and decay at long times and how the coupling alters the polariton condensation. Here, we consider a polariton Josephson junction pumped on one side and study its dynamics within a mean-field theory. The Josephson current is found to give rise to multi-stabili…
In this thesis, we study two different aspects of many-particle physics. In the first part, we study the Bose-Einstein condensation of microcavity exciton-polaritons in different artificial lattices. Bose-Einstein condensation is a quantum phase transition, which allows the system to macroscopically occupy its ground state and develop coherence spontaneously. Often studied in microcavities, which are optical cavities that trap light at specific wavelengths, exciton-polaritons are a kind of quasiparticle arising from the strong coupling between quantum well excitons and cavity photons. By perio…
Microcavity-polaritons in two-dimensional lattice geometries have been used to study a wide range of interesting physics. Meanwhile, organic materials have shown great promise on the road towards polaritonic devices, as the strong binding energy of their Frenkel excitons permits room temperature condensation and lasing. Whilst there are theoretical treatments of the condensation processes in planar organic microcavities, models of lattice geometries are lacking. Here, we introduce a model for describing the dynamics of lattices of zero-dimensional organic microcavities, where the dominant cond…
For dipole-carrying excitations observed in a high-quality resonator, strong-coupling modes can appear as composite bosons with the spontaneous formation of quantized vortices in the condensed phase of a polariton fluid. In exciton-polaritons, in particular, it leads to sustained trapping of the emitted photon. In this paper, we show that magnon-polaritons can be realized due to magnon condensation caused by magnetic dipole-dipole interaction. In a quasi-2D ferrite disk placed in a microwave cavity, one observes quantum confinement effects of magnetic-dipolar-mode (MDM) oscillations. These mod…
We consider polariton condensation in a generalized Dicke model, describing a single-mode cavity containing quantum dots, and extend our previous mean-field theory to allow for finite-size fluctuations. Within the fluctuation-dominated regime the correlation functions differ from their (trivial) mean-field values. We argue that the low-energy physics of the model, which determines the photon statistics in this fluctuation-dominated crossover regime, is that of the (quantum) anharmonic oscillator. The photon statistics at the crossover are different in the high- and low- temperature limits. Whe…
The emergence of two-dimensional crystals has revolutionized modern solid-state physics. From a fundamental point of view, the enhancement of charge carrier correlations has sparked enormous research activities in the transport- and quantum optics communities. One of the most intriguing effects, in this regard, is the bosonic condensation and spontaneous coherence of many-particle complexes. Here, we find compelling evidence of bosonic condensation of exciton-polaritons emerging from an atomically thin crystal of MoSe2 embedded in a dielectric microcavity under optical pumping. The formation o…
It is shown theoretically that Bose condensation of spin-degenerated exciton-polaritons results in spontaneous buildup of the linear polarization in emission spectra of semiconductor microcavities. The linear polarization degree is a good order parameter for the polariton Bose condensation. If spin-degeneracy is lifted, an elliptically polarized light is emitted by the polariton condensate. The main axis of the ellipse rotates in time due to self-induced Larmor precession of the polariton condensate pseudospin. The polarization decay time is governed by the dephasing induced by the polariton-p…
A model for direct two band excitons in a disordered quantum well coupled to light in a cavity is investigated. In the limit in which the exciton density is high, we assess the impact of weak `pair-breaking' disorder on the feasibility of condensation of cavity polaritons. The mean-field phase diagram shows a `lower density' region, where the condensate is dominated by electronic excitations and where disorder tends to close the condensate and quench coherence. Increasing the density of excitations in the system, partially due to the screening of Coulomb interaction, the excitations contributi…
The Bose-Einstein condensation (BEC) of magnetoexcitonic polaritons in two-dimensional (2D) electron-hole system embedded in a semiconductor microcavity in a high magnetic field $B$ is predicted. There are two physical realizations of 2D electron-hole system under consideration: a graphene layer and quantum well (QW). A 2D gas of magnetoexcitonic polaritons is considered in a planar harmonic potential trap. Two possible physical realizations of this trapping potential are assumed: inhomogeneous local stress or harmonic electric field potential applied to excitons and a parabolic shape of the s…
The Bose-Einstein condensation (BEC) of the two-dimensional (2D) magnetoexciton-polaritons in microcavity, when the Landau quantization of the electron and hole states accompanied by the Rashba spin-orbit coupling plays the main role, were investigated. The Landau quantization levels of the 2D heavy holes with nonparabolic dispersion law and third order chirality terms both induced by the external electric field perpendicular to the semiconductor quantum well as the strong magnetic field B gives rise to the nonmonotous dependence on B of the magnetoexciton energy levels and of the polariton en…
Microcavity exciton polariton systems can have a wide range of macroscopic quantum effects that may be turned into better photonic technologies. Polariton Bose-Einstein condensation and photon lasing have been widely accepted in the limits of low and high carrier densities, but identification of the expected Bardeen-Cooper-Schrieffer (BCS) state at intermediate densities remains elusive, as the optical-gain mechanism cannot be directly inferred from existing experiments. Here, using a microcavity with strong polarization selectivity, we gain direct experimental access to the reservoir absorpti…
