Observation of a supersolid phase in a spin-orbit coupled exciton-polariton Bose-Einstein condensate at room temperature
Marcin Muszyński, Pavel Kokhanchik, Rafał Mirek, Darius Urbonas, Pietro Tassan, Piotr Kapuściński, Przemysław Oliwa, Ioannis Georgakilas, Thilo Stöferle, Rainer… 展开作者
Marcin Muszyński, Pavel Kokhanchik, Rafał Mirek, Darius Urbonas, Pietro Tassan, Piotr Kapuściński, Przemysław Oliwa, Ioannis Georgakilas, Thilo Stöferle, Rainer F. Mahrt, Michael Forster, Ullrich Scherf, Dmitriy Dovzhenko, Rafał Mazur, Przemysław Morawiak, Wiktor Piecek, Przemysław Kula, Barbara Piętka, Dmitry Solnyshkov, Guillaume Malpuech, Jacek Szczytko
In Bose-Einstein condensates (BEC), spin-orbit coupling (SOC) produces supersolidity. It is a peculiar state of matter, which, in addition to the superfluid behaviour shows periodic density modulation typical for crystals. Here, we report the fabrication of a new type of optical microcavity allowing to achieve room-temperature supersolidity for a quantum fluid of light. The microcavity is filled with a nematic liquid crystal (LC) and two layers of the organic polymer MeLPPP hosting exciton resonances. We demonstrate exciton-polariton condensation in the two distinct degenerate minima of the dispersion created by the LC induced Rashba-Dresselhaus (RD) SOC. The condensate real-space distribution shows density stripes located randomly from one condensate realization to another despite the presence of a random disorder potential. This demonstrates the immunity of stripes against disorder (that is, superfluidity) and the spontaneous breaking of translational invariance. We also report the random appearance of vortices via the Kibble-Zurek mechanism, another smoking gun of superfluidity.
Collective Excitations and Stability of Nonequilibrium Polariton Supersolids
Abrikosov Center for Theoretical Physics, Moscow Center for Advanced Studies（莫斯科高级研究中心阿布里科索夫理论物理中心）；National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)（莫斯科工程物理国立研究核大学）；Russian Quantum Center, Skolkovo IC（俄罗斯量子中心斯科尔科沃创新中心）
We investigate the ground states of a Bose-Einstein condensate of indirect excitons coupled to an electron gas. We show that in a properly designed system, the crossing of a roton minimum into the negative energy domain can result in the appearance of the supersolid phase, characterized by periodicity in both real and reciprocal space. Accounting for the spin-dependent exchange interaction of excitons we obtain ferromagnetic supersolid domains. The Fourier spectra of excitations of weakly perturbed supersolids show pronounced diffraction maxima which may be detected experimentally.
A supersolid, a counter-intuitive quantum state in which a rigid lattice of particles flows without resistance, has to date not been unambiguously realised. Here we reveal a supersolid ground state of excitons in a double-layer semiconductor heterostructure over a wide range of layer separations outside the focus of recent experiments. This supersolid conforms to the original Chester supersolid with one exciton per supersolid site, as distinct from the alternative version reported in cold-atom systems of a periodic modulation of the superfluid density. We provide the phase diagram augmented by…
We investigate the ground state of a balanced electron-hole system in the quantum Hall regime using mean-field theory and obtain a rich phase diagram as a function of interlayer distance d and the filling factor within a layer. We identify an excitonic condensate phase, an excitonic supersolid phase, as well as uncorrelated Wigner crystal states. We find that balanced electron-hole system exhibits a supersolid phase a wide range of filling factors, with different crystal structure ground states. We obtain the ground state stiffness in the excitonic phases and show that the phase transitions fr…
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.
Heterobilayer transition metal dichalcogenide (TMDC) moiré systems provide an ideal framework to investigate strongly correlated physics. Here we theoretically study bosonic many-body phases of excitons in moiré TMDCs. By using two moiré models and cluster mean-field theory, we reveal that, due to non-local Coulomb interactions, moiré excitons can feature exotic supersolid phases, i.e. superfluids of broken translational invariance, and correlated insulating states. The correlated phases exist at experimentally accessible temperatures and are tunable via the twist angle and exciton density.
We investigate the microscopic description of exciton-polaritons that involves electrons, holes and photons within a two-dimensional microcavity. We show that in order to recover the simplified exciton-photon model that is typically used to describe polaritons, one must correctly define the exciton-photon detuning and exciton-photon (Rabi) coupling in terms of the bare microscopic parameters. For the case of unscreened Coulomb interactions, we find that the exciton-photon detuning is strongly shifted from its bare value in a manner akin to renormalization in quantum electrodynamics. Within the…
We provide a many-body theory for the interactions of two-dimensional excitons and polaritons beyond the Born approximation. Taking into account Gaussian quantum fluctuations via the Bogoliubov theory, we find that the two-body interaction strength in two-dimensions has an inverse logarithmic dependence on the scattering length and ground state energy. This leads to a vanishing exciton interaction strength in the zero-momentum limit but a finite polariton interaction strength due to strong light-matter coupling. We also derive the exact Tan relations for exciton-polaritons and calculate Tan's …
We predict the spontaneous modulated emission from a pair of exciton-polariton condensates due to coherent (Josephson) and dissipative coupling. We show that strong polariton-polariton inter- action generates complex dynamics in the weak-lasing domain way beyond Hopf bifurcations. As a result, the exciton-polariton condensates exhibit self-induced oscillations and emit an equidistant frequency comb light spectrum. A plethora of possible emission spectra with asymmetric peak dis- tributions appears due to spontaneously broken time-reversal symmetry. The lasing dynamics is affected by the shot n…
Collective (elementary) excitations of quantum bosonic condensates, including condensates of exciton polaritons in semiconductor microcavities, are a sensitive probe of interparticle interactions. In anisotropic microcavities with momentum-dependent TE-TM splitting of the optical modes, the excitations dispersions are predicted to be strongly anisotropic, which is a consequence of the synthetic magnetic gauge field of the cavity, as well as the interplay between different interaction strengths for polaritons in the singlet and triplet spin configurations. Here, by directly measuring the disper…
Atomically-thin transition metal dichalcogenide crystals (TMDCs) hold great promise for future semiconductor optoelectronics due to their unique electronic and optical properties. In particular, electron-hole pairs (excitons) in TMDCs are stable at room temperature and interact strongly with light. When TMDCs are embedded in an optical microcavity, the excitons can hybridise with cavity photons to form exciton polaritons (polaritons herein), which display both ultrafast velocities and strong interactions. The ability to manipulate and trap polaritons on a microchip is critical for future appli…
The dynamics of an exciton-polariton superfluid resonantly pumped in a semiconductor microcavity are investigated by mean-field theory. Modulational instability develops into crystalline order and then ordered and disordered states alternately form. A supersolid-like state is also found, in which superflow coexists with crystalline order at rest.
Bilayer electron-hole systems, where carriers in one layer are electrons and carriers in the other are holes, have been actively investigated in recent years with the focus on Bose-Einstein condensation of excitons. This condensation is expected to occur when the layer separation d is much smaller than the interparticle distance r_sa_B within each layer. In this Brief Report, we argue for the existence of a state, Wigner supersolid, in which excitons are phase-coherent but form a Wigner crystal due to dipolar repulsion. We present the qualitative phase diagram of a bilayer system, and discuss …
We theoretically analyze exciton-photon oscillatory dynamics within a homogenous polariton gas in presence of energy detuning between the cavity and quantum well modes. Whereas pure Rabi oscillations consist of the particle exchange between the photon and excitons states in the polariton system without any oscillations of the phases of the two sub-condensates, we demonstrate that any non-zero detuning results in oscillations of the relative phase of the photon and exciton macroscopic wave functions. Different initial conditions reveal a variety of behaviors of the relative phase between the tw…
Time resolved photoluminescence is a powerful technique to study the collective dynamics of excitons and polaritons in semiconductor nanostructures. We present a two excitation pulses technique to induce the ultrafast and controlled quenching of the exciton emission in a quantum well. The depth of the dip is given by the magnitude of the warming of the carriers induced by the arrival of a laser pulse when an exciton population is already present in the sample. We use this technique to study the relaxation mechanisms of polaritons in semiconductor microcavities, which are of great importance to…
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.
Strong light matter coupling between excitons and microcavity photons, as described in the framework of cavity quantum electrodynamics, leads to the hybridization of light and matter excitations. The regime of collective strong coupling arises, when various excitations from different host media are strongly coupled to the same optical resonance. This leads to a well-controllable admixture of various matter components in three hybrid polariton modes. Here, we study a cavity device with four embedded GaAs quantum wells hosting excitons that are spectrally matched to the A-valley exciton resonanc…
The crossover between low and high density regimes of exciton-polariton condensates is examined using a BCS wavefunction approach. Our approach is an extension of the BEC-BCS crossover theory for excitons, but includes a cavity photon field. The approach can describe both the low density limit, where the system can be described as a Bose-Einstein condensate (BEC) of exciton-polaritons, and the high density limit, where the system enters a photon dominated regime. In contrast to the exciton BEC-BCS crossover where the system approaches an electron-hole plasma, the polariton high density limit h…
Self-rotation occurs in an exciton-polariton condensate in a two-dimensional semiconductor microcavity pumped by a nonresonant Gaussian laser beam. A wave packet of the condensate spontaneously rotates around the center of the pumped region at a constant frequency breaking the rotation symmetry of the system. When two self-rotating condensates are created with an appropriate distance, synchronization occurs between the dynamics of the self-rotating condensates.
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 theoretically study two-dimensional exciton-polariton lattices and predict that non-Hermitian topological corner modes can be formed under non-resonant pumping. As a generalization of the non-Hermitian skin effect, all eigenstates are localized at the two corners in our model. This is also a higher dimensional topology compared to other proposals in exciton-polariton systems and we find that it allows propagating signals in the bulk of the system to travel around defects, which is not possible in one-dimensional topological lattices or two-dimensional lattices with Hermitian edge states. Fu…
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 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.
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 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…
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…
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 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…
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 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 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 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 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…
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 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 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…
