Exciton-polaritons (polaritons herein) offer a unique nonlinear platform for studies of collective macroscopic quantum phenomena in a solid state system. Shaping of polariton flow and polariton confinement via potential landscapes created by nonresonant optical pumping has gained considerable attention due to the degree of flexibility and control offered by optically-induced potentials. Recently, large density-dependent energy shifts (blueshifts) exhibited by optically trapped polaritons at low densities, below the bosonic condensation threshold, were interpreted as an evidence of strong polariton-polariton interactions [Nat. Phys. 13, 870 (2017)]. In this work, we further investigate the origins of these blueshifts in optically-induced circular traps and present evidence of significant blueshift of the polariton energy due to reshaping of the optically-induced potential with laser pump power. Our work demonstrates strong influence of the effective potential formed by an optically-injected excitonic reservoir on the energy blueshifts observed below and up to the polariton condensation threshold and suggests that the observed blueshifts arise due to interaction of polaritons with the excitonic reservoir, rather than due to polariton-polariton interaction.
Equilibrium Bose-Einstein condensation of exciton-polaritons, demonstrated with a long-lifetime microcavity [Phys. Rev. Lett. 118, 016602 (2017)], has proven that driven-dissipative systems can undergo thermodynamic phase transitions in the limit where the quasiparticle lifetime exceeds the thermalization time. Here, we identify the role of dimensionality and polariton interactions in determining the degree of thermalization in optically generated traps. To distinguish the effect of trapping from interactions and lifetimes, we measured the polariton distribution under four nonresonant Gaussian…
Bosonic condensates of exciton polaritons (light-matter quasiparticles in a semiconductor) provide a solid-state platform for studies of non-equilibrium quantum systems with a spontaneous macroscopic coherence. These driven, dissipative condensates typically coexist and interact with an incoherent reservoir, which undermines measurements of key parameters of the condensate. Here, we overcome this limitation by creating a high-density exciton-polariton condensate in an optically-induced "box" trap. In this so-called Thomas-Fermi regime, the condensate is fully separated from the reservoir and i…
We develop a quantum field theory for parametrically pumped polaritons using Keldysh Green's function techniques. By considering the mean-field and Gaussian fluctuations, we find that the low energy physics of the highly non-equilibrium phase transition to the optical parametric oscillator regime is in many ways similar to equilibrium condensation. In particular, we show that this phase transition can be associated with an effective chemical potential, at which the system's bosonic distribution function diverges, and an effective temperature. As in equilibrium systems, the transition is achiev…
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.
Controlled Switching of Bose-Einstein Condensation in a Mixture of Two Species of Polaritons
Joint Quantum Institute, University of Maryland（马里兰大学联合量子研究所）；Department of Physics, University of Pittsburgh（匹兹堡大学物理系）；Department of Electrical Engineering, Princeton University（普林斯顿大学电气工程系）
Optical trapping and manipulation of microcavity exciton polaritons rely on effective potentials induced by the interaction of polaritons with a reservoir of high energy excitonic particles injected by an off-resonant optical pump. Here, we experimentally investigate possible mechanisms responsible for reshaping of these effective potentials in the low-density exciton-polariton regime. We infer the spatial distribution of the reservoir from the spatially resolved energy of exciton-polariton emission measured at zero momentum (zero kinetic energy). Power-dependent shape analysis of the potentia…
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…
Exciton-polaritons in semiconductor microcavities have been used to demonstrate quantum effects such as Bose-Einstein condensation, superfluity, and quantized vortices. However, in these experiments, the polaritons have not reached thermal equilibrium when they undergo the transition to a coherent state. This has prevented the verification of one of the canonical predictions for condensation, namely the phase diagram. In this work, we have created a polariton gas in a semiconductor microcavity in which the quasiparticles have a lifetime much longer than their thermalization time. This allows t…
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…
Exciton-polaritons are a coherent electron-hole-photon (e-h-p) system where condensation has been observed in semiconductor microcavities. In contrast to equilibrium Bose-Einstein condensation (BEC) for long lifetime systems, polariton condensates have a dynamical nonequilibrium feature owing to the similar physical structure that they have to semiconductor lasers. One of the distinguishing features of a condensate to a laser is the presence of strong coupling between the matter and photon fields. Irrespective of its equilibrium or nonequilibrium nature, exciton-polariton have been observed to…
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…
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…
The classic Bogoliubov theory of weakly interacting Bose gases rests upon the assumption that nearly all the bosons condense into the lowest quantum state at sufficiently low temperatures. Here we develop a generalized version of Bogoliubov theory for the case of a driven-dissipative exciton-polariton condensate with a large incoherent uncondensed component, or excitonic reservoir. We argue that such a reservoir can consist of both excitonic high-momentum polaritons and optically dark superpositions of excitons across different optically active layers, such as multiple quantum wells in a micro…
Condensation of bosons into a macroscopic quantum state belongs to the most intriguing phenomena in nature. It was first realized in quantum gases of ultra-cold atoms, but more recently became accessible in open-dissipative, exciton-based solid-state systems at elevated temperatures. Semiconducting monolayer crystals have emerged as a new platform for studies of strongly bound excitons in ultimately thin materials. Here, we demonstrate the formation of a bosonic condensate driven by excitons hosted in an atomically thin layer of MoSe2, strongly coupled to light in a solid-state resonator. The …
Estimating the conditions for polariton condensation in organic thin-film microcavities
我们研究了在有机量子阱中观察受限二维极化激元气体玻色凝聚的可能性。我们推导出一个合适的参数化模型哈密顿的基础上的腔的几何形状，双激子结合能，和类似的光谱和结构数据。通过转换的总和在$d$维相空间的半经典积分的状态，我们表明，虽然一个理想的2-D玻色气体将不会发生凝聚，与Bogoliubov色散$H(p)\approx s p$接近$p=0$的相互作用的气体将发生玻色凝聚在一个给定的临界密度和温度。我们发现，$T_c/\sqrt{ρ_c}$是敏感的腔的几何形状和双激子结合能。特别是对于强束缚的双激子，Gross-Pitaevskii方程中的非线性相互作用项变为负值，从而得到的基态将是定域孤子态而不是离域玻色凝聚态.
Phase transitions, where observable properties of a many-body system change discontinuously, can occur in both open and closed systems. Ultracold atoms have provided an exemplary model system to demonstrate the physics of closed-system phase transitions, confirming many theoretical models and results. Our understanding of dissipative phase transitions in quantum systems is less developed, and experiments that probe this physics even less so. By placing cold atoms in optical cavities, and inducing strong coupling between light and excitations of the atoms, one can experimentally study phase tra…
Photonic materials are a rapidly growing platform for studying condensed matter physics with light, where the exquisite control capability is allowing us to learn about the relation between microscopic dynamics and macroscopic properties. One of the most interesting aspects of condensed matter is the interplay between interactions and the effect of an external magnetic field or rotation, responsible for a plethora of rich phenomena -- Hall physics and quantized vortex arrays. At first sight, however, these effects for photons seem vetoed: they do not interact with each other and they are immun…
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 study the dynamics of phase defects trapped in a finite optically imprinted ring lattice in binary polariton condensates, under the influence of the cross-interaction (CI) between the condensates in different spin components and the spin-orbit interaction (SOI). In this configuration, we find that a vortex circulates unidirectionally in optically induced orbits because of the Magnus force acting in the polariton fluid, and the vortex' angular velocity is influenced by the SOI and CI. Interestingly, in our system, these two interactions can also lead to elongated and frozen phase defects, fo…
Semiconductor-microcavity polaritons are composite quasiparticles of excitons and photons, emerging in the strong coupling regime. As quantum superpositions of matter and light, polaritons have much stronger interparticle interactions compared with photons, enabling rapid equilibration and Bose-Einstein condensation (BEC). Current realizations based on 1D photonic structures, such as Fabry-Pérot microcavities, have limited light-trapping ability resulting in picosecond polariton lifetime. We demonstrate, theoretically, above-room-temperature (up to 590 K) BEC of long-lived polaritons in MoSe$_…
Bose-Einstein Condensation and Spin Mixtures of Optically Trapped Metastable Helium
本文报道了亚稳态氦-4原子（4 He *）在全光势下的BEC的实现。多达10^5个自旋极化的4 He * 原子被凝聚在由单个聚焦的垂直传播的远离共振的激光束形成的光学偶极阱中。垂直阱的几何形状被选择为最好地匹配的延迟线阳极微通道板检测器的分辨率特性能够登记单个He* 原子。我们还确认了某些自旋状态组合的4 He * 两体非弹性过程的不稳定性，这必然会影响未来的实验范围，使用光学捕获自旋混合物。为了更好地量化这一约束，我们测量自旋态分辨的两体非弹性损耗率系数的光阱。
Modulational instabilities play a key role in a wide range of nonlinear optical phenomena, leading e.g. to the formation of spatial and temporal solitons, rogue waves and chaotic dynamics. Here we experimentally demonstrate the existence of a modulational instability in condensates of cavity polaritons, arising from the strong coupling of cavity photons with quantum well excitons. For this purpose we investigate the spatiotemporal coherence properties of polariton condensates in GaAs-based microcavities under continuous-wave pumping. The chaotic behavior of the instability results in a strongl…
Coherent bosonic ensembles offer the promise of harnessing quantum effects in photonic and quantum circuits. In the dynamic equilibrium regime, the application of polariton condensates is hindered by exciton-polariton scattering induced de-coherence in the presence of a dark exciton reservoir. By spatially separating the condensate from the reservoir, we drive the system into the weak interaction regime, where the ensemble coherence time exceeds the individual particle lifetime by nearly three orders of magnitude. The observed nanosecond coherence provides an upper limit for polariton self-int…
We describe photonic crystal microcavities with very strong light-matter interaction to realize room-temperature, equilibrium, exciton-polariton Bose-Einstein condensation (BEC). This is achieved through a careful balance between strong light-trapping in a photonic band gap (PBG) and large exciton density enabled by a multiple quantum-well (QW) structure with moderate dielectric constant. This enables the formation of long-lived, dense 10~$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…
We propose a method to enhance the spatial coupling between ballistic exciton-polariton condensates in a semiconductor microcavity based on available spatial light modulator technologies. Our method, verified by numerically solving a generalized Gross-Pitaevskii model, exploits the strong nonequilibrium nature of exciton-polariton condensation driven by localized nonresonant optical excitation. Tailoring the excitation beam profile from a Gaussian into a polygonal shape results in refracted and focused radial streams of outflowing polaritons from the excited condensate which can be directed to…
Exciton-polaritons in a microcavity are composite two-dimensional bosonic quasiparticles, arising from the strong coupling between confined light modes in a resonant planar optical cavity and excitonic transitions, typically using excitons in semiconductor quantum wells (QWs) placed at the antinodes of the same cavity. Quantum phenomena such as Bose-Einstein condensation (BEC), quantized vortices, and macroscopic quantum states have been reported at temperatures from tens of Kelvin up to room temperatures, and polaritonic devices such as spin switches \cite{Amo2010} and optical transistors hav…
In this letter, we give an analytical quantum description of a non-equilibrium polariton Bose-Einstein condensate (BEC) based on the solution of the master equation for the full polariton density matrix in the limit of fast thermalization. We find the density matrix of a non-equilibrium BEC, that takes into account quantum correlations between all polariton states. We show that the formation of BEC is accompanied by the build-up of cross-correlations between the ground state and the excited states reaching their highest values at the condensation threshold. Despite the non-equilibrium nature o…
Room-temperature polariton condensate in a two-dimensional hybrid perovskite
Carl von Ossietzky Universität Oldenburg（奥格斯堡卡尔冯奥西茨基大学）；University of Valencia（瓦伦西亚大学）；University of Exeter（埃克塞特大学）；Fraunhofer-Institute for Applied Optics and Precision Engineering IOF（弗劳恩霍夫应用光学和精密工程研究所IOF）；Friedrich Schiller University（弗里德里希·席勒大学）；Bar-Ilan Univ.（巴伊兰大学）；Weizmann Institute of Science（魏茨曼科学研究所）
Microcavity exciton-polaritons, known to exhibit non-equilibrium Bose condensation at high critical temperatures, can be also brought in thermal equilibrium with the surrounding medium and form a quantum degenerate Bose-Einstein distribution. It happens when their thermalization time in the regime of positive detunings -- or, alternatively, for high-finesse microcavities -- becomes shorter than their lifetime. Here we present the self-consistent finite-temperature Hartree-Fock-Bogoliubov description for such a system of polaritons, universally addressing the excitation spectrum, momentum-depen…
Exciton-polaritons in semiconductor microcavities have advanced to become a model system for studying dynamical Bose-Einstein condensation, macroscopic coherence, many-body effects, nonclassical states of light and matter, and possibly quantum phase transitions in a solid state. Being low mass bosons, these light-matter quasiparticles can condense at comparably high temperatures up to 300K, while preserving fundamental properties such as coherence in space and time domain even when they are out of equilibrium with the environment. Although the presence of an in-plane polariton confinement pote…
