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) [1, 2], superfluidity [3], quantized vortices [4][5][6][7][8], and macroscopic quantum states [9, 10] have been realized at temperatures from tens of Kelvin up to room temperatures [11][12][13], and polaritonic devices such as spin switches [14] and optical transistors [15] have also been reported. Many of these effects of exciton-polaritons depend crucially on the polariton-polariton interaction strength. Despite the importance of this parameter, it has been difficult to make an accurate experimental measurement, mostly because of the difficulty of determining the absolute densities of polaritons and bare excitons. Here we report the direct measurement of the polariton-polariton interaction strength in a very high-Q microcavity structure. By allowing polaritons to propagate over 40 µm to the center of a lasergenerated annular trap, we are able to separate the polariton-polariton interactions from polariton-exciton interactions. The interaction strength is deduced from the energy renormalization of the polariton dispersion as the polariton density is increased, using the polariton condensation as a benchmark for the density. We find that the interaction strength is about two orders of magnitude larger than previous theoretical estimates, putting polaritons squarely into the strongly-interacting regime. When there is a condensate, we see a sharp transition to a different dependence of the renormalization on the density, which is evidence of many-body effects.Much of the physics of polaritons is dominated by the fact that they have extremely light effective mass. When an exciton is mixed with a cavity photon to become an excitonpolariton, it has an effective mass about four orders of magnitude less than a vacuum electron, and about three orders of magnitude less than a typical semiconductor quantum well exciton. (The Supplementary Information gives a basic introduction to the properties of exciton-polaritons.) Therefore one can view the polaritons as excitons which are given much longer diffusion length, with propagation distance of polaritons up to millimeters [16,17]; this may have implications for solar cells, which depend crucially on the diffusive 2 migration of excitons [18]. Alternatively, exciton-polaritons can be viewed as photons with nonlinear interactions many orders of magnitude higher than in typical optical materials, due to their excitonic components [19]. The light effective mass of the polaritons (typically 10 −8 that of a hydrogen atom) allows for quantum phenomena to be realized at much higher temperatures than in cold atomic gases.Interactions among polaritons. The interaction of exciton-polaritons is presumed to come...

The experimental realization of Bose-Einstein condensation (BEC) with atoms and quasiparticles has triggered wide exploration of macroscopic quantum effects. Microcavity polaritons are of particular interest because quantum phenomena such as BEC and superfluidity can be observed at elevated temperatures. However, polariton lifetimes are typically too short to permit thermal equilibration. This has led to debate about whether polariton condensation is intrinsically a nonequilibrium effect. Here we report the first unambiguous observation of BEC of optically trapped polaritons in thermal equilibrium in a high-Q microcavity, evidenced by equilibrium Bose-Einstein distributions over broad ranges of polariton densities and bath temperatures. With thermal equilibrium established, we verify that polariton condensation is a phase transition with a well-defined density-temperature phase diagram. The measured phase boundary agrees well with the predictions of basic quantum gas theory. DOI: 10.1103/PhysRevLett.118.016602 The realization of exciton-polariton condensation in semiconductor microcavities from liquid-helium temperature [1,2] all the way up to room temperature [3][4][5] presents great opportunities both for fundamental studies of many-body physics and for all-optical devices on the technology side. Polaritons in a semiconductor microcavity are admixtures of the confined light modes of the cavity and excitonic transitions, typically those of excitons in semiconductor quantum wells placed at the antinodes of the cavity. Quantum effects such as condensation [1][2][3][4][5], superfluidity [6], and quantized vortices [7][8][9][10][11] have been reported. The dual light-matter nature permits flexible control of polaritons and their condensates, facilitating applications in quantum simulation. It is also straightforward to measure the spectral functions, Aðk; ωÞ, of polaritons, which can provide insights into the dynamics of many-body interactions in polariton systems. For cold atoms, the equilibrium occupation numbers can be measured [12], but the spectral function is not readily accessible. Observations of non-Hermitian physics [13] and phase frustration [14] have shown that polaritons are an important complement to atomic condensates.However, in most previous experiments, the lifetime of the polaritons in microcavities has been 30 ps or less [15] due to leakage of the microcavity. Thus, although there have been claims to partial thermalization of polaritons [16,17], no previous work has unambiguously shown a condensation in thermal equilibrium, leading to the common description of polariton condensates as "nonequilibrium condensates" [18][19][20]. The theory of nonequilibrium condensation is still an active field [21][22][23][24]. Although polariton experiments and theory have shown that a great number of canonical features of condensation persist in nonequilibrium, e.g., superfluid behavior [22,23], some aspects may not [25,26], and debates persist over whether polariton condensates can be called Bose-Einstein c...

This corrects the article DOI: 10.1103/PhysRevLett.118.016602.

The surface reconstruction of SrTiO3 (110) is studied with scanning tunneling microscopy and density functional theory (DFT) calculations. The reversible phase transition between (4×1) and (5×1) is controlled by adjusting the surface metal concentration [Sr] or [Ti]. Resolving the atomic structures of the surface, DFT calculations verify that the phase stability changes upon the chemical potential of Sr or Ti. Particularly, the density of oxygen vacancies is low on the thermodynamically stabilized SrTiO3(110) surface.PACS numbers: 68.47. Gh, 68.37.Ef, 68.35.Fx Perovskite oxides have attracted intensive interests in the fields of fundamental condensed matter physics, photocatalysis chemistry, material science, as well as electronics applications, due to their rich phase diagrams and remarkable functionalities. The related research becomes even more exciting since the recent discovery of a quasitwo-dimensional electron gas (2DEG) between two insulating materials, SrTiO 3 and LaAlO 3 [1]. Subsequently, a tremendous amount of evidence has shown that the perovskite oxides in the low-dimensional (LD) form such as interfaces, thin films, or heterostructures display an equally rich diversity of exotic phenomena that is related, but not identical to the bulk [2], indicating a great opportunity for novel oxide-based devices [3]. One of the most important and intriguing discoveries is that the atomic arrangement on the surface or at the interface is determinant for the properties of the entire artificial structure. Hwang et al. found that the formation of 2DEG critically depends on the type of atomic termination layer at the interface [1]. O vacancies (V O 's) also sensitively influence the density and mobility of the charge carriers at the heterointerface of LaAlO 3 and SrTiO 3 [4]. Therefore, to clarify the origin of the emergent properties in LD oxides and ultimately to tune them for the fabrication of functionalized devices, the detailed knowledge on their microscopic structures and the high-precision growth technique are the key issues.Single crystalline SrTiO 3 is widely used as the epitaxial substrate for perovskite oxide films. In order to improve the growth quality, much effort has been made to obtain the atomically flat and ordered SrO or TiO 2 terminated (100) surface [5,6]. In contrast to the electrically neutral (100) surface, the formation process of SrTiO 3 (110) surface structure is much more complicated since it is inherently unstable due to the perpendicular macroscopic dipole formed by alternatively stacked (SrTiO) 4+ and (O 2 ) 4− layers [7]. The (110) surface stoichiometry often deviates from that in the ideal crystal, which leads to the formation of mixed phases of reconstruction [8]. V O 's may also be responsible for the stabilization of the (110) surface [9]. Recently Russell et al. obtained an (n×1) (n=3,4,6) family of reconstructions at varying annealing temperatures, which was described as a homologous series with the TiO 4 tetrahedra model [10,11]. However, it is still challenging to unders...