After the first demonstration of Bose-Einstein condensation in the solid state in 2006 and the establishment of exciton-polariton condensates in the wider scientific community, there has been an intense interest in this phenomenon at both the theoretical and experimental level. It is the object of this work to expand on the demonstration of polariton condensation and study in more detail different aspects of fundamental importance related to polariton condensation.
This book initially presents the basic concepts for excitons, polaritons, and condensates in and out of equilibrium. The following part focuses on the presentation of the experimental methods. The book is separated in two conceptual parts: one for the experiments done under continuous wave excitation and one dedicated to the dynamical properties of polariton condensates.
The appearance of a single condensate, despite the presence of disorder, is initially presented with the study of the mode synchronization of neighboring condensates. Then the coexistence of multiple condensates is demonstrated, a phenomenon that had been previously unperceived due to the noise of the excitation laser. The use of a low noise excitation source reveals spectral characteristics that were “hidden” in the previously broad spectra and a detailed experimental analysis is performed in order to study the full real and momentum space distribution of the individual condensates and their long range spatial coherence.
Interferometric measurements, which give access to the long range spatial coherence and the condensate phase, revealed the existence of pinned singularities. These were further investigated and were identified as the commonly known singly quantized vortices, here shown for the first time in a polariton condensate.
Up to this point most of the studies demonstrated that the polarization of polariton condensates was preferentially linearly polarized. A more detailed analysis that was pursued in this work showed that the degree of linear polarization is not necessarily high, but there are regions on the sample where it is rather poor. In certain areas where we do not observe a lift of degeneracy in polarization, the polariton condensates have to be considered as spinor objects. This unique property permitted the first observation of the celebrated case of fractional vortices which constitute the elementary excitations of spinor superfluids. In the second part of the book, the work is focused on the dynamics of polariton condensates. Beginning with the dynamics of singly quantized vortices, it is shown that vortices present traceable-in-time trajectories from their nucleation positions all the way to their pinning locations.
Finally taking advantage of the inherent disorder of the sample, a naturally occurring coupled double well system is investigated. The observation of oscillating polariton currents between the two wells was demonstrated. This phenomenon is analogous to the well-known Josephson oscillations. Most, if not all, of the studied phenomena are a complex interplay of the disorder, the driven-dissipative character of the polariton condensates, and the nonlinearities occurring in the system. A detailed theoretical analysis that supports the observed experimental findings is finally provided.
FROM ELECTRONICS TO OPTOELECTRONICS
The huge success of semiconductor electronics came from the fact that semiconductors can have a miniscule size and can dynamically change their conduction properties, leading to an elegant successor of the previously used vacuum tubes. After the first demonstration of the dynamically tunable conductance of a germanium based transistor by J. Bardeen and W. Brattain in the group Laboratories, there was a huge effort on the growth, miniaturization, and improvement of the modulation speed of semiconductor based devices. The use of silicon was widely spread and is nowadays the main material used in most electronic components. Computer processing units (CPUs) are one of the most notable examples of the use of silicon, where the modulation speed has now reached its physical limits. The physically induced limits on the bandwidth of the modulation of electronic signals presents serious limitations on the amount of information transferred and processed and, thus, new technologies needed to be found.
Using optical signals presents serious advantages and the idea of combining optics with electronics gave birth to a new category of devices: optoelectronics. However, creating, capturing, and modulating optical signals is complicated, especially when done with silicon which is an indirect bandgap material. The use of direct bandgap semiconductors was the key to this problem, which established III-V compounds in optoelectronics. The subsequent improvement of the growth techniques and quality allowed for the development of complicated structures, with the most remarkable being the semiconductor laser, dating back to the 1960s. Many years later, lasing from a Vertical Cavity Surface Emitting Laser (VCSEL) was demonstrated. The motivation behind VCSELs was to lower the lasing threshold and to force single mode emission which led to the creation of microcavity structures characterized by the weak coupling regime. The increasing quality of the materials and the narrowing linewidths allowed for the crossover from the weak to strong coupling regime. The first demonstration of strong coupling in a planar microcavity was done for the first time by C. Weisbuch . The new eigenstates that occur in this type of structure are occupied by bosonic quasi particles with extremely low mass.
They were first conceived for bulk volumes by Hoppfield in 1958 who considered the coupling of propagating photons with matter excitations. Microcavities in the strong coupling regime are inherently interesting systems: not only are they a textbook example of light-matter interactions and normal mode splitting, but the quasiparticles (exciton-polaritons) that are formed in this type of structures have an interesting dispersion in the form of a trap in momentum space and an extremely low mass on the order 1/100,000 (10-5) the free electron mass. The ease of the addressability of this type of dispersion, the polarization properties, the inherent possibility of non-linear scattering processes, and the bosonic nature of the polaritons has made these systems an extremely agile and alluring subject of study with numerous applications and rich fundamental physics.
FROM LOUIS DE BROGLIE TO CONDENSATION OF DILUTE ATOMIC GASES
It was in 1924 that Louis de Broglie proposed in his Ph.D. thesis the concept of the wave nature of particles stating that each particle has a wave associated to it. One year later, Einstein, who had fully endorsed the wave particle duality, came across the work of Bose on the statistics for photons and it was then that he realized that dilute atomic gases (matter) are expected to undergo a phase transition to a condensed state with the lowest possible energy if their interatomic distances become comparable to the thermal de Broglie wavelength.
This idea became widely accepted by the scientific community only after the first observation of superfluidity by Kapitsa in 1938, after which London had intuitively done the connection of superfluidity with the phenomenon of condensation described by Einstein. Lots of efforts to create a consistent theory to describe superfluidity and condensation were made, in the course of which, quantized vortices were first predicted by Onsager, then later revisited by Feynman, and experimentally observed for the first time in 1960 by Hall and Vinen. In 1975 Volovik and Mineev and a few months later Cross and Brinkman, taking into account the spinor nature for superfluids, predicted a new type of excitation, the half quantum vortex. Condensation of dilute atomic gases was first reported in 1995 when the groups of Ketterle and Cornell, using a combination of cooling techniques that were developed previously, succeeded in getting the right conditions for the observation of condensation using sodium and rubidium atoms respectively In 1996, the long predicted half quantum vortices are reported for the first time by Kirtley in high temperature superconductors. In the following years, a huge amount of work has been done on condensates of dilute atomic gases of various species for both theory and experiment and a deep understanding of the properties of equilibrium condensates is achieved.
CONDENSATION AND OPTOELECTRONICS: A DREAM BECOMES REALITY
The phenomenon of condensation has not only resided in the atomic or superfluid helium community but it has rather stimulated the semiconductor community from the early years. As early as 1962, excitons were proposed by Blatt and Moskalenko as promising candidates for the demonstration of Bose- Einstein condensation. The bosonic nature of these quasiparticles – that are made of electrons and holes held together by the coulomb interaction – and their light mass, were the main reasons for the long but fruitless efforts to demonstrate condensation.
After the demonstration of strong coupling in semiconductor microcavities and the creation of polaritons that are composite bosons with a half exciton-half photon nature, a new wave of excitement rushed through the solid state community. The polariton dispersion could act as a trap in momentum space and the mass of polaritons was four orders of magnitude lighter than that of excitons, theoretically allowing condensation even at room temperature.
Polariton non-equilibrium condensation was proposed first by Imamoglu et al. Several indications of the bosonic nature were found in pioneering experiments by the group of Baumberg, Scolnick and Deveaud. The weak exciton binding energy of the first generation samples did not allow observation of macroscopic occupations of the lower bottom polariton branch, as the systems lost the strong coupling. The breakthrough came by the samples of R. André which were based on II-VI compounds (CdTe, CdMnTe, CdMgTe) where, because of the higher exciton binding energies, convincing indications of macroscopic occupation in the strong coupling regime were reported. The pioneering work of Richard et al. although truly outstanding, it lacked experimental evidence of macroscopic phase coherence (long range order) and therefore did not eliminate all ambiguity. The first comprehensive and irrefutable evidence for condensation of exciton polaritons was reported in 2006 by the work of Kasprzak and Richard et al. This observation triggered a massive wave of excitement and immediately afterwards, condensation of exciton polaritons was reported for GaAs microcavities under stress and, more recently, for planar GaAs microcavities under non-resonant pumping. Large efforts have been also devoted to get the same effects at room temperature and already solid indications are reported using large bandgap materials like GaN and, more recently, ZnO materials.
The object of this book is to reveal fundamental properties of exciton polariton condensates in CdTe microcavities. After the demonstration of condensation of microcavity polaritons by Kasprzak et al. in 2006, many questions needed to be answered. Triggered by these questions, the experimental investigations that were pursued in the years to come revealed many fundamental aspects of polariton condensates. In addition, intense interactions with different theoretical groups has proved very fruitful as most of the observed phenomena were better understood after the reproduction of the observed phenomenology by theory. The main characteristic of polariton condensates in CdTe microcavities is that condensation takes place in the existent disorder of the sample acquired during epitaxial growth.
Disorder is thus expected to play a major role on the behavior of the condensates depending on its characteristics. In addition, the short lifetime of the polaritons renders polariton condensates out of equilibrium, because the steady state is a balance between losses (outgoing flows) and pumping from the excitonic reservoir (incoming flows).
The complex interplay of both the disorder and the non-equilibrium character has given rise to a very rich phenomenology. Chapter 2 gives a brief account of the basics of microcavity polaritons and polariton condensates and Chapter 3 is dedicated to the sample and the methods used during this work. Chapters 4 and 5 investigate the spectral properties of polariton condensates and their connection with the observation of long range spatial coherence.
They show the diversity that one can find in polariton condensates as a function of the disorder and the reservoir dynamics. Chapters 6 and 8 are a series of experiments on the observation of quantized conventional vortices and their behavior in CW and time resolved experiments showing that disorder and non-equilibrium can lead to the creation and pinning of vortices without the need to stir the condensates.Chapter 7 deals with a new type of vortex in polariton condensates when under specific circumstances the spinor nature of the condensates comes into play and the conventional full vortices are too costly to form. It is an account on the observation of the celebrated case of half quantum vortices. Finally Chapter 9 is dedicated to the temporally and spectrally resolved studies of a polaritonic Josephson junction where evidence of oscillating currents is provided by density and phase studies.
Extract from The Physics of Exciton-Polariton Condensates By Konstantinos Lagoudakis Published by the Presses polytechniques et universitaires romandes