The transition of atomic, electronic, or e-h systems to quantum phases is an extraordinary process when both microscopic and macroscopic properties of the system undergo fundamental changes. Bose-Einstein condensation, has been observed in a number of physical systems, including super-cold atomic gases and solid- state quasiparticles. The most typical example of equilibrium condensation is the superconducting state of Cooper pairs in metals. However, in many cases the lifetime of particles or quasiparticles under study is finite, ranging from picoseconds to milliseconds. And even in this case condensation is possible. It is generally understood at present that coherence and off-diagonal long-range order in the density matrix are the most important characteristic features of condensed quantum states. Phase coherence established over microscopic distances is an intrinsic property of all Bose condensates. Experiments featuring interference between either two condensates or two separate parts of the same condensate are often considered as more convincing than observation of the macroscopic occupation of the ground state. The formation of long-range order and spatial phase coherence can be measured by studying interference patterns using either a Michelson interferometer or Young double slit arrangement. Here we present experimental results of observation of long-range temporal and spatial coherence of a macroscopically ordered state of a high-density e-h system in GaAs during the generation of femtosecond superradiant emission at room temperature
The transition of atomic, electronic, or e-h systems to quantum phases is an extraordinary process when both microscopic and macroscopic properties of the system undergo fundamental changes. Bose-Einstein condensation, has been observed in a number of physical systems, including super-cold atomic gases and solid- state quasiparticles. The most typical example of equilibrium condensation is the superconducting state of Cooper pairs in metals. However, in many cases the lifetime of particles or quasiparticles under study is finite, ranging from picoseconds to milliseconds. And even in this case condensation is possible. It is generally understood at present that coherence and off-diagonal long-range order in the density matrix are the most important characteristic features of condensed quantum states. Phase coherence established over microscopic distances is an intrinsic property of all Bose condensates. Experiments featuring interference between either two condensates or two separate parts of the same condensate are often considered as more convincing than observation of the macroscopic occupation of the ground state. The formation of long-range order and spatial phase coherence can be measured by studying interference patterns using either a Michelson interferometer or Young double slit arrangement. Here we present experimental results of observation of long-range temporal and spatial coherence of a macroscopically ordered state of a high-density e-h system in GaAs during the generation of femtosecond superradiant emission at room temperature
Summary form only given. Bosons can populate quantum states macroscopically, forming various kinds of thermal-equilibrium, and quasi-equilibrium condensates, which exhibit a wide range of collective phenomena including superfluidity and macroscopic coherence in matter. Interferometry has been employed to demonstrate long-range off-diagonal order in cold-atom systems, and, recently, in the rapidly developing field of exciton-polariton condensates. However, all such interferometric measurements have been performed on steady-state condensates, unable to access the temporal off-diagonal order and non-equilibrium dynamics. Moreover, in solid-state systems, interference between two separate condensates has not been observed before. Here we use optical injection to resonantly generate two dynamic exciton-polariton condensates with distinct momenta and at different times. We characterize the interference between condensates, demonstrating their long-range temporal order. We show that the build-up of the temporal long-range order strongly depends on the strength of polariton interactions, as well as the temperature and particle density. Moreover, polariton interactions yield a blue shift of the dynamic condensate energy, acting as an extremely large optical nonlinearity. These results provide direct evidence of temporal long-range order in dynamic condensates as well as demonstrate a new approach for probing the ultrafast coherent dynamics of exciton-polaritons, opening new directions in the fundamental study of coherence in matter as well as in practical applications such as quantum information processing and ultrafast logic.
A review of an experimental study of superradiance in semiconductor inorganic structures is presented. It is demonstrated that unique properties of superradiant emission are determined by unusual properties of electrons and holes, namely, the formation of BCS-like state in a system of collectively paired electrons and holes. This can adequately explain all features of superradiance, including its femtosecond pulse duration, record peak power, optical spectrum, spatial and temporal coherency and macroscopically large fluctuations. The effect of non-equilibrium condensation of electrons and holes in the phase domain at room temperature is experimentally demonstrated. The critical temperature of condensation in a strongly degenerate system of electrons and holes is finally theoretically estimated.
We have experimentally investigated the formation of off-diagonal long-range order in a gas of ultracold atoms. A magnetically trapped atomic cloud prepared in a highly nonequilibrium state thermalizes and thereby crosses the Bose-Einstein condensation phase transition. The evolution of phase coherence between different regions of the sample is constantly monitored and information on the spatial first-order correlation function is obtained. We observe the growth of the spatial coherence and the formation of long-range order in real time and compare it to the growth of the atomic density. Moreover, we study the evolution of the momentum distribution during the nonequilibrium formation of the condensate.
This thesis features fundamental experiments on the coherence properties of Bose-Einstein condensates (BEC) and atom lasers, made possible by a newly developed apparatus combining a Bose-Einstein condensate with an ultrahigh nesse optical cavity.Using the cavity as a single atom detector, atoms extracted from a trapped cloud are detected with unprecedented sensitivity, and the rst time-resolved counting of single atoms from a quantum degenerate source was demonstrated.O-diagonal long-range order is a dening property of a BEC and equivalent to longrange phase coherence.Its formation is a complex process accompanied by spontaneous symmetry breaking.We witnessed this formation in an ultracold cloud of 87 Rb atoms crossing the phase transition of BEC.Two overlapping atomic beams originating from dierent positions inside the condensate propagated downwards into the cavity.They showed a matter wave interference pattern with a visibility determined by the coherence of the probed regions.The modulation of the ux of atoms, recorded with single-atom resolution, yields the visibility, whereas its mean value gives information about the density of the sample.By shock cooling, a cloud of atoms was prepared in a highly nonequilibrium state slightly above the phase transition.While the ensemble subsequently relaxed, it crossed the phase transition into an equilibrium with a small condensate fraction.Employing our minimally invasive measurement method, the growth of both the rst-order coherence and the density of the sample was tracked in real time while the system crossed the phase transition.The growth of the coherence was found to start later, proceed faster and nish earlier than the increase in density.The coherent region increased at one fth of the speed of sound.Employing time-resolved single atom counting with the cavity detector, the full counting statistics of an atom laser beam was recorded.In a Hanbury Brown and Twiss type experiment, the second-order correlation function was found to be constant g (2) (τ ) = 1.00±0.01,proving the atom laser's second-order coherence and the absence of excess intensity uctuations that were observed in a pseudothermal beam.An analysis of the time interval distributions of atoms in the beam conrmed these ndings.The iii
Macroscopic coherence of Bose condensates is a fundamental and practical phenomenon in many-body systems, such as the long-range correlation of exciton-polariton condensates with a dipole density typically below the exciton Mott-transition limit. Here we extend the macroscopic coherence of electron-hole-photon interacting systems to a new region in the phase diagram-the high-density plasma region, where long-range correlation is generally assumed to be broken due to the rapid dephasing. Nonetheless, a cooperative state of electron-hole plasma does emerge through the sharing of the superfluorescence field in an optical microcavity. In addition to the in situ coherence of e-h plasma, a long-range correlation is formed between two 8-μm-spaced plasma ensembles even at room temperature. Quantized and self-modulated correlation modes are generated for e-h ensembles in the plasma region. By controlling the distance between the two ensembles, multiple coupling regimes are revealed, from strong correlation to perturbative phase correlation and finally to an incoherent classical case, which has potential implications for tunable and high-temperature-compatible quantum devices.
The kinetics of the formation of coherent correlation properties associated with Bose condensation is studied in detail. The evolution of a nonequilibrium state with no “condensate-seed” is related to a hierarchy of relaxation times. At the first stage, a particle flux in energy space toward low energies sets in. The evolution in this case is described by a nonlinear Boltzmann equation, with a characteristic time given by interparticle collisions. When the particles which will later form the condensate have a kinetic energy which is less than the potential energy, a quasicondensate starts to form. In this stage, fluctuations of the density (but not of the phase) are suppressed and short-range coherent correlation properties are governed by the equation of motion for a quasiclassical complex field. The next stage is connected with the formation of the long-range order. The time for forming topological order and therefore genuine superfluidity proves to be dependent on the system size. The off-diagonal long-range order, arising after the attenuation of long-wave phase fluctuations, has a size-dependent relaxation time as well. Introduction The problem of Bose–Einstein Condensation (BEC) kinetics, being interesting in itself, has acquired a special significance in connection with experimental efforts to observe this condensation in a number of systems with particles with a finite lifetime. Such systems include spin-polarized atomic hydrogen [1], excitons [2] and biexcitons [3] in semiconductors and, more recently, laser-cooled atomic systems [4].