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arXiv:1312.6772 · Physical Review A

Second-order coherence of superradiance from a Bose-Einstein condensate

Raphael Lopes, Almazbek Imanaliev, Marie Bonneau, Josselin Ruaudel, Marc Cheneau, Denis Boiron, Christoph Ira Westbrook

Published Jul 16, 2014• 14 citations
arXivHTMLPDF

Abstract

We have measured the two-particle correlation function of atoms from a Bose-Einstein condensate participating in a superradiance process, which directly reflects the second-order coherence of the emitted light. We compare this correlation function with that of atoms undergoing stimulated emission. Whereas the stimulated process produces correlations resembling those of a coherent state, we find that superradiance, even in the presence of strong gain, shows a correlation function close to that of a thermal state, just as for ordinary spontaneous emission.

DOI
10.1103/physreva.90.013615

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We have measured the two-particle correlation function of atoms from a Bose-Einstein condensate participating in a superradiance process, which directly reflects the second-order coherence of the emitted light. We compare this correlation function with that of atoms undergoing stimulated emission. Whereas the stimulated process produces correlations resembling those of a coherent state, we find that superradiance, even in the presence of strong gain, shows a correlation function close to that of a thermal state, just as for ordinary spontaneous emission.
Second-order time correlation measurements with a temporal resolution better than 3 ps were performed on a CdTe microcavity where spontaneous Bose-Einstein condensation is observed. After the laser pulse, the nonresonantly excited thermal polariton population relaxes into a coherent polariton condensate. Photon statistics of the light emitted by the microcavity evidences a clear phase transition from the thermal state to a coherent state, which occurs within 3.2 ps after the onset of stimulated scattering. Following this very fast transition, we show that the emission possesses a very high coherence that persists for more than 100 ps after the build-up of the condensate.
A major advance in understanding the behavior of light was to describe the coherence of a light source by using correlation functions that define the spatio-temporal relationship between pairs and larger groups of photons. Correlations are also a fundamental property of matter. We performed simultaneous measurement of the second- and third-order correlation functions for atoms. Atom bunching in the arrival time for pairs and triplets of thermal atoms just above the Bose-Einstein condensation (BEC) temperature was observed. At lower temperatures, we demonstrated conclusively the long-range coherence of the BEC for correlation functions to third order, which supports the prediction that like coherent light, a BEC possesses long-range coherence to all orders.
The first-order coherence properties of strongly coupled systems supporting polariton lasing and Bose-Einstein condensation (BEC) have been thoroughly studied and show consistent results. In contrast, second-order coherence properties have been found to vary for different systems, and the second-order coherence function can deviate from the value of one, typical for atomic BEC, revealing super-Poissonian fluctuations even above the BEC/polariton lasing threshold. This calls for a deeper understanding of the emission statistics and dynamics in light-based condensates, especially in the non-equilibrium regime. Here we demonstrate a coherent state of polariton emission from a plasmonic lattice measured as the second-order coherence function value separately for Γ\mathrmΓΓ- and non-Γ\mathrmΓΓ-point radiation (ground state and high-energy tail). We observe a high degree of coherence with the value g(2)(τ=0)−1<10−4g^{(2)}(τ=0)-1<10^{-4}g(2)(τ=0)−1<10−4. We also demonstrate the ultrafast ($>$1 THz) nature of the dynamics. The process can be interpreted as a BEC with ultrafast, sub-50-fs thermalization, but we also suggest an alternative explanation as superradiance in a system where the emitters have vibrational degrees of freedom.
The atom - electromagnetic field interaction is studied in the Dicke model, wherein a single field mode is interacting with a collection of two level atoms at thermal equilibrium. It is found that in the superradiant phase of the system, wherein the Bose-Einstein condensation of photons takes place, the notion of photon as an elementary electromagnetic excitation ceases to exist. The phase and intensity excitations of the condensate are found to be the true excitations of electromagnetic field. It is found that in this phase, the atom interacts with these excitations in a distinct coherent transition process, apart from the known stimulated emission/absorption and spontaneous emission processes. In the coherent transition it is found that while the atomic state changes in course of the transition process, the state of electromagnetic field remains unaffected. It is found that the transition probability of such coherent transition process is macroscopically large compared to other stimulated emission/absorption and spontaneous emission processes.
Summary form only given. Bose-Einstein condensed atomic gases are a new class of quantum fluids with many novel properties. We have studied collective modes and dissipation by perturbing the condensate with focused laser beams. The scattering of photons imparts momentum to the condensate and creates excitations. Consequently, the coherence and collective behavior of the condensate can strongly affect optical properties. We used light scattering to demonstrate that the coherence length of a condensate is equal to its physical size, and obtained dramatic evidence for the presence of correlated momentum excitations in the many-body condensate wavefunction. At higher laser intensity, a new form of superradiance was found which provided a gain mechanism for the generation of directed beams of atoms and light. This process amplified matter waves in a phase coherent way.
Due to its coherence properties and high optical depth, a Bose–Einstein condensate [BEC] provides an ideal setting to investigate collective atom-light interactions. Superradiant light scattering [SLS] in a BEC is a fascinating example of such an interaction. It is an analogous process to Dicke superradiance, in which an electronically inverted sample decays collectively, leading to the emission of one or more light pulses in a well-defined direction. Through time-resolved measurements of the superradiant light pulses emitted by an end-pumped BEC, we study the close connection of SLS with Dicke superradiance. A 1D model of the system yields good agreement with the experimental data and shows that the dynamics result from the structures that build up in the light and matter-wave fields along the BEC. This paves the way for exploiting the atom–photon correlations generated by the superradiance.