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arXiv:1505.01732 · Physical Review A

Theory for Bose-Einstein condensation of light in nanofabricated semiconductor microcavities

Arie‐Willem de Leeuw, E. C. I. van der Wurff, R. A. Duine, D. van Oosten, Henk T. C. Stoof

Published Jul 22, 2016• 9 citations
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Abstract

We construct a theory for Bose-Einstein condensation of light in nanofabricated semiconductor microcavities. We model the semiconductor by one conduction and one valence band which consist of electrons and holes that interact via a Coulomb interaction. Moreover, we incorporate screening effects by using a contact interaction with the scattering length for a Yukawa potential and describe in this manner the crossover from exciton gas to electron-hole plasma as we increase the excitation level of the semiconductor. We then show that the dynamics of the light in the microcavities is damped due to the coupling to the semiconductor. Furthermore, we demonstrate that on the electron-hole plasma side of the crossover, which is relevant for the Bose-Einstein condensation of light, this damping can be described by a single dimensionless damping parameter that depends on the external pumping. Hereafter, we propose to probe the superfluidity of light in these nanofabricated semiconductor microcavities by making use of the differences in the response in the normal or superfluid phase to a sudden rotation of the trap. In particular, we determine frequencies and damping of the scissors modes that are excited in this manner. Moreover, we show that a distinct signature of the dynamical Casimir effect can be observed in the density-density correlations of the excited light fluid.

DOI
10.1103/physreva.94.013615

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Conference on Lasers and Electro-Optics•Nov 27, 2002•0 citations
We construct a theory for Bose-Einstein condensation of light in nanofabricated semiconductor microcavities. We model the semiconductor by one conduction and one valence band which consist of electrons and holes that interact via a Coulomb interaction. Moreover, we incorporate screening effects by using a contact interaction with the scattering length for a Yukawa potential and describe in this manner the crossover from exciton gas to electron-hole plasma as we increase the excitation level of the semiconductor. We then show that the dynamics of the light in the microcavities is damped due to the coupling to the semiconductor. Furthermore, we demonstrate that on the electron-hole plasma side of the crossover, which is relevant for the Bose-Einstein condensation of light, this damping can be described by a single dimensionless damping parameter that depends on the external pumping. Hereafter, we propose to probe the superfluidity of light in these nanofabricated semiconductor microcavities by making use of the differences in the response in the normal or superfluid phase to a sudden rotation of the trap. In particular, we determine frequencies and damping of the scissors modes that are excited in this manner. Moreover, we show that a distinct signature of the dynamical Casimir effect can be observed in the density-density correlations of the excited light fluid.
In this thesis we study Bose-Einstein condensation of photons. In Chapter 1 we describe the current experimental set-up and we explain the two important features of the Bose-Einstein condensate of light: dissipation through the interaction with the external reservoir of dye molecules and driving by the external pumping. In Chapter 2 we use the Schwinger-Keldysh formalism to describe the complete time evolution of the light. We show that the finite-lifetime effects of the photons due to the interaction with the dye can be characterized by a single dimensionless parameter, that depends on the power of the external laser pumping the dye. We also determine spectral functions and collective modes of the photon gas in both the normal and the Bose-Einstein condensed phases. In Chapter 3 we demonstrate that the finite-lifetime effects on the spatial first-order correlation functions of the condensed light are negligible, but are important for the temporal first-order correlations. Furthermore, we show that in the normal state the first-order correlations of the photons are suppressed by the interaction with the dye. In Chapter 4 we develop a model to describe the effect of interactions on the number fluctuations in Bose-Einstein condensates. We find good agreement between the observed number fluctuations in the light Bose-Einstein condensate and the results of our model for different interaction strenghts. In Chapter 5 we propose an experiment to observe phase diffusion in the Bose-Einstein condensate of photons and we predict the outcome of individual measurements. In our model we incorporate quantum and thermal fluctuations as well as the finite-lifetime effects. In Chapter 6 we investigate the light in the presence of a periodic potential and we study the transition from a superfluid to a Mott-insulator. We demonstrate that in this system the true Mott-insulating state is longer present due the interactions with the dye molecules. Finally, in Chapter 7 we consider Bose-Einstein condensation of light in nano-fabricated semiconductor microcavities. We demonstrate that in this system there is also a single dimensionless damping parameter that depends on the external pumping. We propose to use the experimental freedom to investigate the superfluidity of the photons via the excitation of scissors modes. We determine the frequency and damping of these scissors modes. We also calculate the density-density correlations of the excited light fluid and we show that this contains a signature of the dynamical Casimir effect.
When particles with integer spin accumulate at low temperature and high density they undergo Bose-Einstein condensation (BEC). Atoms, solid-state excitons and excitons coupled to light all exhibit BEC, which results in high coherence due to massive occupation of the respective system's ground state. Surprisingly, photons were shown to exhibit BEC much more recently in organic dye-filled optical microcavities, which, owing to the photon's low mass, occurs at room temperature. Here we demonstrate that photons within an inorganic semiconductor microcavity also thermalise and undergo BEC. Although semiconductor lasers are understood to operate out of thermal equilibrium, we identify a region of good thermalisation in our system where we can clearly distinguish laser action from BEC. Based on well-developed technology, semiconductor microcavities are a robust system for exploring the physics and applications of quantum statistical photon condensates. Notably, photon BEC is an alternative to exciton-based BECs, which dissociate under high excitation and often require cryogenic operating conditions. In practical terms, photon BECs offer their critical behaviour at lower thresholds than lasers. Our study shows two further advantages of photon BEC in semiconductor materials: the lack of dark electronic states allows these BECs to be sustained continuously; and semiconductor quantum wells offer strong photon-photon scattering. We measure an unoptimised interaction parameter, g~=0.0023±0.0003\tilde{g}=0.0023\pm0.0003g~​=0.0023±0.0003, which is large enough to access the rich physics of interactions within BECs, such as superfluid light or vortex formation.
Abstract When particles with integer spin accumulate at low temperature and high density, they undergo Bose–Einstein condensation (BEC). Atoms, magnons, solid-state excitons, surface plasmon polaritons and excitons coupled to light exhibit BEC, which results in high coherence due to massive occupation of the respective system’s ground state. Surprisingly, photons were shown to exhibit BEC recently in organic-dye-filled optical microcavities, which—owing to the photon’s low mass—occurs at room temperature. Here we demonstrate that photons within an inorganic semiconductor microcavity also thermalize and undergo BEC. Although semiconductor lasers are understood to operate out of thermal equilibrium, we identify a region of good thermalization in our system where we can clearly distinguish laser action from BEC. Semiconductor microcavities are a robust system for exploring the physics and applications of quantum statistical photon condensates. In practical terms, photon BECs offer their critical behaviour at lower thresholds than lasers. Our study shows two further advantages: the lack of dark electronic states in inorganic semiconductors allows these BECs to be sustained continuously; and quantum wells offer stronger photon–photon scattering. We measure an unoptimized interaction parameter ( g~\tilde{{{{{g}}}}}g~​ g ̃ ≳ 10–3), which is large enough to access the rich physics of interactions within BECs, such as superfluid light.
Different aspects of the photoluminescence from semiconductor quantum-confined structures are studied in this dissertation, for a better understanding of fundamental physics of semiconductors.The precursor of any photoluminescence study is the characterization of the linear optical properties of the semiconductor structure. High resolution absorption measurements were performed in order to study the interplay of disorder and acoustic phonon scattering in a quantum well. Also, reflectivity measurements, together with a fitting procedure based on the transfer matrix formalism, are used to determine the thickness of samples.Excitons are atom-like quasi-particles, formed from a bound electron-hole pair. They follow a Bose-Einstein statistic, so in principle it is possible to achieve an excitonic Bose-Einstein condensate. Time resolved photoluminescence measurements were performed over an extensive range of lattice temperatures and carrier concentrations, in order to determine the fraction of excitons formed from the electron-hole plasma in a quantum well, after non-resonant excitation. The experimental spectra were compared to a pure plasma calculation first, then excitons were taken into account. The highest fraction of formed excitons is found for low temperatures and intermediate carrier densities. This fraction is found to be very small, and this has clear implications on the excitonic Bose-Einstein condensation studies.The photoluminescence emitted left and right from a quantum well is interfered in a modified Mach-Zender interferometer. It is shown that the light emitted on the two paths will interfere for a V-shape geometry and will not for any other paths.A structure formed by placing a quantum well in a field antinode of a resonant planar microcavity exhibits normal mode coupling: splitting of the resonance spectral line. The coherence properties of the photoluminescence from a normal-mode-coupling microcavity are studied using another version of the Mach-Zender interferometer. The degree of coherence measured in this way depends greatly on the pump wavelength and intensity, ranging from zero to 0.8. However, direct observation of the emission speckle shows significant coherence in all cases. The difference is explained by the different methods used to evaluate the coherence.The strong coupling between a quantum dot and a photonic crystal nanocavity is investigated by observation of photoluminescence. A new method of tunning the cavity wavelength by deposition of a thin film of solid Xenon on all the surfaces of the sample is presented. The method allows the scanning of the cavity wavelength with about 5 nm without a decrease in the quality factor and without changing the temperature.Finally, an extensive study of the quality factors of quantum dot photonic crystal nanocavities is presented. The role of the quantum dot ensemble absorption is investigated. At higher excitation levels, lasing is observed and discussed.
Photon condensation in semiconductor microcavities is a transformative technique for engineering quantum states of light at room temperature by tailoring strong but incoherent light-matter interactions. While continuous-wave and electrical pumping offer exceptional prospects for miniaturized quantum photonic technologies, harnessing these requires conceptual advances in understanding nonequilibrium light-matter dynamics in semiconductors. We resolve this challenge through an \textit{ab initio} quantum kinetic theory capturing how Coulomb interactions of optically excited carriers and phonon scattering mediate photon thermalization and condensation in semiconductors. Our microscopic model shows that at high carrier densities, thermalization is dominated by carrier-carrier Coulomb scattering, in clear contrast to the rovibrational relaxation that governs dye-based photon condensates. The theory predicts a rich nonequilibrium phase diagram with thermal, Bose-condensed, multimode, and lasing phases, quantitatively in agreement with recent experiments. Crucially, we identify how cavity detuning controls transitions between equilibrium and gain-dominated regimes, enabling tailored design of coherent light sources. This work thus provides the foundation for semiconductor-based quantum photonic devices operating beyond conventional laser paradigms.
Summary form only given.Recent experiments show signatures of exciton Bose-Einstein condensation in semiconductors. Thus a device that creates a coherent population of excitons while being pumped by a thermal source may be possible. Such an exciton matter laser could consist of a quantum well, possibly embedded in an optical microcavity. In it hot excitons slightly below the bandgap are created by a thermal distribution of free electrons and holes (generated by electrical injection or optical pumping). The excitons interact with (LA) phonons. At low densities excitons are bosonic, and their scattering is affected by statistical enhancement into states with large occupation. Under certain conditions the excitons can condense into a single state, with statistics similar to a coherent state. Light emitted by radiative recombination has the coherence properties of the condensate and is similar to laser light. However, the electronic population in the device does not need to be inverted. We consider 1S heavy-hole excitons in a two-dimensional harmonic trap, realized by a quantum well where interface roughness inevitably localizes low-energy excitons, or by strain fields in lattice mismatched structures. We treat the lowest two trap levels quantum mechanically, and the higher lying states act as a reservoir. Our model is valid at low density, where phase space filling and collisions are negligible. While simplistic, the model displays the main features of an exciton matter laser. Our model is described by the master equation.