Spectrum and thermal fluctuations of a microcavity polariton Bose-Einstein condensate

Sarchi, Davide; Savona, Vincenzo

doi:10.1103/physrevb.77.045304

Cited by 39 publications

(42 citation statements)

References 32 publications

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“…21 In this approach and considering a coherent monochromatic optical pump F͑r , t͒ = e −it F 0 ͑r͒, the coherent exciton and photon fields ⌽ x,c ͑r , t͒ evolve with the frequency of the laser source as ⌽ x,c ͑r , t͒ = e −it ⌽ x,c 0 ͑r͒. Their steady-state shape ⌽ x,c 0 ͑r͒ obeys a set of two coupled Schrödinger-like equations for the excitonphoton problem 19,21 …”

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Coherent optical control of the wave function of zero-dimensional exciton polaritons

et al. 2009

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Control of the wave function of confined microcavity polaritons is demonstrated experimentally and theoretically by means of tailored resonant optical excitation. Three dimensional confinement is achieved by etching mesas on top of the microcavity spacer layer. Resonant excitation with a continuous-wave laser locks the phase of the discrete polariton states to the phase of the laser. By tuning the energy and momentum of the laser, we achieve precise control of the momentum pattern of the polariton wave function. This is an efficient and direct way for quantum control of electronic excitations in a solid.Polaritons in semiconductor microcavities are hybrid quasiparticles consisting of a superposition of photons and excitons. Due to their photon component, polaritons are characterized by a quantum coherence length in the several micron range. Owing to their exciton content, they display sizeable interactions, both mutual and with other electronic degrees of freedom. These unique features have produced striking matter wave phenomena, such as Bose-Einstein condensation, 1,2 or parametric processes 3,4 able to generate entangled polariton states. 5,6 The key feature of polaritons with respect to confinement is their very small effective mass, which is about 10 5 times smaller than the free-electron mass. Hence, confinement within micrometer sized traps is sufficient to produce an atomlike spectrum with discrete energy levels. Recently, several paradigms for spatial confinement of polaritons in semiconductor devices have been established. 7-10 This opens the way to quantum devices in which polaritons can be used as a vector of quantum information. 11 Their electronic component can be accessed and controlled optically, through their photonic component. This holds promise for preparation of quantum states, which might then be transferred to longer lived elements of quantum storage ͑e.g., localized spins͒, or as a mechanism for mediating interactions between such elements over long distances, as proposed in Ref. 12. Precise control of the polariton wave function is then an essential requirement.In this Rapid Communication we demonstrate the manipulation of the wave function of confined zero-dimensional ͑0D͒ exciton polaritons under resonant optical excitation. The excited wave functions are monitored by collecting the coherent emission from the polariton traps. Control of the spatial and momentum probability distribution of the confined polaritons is achieved by tuning either the incidence angle or the energy of the excitation beam. Our results are supported by numerical simulations based on the coupled Gross-Pitaevskii equations for excitons and photons.The sample we used to carry out our studies consists of a single quantum well embedded in a planar microcavity with a pattern of differently sized round mesas on the spacer layer. 13 Patterning the cavity thickness results in a modulation of the photon resonance energy, which corresponds to a potential trap, with finite-energy barriers, able to confine polaritons. The con...

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Coherent optical control of the wave function of zero-dimensional exciton polaritons

et al. 2009

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“…Polariton condensates can be generated in zero dimensional micropillars [11] or in arrays of pillars with fully controlled coupling [16,17]. In this configuration, the non-equilibrium nature of polariton condensates should allow the realization of metastable collective states, such as the self-trapped states in a bosonic Josephson junction [18][19][20].In the present paper we investigate polariton condensation in photonic molecules obtained by coupling two micropillars. We demonstrate that polariton interactions strongly affect the way condensation occurs in such coupled system, not only modifying the wavefunction of the polariton condensate, but also the relaxation dynamics.…”

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Polariton Condensation in Photonic Molecules

et al. 2012

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We report on polariton condensation in photonic molecules formed by two coupled micropillars. We show that the condensation process is strongly affected by the interaction with the cloud of uncondensed excitons. Depending on the spatial position of these excitons within the molecule, condensation can be triggered on both binding and anti-binding polariton states of the molecule, on a metastable state or a total transfer of the condensate into one of the micropillars can be obtained. Our results highlight the crucial role played by relaxation kinetics in the condensation process.PACS numbers: 71.36.+c, 67.85.Hj, 78.67.Pt, 78.55.Cr Most of the experimental studies in atomic Bose condensates have explored conditions of thermodynamic equilibrium since typical condensate lifetimes are much longer than interaction times. Recent theoretical proposals have shown that out of equilibrium bosonic systems present qualitatively new behaviors [1]. One proposed way to reach this regime is the use of photonic systems with effective photon-photon interactions and dissipation provided by inherent optical losses [2]. Localized to delocalized phase transitions [3,4], highly entangled states [5], or fermionisation effects in a ring of coupled sites [6] are predicted in such systems.Microcavity polaritons are a model system for the investigation of the physics of driven-dissipative boson condensates [7][8][9][10][11][12][13]. They are the quasi-particules arising from the strong coupling between excitons confined in quantum wells and the optical mode of a microcavity. Because of their light-matter nature, polaritons present peculiar properties: they interact efficiently with their environment through their excitonic part [14,15] while their photonic part enables efficient coupling with the free space optical modes. Polariton condensates can be generated in zero dimensional micropillars [11] or in arrays of pillars with fully controlled coupling [16,17]. In this configuration, the non-equilibrium nature of polariton condensates should allow the realization of metastable collective states, such as the self-trapped states in a bosonic Josephson junction [18][19][20].In the present paper we investigate polariton condensation in photonic molecules obtained by coupling two micropillars. We demonstrate that polariton interactions strongly affect the way condensation occurs in such coupled system, not only modifying the wavefunction of the polariton condensate, but also the relaxation dynamics. This effect, specific to an out-of-equilibrium bosonic system, is illustrated by considering different positions of the non resonant excitation within the molecule. When the excitation spot is placed at the center of the molecule, polariton condensation is observed on both binding and anti-binding states. Interactions induce strong changes in the condensate wavefunction, the most important one being the change in its spatial anisotropy.When the excitation spot is positioned on one of the two coupled micropillars, condensation occurs in a very diffe...

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“…Indeed, theory predicts the manifestation of the superfluid behavior at lower densities and temperatures than the ones commonly explored. 9,10 In planar microcavities, due to the short radiative lifetime of polaritons and the very inefficient mechanisms of energy relaxation and thermalization, the deviations from equilibrium are very important. Indeed, in planar microcavities, thermalization is only possible in the regime of high polariton densities, where the polariton-polariton scattering becomes efficient enough.…”

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Enhancement of microcavity polariton relaxation under confinement

et al. 2009

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We experimentally investigate the relaxation of spatially confined microcavity polaritons. We measure the time-and energy-resolved photoluminescence under resonant excitation and in the low-density regime. In this way, we have access to the time evolution of the energy distribution of the polariton population. We show that, when one confined level is resonantly excited, after an initial transient, the population of the confined levels is thermally distributed. The reported efficiency of the relaxation process strongly depends on the confinement size. These experimental findings are well reproduced by a theoretical model accounting for the coupling between the confined states and a bath of acoustic phonons. Our results thus suggest that the phonon-mediated relaxation mechanisms are enhanced in the presence of spatial confinement.

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Spectrum and thermal fluctuations of a microcavity polariton Bose-Einstein condensate

Cited by 39 publications

References 32 publications

Coherent optical control of the wave function of zero-dimensional exciton polaritons

Coherent optical control of the wave function of zero-dimensional exciton polaritons

Polariton Condensation in Photonic Molecules

Enhancement of microcavity polariton relaxation under confinement

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