Long-range order in the Bose-Einstein condensation of polaritons

Sarchi, Davide; Savona, Vincenzo

doi:10.1103/physrevb.75.115326

Cited by 47 publications

(45 citation statements)

References 38 publications

(92 reference statements)

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“…Recently, a similar phase transition has been reported for the lower branch of exciton-polaritons (LPs) in planar semiconductor microcavities [5,6,7,8,9,10,11,12], and supporting theoretical frameworks have been developed [13,14,15,16,17,18,19,20]. Interestingly, LPs are free particles in a two dimensional (2D) system where genuine BEC exists only at zero temperature in the thermodynamic limit [21,22].…”

Section: Pacs Numbersmentioning

confidence: 55%

Spatial Coherence of a Polariton Condensate

et al. 2007

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We perform a Young's double-slit experiment to study the spatial coherence properties of a twodimensional dynamic condensate of semiconductor microcavity polaritons. The coherence length of the system is measured as a function of the pump rate, which confirms a spontaneous build-up of macroscopic coherence in the condensed phase. An independent measurement reveals that the position and momentum uncertainty product of the condensate is close to the Heisenberg limit. An experimental realization of such a minimum uncertainty wavepacket of the polariton condensate opens a door to coherent matter-wave phenomena such as Josephson oscillation, superfluidity, and solitons in solid state condensate systems. PACS numbers:Simple, yet profoundly connected to the foundation of quantum physics, the Young's double-slit experiment has been a benchmark demonstration of macroscopic spatial coherence -off-diagonal long range order (ODLRO) of a macroscopic number of particles [1] -in Bose-Einstein Condensation (BEC) of cold atoms [2,3,4]. Recently, a similar phase transition has been reported for the lower branch of exciton-polaritons (LPs) in planar semiconductor microcavities [5,6,7,8,9,10,11,12], and supporting theoretical frameworks have been developed [13,14,15,16,17,18,19,20]. Interestingly, LPs are free particles in a two dimensional (2D) system where genuine BEC exists only at zero temperature in the thermodynamic limit [21,22]. A quasi-BEC can be defined for a 2D system of a finite size if a macroscopic number of particles occupy a single ground state and if an ODLRO is established throughout the system [23,24]. Yet in the LP experiments to date, the system size is ambiguously defined by the spot size of the pump laser, and there is no quantitative study of the relation between the size and the coherence length of a condensate [10,11]. In this work, we perform a Young's double slit experiment on a LP gas to measure its spatial coherence properties across the phase transition, and compare the measured coherence length with the condensate size. We also measure the position-momentum uncertainty product of the condensate and compare it to the Heisenberg limit.A sketch of the setup is shown in Fig. 1. The microcavity sample is first magnified by a factor of 37.5 and imaged to a plane A, which is in turn imaged by a lens II to a charge-coupled-device (CCD) at plane C for measurement of spatial distribution. For the double-slit experiment, we insert a pair of rectangular slits at plane A, and move the lens II such that the image of plane A (denoted by plane B ) is a distance D behind plane C. Effectively, we observe on the CCD the interference pattern of the LP emission passing through the double- slit. In our experiment, D = 6.7 cm, the width of the slit image at plane B is δ = 53 µm, and the average wavelength of the LP emission is λ ∼ 778.5 nm. Correspondingly, the Fresnel number δ 2 Dλ = 0.05 ≪ 1, thus the far-field condition is satisfied at plane C. When mapped onto the sample surface, the slit width seen by the LPs is ∆r ≈ ...

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Section: Pacs Numbersmentioning

confidence: 55%

Spatial Coherence of a Polariton Condensate

et al. 2007

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“…[11][12][13] Recently, it has been suggested that the presence of spatial confinement could have an impact on the thermalization process. 14 This is confirmed by pioneering experimental observations in micropillars, where the spontaneous quantum degeneracy of microcavity polaritons seems to be reached at lower excitation densities than in planar microcavities. 15 In order to clarify this point, a detailed investigation of the efficiency of relaxation and thermalization of polaritons in spatially confined structures is required.…”

Section: Introductionmentioning

confidence: 53%

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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“…The real part g 0 is associated with an energy renormalization, while the imaginary part g represents the strength of EID, which is also referred to as collisional broadening. The ratio of the constants is estimated as 2g pae /g 0 /6n s E b a 2 0 , where n s is the saturation density of excitons [26]. E b and a 0 are respectively the exciton binding energy and Bohr radius.…”

Section: Theorymentioning

confidence: 99%

Dephasing effects on coherent exciton-polaritons and the breakdown of the strong coupling regime

et al. 2015

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Using femtosecond pump-probe spectroscopy, we identify excitation-induced dephasing as a major mechanism responsible for the breakdown of the strong coupling between excitons and photons in a semiconductor microcavity. The effects of dephasing are observed on the transmitted probe-pulse spectrum as a density-dependent broadening of the exciton-polariton resonances and the emergence of a third resonance at high excitation density. A striking asymmetry in the energy shift between the upper and the lower polaritons is also evidenced. Using the excitonic Bloch equations, we quantify the respective contributions to the energy shift of many-body effects associated with Coulomb fermion exchange and photon assisted exchange processes and the contribution to collisional broadening.

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Long-range order in the Bose-Einstein condensation of polaritons

Cited by 47 publications

References 38 publications

Spatial Coherence of a Polariton Condensate

Spatial Coherence of a Polariton Condensate

Enhancement of microcavity polariton relaxation under confinement

Dephasing effects on coherent exciton-polaritons and the breakdown of the strong coupling regime

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