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Physical Review A

Evolution of excitonic bands in fluid xenon

P. Laporte, I. T. Steinberger

Published Jun 1, 1977• 36 citations
Publisher

Abstract

Reflection spectra of homogeneous fluid xenon are presented for the wavelength region $115<\ensuremath{\lambda}<165$ nm and densities ranging from that near the critical point to that at the triple point. For each atomic line in this spectral region two bands are observed: one broadened and somewhat shifted band corresponding to the atomic transition, and another distinct band corresponding in position to that of the exciton observed in the triple-point liquid. Dispersion analysis of the two (atomic and excitonic) $^{3}P_{1}$ bands yielded the optical constants ${\ensuremath{\epsilon}}^{\ensuremath{'}}$, ${\ensuremath{\epsilon}}^{\ensuremath{'}\ensuremath{'}}$, $n$, and $k$ as a function of photon energy as well as parameters of the absorption bands. The results are interpreted in terms of exciton transitions appearing in momentary clusters of the fluid. The analysis of the parameters of the absorption bands was compared with the statistical fluctuations of the fluid density. It was estimated from this comparison that the $^{3}P_{1}$ exciton can be formed in a momentary cluster of atoms provided two conditions are fulfilled: the cluster has at least the volume of 1.5\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}21}$ ${\mathrm{cm}}^{3}$ and contains at least ten atoms.

DOI
10.1103/physreva.15.2538

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Reflection spectra of homogeneous fluid xenon are presented for the wavelength region 115<\ensuremathλ<165115<\ensuremath{\lambda}<165115<\ensuremathλ<165 nm and densities ranging from that near the critical point to that at the triple point. For each atomic line in this spectral region two bands are observed: one broadened and somewhat shifted band corresponding to the atomic transition, and another distinct band corresponding in position to that of the exciton observed in the triple-point liquid. Dispersion analysis of the two (atomic and excitonic) 3P1^{3}P_{1}3P1​ bands yielded the optical constants \ensuremathϵ\ensuremath′{\ensuremath{\epsilon}}^{\ensuremath{'}}\ensuremathϵ\ensuremath′, \ensuremathϵ\ensuremath′\ensuremath′{\ensuremath{\epsilon}}^{\ensuremath{'}\ensuremath{'}}\ensuremathϵ\ensuremath′\ensuremath′, nnn, and kkk as a function of photon energy as well as parameters of the absorption bands. The results are interpreted in terms of exciton transitions appearing in momentary clusters of the fluid. The analysis of the parameters of the absorption bands was compared with the statistical fluctuations of the fluid density. It was estimated from this comparison that the 3P1^{3}P_{1}3P1​ exciton can be formed in a momentary cluster of atoms provided two conditions are fulfilled: the cluster has at least the volume of 1.5\ifmmode\times\else\texttimes\fi{}10\ensuremath−21{10}^{\ensuremath{-}21}10\ensuremath−21 cm3{\mathrm{cm}}^{3}cm3 and contains at least ten atoms.
Reflectivity spectra of MgF2{\mathrm{F}}_{2}F2​---fluid-xenon interfaces obtained for a wide range of densities revealed that the n=2n=2n=2 Wannier exciton starts to appear at densities above 400 amagat (1 amagat of density for xenon corresponds to 2.7067\ifmmode\times\else\texttimes\fi{}1019{10}^{19}1019 atoms/cm3{\mathrm{cm}}^{3}cm3). The ${n}^{\ensuremath{'}}=1$ exciton appears at densities above about 100 amagats on the low-energy side of the parent 5p56s5{p}^{5}6s5p56s [K=12K=\frac{1}{2}K=21​] atomic state. The occurrence and evolution of these bands and of the previously reported n=1n=1n=1 band with density are discussed with use of conductivity relaxation times obtained by Huang and Freeman.
Bose-Einstein condensation, an effect long known for material particles as cold atomic gases, has in recent years also been observed for photons in microscopic optical cavities. Here, we report absorption and emission spectroscopic measurements on the lowest electronic transition ($5{p}^{6}\ensuremath{\rightarrow}5{p}^{5}6s$) of xenon, motivated by the search for a thermalization medium for photon Bose-Einstein condensation in the vacuum-ultraviolet spectral regime. We have recorded pressure-broadened xenon spectra in the 135- to 190-nm wavelength regime at conditions near the critical point. The explored pressure and temperature ranges include high-pressure gaseous xenon below the critical pressure and supercritical xenon at room temperature as well as liquid xenon close to the boiling point near the critical pressure.
The experiment demonstrates at low pressure the resonant excitation of the 3 P 1 atomic state of xenon by three-photon absorption; as the pressure increases the xenon molecules in the ground state intervene in the absorption process. The emission spectra present the VUV continua characteristic of the excimer. In the same experimental conditions but with observation along the excitation axis, the frequency tripling phenomenon is seen close to the resonance line at 147 nm and the authors have measured new values of the phase matching parameter C Xe between 145 and 147 nm.
We show that a laser beam, tuned in the transparency region of a direct-gap semiconductor, not only shifts but also splits the exciton levels. This splitting originates from the degeneracy of the valence band as the (${\ensuremath{\sigma}}_{+},{\ensuremath{\sigma}}_{\ensuremath{-}}$) parts of the light are not similarly coupled to the various exciton components. In the case of a fourfold-degenerate valence band, we find that, at large detuning, the shifts of the (2\ifmmode\times\else\texttimes\fi{}4) eightfold exciton are exactly the shifts of a (2+4) six-level atom. This is just the generalization of the simple band-structure case with one electron and one hole band in which the large detuning excitonic shift has the same value as that of the two-level (dressed) atom. We give the selection rules to observe the various shifted lines for typical pump-probe experiments. We also discuss the experimental conditions necessary to see an exciton red shift at the two-photon absorption threshold, when the molecular biexciton is stable.
In a first part, a brief review of some excitonic properties is presented, with the accent put on their relevance with respect to the possibility of Bose-Einstein condensation. In a second part, recent experimental evidence is described, which supports the idea that excitonic particles may form a highly quantum fluid. In Cu20, the analysis of the exciton decay spectrum shows a gradual evolution of the gas from a classical regime at low densities up to a strongly degenerate one at high densities, with a chemical potential µ ~ 0. In CuCl excitons are unstable against formation of molecules (biexcitons). It is possible to generate directly a high density gas of biexcitons with momentum K ~ 0 by giant two-photon absorption. At low excitation, the observed molecular emission is in agreement with Maxwell -Boltzmann statistics. At high densities, strong deviations occur. In particular, the appearance of a sharp emission line is attributed to the presence of a Bose-Einstein condensate of excitonic molecules.