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Physical Review A

Birefringence arising from the reorientation of the polarizability anisotropy of molecules in collisionless gases

Chinlon Lin, J.P. Heritage, T. Kenneth Gustafson, R. Y. Chiao, John P. McTague

Published Feb 1, 1976• 79 citations
Publisher

Abstract

The refractive-index change in a collisionless gas is evaluated from the Stark shifts of the rotational energy levels that arise from the polarizability anisotropy. In the limit of an extremely-short-duration excitation, a multilevel coherent effect results in delayed refractive-index bursts. Both stationary and transient responses of this birefringence to an optical field are considered for symmetric-top molecules, with particular emphasis on the special case of linear molecules.

DOI
10.1103/physreva.13.813

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Journal of Physics B Atomic and Molecular Physics•Dec 14, 1979•12 citations
The refractive-index change in a collisionless gas is evaluated from the Stark shifts of the rotational energy levels that arise from the polarizability anisotropy. In the limit of an extremely-short-duration excitation, a multilevel coherent effect results in delayed refractive-index bursts. Both stationary and transient responses of this birefringence to an optical field are considered for symmetric-top molecules, with particular emphasis on the special case of linear molecules.
We present a theoretical study of the induced transient birefringence of a low density homogeneous molecular gas in a resonant pump–probe experiment. The molecular coherent state induced by the resonant pump field is described by second-order perturbation theory. The induced birefringence can be detected by a delayed probe pulse propagating through the molecular medium after illumination by the pump pulse. In the case of a nonresonant probe, the birefringence is linearly proportional to the mean value of the electronic polarizability of the molecular gas. The birefringence signal is composed of distinct components due to population change and those of rotational, vibrational, and mixed vibrational–rotational origins. This is demonstrated by numerical simulations on Li2 gas. Moreover, the quantum beats contained in the birefringence, as a function of the time delay between the pump and probe pulses, is dominated by the pure rotational motion. Finally, the birefringence is sensitive to the shape of the applied pump pulse and dependent on the spectral phase of the pump pulse.
We have observed short-duration birefringence in CS2{\mathrm{S}}_{2}S2​ vapor 38 and 76 psec after excitation with a mode-locked (\ensuremath{\sim} 5 psec duration) 1.06-\ensuremath{\mu}m glass: Nd3+{\mathrm{Nd}}^{3+}Nd3+ laser pulse. These bursts are attributed to the time evolution of a coherent sum of rotational superposition states.
We show that molecules and nuclei with well-expressed rotational degrees of freedom can be excited by means of a multistep process, initiated by a short and sufficiently strong electromagnetic pulse, into a coherent superposition of rotational states. Properties of a molecule or a nucleus in such a nonstationary state change (quasi-) periodically in time, due to the fact that the energies of the rotational states satisfy (approximately) the rule \ensuremath{\omega}J(J+1). Accordingly, their interaction with an electromagnetic field or with other particles changes (quasi-) periodically in time. A gas of molecules in a coherent state exhibits a (quasi-) periodic change of the refractive index, an effect which has been observed for the case of CS2{\mathrm{CS}}_{2}CS2​ gas at 325 K. The nuclear case does not lead to direct experimental detection, because of its short coherence period.
We have observed the Doppler-free dichroism and birefringence induced by a linearly polarized laser beam (pump beam) by monitoring the polarization and amplitude changes of a weak probe beam through an analyzer. The effects have been observed in two-level systems and also in three-level systems of Ne I. At rather low pump power, a typical refractive-index anisotropy of 10−8 has been measured. We have shown that, when the normal resonance curve exhibits a broad background due to collisions, our method allows the elimination of this background. In addition, using a rotating analyzer, we have obtained simultaneously the dichroism and birefringence curves, i.e., the imaginary and real part of the anisotropic-induced susceptibility.
A great variety of coherent transient processes in atomic and molecular gases is investigated. The degeneracy with respect to magnetic sublevels, which is typical of working levels of atomic and molecular transitions in gases, leads to new phenomena. In particular, the non-Faraday rotation of the coherent-response polarization vector at the 0 ↔ 1 transition is investigated in the presence of the longitudinal magnetic field in the 174 Yb vapor for both photon echo and stimulated photon echo. A specific relaxation channel that involves the depolarizing collisions emerges in a gas due to the degeneracy of working levels. Such collisions are especially important for atoms and are also observed in molecules. The anisotropy of the depolarizing collisions leads to a new phenomenon of the collision photon echo, which is experimentally demonstrated for the 0 ↔ 1 transition in the 174 Yb mixtures with atomic buffers. The velocity-dependent relaxation rates are observed for various coherent phenomena in molecular gases. The coherent control of a few coherent transient processes is implemented.
By means of a time-resolved microwave spectroscopy experiment using the Stark switching technique, the authors have pointed out an exchange of rotational coherence from a level pair (a-a') of an A molecule to a level pair (b-b') of a B molecule in a gas at low pressure. The experiment exploits the linear Stark effect of the (a-a') line, the frequency of which is successively switched on resonance with the applied CW field to bring a coherence on the (a-a') level pair or with the (b-b') line frequency which is Stark insensitive and always off resonance with the applied CW field. The coherence exchange efficiency is maximum when the two line frequencies (a-a') and (b-b') are switched in exact resonance during a time around the transverse relaxation time T2. The radiation trapping effects are calculated and explain fairly well the experimental results obtained in a long cell. The collisional effects are shown to give a contribution which differs from the previous one only by its phase and its cell-length dependence. An experiment in a short cell is exploited to give a tentative upper limit for the collisional coherence transfers.