Coherent Radiative Decay of Molecular Rotations: A Comparative Study of Terahertz-Oriented versus Optically Aligned Molecular Ensembles

The decay of field-free rotational dynamics is experimentally studied by two complementary methods: laser-induced molecular alignment and terahertz-field-induced molecular orientation. A comparison between the decay rates of different molecular species at various gas pressures reveals that oriented molecular ensembles decay faster than aligned ensembles. The discrepancy in decay rates is attributed to the coherent radiation emitted by the transiently oriented ensembles and is absent from aligned molecules. The experimental results reveal the dramatic contribution of coherent radiative emission to the observed decay of rotational dynamics and underline a general phenomenon expected whenever field-free coherent dipole oscillations are induced.

Figure 1

Representative experimental data for ${\mathrm{CH}}_3\mathrm{I}$ at the pressure of 20 torr measured in the (a) time-resolved birefringence setup and (b) time-resolved terahertz emission setup. The revival period of ${\mathrm{CH}}_3\mathrm{I}$ is $T_{\mathrm{rev}}=66.7\mathrm{ps}$ ($B=0.25{\mathrm{cm}}^{-1}$). Birefringence modulations are observed twice in each period (separated by $T_{\mathrm{rev}}/2$), while the terahertz emission events occur only at integer revival times. Strong centrifugal distortion of ${\mathrm{CH}}_3\mathrm{I}$ results in “signal smearing” transforming the nearly single oscillation observed at the $1/2T_{\mathrm{rev}}$ [in (a)] and at $1T_{\mathrm{rev}}$ [in (b)] to multiple oscillations at $4T_{\mathrm{rev}}$ as depicted in both figures. Note the change in the birefringence background signal [enlarged inset in (a)] due to the nonthermal rotational population that is induced by the optical pulse. An artifact birefringence signal arising from the overlap of the pump and probe pulses in the cell window (marked “Window”) is also observed in the vicinity of the zero time.

Figure 2

Simulated alignment dynamics for OCS at 300 K and signal decay analysis using the two metric schemes. (a) Time-dependent change ($\mathrm{\Delta }⟨{\cos }^2\theta ⟩=⟨{\cos }^2\theta ⟩-1/3$) in alignment following an interaction with an ultrashort laser pulse. The observed decrease in signal amplitudes and changes in the signal shape result from centrifugal distortion. (b) The same simulation as in (a) multiplied by an exponential decay $\exp (-\gamma t)$ with $\gamma =0.002{\mathrm{ps}}^{-1}$. (c) An analysis of the signal in (a) using both metrics retrieves $\gamma =0$ (no decay). (d) An analysis of the decaying signal in (b) retrieves the correct decay values of $\gamma =4\times {10}^{-3}{\mathrm{ps}}^{-1}$ (metric 1) and $\gamma =2\times {10}^{-3}{\mathrm{ps}}^{-1}$ (metric 2) as expected, since metric 1 integrates over the square of the time-domain signal while metric 2 integrates over the fundamental frequency amplitudes following the Fourier transformation of the simulated time-domain signal.

Figure 3

Experimental decay rates of field-free alignment (red triangles) and orientation (blue circles) as a function of sample pressure measured for three molecular gases (a) ${\mathrm{N}}_2\mathrm{O}$, (b) OCS, and (c) ${\mathrm{CH}}_3\mathrm{I}$. The pressure-dependent decay rates of the alignment and orientation dynamics were fitted by a linear curve and yielded the slopes noted in the figures (for the fit details, see [17]). All of the measurements were performed in a 10 cm long static gas cell at the ambient temperature of the lab (295 K).

Figure 4

Simulated responses of a thermal ensemble of linear molecules excited by a single cycle terahertz field with ${\omega }_0=0.6\mathrm{THz}$, $\mathrm{FWHM}=1.5\mathrm{ps}$ with a Gaussian time envelope. We simulated for $B=0.7{\mathrm{cm}}^{-1}$, $D=3.5\times {10}^{-6}{\mathrm{cm}}^{-1}$ at the temperature of 150 K to span a transition bandwidth comparable to that of OCS at 300 K but with sparser frequencies for the sake of a clearer graphical presentation. (a) Field-free orientation with the typical (red) and (b) the modified (blue) Hamiltonian. (c),(d) Decay analysis of (a),(b), respectively, using metric 1. Note that time is given in units of the revival period ($T_{\mathrm{rev}}$).