Absolute absorption spectroscopy based on molecule interferometry

We propose a method to measure the absolute photon absorption cross section of neutral molecules in a molecular beam. It is independent of our knowledge of the particle beam density, nor does it rely on photoinduced fragmentation or ionization. The method is based on resolving the recoil resulting from photon absorption by means of near-field matter-wave interference, and it thus applies even to very dilute beams with low optical densities. Our discussion includes the possibility of internal state conversion as well as fluorescence. We assess the influence of various experimental uncertainties and show that the measurement of absolute absorption cross sections is conceivable with high precision and using existing technologies.

Figure 1

Setup of the proposed measurement scheme. The molecular beam enters from the left through a material grating, and the transmitted molecules are counted after passing the grating mask on the right-hand side. In the center, a standing light field created by the grating laser serves as a diffraction element for near-field Talbot-Lau interference of the molecular matter waves. When the molecules pass the recoil laser beam they may absorb an integer number of photons, thus effecting a probabilistic modification of the interference pattern. For an appropriate choice of the distance $D$, the nanostructured, periodic form of the interference pattern thus enables a robust and precise extraction of the molecular absorption cross section by observing how the quantum interference contrast reduces as a function of the recoil laser power.

Figure 2

Effect of a half-period recoil shift on the interference signal of a TLI setup composed of three metallic gratings with a period of $991\mathrm{nm}$ and an open fraction of $f=1∕5$, implying a slit width of $a=198.2\mathrm{nm}$. The plots show the expected signal as a function of the transverse position of the third grating, normalized to the flux of the molecular beam entering the interferometer. The dashed line in panel (a) shows the peaked fringe pattern for tetraphenylporphyrin $\left({\mathrm{H}}_2\mathrm{TPP}\right)$ molecules passing the interferometer at fixed velocity of $175\mathrm{m}∕\mathrm{s}$. It is changed to the solid line by a $420\mathrm{nm}$ recoil laser of $0.5\mathrm{W}$ power that shifts the pattern by half a period per absorbed photon. Panel (b) shows an analogous situation, where the molecular beam displays a Gaussian velocity distribution centered at ${\overline{v}}_z=175\mathrm{m}∕\mathrm{s}$ with a relative width of $\Delta v∕{\overline{v}}_z=5\%$.

Figure 3

Monte Carlo simulation of the proposed measurement of the absorption cross section of ${\mathrm{H}}_2\mathrm{TPP}$ at $420\mathrm{nm}$ (see text). The results (including error bars at a 95% confidence level) are plotted versus the relative width $\Delta v_z∕{\overline{v}}_z$ of a Gaussian velocity distribution of the molecules underlying the simulation. The dotted line marks the true value of the absorption cross section ${\sigma }_{\mathrm{abs}}=15{\mathrm{\AA }}^2$ [33]. It is well reproduced by the simulated measurement for velocity spreads below 10%.

Figure 4

Influence of fluorescence on the KDTLI contrast reduction by the recoil laser. The theoretical values of the negative logarithm of the contrast reduction factor (12) are plotted versus the power of the recoil laser for ${\mathrm{H}}_2\mathrm{TPP}$ molecules at $v_z=175\mathrm{m}∕\mathrm{s}$, with all experimental parameters the same as in Fig. 3. The solid line corresponds to the case without fluorescence, $P_{\mathrm{fluo}}=0$, while the dashed line represents the case of a realistic quantum yield $P_{\mathrm{fluo}}=11\%$ and the dotted line corresponds to maximally possible value $P_{\mathrm{fluo}}=100\%$.