Two-Pulse Field-Free Orientation Reveals Anisotropy of Molecular Shape Resonance

We report the observation of macroscopic field-free orientation, i.e., more than 73% of CO molecules pointing in the same direction. This is achieved through an all-optical scheme operating at high particle densities ($>10^{17}{\mathrm{cm}}^{-3}$) that combines one-color ($\omega$) and two-color ($\omega +2\omega$) nonresonant femtosecond laser pulses. We show that the achieved orientation solely relies on the hyperpolarizability interaction as opposed to an ionization-depletion mechanism, thus, opening a wide range of applications. The achieved strong orientation enables us to reveal the molecular-frame anisotropies of the photorecombination amplitudes and phases caused by a shape resonance. The resonance appears as a local maximum in the even-harmonic emission around 28 eV. In contrast, the odd-harmonic emission is suppressed in this spectral region through the combined effects of an asymmetric photorecombination phase and a subcycle Stark effect, generic for polar molecules, that we experimentally identify.

Figure 1

(a) Experimental setup for high-harmonic spectroscopy of molecules oriented with the two-pulse scheme. Calculated time evolution of (b) $⟨\cos \theta ⟩$ for CO oriented by a single two-color laser pulse and of (c) $⟨{\cos }^2\theta ⟩$ for CO aligned by a single one-color laser pulse. The contributions of rotational levels with even or odd angular momentum quantum number ($J$) and their sum are shown separately in both panels.

Figure 2

(a) High-harmonic spectrum of CO [$(2.2\pm 0.1)\times 10^{14}\mathrm{W}/{\mathrm{cm}}^2$] oriented by the two-pulse scheme. (b) High-harmonic spectrum of CO oriented by the one-pulse scheme recorded under conditions otherwise identical to the upper spectrum. (c) Variation of the intensity of a representative even harmonic (H18) with pump-probe delay for the two-pulse scheme. The intensity was normalized to the intensity of the next higher odd harmonic (H19) at the delay of maximal orientation. (d) Calculated evolution of $⟨\cos \theta {⟩}^2$ including only the hyperpolarizability mechanism of molecular orientation, only the ionization depletion mechanism, or both mechanisms.

Figure 3

(a) Experimental and calculated even-to-odd ratio. The ratio was calculated with and without taking the Stark phase into account. (b) Oriented axis distribution. (c) Calculated evolution of $⟨{\cos }^2\theta ⟩$. [(d) and (e)] Measured evolution of the odd harmonic intensities as function of the pump-probe delay. The time of maximal alignment is marked with an arrow in the panels (c)–(e).

Figure 4

(a) Molecular-frame photoionization cross section for the HOMO of CO as function of the alignment angle and the harmonic order. (b) Decomposition of the photoionization cross section into partial waves ($\ell =1,2,3$) for parallel alignment of the molecule and differential photoionization cross sections for electron emission from the O side (0°) or the C side (180°) of the molecule. (c) Phase difference $\mathrm{\Delta }\phi$ of high-harmonic emission from the C or O sides of the molecule. (d) Squared magnitude of the sum and difference of the recombination dipoles including the Stark-phase contributions, reflecting the envelope of odd- and even-harmonic spectra, respectively.