Field-free long-lived alignment of molecules with a two-dimensional optical centrifuge

We introduce an optical tool—a “two-dimensional optical centrifuge”—capable of aligning molecules in extreme rotational states. The alignment is studied in oxygen under ambient conditions, and in a cold jet of nitrogen. Unlike the conventional centrifuge, which confines the molecules in the plane of their rotation, its two-dimensional version aligns the molecules along a well-defined axis, similar to the effect of a single linearly polarized laser pulse, but at a much higher level of rotational excitation. We observe long lifetimes of the created alignment due to the increased robustness of ultrahigh rotational states with respect to collisions. The adiabatic nature of the centrifuge excitation provides a means of generating stationary aligned states.

Figure 1

(a) Illustration of the concept of a “two-dimensional (2D) centrifuge.” The three-dimensional corkscrew-shaped surface represents the field of a conventional “3D centrifuge,” propagating from right to left. Shown in blue is the field of a 2D centrifuge, created by passing the 3D centrifuge through a linear polarizer. (b) Scheme of the experimental setup for Raman spectroscopy and the detection of the centrifuge-induced optical birefringence. ${\mathrm{O}}_2$ molecules are rotationally excited by a pump beam (thick red line) focused by a focusing lens (FL) in the middle of a gas cell (black circle). Probe pulses are delayed with respect to the pump pulses, and either directed collinearly with the pump beam by means of a dichroic mirror (DM) or sent perpendicularly to it (thin blue and dashed green lines, respectively). In the longitudinal or transverse geometry, the probe light is used to image the interaction region onto an input slit of a spectrometer (Spe) or a charge-coupled device camera (CCD), respectively, with an imaging lens (IL). Linear polarizers (LP) and quarter-wave plates are used to create different combinations of linear and circular polarizers and analyzers, as described in the text. A typical image of the cloud of centrifuged molecules is shown in the lower right corner, with a horizontal bar representing the distance of $200\mu \mathrm{m}$.

Figure 2

(a) Rotational Raman spectra of the centrifuged oxygen molecules at room temperature and atmospheric pressure recorded with a linearly polarized probe light. From top to bottom, the spectra correspond to the excitation by a single femtosecond pulse (black), a “truncated” (see text) 2D centrifuge (green), a full 2D centrifuge (red), and a full 3D centrifuge (blue) with a terminal rotational frequency around 10 THz. The spectra have been recorded at the delay times of 400 ps. (b) Rotational Raman spectra of the centrifuged oxygen molecules recorded with a circularly polarized probe light. Upper red and lower blue curves correspond to the 2D and 3D centrifuge, respectively. The spectra have been recorded at the delay time of 400 ps.

Figure 3

Simulated molecular distribution after the rotational excitation by a 2D (a) and a 3D (b) optical centrifuge, propagating along the $\widehat{x}$ axis. See text for details.

Figure 4

Decay of the permanent birefringence of the rotationally excited oxygen gas at room temperature and atmospheric pressure in $yz$ (a) and $xz$ (b) planes. Red diamonds and blue circles correspond to the excitation by a 2D and a 3D centrifuge, respectively. Incident probe polarization, shown by the black arrow, is at 45 deg to $\widehat{z}$. The calculated distributions of molecular axes are shown to illustrate the anticipated linear anisotropy for each case. (c) Comparison of the birefringence decay for the 2D centrifuge with a full spectral bandwidth of 20 THz (red diamonds) and with its bandwidth truncated at $\approx 10\mathrm{THz}$ (purple triangles) and $\lesssim 5\mathrm{THz}$ (green squares). Black circles represent the case of a 1D kick. In all plots, solid lines show the fits by exponential decays.

Figure 5

(a) VMI setup, used for measuring the degree of molecular alignment of ${\mathrm{N}}_2$, induced by a 2D centrifuge. See text for details. Ion images of nitrogen molecules prior to any rotational excitation (b), and following the excitation by a 3D (c) and a 2D (d) centrifuge. Calculated molecular distributions are shown above the respective images.

Figure 6

(a) Definition of the spherical coordinates $(r,\theta ,\varphi )$ and polar coordinates $(R,\mathrm{\Theta })$ used to describe the full molecular distribution and its two-dimensional projection on the $\left(xz\right)$ plane of the ion detector. (b) $R$ dependence of the extracted alignment factor, with the shaded region indicating the experimental error. (c) Ion image of ${\mathrm{N}}_2$ molecules aligned with a 2D optical centrifuge. The black dotted and white dashed lines show the circular cross sections at the radius of a maximum ion signal $R=R_{\text{max}}$, and the bigger radius used for estimating the true two-dimensional alignment factor, respectively. The latter is also marked by the red dashed line in (b).