Researchers at the Ernest Orlando Lawrence Berkeley National Laboratory (LBL; Berkeley, CA) are completing a device that they hope will help them find order in quantum chaos. After almost five years of design and development work, the researchers are now within months of completing a soft x-ray interferometer with enough resolution to probe correlated motion between the two electrons in a helium atom that have been excited to high-energy Rydberg states.
At the 65-eV energy level of the Rydberg states, currently available grating-based spectrometers provide a resolving power on the order of 64,000. The Berkeley researchers expect to boost that resolving power to about 1 million by replacing the grating-based spectrometer with a Fourier-transform (FT)-based spectrometer.
"A Fourier-transform-based spectrometer can, in principle, get a much higher resolution than a grating-based spectrometer," said Edward Moler, a research fellow at the Advanced Light Source at LBL. "The challenge in this project is [in achieving] the alignment tolerance." Working with 20-nm x-ray wavelengths calls for alignment tolerances on the scale of a microradian, he said.
The advantage of the FT-based device comes from the fact that resolution is determined by the greatest path-length difference introduced between the beams. For a grating, resolution is related to the distance between the first and last grooves, and for an interferometer, it is a function of the translation of the mirrors. A grating can only subtend a finite angle, but interferometer mirrors can be moved an arbitrary distance, Moler said. The technological challenge for FT devices lies in moving the mirrors over a significant distance while maintaining precise alignment. In the case of the Berkeley device, the significant distance is 1 cm.
"The resolving power is approximately equal to the number of periods in the delay caused by the path-length difference introduced by the spectrometer," Moler said. "For our nominal wavelength target of 20 nm and a desired resolving power of 1 million, we must introduce a path-length difference of 2 cm. Accounting for the geometrical factors of the optical layout, we arrived at the necessity of moving the mirrors linearly by about 1 cm."
System configuration
The device consists of four mirrors on a moving stage and two beamsplitters. One beamsplitter splits the beam into two parts before it enters the mirror assembly. As the split beams emerge from the mirror assembly, the second beamsplitter recombines them coherently.
To meet the requirement for less than a microradian of tilt across a centimeter of translation, mechanical engineer Robert Duarte devised a metal flexure system using a special military steel that could bend the required distance without breaking, cracking, or deforming.
A prototype hydraulic drive system for the mirror stage was chosen initially to provide baseline stick-slip measurements prior to building a sophisticated driver. The prototype was pressed into permanent service, however, after John Spring, a graduate student at San Francisco State University (San Francisco, CA), managed to tweak the stick-slip effects down to the angstrom range on a millisecond time scale, which is at the limit of the system used to measure the stage motion.
The need to split the 5-mm square beam into two parts and then recombine it coherently required a special set of beamsplitters, which were fabricated by the Rocketdyne division of Rockwell (Albuquerque, NM). Each of the beamsplitters was made from a single crystal of silicon (about 24 × 95 mm in area) polished x-ray flat (surface finish less than 2 Å rms and a surface slope error less than 0.5 µrad). Alternating slots (each 2 cm long and 50 µm wide) were etched into the substrate between reflective bars of the same size. After etching, molybdenum was deposited as the optical coating for the required 65 eV reflection energy.
Mirrors are aligned in the assembled device within a tolerance of 0.6 µrad by attaching the lower portion of each mirror to a solid glass prism. A HeNe laser interferometer is used initially to align the beamsplitters within an angular tolerance of about 0.5 millirad and a translational tolerance of a few hundred microns. The required fine tolerances of about 1 µrad angular and 30 µm translational are achieved in a two-step process developed by Scott Locklin, a graduate student at the University of California-Davis (Davis, CA).
The first step uses piezoelectrically driven screws (New Focus; Santa Clara, CA) with linear voltage differential transformers added to gauge translational distance. The second step of making fine angular adjustments of the assembled system—alignment of beamsplitters to each other and to the mirror assembly—is performed with a metal flexure system. The researchers have begun to test and refine the device using visible and UV spectra and hope to have a working soft x-ray spectrometer in a matter of months, Moler said.
Once the system is fully characterized, possible experiments include assessing the behavior of highly correlated electron systems to gain insight into chemical reactions and phenomena such as superconductivity, studying quantum chaos phenomena at high magnetic fields on the order of several Tesla, studying multiple electron excitations of atoms more complex than helium and of atoms in molecules, and performing high-resolution studies of inelastic scattering from solids.
"Once you demonstrate the usefulness of an instrument like this, people will start coming to you with ideas," Duarte said.