A high phase-space-density gas of polar molecules.

A quantum gas of ultracold polar molecules, with long-range and anisotropic interactions, not only would enable explorations of a large class of many-body physics phenomena but also could be used for quantum information processing. We report on the creation of an ultracold dense gas of potassium-rubidium (40K87Rb) polar molecules. Using a single step of STIRAP (stimulated Raman adiabatic passage) with two-frequency laser irradiation, we coherently transfer extremely weakly bound KRb molecules to the rovibrational ground state of either the triplet or the singlet electronic ground molecular potential. The polar molecular gas has a peak density of 10(12) per cubic centimeter and an expansion-determined translational temperature of 350 nanokelvin. The polar molecules have a permanent electric dipole moment, which we measure with Stark spectroscopy to be 0.052(2) Debye (1 Debye = 3.336 x 10(-30) coulomb-meters) for the triplet rovibrational ground state and 0.566(17) Debye for the singlet rovibrational ground state.

Flatland optics. III. Achromatic diffraction.

In the previous two sections of "Flatland optics" [J. Opt. Soc. Am. A 17, 1755 (2000); 18, 1056 (2001)] we described the basic principles of two-dimensional (2D) optics and showed that a wavelength lambda in three-dimensional (3D) space (x, y, z) may appear in Flatland (x, z) as a wave with another wavelength Lambda=lambda/cos alpha. The tilt angle alpha can be modified by a 3D-Spaceland individual, who then is able to influence the 2D optics in a way that must appear to be magical to 2D-Flatland individuals-in the spirit of E. A. Abbott's science fiction story of 1884 [Flatland, a Romance of Many Dimensions, 6th ed. (Dover, New York, 1952)]. Here we show how the light from a white source can be perceived in Flatland as perfectly monochromatic, so diffraction with white light will be free of color blurring and the contrast of interference fringes can be 100%. The basic considerations for perfectly achromatic diffraction are presented, along with experimental illustration of Talbot self-imaging performed with broadband illumination.

Flatland optics. II. Basic experiments.

In "Flatland optics: fundamentals" [J. Opt. Soc. Am. A 17, 1755 (2000)] we described the basic principles of two-dimensional (2D) optics and showed that a wavelength lambda in three-dimensional (3D) space (x,y,z) may appear in Flatland (x,z) as a wave with another wavelength, lambda = lambda/cosalpha. The tilt angle alpha can be modified by a 3D (Spaceland) individual who then is able to influence the 2D optics in a way that must appear to be magical to 2D Flatland individuals-in the spirit of E. A. Abbott's science fiction story [Flatland, a Romance of Many Dimensions, 6th ed. (Dover, New York, 1952)] of 1884. We now want to establish the reality or objectivity of the 2D wavelength lambda by some basic experiments similar to those that demonstrated roughly 200 years ago the wave nature of light. Specifically, we describe how to measure the 2D wavelength lambda by mean of five different arrangements that involve Young's biprism configuration, Talbot's self-imaging effect, measuring the focal length of a Fresnel zone plate, and letting light be diffracted by a double slit and by a grating. We also performed experiments with most of these arrangements. The results reveal that the theoretical wavelength, as predicted by our Flatland optics theory, does indeed coincide with the wavelength lambda as measured by Flatland experiments. Finally, we present an alternative way to understand Flatland optics in the spatial frequency domains of Flatland and Spaceland.

Wigner formulation of optical processing with light of arbitrary coherence.

A unified mathematical formulation for designing and analyzing even the most general optical processor is presented. It exploits the Wigner distribution function to characterize the illumination, the input, the inherent filter, and the output results. To characterize the propagation of the light through the optical processor setup, we exploit the Wigner matrix formalism, which is appealing because it allows simple geometric analysis. The Wigner distribution function was extended to include illumination of arbitrary coherence so that processors using either coherent light or partially coherent light can be designed and analyzed with the same Wigner formalism. The basic principles, design, and analysis of the imaging and Fourier-transform operations and use of the Wigner formalism to evaluate the performance and tolerances of optical processors are presented.

Flatland optics: fundamentals.

"Flatland" is the title of a 120-year-old science fiction story. It describes the life of creatures living in a two-dimensional (2D) Flatland. A superior creature living in the three-dimensional (3D) spaceland, as we do, can easily inspect, for example, the inside of a Flatland house, as well as the content of a flat man's stomach without leaving any trace. Furthermore, the 3D person has supernatural powers that enable him to change the laws of physics in Flatland. We present here the concept of a 2D Flatland optics with one transversal coordinate x and one longitudinal coordinate z. The other transversal coordinate y allows total inspection of Flatland optics, and the freedom to change the wavelength, without using something like nonlinear optics or a Doppler shift. Monochromatic 3D light can be converted reversibly into polychromatic 2D light. A large variety of 2D systems and 2D effects will be presented here and in follow-up contributions. An epilogue faces the question, how "real" is Flatland optics?

General linear optical coordinate tranformations.

New optical configurations for performing general coordinate transformation operations of shear, rotation, and their combination are presented. These configurations consist of refractive spherical and cylindrical lenses that are readily available. Typically, high-resolution imagery can be obtained, depending on the size of the input object, the illumination wavelength, and the f-number of the lenses. Basic and more general configurations are presented, along with experimental results clearly showing image shearing, rotation, and a combination of these with high-quality output imagery.

Apochromatic optical correlation.

Optical correlation, or matched filtering, can now be applied more widely than before, because the light is now allowed to be totally incoherent, spatially and spectrally. Two such correlators were demonstrated recently. Their state of chromatic correction can be called achromatic, since the scaling error has two zero crossings within the visible range of wavelengths. We present a new apochromatic correlator, in which the scaling error has three zero crossings. The maximum error and the rms error are reduced by a factor of 5. Our apochromatic correlator is composed of two highly dispersive heavy flint lenses that are in contact with two diffractive lenses and two chromatic corrected refractive lenses. The uncommon combination of flint dispersion and diffractive dispersion enabled us to achieve apochromatic correction of the scaling factor of the correlator.

Optical correlation with totally incoherent light.

An optical correlator that can operate with totally incoherent light is presented. Such a correlator can be designed to compensate completely for the inherent chromatic aberrations by resorting to elements with specialized, possibly impractical, dispersion characteristics. Nevertheless, a practical configuration that exploits available achromatic lenses and Fresnel zone plates was designed, built, and tested experimentally. The results reveal that detectable correlation peaks can be obtained with totally incoherent white light. The designs, experimental procedures, and results are presented.