Beyond the ABCDs: A better matrix method for geometric optics by using homogeneous coordinates

Geometric optics is often described as tracing the paths of non-diffracting rays through an optical system. In the paraxial limit, ray traces can be calculated using ray transfer matrices (colloquially, ABCD matrices), which are 2x2 matrices acting on the height and slope of the rays. A known limitation of ray transfer matrices is that they only work for optical elements that are centered and normal to the optical axis. In this article, we provide an improved 3x3 matrix method for calculating paraxial ray traces of optical systems that is applicable to how these systems are actually arranged on the optical table: lenses and mirrors in any orientation or position (e.g.~in laboratory coordinates), with the optical path zig-zagging along the table. Using projective duality, we also show how to directly image points through an optical system using a point transfer matrix calculated from the system's ray transfer matrix. We demonstrate the usefulness of these methods with several examples and discuss future directions to expand applications of this technique.Comment: 15 pages, 10 figures. Accepted to American Journal of Physics. Example code available at https://github.com/corcoted/arXiv-2205.09746-code (Rearranged and clarified based on referee comments.

3D Projection Sideband Cooling

We demonstrate 3D microwave projection sideband cooling of trapped, neutral atoms. The technique employs state-dependent potentials that enable microwave photons to drive vibration-number reducing transitions. The particular cooling sequence we employ uses minimal spontaneous emission, and works even for relatively weakly bound atoms. We cool 76% of atoms to their 3D vibrational ground states in a site-resolvable 3D optical lattice.Comment: 5 pages, 4 figures, Supplemental Material included. To appear in Physical Review Letter

Extreme tunability of interactions in a 7^7Li Bose-Einstein condensate

We use a Feshbach resonance to tune the scattering length a of a Bose-Einstein condensate of 7Li in the |F = 1, m_F = 1> state. Using the spatial extent of the trapped condensate we extract a over a range spanning 7 decades from small attractive interactions to extremely strong repulsive interactions. The shallow zero-crossing in the wing of the Feshbach resonance enables the determination of a as small as 0.01 Bohr radii. In this regime, evidence of the weak anisotropic magnetic dipole interaction is obtained by comparison with different trap geometries

Experimental investigation of the asymmetric spectroscopic characteristics of electron- and hole-doped cuprates

Quasiparticle tunneling spectroscopic studies of electron- (n-type) and hole-doped (p-type) cuprates reveal that the pairing symmetry, pseudogap phenomenon and spatial homogeneity of the superconducting order parameter are all non-universal. We compare our studies of p-type YBa2Cu3O7-delta and n-type infinite-layer Sr(0.9)Ln(0.1)CuO(2) (Ln = La, Gd) systems with results from p-type Bi2Sr2CaCu2Ox and n-type one-layer Nd1.85Ce0.15CuO4 cuprates, and attribute various non-universal behavior to different competing orders in p-type and n-type cuprates

All-Optical Production of a Lithium Quantum Gas Using Narrow-Line Laser Cooling

We have used the narrow $2S_{1/2} \rightarrow 3P_{3/2}$ transition in the ultraviolet (uv) to laser cool and magneto-optically trap (MOT) $^6$Li atoms. Laser cooling of lithium is usually performed on the $2S_{1/2} \rightarrow 2P_{3/2}$ (D2) transition, and temperatures of $\sim$300 $\mu$K are typically achieved. The linewidth of the uv transition is seven times narrower than the D2 line, resulting in lower laser cooling temperatures. We demonstrate that a MOT operating on the uv transition reaches temperatures as low as 59 $\mu$K. Furthermore, we find that the light shift of the uv transition in an optical dipole trap at 1070 nm is small and blue-shifted, facilitating efficient loading from the uv MOT. Evaporative cooling of a two spin-state mixture of $^6$Li in the optical trap produces a quantum degenerate Fermi gas with $3 \times 10^{6}$ atoms a total cycle time of only 11 s.Comment: 5 pages, 4 figure

Optical Bragg, atom Bragg and cavity QED detections of quantum phases and excitation spectra of ultracold atoms in bipartite and frustrated optical lattices

Ultracold atoms loaded on optical lattices can provide unprecedented experimental systems for the quantum simulations and manipulations of many quantum phases and quantum phase transitions between these phases. However, so far, how to detect these quantum phases and phase transitions effectively remains an outstanding challenge. In this paper, we will develop a systematic and unified theory of using the optical Bragg scattering, atomic Bragg scattering or cavity QED to detect the ground state and the excitation spectrum of many quantum phases of interacting bosons loaded in bipartite and frustrated optical lattices. We show that the two photon Raman transition processes in the three detection methods not only couple to the density order parameter, but also the {\sl valence bond order} parameter due to the hopping of the bosons on the lattice. This valence bond order coupling is very sensitive to any superfluid order or any Valence bond (VB) order in the quantum phases to be probed. These quantum phases include not only the well known superfluid and Mott insulating phases, but also other important phases such as various kinds of charge density waves (CDW), valence bond solids (VBS), CDW-VBS phases with both CDW and VBS orders unique to frustrated lattices, and also various kinds of supersolids. The physical measurable quantities of the three experiments are the light scattering cross sections, the atom scattered clouds and the cavity leaking photons respectively. We analyze respectively the experimental conditions of the three detection methods to probe these various quantum phases and their corresponding excitation spectra. We also address the effects of a finite temperature and a harmonic trap.Comment: REVTEX4-1, 32 pages, 16.eps figures, to Appear in Annals of Physic