D. J. Heinzen

Interisotope Determination of Ultracold Rubidium Interactions from Three High-Precision Experiments

Combining the measured binding energies of four of the most weakly bound rovibrational levels of the 87Rb2 molecule with results of two other recent high-precision experiments, we obtain exceptionally strong constraints on the atomic interaction parameters in a highly model independent analysis. The comparison of (85)Rb and (87)Rb data, where the two isotopes are related by a mass scaling procedure, plays a crucial role. We predict scattering lengths, clock shifts, and Feshbach resonances with an unprecedented level of accuracy. Two of the Feshbach resonances occur at easily accessible magnetic fields in mixed-spin channels. One is related to a d-wave shape resonance.

Spin relaxation of optically trapped atoms by light scattering

We study spin relaxation of optically trapped atoms that is due to light scattering from the trap laser. We observe relaxation times greater than 2 s for ground-state hyperfine-level populations of 85Rb atoms trapped in an optical dipole force trap operating as much as 65 nm to the red of the D1 line. The measured relaxation rate can be more than 100 times slower than the atoms’ total spontaneous scatter rate from the trap laser. This enhancement in atomic ground-state lifetime is due to an interference effect in spontaneous Raman scattering far from atomic resonance.

High-precision laser beam shaping using a binary-amplitude spatial light modulator

We have achieved high-precision laser beam shaping by using a binary-amplitude spatial light modulator, a digital micromirror device (DMD), followed by an imaging telescope that contains a pinhole low-pass filter (LPF). An error diffusion algorithm was used to design the initial DMD pixel pattern based on the measured input beam profile. This pattern was iteratively refined by simulating the optically low-pass filtered DMD image and changing DMD pixels to lift valleys and suppress peaks. We noted the gap between the experimental result of 1.4% root-mean-square (RMS) error and the simulated result for the same DMD pattern of 0.3% RMS error. Therefore, we deemed it necessary to introduce iterative refinement based on actual measurements of the output image to further improve the uniformity of the beam. Using this method, we have demonstrated the ability to shape raw, non-spatially filtered laser beams (quasi-Gaussian beams) into beams with precisely controlled profiles that have an unprecedented level of RMS error with respect to the target profile. We have shown that our iterative refinement process is able to improve the light intensity uniformity to around 1% RMS error in a raw camera image for both 633 and 1064 nm laser beams. The use of a digital LPF on the camera image is justified in that it matches the performance of the pinhole filter in the experimental setup. The digital low-pass filtered results reveal that the actual optical beam profiles have RMS error down to 0.23%. Our approach has also demonstrated the ability to produce a range of target profiles as long as they have similar spatial-frequency content (i.e., a slowly varying beam profile). Circular and square cross-section flat-top beams and beams with a linear intensity variation within a circular and square cross section were produced with similarly low RMS errors. The measured errors were about twice the ultimate limit of 0.1% RMS error based on the number of binary DMD pixels that participate in the beam-formation process.

1.5% root-mean-square flat-intensity laser beam formed using a binary-amplitude spatial light modulator

We demonstrate a digital micromirror device (DMD)-based optical system that converts a spatially noisy quasi-Gaussian to an eighth-order super-Lorentzian flat-top beam. We use an error-diffusion algorithm to design the binary pattern for the Texas Instruments DLP device. Following the DMD, a telescope with a pinhole low-pass filters the beam and scales it to the desired sized image. Experimental measurements show a 1% root-mean-square (RMS) flatness over a diameter of 0.28 mm in the center of the flat-top beam and better than 1.5% RMS flatness over its entire 1.43 mm diameter. The power conversion efficiency is 37%. We develop an alignment technique to ensure that the DMD pattern is correctly positioned on the incident beam. An interferometric measurement of the DMD surface flatness shows that phase uniformity is maintained in the output beam. Our approach is highly flexible and is able to produce not only flat-top beams with different parameters, but also any slowly varying target beam shape. It can be used to generate the homogeneous optical lattice required for Bose-Einstein condensate cold atom experiments.

Observation of the saturation effect in continuous-wave coherent anti-Stokes Raman spectroscopy of liquid nitrogen

We report the first observation to our knowledge of the saturation effect in a Raman transition of a liquid, liquid N2. Using cw coherent anti-Stokes Raman spectroscopy, Raman line broadening by a factor of ≃2 is observed. This corresponds to vibrational excitation of up to 30% of the N2 molecules in the interaction volume.

Bragg spectroscopy of a superfluid Bose-Hubbard gas

Bragg spectroscopy is used to measure the excitations of a trapped, quantum-degenerate gas of 87Rb atoms in a three-dimensional (3D) optical lattice. The measurements are carried out over a range of optical lattice depths in the superfluid phase of the Bose?Hubbard model. For a fixed wavevector, the resonant frequency of the excitation is found to decrease with increasing lattice depth. A numerical calculation of the resonant frequencies based on Bogoliubov theory shows a less steep rate of decrease than the measurements.

Photoassociation of 85Rb atoms into 0u+ states near the 5S+5P atomic limits

New photoassociation data on the 0u+ levels of Rb2 below the 5S+5P1/2 limit are combined with older data (Cline et al 1994 Phys. Rev. Lett. 73 632) in a fit to potentials and spin–orbit functions. The P1/2 data exhibit oscillations in the B(v) values due to coupling between the two 0u+ series, as modelled accurately by a coupled potentials approach. The fitted value for the C3 dispersion parameter from the combined data agrees well with the value derived from the pure long-range 0g− state.

Time-independent and time-dependent photoassociation of spin-polarized rubidium

We extract information about collisions of ultra-cold ground-state rubidium atoms from observations of a g-wave shape resonance in the 85Rb + 85Rb system via time-independent and time-dependent photoassociation. The shape resonance arises from a quasi-bound state inside a centrifugal barrier that enhances the excitation to the bound electronically excited state by the photoassociation laser in the time-independent experiment. The shape resonance is sufficiently long-lived that its build-up through the barrier can be observed by first depleting it via a photoassociation laser pulse and then measuring the rate of photoassociation by a second laser pulse with a variable delay time. A combined method of analysis of the time-independent and time- dependent experiments is presented. We discuss the spectroscopy of states of two particles with spin trapped inside a centrifugal barrier, interacting via direct and indirect spin-spin interactions.

Grayscale laser image formation using a programmable binary mask

Abstract. We present grayscale laser image formation from a programmable binary mask using a digital micromirror device (DMD) followed by a telescope with an adjustable pinhole low-pass filter. System performance was measured by comparing the intensity conformity with respect to the target image and by the energy conversion efficiency. A theoretical analysis of image precision proved high-precision image formation and inspired the iterative pattern refinement process based on the point spread function of a single DMD pixel to seek optimized image quality. We derived the diffraction efficiency formula of the DMD and discussed the overall system energy efficiency with operation wavelengths. Actual image precision performance was evaluated by measuring the root-mean-square (RMS) error of a series of sinusoidal-flattop profiles with different system bandwidths. We produced grayscale laser images with different spatial spectral content using intensity profiles of Laguerre-Gaussian, Hermite-Gaussian, and Lena-flattop beams. Measured RMS errors of all examples of various bandwidths were consistent with the image precision of the sinusoidal reference patterns. The ripple effect caused by the sharp-edged pinhole was the major contributor to the residual error in the output images. Error histograms had a zero-mean Gaussian distribution with standard deviation equal to the value of the RMS error.

High-precision laser beam shaping using binary-amplitude DLP spatial light modulators

Laser beams with precisely controlled intensity profiles are essential for many areas of optics and optical physics. We create such beams from real-world lasers: quasi-Gaussian beams obtained directly from a laser and beam-expanding telescope without spatial filtering. Our application is to form optical standing-wave lattices for Bose-Einstein condensates in quantum emulators. This requires controlled amplitude and flat phase, and that the beam be free of temporal modulation from either pixel dithering or refresh cycles. We describe the development of the pattern design algorithms and demonstrate the performance of a high precision beam shaper to make flattop beams and other spatial profiles with similarly low spatial frequency content. The digital micromirror device (DMD) was imaged through a telescope containing a pinhole low-pass filter. An error diffusion algorithm was used to design the initial DMD pixel pattern based on the input beam profile. This pattern was iteratively refined based on output image measurements. We demonstrate forming a variety of beam profiles including flattop beams and beams with 1-D linear intensity variation, both with square and circular cross-sections. Produced beams had less than 0.25% root-mean-square (RMS) error with respect to the target profile and nearly flat phase.