Dian-Jiun Han

Transient compression of a MOT and high intensity fluorescent imaging of optically thick clouds of atoms

Abstract We describe a way to compress Cs atoms in a MOT to temporarily reach spatial densities of 10 12 atoms/cm 3 . The method entails starting off with more atoms than will ultimately be used, and then changing parameters so the atoms rush toward the trap center. For some time during the compression, collisional losses at the center are more than offset by newly arriving atoms. We monitor the compression with a high intensity fluorescent technique that is well suited to providing accurate number and density measurements for large dimension clouds that are very optically thick.

Phase shifting interferometry of cold atoms

We propose a scheme to engage phase shifting interferometry on cold atomic samples and present the simulation results under several experimentally achievable conditions nowadays. This method allows far-detuning, low power probing, and is intrinsically nondestructive. This novel detection means yields image quality superior to the conventional phase contrast imaging at certain conditions and could be experimentally realized. Furthermore, the longitudinal resolution of imaging by this manner is mainly set by optical interference and can be better than the diffraction limit. This scheme also provides special advantages to diagnose the surface-trapped clouds, with which phase imaging on the fabricated wires and atoms altogether is possible as well.

Observation of large group index enhancement in Doppler-broadened rubidium vapor

We report experimental observation of large group index across the Lamb dips of ground hyperfine states in Doppler-broadened 87Rb vapor. By sweeping the laser frequency through each hyperfine transition we measure the saturated absorption and optical phase shift using a phase-locked Mach-Zehnder interferometer. Our measurements provide a direct demonstration of the theoretical prediction by Agarwal et al. [G. S. Agarwal and T. N. Dey, Phys. Rev. A 68, 063816, (2003)] for the first time. An enhancement factor as large as 1005 in group index was observed for Rb vapor at temperature of 85 °C. The experimental data are in good agreement with the theory.

Real-Time Phase Difference Control of Optical Beams Using a Mach-Zehnder Interferometer

We present an experimental scheme for fast phase difference control of optical beams based on a simple, however robust setup of Mach–Zehnder interferometer. We demonstrate to smoothly tune the relative phase by 140° in 275 ms, with an average peak-to-peak phase difference jitter less than 0.9°. The overall achievable tuning range, both for continuous and stepwise scans, can be more than 320°. This scheme is totally immune to intensity fluctuation and allows to engage the conventional phase-shifting imaging. It is especially suitable for real-time configuration control of 2D and 3D optical lattice potentials to study the tunneling and transport effects on cold atomic samples.

Lens-free phase shifting imaging for cold atoms

We propose a lens-free nondestructive imaging method for cold atomic clouds using a Gaussian beam accompanied with phase shifting interferometry. This scheme requires no imaging lens. Hence, aberrations associated with it are completely eliminated and mechanical focusing can be avoided. Compared with the common single-beam nondestructive means, our proposed scheme lowers the energy per probe pulse delivered to the cold samples by almost three orders of magnitude, due to signal enhancement inherently provided in the two-beam configuration. Moreover, higher image resolution is attainable by magnifying the far-field interference distribution using a divergent Gaussian beam. We examine this novel lensless detection means for in situ imaging on typical cold atomic clouds under experimentally achievable conditions. Our simulations show the cloud position can be precisely determined, depending upon the cloud size and probe parameters, with an uncertainty from a few hundreds of micrometers to only a few micrometers, and the spatial resolution of the retrieved phase image can reach the diffraction limit.

Coherent signal amplification of refractive index spectrum in rubidium vapor using phase-shifting interferometry

We have experimentally demonstrated a general method to perform high-precision refractive index spectrum measurement using phase-shifting interferometry in a phase-tunable Mach–Zehnder interferometer. We observed coherent amplification on the refractive spectrum, across the Lamb dips of ground hyperfine states in a Doppler-broadened Rb87 vapor. Most importantly, the spectrum still has a large signal-to-noise ratio when the probe power is in the dark light level under which the method using a single interferogram fails. This experimental scheme is efficient for refractive spectrum measurements and could be extended for 2D phase imaging. It provides many potential applications for optical phase measurements in linear, nonlinear, and quantum optics.

Nondestructive lensless imaging on cold rubidium atoms

We report experimental realization of lensless imaging on cold rubidium atoms confined in a magneto-optical trap. This imaging scheme relies on the off-resonant light refraction from the cold atoms and is employed in a phase-tunable Mach–Zehnder interferometer, accompanied with phase-shifting interferometry. With this setup, it allows obtaining the probe light phase distribution in the far field after passing the atoms, from which the near-field phase image of the atomic cloud is retrieved using the Fresnel–Kirchhoff integral. We show the phase images can be effectively reconstructed, and the measured two-dimensional phase distributions are in good agreement with the theory.

Manipulation of coherent atom waves using accelerated two-dimensional optical lattices

We study the dynamics of Bose–Einstein condensates in accelerated two-dimensional (2D) optical square lattices by numerically solving the Gross–Pitaevskii equation. We consider the regime with negligible mean-field interactions and examine in detail the pulses of atom clouds ejected from the condensate due to Landau–Zener tunnelling. The pulses exhibit patterned structures that can be understood from the momentum–space dynamics of the condensate. Apart from conceiving the realization of a pulsed 2D atom laser, we demonstrate that, by exploring the band structure of the lattice, the Landau–Zener tunnelling and Bragg reflection of the condensate inside the optical lattice can provide a means of manipulation of coherent atom waves.

An adaptive multigrid scheme for Bose-Einstein condensates in a periodic potential

We present a novel multigrid-continuation method for treating parameter-dependent problems. The proposed algorithm which can be flexibly implemented is a generalization of the two-grid discretization schemes [C.-S. Chien, B.-W. Jeng, A two-grid discretization scheme for semilinear elliptic eigenvalue problems, SIAM J. Sci. Comput. 27 (2006) 1287-1304]. That is, approximating points on a solution curve do not necessarily lie on the same fine grid. We apply the algorithm to compute energy levels and superfluid densities of Bose-Einstein condensates (BEC) in a periodic potential. Both positive and negative scattering lengths are considered in our numerical experiments. For positive scattering length, if the chemical potential is large enough, and the domain is properly chosen, the results show that the number of peaks of the first few energy states of the 2D BEC in a periodic potential depends on the wave number of the periodic potential. Moreover, for bright solitons the number of peaks of the ground state solutions is (1d-1)^2 and (1d)^2, where the periodic potential is expressed in terms of the sine or the cosine functions, respectively. However, these formulae do not hold if the scattering length is negative. The numerical study is extended to the two-component, 1D and 2D BEC in a periodic potential.

A controllable double-well magneto-optical trap for Rb and Cs atoms

We experimentally demonstrate a novel scheme to simultaneously confine two atomic species of (87)Rb and (133)Cs with adjustable spatial separation by a controllable double-well magneto-optic trap. Using a single-loop wire and a magnetic bias field, the two clouds, each containing more than 1 x 10(6) atoms, are spatially separated above and below the wire center of the double-well MOT. The cloud interdistance can be controlled by independently varying the wire current and external bias field. This allows to load the double-well magnetic trap, and to study the dynamics of cold collisions between two-species atoms.