A. Kumarakrishnan

A calculation of the time-of-flight distribution of trapped atoms

We consider the ballistic expansion of a cloud of trapped atoms falling under the influence of gravity. Using a simple coordinate transformation, we derive an analytical expression for the time-of-flight signal. The properties of the signal can be used to infer the initial temperature of the cloud. We first assume a point size cloud with an isotropic velocity distribution to explain the physical basis of the calculation. The treatment is then generalized to include a finite-size cloud with an anisotropic velocity distribution, and an exact result for the signal is derived. The properties of the signal are discussed, and an intuitive picture is presented to explain how initial conditions determine the features of the signal.

Measurements of temperature scaling laws in an optically dense magneto-optical trap

We have studied the temperature scaling laws for the conditions under which a cloud of trapped ^85Rb atoms in the sigma+/sigma- configuration makes the transition from the temperature-limited regime to the multiple-scattering regime. Our experimental technique for measuring temperature relies on measuring the ballistic expansion of the cloud after turning off the confining forces and imaging the cloud size as a function of time with two CCD cameras. In the transition regime, the temperature T is shown to depend on the number of atoms N and the peak density n as (T-T_0) proportional N^1/3 and as (T-T_0) proportional n^2/3, in a manner consistent with theoretical predictions. Here T_0 is defined as the equilibrium temperature of a low-density optical molasses. In the multiple-scattering regime we find that T proportional Omega^2/(delta Gamma), where Omega and delta are the Rabi frequency and the detuning of the trapping laser, respectively, and Gamma is the natural linewidth of the cycling transition. We have also measured the ratio of temperatures along the axial and radial directions of the magnetic field gradient coils and find that the temperature is isotropic only if the intensities of the three orthogonal trapping beams are equal, and that the ratio is generally independent of trapping laser intensity and magnetic field gradient. Finally we demonstrate a measurement of the gravitational acceleration precise to approximately 0.1% by tracking the center of the cloud during ballistic expansion.

Measurement of excited-state lifetime using two-pulse photon echoes in rubidium vapor

We report a measurement of the 5P3/2 excited-state lifetime using two-pulse photon echoes in Rb vapor. The measurement is precise to ∼1% and agrees with the best measurement of atomic lifetime in Rb. The results suggest that a measurement precise to ∼0.25% is possible through additional data acquisition and study of systematic effects. The experiment relies on short optical pulses generated from a cw laser using acousto-optic modulators. The excitation pulses are on resonance with the F=3-->F′=4 transition in Rb85 or the F=2-->F′=3 transition in Rb87. The resulting photon echo signal is detected using a heterodyne detection technique. The excited-state lifetime is determined by measuring the exponential decay of the echo intensity as a function of the time between the excitation pulses. We also present a study of the echo intensity as a function of excitation pulse area and compare the results to simulations based on optical Bloch equations. The simulations include the effects of spontaneous emission as well as spatial and temporal variations of the intensities of excitation pulses.

Precise determination of atomic g-factor ratios from a dual isotope magneto-optical trap

We demonstrate a technique, for carrying out precise measurements of atomic g-factor ratios, which relies on measurements of Larmor oscillations from coherences between magnetic sublevels in the ground states of {sup 85}Rb and {sup 87}Rb atoms confined in a dual isotope magneto-optical trap. We show that a measurement of g{sub F}{sup (87)}/g{sub F}{sup (85)} with a resolution of 0.69 parts per 10{sup 6} is possible by recording the ratio of Larmor frequencies in the presence of a constant magnetic field. This represents the most precise single measurement of g{sub F}{sup (87)}/g{sub F}{sup (85)} without correcting for systematic effects.

Collision-induced superfluorescence

We have studied superfluorescence (SF) in Ca vapor evolving on the 3d4s ^3 D_J -4s4p ^3 P_J-1 transitions at 1.9 µm by exciting the 4s^21 S_0 -4s4p ^1 P_1 with a pulsed dye laser. SF is generated following population transfer by spin-changing collisions with an inert gas Ar from the 4s4p ^1 P_1 and 3d4s ^1 D_2 levels. We show for the first time to our knowledge that the time delay for SF evolution follows the 1/sqrt N dependence expected for the case of uniform excitation of the vapor column by collisional transfer. Here, N is the number of participating atoms that was measured directly from the photon yield. The measured photon yield for the signal as a function of Ar pressure was found to be consistent with rate equations that simulate the buildup of populations in the ^3 D_J levels based on known collisional rates. This suggests that collisional rates can be directly inferred on the basis of SF photon yields and the atomic level populations. The pulse shapes for SF show temporal oscillations that depend on two distinct factors. The first is the presence of a number of independently evolving regions in the gain medium, and the second is the presence of spatial modes. Temporal ringing is a well-known effect related to the exchange of energy between the atoms and the radiation field during pulse propagation. However, the temporal ringing observed in this experiment is far more pronounced than in previous SF experiments due to a particular choice of evolution parameters. This should make it feasible to compare our results with detailed numerical simulations that have been carried out previously.

Time-Domain Interferometry with Laser-Cooled Atoms

Abstract A single-state grating echo interferometer offers unique advantages for time-domain studies of light–matter interactions using laser-cooled atoms, including applications that involve precision measurements of atomic recoil, rotation, and gravitational acceleration. To illustrate the underlying physics, we first discuss the output signal of the interferometer in the absence of spontaneous emission. The influence of spontaneous emission, magnetic sublevels, and the spatial profile of excitations beams on matter wave interference in a two-pulse interferometer is described, followed by a discussion of transit time limited experiments using a multipulse technique that offers several advantages. We also examine the enhancement in signal size achieved by a lattice interferometer. The sensitivity of the interferometer to magnetic gradients and gravitational acceleration is discussed along with extensions to frequency-domain studies of atomic recoil and rotation. Applications of coherent transient effects and echo techniques associated with internal state labeled interferometers that utilize magnetic sublevels of a single hyperfine state are considered for precise measurements of magnetic interactions such as atomic g-factor ratios. The article concludes with an overview of the suitability of the traditional two-pulse photon echo technique for measurements of atomic lifetimes and studies of superradiant emission in laser-cooled samples.

A high-speed modulated retro-reflector for lasers

We have used an acousto-optic modulator (AOM) to impose an amplitude-modulation signal on an incident laser beam. The amplitude-modulated beam is retroreflected through the AOM. This beam is diffracted again by the AOM so that it overlaps the incident beam and is frequency shifted with respect to it. The return beam is also orthogonally polarized with respect to the incident beam by a wave plate. These features allow us to detect the amplitude-modulated signal with high signal to noise ratio using heterodyne detection. Since the optical setup is simple and can be made very compact, this device may be ideal for certain forms of high-speed, free-space optical communication. We have used a 60 MHz AOM to demonstrate a 1 MHz communication rate, and studied the performance limitations of this device. Finally, we discuss the realization of a communication rate approaching 1 GHz using this method.

Observation of Superfluorescent Emissions from Laser Cooled Rb Atoms

We present studies of superfluorescent pulses observed at 420.3 nm from a sample of laser cooled rubidium atoms that are excited to the 5D5/2 excited state by a two-photon transition from the 5S1/2 ground state.