Electromagnetic Transition in Waveguide with Application to Lasers

The electromagnetic transition of two-level atomic systems in a waveguide is calculated. Compared with the result in free space, the spontaneous emission rate decrease because the phase space is smaller, and meanwhile, some resonance appears in some cases. Moreover, the influence of non-uniform electromagnetic field in a waveguide on absorption and stimulated emission is considered. Applying the results to lasers, a method to enhance the laser power is proposed.Comment: 4 pages, 2 figure

Relativistic theory for time and frequency transfer to order c^{-3}

This paper is motivated by the current development of several space missions (e.g. ACES on International Space Station) that will fly on Earth orbit laser cooled atomic clocks, providing a time-keeping accuracy of the order of 5~10^{-17} in fractional frequency. We show that to such accuracy, the theory of frequency transfer between Earth and Space must be extended from the currently known relativistic order 1/c^2 (which has been needed in previous space experiments such as GP-A) to the next relativistic correction of order 1/c^3. We find that the frequency transfer includes the first and second-order Doppler contributions, the Einstein gravitational red-shift and, at the order 1/c^3, a mixture of these effects. As for the time transfer, it contains the standard Shapiro time delay, and we present an expression also including the first and second-order Sagnac corrections. Higher-order relativistic corrections, at least O(1/c^4), are numerically negligible for time and frequency transfers in these experiments, being for instance of order 10^{-20} in fractional frequency. Particular attention is paid to the problem of the frequency transfer in the two-way experimental configuration. In this case we find a simple theoretical expression which extends the previous formula (Vessot et al. 1980) to the next order 1/c^3. In the Appendix we present the detailed proofs of all the formulas which will be needed in such experiments.Comment: 11 pages, 2 figures, to appear in Astronomy & Astrophysic

Atomic Resonance and Scattering

Contains research objectives and summary of research on three research projects.Joint Services Electronics Program (Contract DAAB07-75-C-1346)U.S. Air Force Office of Scientific Research (Contract F44620-72-C-0057

Simple Pendulum Revisited

We describe a 8085 microprocessor interface developed to make reliable time period measurements. The time period of each oscillation of a simple pendulum was measured using this interface. The variation of the time period with increasing oscillation was studied for the simple harmonic motion (SHM) and for large angle initial displacements (non-SHM). The results underlines the importance of the precautions which the students are asked to take while performing the pendulum experiment.Comment: 17 pages with 10 figure

Rieffel deformation via crossed products

We start from Rieffel data (A,f,X) where A is a C*-algebra, X is an action of an abelian group H on A and f is a 2-cocycle on the dual group. Using Landstad theory of crossed product we get a deformed C*-algebra A(f). In the case of H being the n-th Cartesian product of the real numbers we obtain a very simple proof of invariance of K-groups under the deformation. In the general case we also get a very simple proof that nuclearity is preserved under the deformation. We show how our approach leads to quantum groups and investigate their duality. The general theory is illustrated by an example of the deformation of SL(2,C). A description of it, in terms of noncommutative coordinates is given.Comment: 39 page

Zeeman Relaxation of Cold Atomic Iron and Nickel in Collisions with 3He

We have measured the ratio of the diffusion cross-section to the angular momentum reorientation cross-section in the colliding Fe-3He and Ni-3He systems. Nickel (Ni) and iron (Fe) atoms are introduced via laser ablation into a cryogenically cooled experimental cell containing cold (< 1 K) 3He buffer gas. Elastic collisions rapidly cool the translational temperature of the ablated atoms to the helium temperature. The cross-section ratio is extracted by measuring the decays of the atomic Zeeman sublevels. For our experimental conditions, thermal energy is comparable to the Zeeman splitting. As a result, thermal excitations between Zeeman sublevels significantly impact the observed decay. To determine the cross-section ratio accurately, we introduce a model of Zeeman state dynamics that includes thermal excitations. We find the cross-section ratio for Ni-3He = 5 x 10^3 and Fe-3He <= 3 x 10^3 at 0.75 K in a 0.8 T magnetic field. These measurements are interpreted in the context of submerged shell suppression of spin relaxation as studied previously in transition metals and rare earth atoms.Comment: 10 pages, 5 figures; submitted to Phys. Rev.

Slipping and Rolling on an Inclined Plane

In the first part of the article using a direct calculation two-dimensional motion of a particle sliding on an inclined plane is investigated for general values of friction coefficient ($\mu$). A parametric equation for the trajectory of the particle is also obtained. In the second part of the article the motion of a sphere on the inclined plane is studied. It is shown that the evolution equation for the contact point of a sliding sphere is similar to that of a point particle sliding on an inclined plane whose friction coefficient is 2/7}\ \mu. If $\mu> 2/7 \tan\theta$, for any arbitrary initial velocity and angular velocity the sphere will roll on the inclined plane after some finite time. In other cases, it will slip on the inclined plane. In the case of rolling center of the sphere moves on a parabola. Finally the velocity and angular velocity of the sphere are exactly computed.Comment: 12 pages, 3 figure

Atomic Resonance and Scattering

Contains reports on eleven research projects.U.S. Air Force - Office of Scientific Research (Grant AFOSR-81-0067

Crossover from weak to strong coupling regime in dispersive circuit QED

We study the decoherence of a superconducting qubit due to the dispersive coupling to a damped harmonic oscillator. We go beyond the weak qubit-oscillator coupling, which we associate with a phase Purcell effect, and enter into a strong coupling regime, with qualitatively different behavior of the dephasing rate. We identify and give a physicaly intuitive discussion of both decoherence mechanisms. Our results can be applied, with small adaptations, to a large variety of other physical systems, e. g. trapped ions and cavity QED, boosting theoretical and experimental decoherence studies.Comment: Published versio

Atomic Resonance and Scattering

Contains research objectives.Joint Services Electronics Programs (U. S. Army, U.S. Navy, and U.S. Air Force) under Contract DA 36-039-AMC-03200(E)Sloan Fund for Basic Research (M.I.T. Grant 95