Time Reversal Techniques for Atomic Waveguides

摘要

The modes of an atomic waveguide are analyzed using both the time reversal symmetry of the system and the Frobenius method of series solution to create a general, physically acceptable, solution of the radial differential equations. The general solution is used to obtain precise energies and wavefunctions by imposing various boundary conditions on the radial solution at some distance from the guide center. The use of the time reversal technique to analyze the mode structure allows for a simplified understanding of the transition between the zero Ioffe field case and the moderate Ioffe field case. By understanding the relation between the two time reversed modes, it is expected that a technique based on the time reversal symmetry of the system can be developed to efficiently model decay mechanisms and other dynamics of atomic guides and guided wave magnetic beam splitters used in chip based atom interferometers.