Excitation probability of the hyperfine ground state of Doppler-broadened muonic hydrogen through dipole-forbidden transition

Abstract

We study the magnetic dipole induced excitation probability of the hyperfine ground state of Doppler-broadened muonic hydrogen (pμ−) by a single nanosecond laser pulse with pulse durations of 20, 2, and 0.2 ns pulses with a Gaussian temporal shape such that the pulse bandwidth is, respectively, narrower than, comparable to, and broader than the Doppler width at 300 K. We numerically solve a set of density matrix equations to obtain the excitation probability at the various laser intensities and detunings. For the resonant 20 ns pulse, the excitation probability increases very slowly as the laser intensity increases. The width of the excitation probability lineshape mainly comes from the Doppler broadening and hardly increases with intensity. For the resonant 0.2 ns pulse a complete population inversion occurs at a certain laser intensity, and the excitation probability oscillates between 0 and unity as the intensity further increases. Owing to the inherent pulse bandwidth the width of the excitation probability lineshape is very broad even at the low intensity, and it increases further as the intensity increases. For the resonant 2 ns pulse at a moderate intensity (∼1011 W/cm2) the excitation probability is higher than those by the 20 and 0.2 ns pulses with a relatively narrow width. Our study can serve as a guideline for the development of the relevant laser source, depending on the purpose to excite muonic hydrogen, i.e., precise measurement of the ground state hyperfine splitting of muonic hydrogen or production of spin-polarized muonic hydrogen.