State-dependent atomic excitation by multiphoton pulses propagating along two spatial modes

Abstract

We investigate the dynamics of a single two-level atom, which interacts with pulses propagating in two spatial modes (right and left) and frequency continuum. Using Heisenberg equations of motion, we present the explicit analytical derivations and general formalisms for atomic excitation with two-spatial-mode multiphoton pulses in both the Fock and coherent states. Based on those formalisms, we show that perfect atomic excitation by a single-photon Fock state pulse can only be realized when it is rising exponentially shaped in the even mode, a balanced superposition of the two spatial modes. A single photon from a single spatial mode can only give half of the maximal atomic excitation probability. We also show that the maximum atomic excitation probability with multiphoton pulses in the even mode is a monotonic function of the average photon number for the coherent state, but not for the Fock states. Furthermore, we demonstrate that the atomic dynamics can be controlled by the initial relative phase between the two counterpropagating coherent state pulses incident on the atom, which is not the case with the two Fock state pulses.