Coherent superposition of states in N-pod systems by hyperbolic-tangent coincident pulses

Abstract

We present an analytically exactly solvable N-pod quantum model, in which the coupling has a hyperbolic-tangent temporal shape and the frequency detuning is constant. The solution is derived by using the Morris–Shore transformation to reduce the N-pod system to a -like one and then to a two state system and a set of decoupled states in two steps. In this work, we use the propagator for a reduced two state system and the inverse transformation to achieve the reduced three state propagator. It is shown that any preselected coherent superposition of all N ground states can be obtained from an initial superposition of M ground states in the presence of detuning. We use a train of tanh coincident pulses and we show that the effect of spontaneous emission is efficiently suppressed by increasing the number of pulses. Besides, we explore that a coherent superposition of ground states from the initial excited state can be implemented using tanh pulses.