Laser-manipulated the multiphoton transitions of a harmonically trapped particle

A single particle magneto-confined in a one-dimensional (1D) quantumwire experiences a harmonic potential, and imposing a sharplyfocused laser beam on an appropriate site shapes a $delta$potential. The theoretical investigation has demonstrated that for asufficiently strong $delta$ pulse the quantum motional stationarystate of the particle is one of the eigenstates of the free harmonicoscillator, and it is determined by the site of the laser beamuniquely, namely a quantum state is admissible if and only if thelaser site is one of its nodes. The numerical computation shows thatall the nodes of the lower energy states with quantum numbers $n le20$, except the coordinate origin, are mutually different. So we canmanipulate the multiphoton transitions between the quantum states byadjusting the position of the laser $delta$ pulse and realize thetransition from an unknown higher excitation state to a requiredlower energy state.