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A driven quantum system can experience Landau-Zener-Stueckelberg-Majorana(LZSM) transitions between its states, when the respective energy levelsquasi-cross. If this quasicrossing is passed repeatedly under periodic driving,the trajectories can interfere either constructively or destructively. In thelatter case, known as coherent destruction of tunneling, the transition betweenthe energy states is suppressed. Even for a double-passage case, theaccumulated phase difference (also referred to as the Stueckelberg phase) canlead to destructive interference, resulting in no transition. In this paper wediscuss a similar process for a single-passage dynamics. We study the LZSMsingle-passage problem starting from a superposition state. The phasedifference of this initial state results in interference. When this isdestructive, resulting in a zero transition probability, such situation can becalled single-passage coherent destruction of tunneling. When the phase ischosen so that the occupation probabilities do not change after the transition,this can be called occupation conservation and this is analogous to the problemof transitionless driving. We demonstrate how varying the system parameters(driving velocity, initial phase, initial detuning) can be used for quantumcontrol.

Tuning the initial phase to control the final state of a driven qubit: single-passage coherent destruction of tunneling