Temporal interferometry: A mechanism for controlling qubit transitions during twisted rapid passage with possible application to quantum computing

Abstract

In an adiabatic rapid passage experiment, the Bloch vector of a two-level system (qubit) is inverted by slowly inverting an external field to which it is coupled, and along which it is initially aligned. In twisted rapid passage, the external field is allowed to twist around its initial direction with azimuthal angle $\ensuremath{\varphi}(t)$ at the same time that it is inverted. For polynomial twist, $\ensuremath{\varphi}(t)\ensuremath{\sim}{\mathrm{Bt}}^{n}.$ We show that for $n>~3,$ multiple avoided crossings can occur during the inversion of the external field, and that these crossings give rise to strong interference effects in the qubit transition probability. The transition probability is found to be a function of the twist strength B, which can be used to control the time separation of the avoided crossings, and hence the character of the interference. Constructive and destructive interference are possible. The interference effects are a consequence of the temporal phase coherence of the wave function. The ability to vary this coherence by varying the temporal separation of the avoided crossings renders twisted rapid passage with adjustable twist strength into a temporal interferometer through which qubit transitions can be greatly enhanced or suppressed. Possible application of this interference mechanism to construction of fast fault-tolerant quantum controlled-NOT and NOT gates is discussed.