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In an adiabatic rapid passage experiment, the Bloch vector of a two-levelsystem (qubit) is inverted by slowly inverting an external field to which it iscoupled, and along which it is initially aligned. In twisted rapid passage, theexternal field is allowed to twist around its initial direction with azimuthalangle $\phi (t)$ at the same time that it is inverted. For polynomial twist:$\phi (t) \sim Bt^{n}$. We show that for $n \geq 3$, multiple avoided crossingscan occur during the inversion of the external field, and that these crossingsgive 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, andhence the character of the interference. Constructive and destructiveinterference are possible. The interference effects are a consequence of thetemporal phase coherence of the wavefunction. The ability to vary thiscoherence by varying the temporal separation of the avoided crossings renderstwisted rapid passage with adjustable twist strength into a temporalinterferometer through which qubit transitions can be greatly enhanced orsuppressed. Possible application of this interference mechanism to constructionof fast fault-tolerant quantum CNOT and NOT gates is discussed.Comment: 29 pages, 16 figures, submitted to Phys. Rev.

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