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All classical and quantum technologies that encode in and retrieveinformation from optical fields rely on the ability to selectively manipulateorthogonal field modes of light. Such manipulation can be achieved with highselectivity for polarization modes and transverse-spatial modes. For thetime-frequency degree of freedom, this could efficiently be achieved for alimited choice of approximately orthogonal modes, i.e. non-overlapping bins intime or frequency. We recently proposed a method that surmounts the selectivitybarrier for sorting arbitrary orthogonal temporal modes [Opt. Lett. {\bf 39},2924 (2014)] using cascaded interferometric quantum frequency conversion innonlinear optical media. We call this method temporal-mode interferometry, asit has a close resemblance to the well-known separated-fields atomicinterferometry method introduced by Ramsey. The method has importantimplications for quantum memories, quantum dense coding, quantum teleportation,and quantum key distribution. Here we explore the inner workings of the methodin detail, and extend it to multiple stages with a concurrent asymptoticconvergence of temporal-mode selectivity to unity. We also complete ouranalysis of pump-chirp compensation to counter pump-induced nonlinearphase-modulation in four-wave mixing implementations.

Sorting photon wave packets using temporal-mode interferometry based on multiple-stage quantum frequency conversion