Phase-Only Temporal Mode Transformations with Complex Spectral and Temporal Phases

Spectral-temporal modes of quantum light have been recognized as a promising platform for quantum information processing (QIP) and metrology [1], [2]. However, a simple general tool for efficient conversion between spectral-temporal modes is still missing. A phase-only, i.e. in-principle lossless, approach is required for quantum light. The existing phase-only approaches for converting a given input spectral-temporal mode to a given target spectral-temporal mode rely on sequences of complex temporal phase modulations interleaved with propagation in second order dispersive medium, yielding complex setups with often formidable insertion losses. Here we show that such a transformation can be carried out by a single application of a complex temporal phase modulation, and a single application of complex spectral phase modulation.