Quantum temporal imaging: application of a time lens to quantum optics

We consider application of a temporal imaging system, based on the sum-frequency generation (SFG), to a nonclassical, squeezed optical temporal waveform. We analyze restrictions on the pump and the phase-matching condition in the summing crystal, which are necessary for preserving the quantum features of the initial waveform. We show that modification of the notion of the field of view (FOV) in the quantum case is necessary, and that the quantum FOV is much narrower than the classical one for the same temporal imaging system. These results are important for temporal stretching and compressing of squeezed fields, which are used in quantum-enhanced metrology and quantum communications.