Space-time duality and quantum temporal imaging

TL;DR

This paper extends quantum temporal imaging theory by incorporating finite aperture effects, analyzing vacuum fluctuation contributions, and applying the framework to preserve squeezing in broadband quantum light.

Contribution

It introduces a quantum theory of temporal imaging with finite aperture effects, highlighting vacuum fluctuations' role and criteria for preserving quantum properties like squeezing.

Findings

Finite aperture affects quantum temporal imaging performance.

Vacuum fluctuations influence nonclassical waveform imaging.

Criteria established for maintaining squeezing in broadband quantum light.

Abstract

Using the space-time analogy, we compare the performance of quantum temporal imaging with its classical counterpart. We consider a temporal imaging scheme, based on the sum-frequency generation (SFG) time lens, but our results can be applied to other temporal imaging schemes such as, for instance, four-wave mixing. Extending the theory presented in our previous publications, in this paper we take into account the finite time aperture of the imaging system, characterized by its pupil function. Using the quantum theory, we obtain a unitary transformation of the quantum field from the input to the output of the imaging scheme and identify the contribution of the vacuum fluctuations missing in the classical theory. This contribution plays a key role in the quantum temporal imaging of nonclassical temporal waveforms, characterized by nonclassical fluctuations of the electromagnetic field. As an example, we consider quantum temporal imaging of broadband squeezed light and formulate the criteria for conservation of its squeezing properties at the output of the system.