Unidimensional Time Domain Quantum Optics

TL;DR

This paper develops a time domain first quantization framework in quantum optics, clarifying the relationship between electromagnetic and photonic fields, and extending quadrature concepts to all bases, enhancing interpretation of short waveform experiments.

Contribution

It introduces a novel time domain first quantization approach, deriving the relation between electromagnetic and photonic fields and extending quadratures to all bases, which was not previously established.

Findings

Derived the relation between electromagnetic and photonic fields in time domain.

Calculated photon detection statistics for specific states like single photon Fock state.

Extended the concept of quadratures to all first quantization bases.

Abstract

Choosing the right first quantization basis in quantum optics is critical for the interpretation of experimental results. The usual frequency basis is, for instance, inappropriate for short, subcycle waveforms. Deriving first quantization in time domain shows that the electromagnetic field is not directly proportional, nor even causally related, to the photonic field (the amplitude probability of a photon detection). We derive the relation between the two and calculate the statistics of the electromagnetic field for specific states in time domain, such as the single photon Fock state. We introduce the dual of the Hamiltonian in time domain and extend the concept of quadratures to all first quantization bases.