Information-theoretic perspective on energy conservation in high harmonic generation

The use of energy conservation arguments is ubiquitous in understanding the process of high harmonic generation, yet a complete quantum optical description of exact photon number exchange remained elusive. Here, we solve this gap in description by introducing the energy conserving subspace in high harmonic generation in which many photons of the driving field are absorbed to generate a single photon of higher energy. The presented solution to energy conservation in quantum optical high harmonic generation naturally results in highly entangled states of light with non-classical properties in their marginals and photon statistics. This new technique can be seen as an information-theoretic approach to the problem of photon exchange between field modes, providing a new kind of selection rule imposed on the quantum optical state by the structure of the Hilbert space. In addition to providing the quantum state satisfying exact energy conservation, it allows to explain recent experimental results for quantum state engineering of optical cat states.