We propose to use the quantum-electrodynamical description in the time domain to investigate theoretically novel quantum states of light which can be generated by means of modern ultrafast photonics when pushing the time-resolution and signal sensitivity to their fundamental limits. The quantum nature of light is crucial for applications ranging from novel spectroscopies of complex many-body phenomena in condensed matter to quantum information processing. In recent years we experience an unprecedented progress in generation of ultrashort light pulses (down to attoseconds) and control of their classical properties. In the current project we aim to explore now the quantumness of pulsed light fields at ultrafast, subcycle (shorter than the optical cycle) time scales. Subcycle access to nonclassical states of light and the possibility to govern them with such temporal resolution might, in fact, revolutionize parts of the fields of quantum optics and ultrafast photonics. The planned research intends to provide the necessary theoretical framework. The consideration will be based on the realistic description of wave-mixing processes of quantized fields in nonlinear optical crystals, in close connection to situations in the actual running experiments.Manipulation of light on ultrafast time scales and short (sub-wavelength) distances is intrinsically connected with modifications of the probed space-time. An appropriate description naturally evokes the connection to the concepts of the relativity theory. We are going to test the surmise that the appearance of pulsed squeezed photon states out of the bare vacuum can be associated with the famous Hawking-Unruh radiation. With the direct connection to general relativity, other cosmological predictions, such as scaling laws in the sub-wavelength regime, will also be examined. Modification of the generated quantum light via the interaction with elementary excitations in matter will be studied as well, whereby the causal response of massive modes should manifest an essential and nontrivial role. The fundamental physical aspects and interplay of relativity and causality arising in the generation, detection and interaction processes of nonlinear quantum electrodynamics should be addressed in this project.
