Theory of entanglement and measurement in high harmonic generation

Abstract

Quantum information science and intense laser matter interaction are two apparently unrelated fields. However, the recent developments of the quantum optical description of the intense laser driven process of high harmonic generation allow to conceive new light engineering protocols. Here, we introduce the notion of quantum information theory to intense laser driven processes by providing the quantum mechanical description of measurement protocols for high harmonic generation in atoms. We explicitly evaluate conditioning experiments on individual optical field modes, and provide the corresponding quantum operation for coherent states. The associated positive operatorvalued measures are obtained, and give rise to the quantum theory of measurement for the generation of high dimensional entangled states, and coherent state superposition with controllable non-classical features on the attosecond timescale.

Quantum optical analysis of high-harmonic generation in solids within a Wannier-Bloch picture

“…Finally, we introduce the so-called conditioning to HHG operation that has been theoretically studied and experimentally implemented in Refs. [58,61,62,64,65], and proceed to characterize the state of the system after such operation.…”

“…In a similar basis to what was presented in Refs. [61,64], one could experimentally condition on the state of the fundamental instead of the XUV modes, such that non-classical states of light could be potentially obtained in the latter. Based on this, we project the fundamental mode onto |α so that Eq.…”

“…On the other hand, from a quantum optical perspective, strong-field processes have been studied experimentally and theoretically, so far, only for atomic ensembles [52][53][54][55][56][57][58][59][60][61][62][63]. These works have shown that, strong laser-matter interaction processes can lead to the generation of highphoton number non-classical states of light [55,58,62], where the generated harmonics are entangled between them [61,62,64] and with the electron that gets ionized [60]. Thus, it is of interest to understand to what extent the features that are observed in the atomic regime can be found in the solid-state scenario.…”

“…Thus, it is of interest to understand to what extent the features that are observed in the atomic regime can be found in the solid-state scenario. With that purpose in mind, in this work we apply the conditioning operations that allow for the generation of non-classical states of light in gaseous HHG [55,58,61,64] to its solid-state counterpart, and study the properties of the obtained state.…”

“…In Section III we present the results, which are divided into three subsections. Firstly, we study how the dynamics of the electron in the valence and conduction bands affect the quantum optical state of the system; secondly, we focus on the high-harmonic generation processes, and study the photon number probability of finding a harmonic photon in one of the field modes; thirdly, we introduce the conditioning to HHG operation as experimentally implemented in [58,65], and theoretically described in [61,62,64], to study non-classical properties of the obtained quantum state. Finally, we end our contribution with conclusions and a brief outlook in Section IV, where we also discuss how decoherence effects in solidstate systems may affect the measured quantum optical observables.…”