Macroscopic Manipulation of High-Order-Harmonic Generation Through Bound-State Coherent Control

We propose a paradigm for macroscopic control of high-order harmonic generation by modulating the bound-state population of the medium atoms. A unique result of this scheme is that apart from regular spatial quasi-phase-matching (QPM), also purely temporal QPM of the emitted radiation can be established. Our simulations demonstrate temporal QPM by inducing homogenous Rabi oscillations in the medium and also spatial QPM by creating a grating of population inversion using the process of rapid adiabatic passage. In the simulations a scaled version of high-order harmonic generation is used: a far off-resonance $2.6\mu \mathrm{m}$ source generates UV-visible high-order harmonics from alkali-metal-atom vapor, while a resonant near IR source is used to coherently control the medium.

Figure 1

Four channels of HHG from a two-level system. $g$ is the ground state of the atom, $e$ is the first excited state, and $c$ represents continuum states. Each channel includes the ionization of an electron from one of the bound states to the continuum and its recombination into a bound state, e.g., $ge$ means that an electron is ionized from the ground state of the atom and recombines into the excited state. The dashed line separates channels which have different phase mismatch values in case the index of refraction changes during the interaction.

Figure 2

Proposed setup for QPM of HHG using bound-states coherent control: A HHG pump pulse propagates along the interaction axis generating high-order harmonics. A coherent control pulse is focused uniformly using a cylindrical lens upon the interaction axis within an interaction cell, modulating the atomic population of the medium either in space by generating a quasi-static spatial population grating (with the aid of the additional mask) or in time by generating a temporal population grating through Rabi oscillations (without the mask).

Figure 3

Rabi oscillations induced by a coherent control electric field propagating in the medium. The black dashed line shows the coherent control field envelope after propagating 5 mm in the medium. The blue solid line shows the population inversion in the medium induced by the coherent control field. The inset shows a close up of the population inversion around the peak of the pulse, showing periodic oscillations with the desired generalized Rabi frequency.

Figure 4

QPM of HHG using bound states’ coherent control. (a) Harmonic spectrum at the end of the interaction cell, normalized to the strongest harmonic emission. (b) Thirteenth harmonic evolution along the HHG pump propagation direction, normalized to the strongest enhancement during the propagation. The solid black line represents propagation in a medium with no QPM, the dashed blue line represents propagation in a medium with temporal QPM prepared with Rabi oscillations and the dash-dotted red line represents propagation in a medium with spatial QPM prepared with RAP and a mask of slits. (c),(d),(e): Evolution of the HHG spectrum, normalized for each harmonic order separately, with (c) no QPM, (d) spatial QPM, and (e) temporal QPM.