High Photon Number Entangled States and Coherent State Superposition from the Extreme Ultraviolet to the Far Infrared

Theory of entanglement and measurement in high harmonic generation

“…The field amplitude of the driving laser is typically in the range of |α| ∼ 10 7 . The interaction of the field with the atomic medium conditioned on the electronic ground state (leading to HHG) can then be described as an effective multimode displacement operation (see Methods) [16][17][18]…”

“…The associated induced time-dependent dipole moment d(t) = g| d(t) |g makes the respective shifts of the modes correlated. In fact, the actual mode which is populated during the HHG process is a wavepacket mode taking into account these correlations [16,18], and can be described by the corresponding number states |ñ . To account for the process of HHG, we express the state in (6) in terms of the number states of the wavepacket mode…”

“…The drawback of this scheme is that some fraction of the optical field needs to be detected, and is thus inevitably interacting with additional optical devices leading to decoherence and amplitude reduction. Nonetheless, this scheme is very powerful to generate non-classical optical cat states with high photon numbers [16][17][18][19].…”

“…which can interpolate between an optical kitten or cat state with non-classical signatures in the corresponding Wigner function [16,17]. Note that similar operation can be performed on other field modes in order to generate optical cat states towards the XUV regime [18]. The influence of the harmonic modes, which can be considered as an environment on which conditioning measurements are performed, is captured in the decoherence factor Ω.…”

“…However, recent advances in the quantum optical analysis of HHG has established a new direction in the investigation of strong field physics. This allows to study the quantum mechanical properties of the harmonic radiation, or to take into account the backaction on the driving field [10][11][12][13][14][15][16][17][18][19][20]. In particular, it was shown that conditioning procedures on processes induced by intense laser-matter interaction can lead to the generation of high-photon number controllable non-classical field states in a broad spectral range [16][17][18][19].…”