Correlation-induced phase shifts and time delays in resonance-enhanced high-harmonic generation

We investigate resonance-enhanced high-harmonic generation (rHHG) in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:msup> <a:mrow> <a:mi>Cr</a:mi> </a:mrow> <a:mo>+</a:mo> </a:msup> </a:math> by comparing a one-dimensional (1D) shape-resonant model, time-dependent density functional theory (TDDFT), and independent particle approximation (IPA) simulations. Previous studies linked rHHG to the <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:mn>3</b:mn> <b:mi>p</b:mi> <b:mo>→</b:mo> <b:mn>3</b:mn> <b:mi>d</b:mi> </b:mrow> </b:math> giant resonance, suggesting a modified four-step model where recolliding electrons are first captured in the autoionization state before recombining into the ground state, potentially leading to an emission delay associated with the resonance lifetime. While both the 1D model and TDDFT reproduce experimental spectra, TDDFT reveals that rHHG counterintuitively originates from spin-down <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mn>3</c:mn> <c:mi>p</c:mi> </c:mrow> </c:math> states, while spin-up <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:mn>3</d:mn> <d:mi>d</d:mi> </d:mrow> </d:math> electrons negligibly contribute. The IPA fails to reproduce rHHG, highlighting the significance of electron correlations. Furthermore, TDDFT revealed a correlation-induced <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mrow> <e:mo>∼</e:mo> <e:mspace width="0.16em"/> <e:mn>480</e:mn> </e:mrow> </e:math> as time delay, accompanied by a strong phase shift across the resonance, potentially explaining earlier reconstruction of attosecond beating by interference of two-photon transitions measurements. Our work sheds light on long-standing open questions in rHHG and should advance ultrafast spectroscopies of electron correlations and resonances.