Origin of heart-shaped intra-cycle temporal-shift interference patterns in RESI with few-cycle pulses

Determine the physical origin and mechanism of the heart-shaped interference structures that appear in intra-cycle temporal-shift interference maps for recollision-excitation with subsequent ionization (RESI) driven by few-cycle sin^2 pulses. Specifically, derive analytic conditions connecting these shapes to the temporal-shift phase-difference components—α^(A^2)_{Δτ}(t',t''), α^(pond)_{Δτ}(t,t''), α^(ene)_{Δτ}, and α^{(p1,p2)}_{Δτ}(t,t')—and identify the carrier-envelope phase and event-dominance regimes under which these structures emerge or vanish.

Background

In this work, the authors analyze single-channel quantum interference in nonsequential double ionization (NSDI) via the RESI mechanism using few-cycle laser pulses, deriving generalized phase-difference conditions for exchange and event (temporal-shift) interference. They identify multiple field-dependent building blocks for event interference, including terms from the squared vector potential, ponderomotive energy, bound-state and kinetic energies, and momentum–field couplings.

While dissecting interference patterns associated with purely temporal shifts, the authors observe distinctive wing-like and heart-shaped structures in the first or third quadrants (depending on dominant events), alongside static-like patterns in the opposite quadrants. Despite proposing that these heart-shaped patterns likely result from combinations of field-dependent temporal-shift phases, they explicitly state that the origin of this shape is unclear, highlighting a concrete unresolved question about its mechanism and analytic description.