The multi-photon induced Fano effect
An international team of researchers demonstrated that Fano structure may also be induced without need of auto-ionization, by dressing the continuum with an ordinary bound state in any atom by a coupling laser, in this case the Free Electron Laser FELIX, which emits tunable picosecond pulses of high intensity. Using multi-photon processes gives complete, ultra-fast control over the interference. Since the Fano lineshape has both constructive and destructive interference, the laser control opens the possibility of state-selective detection with enhancement on one side of resonance and invisibility on the other. The results are published in Nature Communications.
a Here, |g⟩|g⟩ is the ground state, |c⟩|c⟩ (the orange band) is the one-electron continuum, and |a⟩|a⟩ is an auto-ionizing state, i.e., it is discrete and localized, but it has enough total energy that one electron can be kicked out of the atom into |c⟩|c⟩. |kω⟩|kω⟩ (dashed blue line) is the state within the continuum that is resonant with excitation from |g⟩|g⟩ by dipole allowed transitions with perturbation Hamiltonian D at frequency ω, indicated here such that |kω⟩|kω⟩ is above the level of |a⟩|a⟩, i.e., positive detuning, Δ. V is an energy-conserving perturbation (such as a configuration interaction) that couples |a⟩|a⟩ with |c⟩|c⟩, and creates a second pathway from |g⟩→|kω⟩|g⟩→|kω⟩ via |a⟩|a⟩ and the pathways interfere. As the detuning Δ is tuned across the resonance with |a⟩|a⟩, the interference between the pathways changes sign. Resonance-Enhanced Multi-Photon Ionization (RE-MPI) is similar to the Fano process, involving an intermediate state. In Laser-Induced Continuum Structure (LICS), V is a dipole transition from a bound state |b⟩|b⟩ and now |g⟩→|kω⟩|g⟩→|kω⟩ interferes with a third-order process |g⟩→|k⟩→|b⟩→|kω⟩|g⟩→|k⟩→|b⟩→|kω⟩, where |k⟩|k⟩ is a virtual intermediate state and no autoionizing state is involved. In Multi-Photon Induced Continuum Structure (MPICS), interference occurs between two second-order processes |g⟩→|b⟩→|k2ω⟩|g⟩→|b⟩→|k2ω⟩ and |g⟩→|k⟩→|k2ω⟩|g⟩→|k⟩→|k2ω⟩, where the latter is a two-photon transition via a virtual intermediate state with Hamiltonian D(2). In degenerate MPICS (used in this work), V = D. b The pump-probe experiment geometry in time and space. The pulse duration tp and delay time t are indicated. c The primary processes in a standard pump-probe experiment (black) and the additional ionization-related processes (blue) of interest here.
The multi-photon induced Fano effect, K. L. Litvinenko, Nguyen H. Le, B. Redlich, C. R. Pidgeon, N. V. Abrosimov, Y. Andreev, Zhiming Huang & B. N. Murdin, Nature Communications 12, 454 (2021)