Bringing weak transitions to light

Abstract

Weak transitions between quantum states are of fundamental importance for a broad range of phenomena from analytical biochemistry to precision physics, but generally challenge experimental detection. Due to their small cross sections scaling with the absolute square of their transition matrix elements, spectroscopic measurements often fail in particular in the presence of competing background processes. Here we introduce a general concept to break this scaling law and enhance the transition probability by exploiting a stronger laser-coupled pathway to the same excited state. We demonstrate the concept experimentally by attosecond transient absorption spectroscopy in helium atoms. The quasi-forbidden transitions from the ground state 1s² to the weakly coupled doubly excited 2p3d and sp_2,4- states are boosted by an order of magnitude. Enhancing single-photon-suppressed transitions can find widespread applicability, from spectral diagnostics of complex molecules in life and chemical sciences to precision spectroscopy of weak transitions in metastable atomic nuclei in the search for new physics.

Fig. 1. Schematic illustration of the concept of enhancing spectroscopically weak transitions.

a Laser 1 creates a coherent superposition of ground and excited states, with state $∣1⟩$ being very weakly excited compared to state $∣2⟩$ as a result of a vanishingly small transition matrix element ∣T_g1∣ ≪ ∣T_g2∣. Laser 2 opens an additional pathway by coupling state $∣1⟩$ to the more strongly populated excited state $∣2⟩$. The resulting spectral signal on the originally weak transition $∣g⟩\to ∣1⟩$ gets enhanced as shown in panel (b). Parameters for the calculation results shown in panel (b) are as follows: state $∣1⟩$ (E_g1 = 62 eV, 400-fs decay time); state $∣2⟩$ (E_g2 = 60 eV, 17-fs decay time); transition matrix elements for T_g1, T_g2, and T₂₁ are 0.0008, 0.04, and 2 a.u., respectively; laser 1 [0.2-fs FWHM (full width at half maximum) duration, 9.1-eV spectral bandwidth, 1 × 10¹¹-W/cm² peak intensity, 60 eV central frequency] overlaps temporally with laser 2 (4-fs FWHM duration, 2 × 10¹²-W/cm² peak intensity, 700 nm central wavelength).

Fig. 2. Outline of the attosecond transient absorption measurement.

a Illustration of the experimental setup. CCD, charge-coupled device. b Relevant energy-level diagram in helium. c Absorption profile at 1.5-fs time delay (reddish-orange line) along with the result in the absence of the VIS pulse (blue line).

Fig. 3. Experimental and theoretical demonstration.

a Upper panel: measured transient absorption spectrum in the vicinity of the 2p3d and sp_2,4− states; lower panel: absorption profiles at two representative time delays [blue (reddish-orange) line: negative (positive) time delay] marked as white dashed lines in the upper panel. b Simulated spectrum and absorption profiles after implementing the spectral broadening and the spectrometer resolution.