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Annals of Physics

Coupled field induced conversion between destructive and constructive quantum interference

Xiangqian Jiang, Xiudong Sun

Published Oct 10, 2016• 8 citations
Publisher
DOI
10.1016/j.aop.2016.10.002

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The sum-frequency generation process using strong-field coupling and quantum interference is described systematically using atomic hydrogen both in theory and experiment. It is shown that strong coupling at the 3p-2s transition creates destructive interference to reduce the linear susceptibility at the resonant 3p\ensuremath{\leftarrow}1s transition. Simultaneously, two-photon coupling of the 2s and 1s states produces constructive interference to resonantly enhance the nonlinear susceptibility for sum-frequency generation at the 3p\ensuremath{\rightarrow}1s (Lyman-\ensuremath{\beta}) transition. Experimental results clearly demonstrate the theoretical predictions. When the Rabi frequency for the 3p-2s coupling exceeds the Doppler tail of the medium, the photoion signals on resonance are suppressed significantly because of induced transparency. The generated Lyman-\ensuremath{\beta} radiation grows rapidly by a factor of 250 at an atom density of 1015{10}^{15}1015 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ and interaction length of 3.5 cm, resulting in a conversion efficiency of 2\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}4}$.
We present experimental data on quantum interferences in resonantly enhanced frequency up-conversion towards the vacuum-ultraviolet spectral regime. The process is driven in xenon atoms by ultrashort (picosecond) laser pulses. We use two simultaneous frequency conversion pathways via an excited intermediate state, i.e., fifth harmonic generation of the fundamental wavelength and four-wave mixing of the fundamental and two photons of its second harmonic wavelength. Both conversion pathways yield radiation at 102 nm. The two pathways interfere, depending on the relative phase of the fundamental and second harmonic. By appropriate choice of the phase we get constructive interference (resulting in increased conversion efficiency) or destructive interference (resulting in reduced conversion efficiency). The total conversion yield shows very pronounced constructive and destructive quantum interference with a visibility of roughly 90%. A stable and highly accurate phase control setup enables such strong quantum interferences for more than 260 oscillation cycles. In an extension of the experiment, simultaneously to frequency conversion we also monitor laser-induced fluorescence as a measure for the excitation probability to the excited intermediate state. Also, in the excitation probability we observe strong quantum interferences. As an interesting feature, a small phase lag occurs between the quantum interference patterns of frequency conversion and population transfer. This is due to an additional atomic phase acquired during frequency conversion.
We investigate a four-state system interacting with long and short laser pulses in a weak probe beam approximation. We show that when all lasers are tuned to the exact unperturbed resonances, part of the four-wave mixing (FWM) field is strongly absorbed. The part that is not absorbed has the exact intensity required to destructively interfere with the excitation pathway involved in producing the FWM state. We show that with this three-photon destructive interference, the conversion efficiency can still be as high as 25%. Contrary to common belief, our calculation shows that this process, where an ideal one-photon electromagnetically induced transparency is established, is not most suitable for high-efficiency conversion. With appropriate phase matching and propagation distance, and when the three-photon destructive interference does not occur, we show that the photon flux conversion efficiency is independent of probe intensity and can be close to 100%. In addition, we show clearly that the conversion efficiency is not determined by the maximum atomic coherence between two lower excited states, as commonly believed. It is the combination of phase matching and constructive interference involving the two terms arising in producing the mixing wave that is the key element for the optimized FWM generation. Indeed, in this scheme no appreciable excited state is produced, so that the atomic coherence between states |0〉 and |2〉 is always very small.