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Optics Communications

Second harmonics conversion and primary and second harmonics echoes from a resonant two-photon three-level atom system

Jamal T. Manassah, Barry M. Gross

Published Dec 1, 1994• 0 citations
Publisher
DOI
10.1016/0030-4018(94)90614-9

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With the assistance of a cyclic three-level artificial atom of a superconducting flux quantum circuit interacting with a two-mode superconducting transmission-line resonator, we study theoretically the degenerate microwave parametric down-conversion (PDC) in a circuit-QED system. By adiabatically eliminating the excited states of the three-level artificial atom, we obtain an effective microwave PDC Hamiltonian for the two resonator modes (i.e., the fundamental and second-harmonic modes). The corresponding PDC efficiency in our model can be much larger than that in the similar circuit-QED system based on a single two-level superconducting qubit [K. Moon and S. M. Girvin, Phys. Rev. Lett. 95, 140504 (2005)]. Furthermore, we investigate the squeezing and bunching behavior of the fundamental resonator mode resulting from the coherent driving to the second-harmonic one.
Motivated by recent experiments on second-harmonic generation in three-level systems [K. S. Yngvesson and E. L. Kollberg, Appl. Phys. Lett. 36, 104 (1980)], a semiclassical description of resonant three-wave parametric interactions in three nondegenerate levels is considered. Within the limitations of the rotating-wave approximation, analytical nonperturbative solutions for the nonlinear polarization are derived, which are then coupled to Maxwell's equations and integrated numerically. The results of sample calculations for second-harmonic generation show (a) a maximum harmonic conversion occurs on full resonance, (b) the conversion efficiency can be > 50% but requires a strongly saturating pump, (c) the conversion distance increases with pumping intensity, and (d) the inclusion of ac Stark splittings is crucial for the achievement of high conversion efficiency. The role of level splittings is further explored for the case of a resonant parametric oscillator.
Two-photon transitions in a nearly resonant three-level spin system are experimentally investigated at microwave frequencies by detecting the second harmonic (SH) wave emitted by a resonant paramagnetic spin sample. The dependence of the SH intensity and lineshape on the detuning of the intermediate level from the resonance is measured in a dilute ruby sample (Cr 3+ :Al 2 O 3 ). It is shown that the SH output is the coherent superposition of two different contributions which come, respectively, from processes which involve all three levels and from Raman-like processes to which the intermediate level does not take part. The dependence on the intensity and polarisation of the input radiation is measured for each one of the two kinds of processes and interference effects between them are detected.