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Physical Review A

Dynamics of multiphoton scattering in a two-level mixer

Andrei Vladimirovich Vasenin, A. Yu. Dmitriev, Shamil Kadyrmetov, Aleksey N. Bolgar, O. V. Astafiev

Published Oct 21, 2022• 2 citations
Publisher

Abstract

Mixing of coherent pulses with different carrier frequencies by a two-level atom results in a finite number of sidebands in the emitted spectrum. The authors studied the dynamics of mixing side components in response to characteristics of the coherent pulses such as their number, amplitudes, durations, and overlapping.
DOI
10.1103/physreva.106.l041701

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A superconducting qubit in a waveguide behaves as a point-like nonlinear element. If irradiated with nearly resonant microwave pulses, the qubit undergoes quantum evolution and generates coherent fields at sideband frequencies due to elastic scattering. This effect is called Quantum Wave Mixing (QWM), and the number of emerged side components depends on the number of interacting photons. By driving a superconducting qubit with short pulses with alternating carrier frequencies, we control the maximal number of photons simultaneously interacting with a two-level system by varying the number and duration of applied pulses. Increasing the number of pulses results in consecutive growth of the order of non-linearity, which manifests in additional coherent side peaks appearing in the spectrum of scattered radiation while the whole spectrum maintains its asymmetry.
We present a theoretical analysis of the spectral features of coherent light pulses traveling in a one-dimensional waveguide with an embedded two-level quantum system. In particular, we clarify and explain the relevant physical mechanisms that lead to a rich variety of distinct features in the spectrum of the scattered light. This includes the phenomenon of discrete steps in the transmitted intensity as a function of the excitation amplitude, frequency mixing as a consequence of cascaded nonlinear processes, and the role of atom-photon bound states.
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Summary form only given. It is well-known that the steady-state four-wave mixing (FWM) spectrum, obtained when a two-level atomic system interacts with a coherent pump of arbitrary intensity and a weak probe, is symmetrical and consists of three peaks: a central peak and two Rabi sidebands. Previously, we showed for temporally nonoverlapping pulses, that the spectrum becomes extremely asymmetrical and that only the Rabi sideband near the resonance frequency survives, in the case where the probe precedes the pump. For the opposite case, where the pump precedes the probe, no FWM spectrum is obtained at all. It should be noted that these results hold true provided the pump and probe pulses are much shorter than the transverse relaxation time T/sub 2/ and the pump-probe time delay /spl Delta/t/sub 0/ (/spl Delta/t/sub 0/<0 when the probe precedes the pump). We have also shown that T/sub 2/ can be determined from the slope of the semilog plot of the FWM intensity, near the resonance sideband, versus the pump-probe time delay /spl Delta/t/sub 0/ (for the case /spl Delta/t/sub 0/<0).