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The European Physical Journal B

Quantum aspects of chaos for three-level atoms interacting with two harmonic oscillators

K.D. Harms, Fritz Haake

Published Feb 1, 1990• 4 citations
Publisher
DOI
10.1007/bf01387837

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We study the interaction between a two-level system and a harmonic oscillator without the rotating-wave approximation (RWA). In quantum optics, this model (sometimes called the spin-boson model) is traditionally thought of as a two-Ievel atom coupled to a single-mode radiation field, but it could also describe (1) a two-level ion in a trap coupled to the motion of its own center of mass or (2) a two-level particle in a solid coupled to a phonon mode. For sufficiently strong coupling, this model is known to exhibit chaos in a variety of semi-classical approximations.1
In this paper, the out-of-time-order correlators (OTOC) in quantum harmonic oscillators are calculated analytically by second quantization method in perturbative approximation. We consider the coupled harmonic oscillators and anharmonic (quartic) oscillators. The analytic formulas of microcanonical OTOC in the leading order of interaction are obtained. From these results we clearly see that the interactions can enhance the correlation to very large values over time and is proportional to the energy level. The growth of OTOC signatures the quantum chaos therein. The microcanonical OTOC which is an increasing oscillation becomes a simple increasing function in thermal OTOC after sum over all energy level, as different level oscillates with different frequency. The property that, at late time stage OTOC saturates to a constant value, however, does not show in the first-order perturbation studied in this paper.
A single superconducting artificial atom can be used for coupling electromagnetic fields up to the single-photon level due to an easily achieved strong coupling regime. Bringing a pair of harmonic oscillators into resonance with the transitions of a three-level atom converts atomic spontaneous processes into correlated emission dynamics. We present the experimental demonstration of two-mode correlated emission lasing in harmonic oscillators coupled via a fully controllable three-level superconducting quantum system (artificial atom). The correlation of emissions with two different colors reveals itself as equally narrowed linewidths and quenching of their mutual phase diffusion. The mutual linewidth is more than 4 orders of magnitude narrower than the Schawlow-Townes limit. The interference between the different color lasing fields demonstrates that the two-mode fields are strongly correlated.