Magnetic Field Control of the Quantum Chaotic Dynamics of Hydrogen Analogs in an Anisotropic Crystal Field

Abstract

We report magnetic field control of the quantum chaotic dynamics of hydrogen analogues in an anisotropic solid state environment. The chaoticity of the system dynamics was quantified by means of energy level statistics. We analyzed the magnetic field dependence of the statistical distribution of the impurity energy levels and found a smooth transition between the Poisson limit and the Wigner limit, i.e. transition between regular Poisson and fully chaotic Wigner dynamics. Effect of the crystal field anisotropy on the quantum chaotic dynamics, which manifests itself in characteristic transitions between regularity and chaos for different field orientations, was demonstrated.PACS numbers: 05.45. Mt, 05.45.Gg, The control and anti-control of chaos have been the subject of growing interdisciplinary interest in the past decades [1,2]. The possibility of controlling chaos is not only interesting from the point of view of fundamental physics, but also of immense practical importance. A number of techniques have been developed to control chaos since the seminal work of Ott, Grebogi, and Yorke [3], many of which have been verified experimentally and found applications in a wide variety of fields, e.g. in electronic circuits, non-linear optics, biological systems etc [1,2,4,5]. On the other hand, the presence of chaos in quantum mechanics (sometimes referred to as quantum chaos) has been demonstrated and can be found in quantum systems [6,7]. A large amount of work has been stimulated since its introduction in 1970s. However, understanding the underlying physics of such quantum chaotic systems and finding ways of controlling them remain a major scientific challenge in this field.Highly excited Rydberg atoms in strong magnetic fields are particularly suitable for studying the quantum manifestation of underlying chaotic dynamics, among which hydrogenic atoms received the most attention due to their physical simplicity and experimental feasibility [8]. However, our understanding of chaotic atoms is still far from being complete, not to mention chaotic atom analogues. The quantum manifestation of underlying chaotic dynamics and its control mechanism for atom analogues in solid state environment remain mysterious, despite their fundamental importance.It is now generally known that atom analogues can be well produced in a solid state environment [6]. Perhaps, the physically most appealing conservative system exhibiting underlying chaotic dynamics is the analogue of the hydrogen atom in a semiconductor crystal. Studies have shown that hydrogenlike shallow impurities in semiconductor resemble the energy level structures of the hydrogen atom but with a much smaller energy scale due to the small electron effective mass and large dielectric constants [6,9,10]. The impurity electron feels the external field much more sensitively than in real atoms and thus efficiencies for the control of chaos can be greatly enhanced. Another significant difference from real atoms in vacuum is that series of material parameters can be manipulated, e....

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