Control of anomalous diffusion of a Bose polaron

Christos Charalambous1, Miguel Ángel García-March1,2, Gorka Muñoz-Gil1, Przemysław Ryszard Grzybowski3, and Maciej Lewenstein1,4

1ICFO – Institut de Ciéncies Fotóniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
2Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, E-46022 València, Spain
3Faculty of Physics, Adam Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland
4ICREA, Lluis Companys 23, E-08010 Barcelona, Spain

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Abstract

We study the diffusive behavior of a Bose polaron immersed in a coherently coupled two-component Bose-Einstein Condensate (BEC). We assume a uniform, one-dimensional BEC. Polaron superdiffuses if it couples in the same manner to both components, i.e. either attractively or repulsively to both of them. This is the same behavior as that of an impurity immersed in a single BEC. Conversely, the polaron exhibits a transient nontrivial subdiffusive behavior if it couples attractively to one of the components and repulsively to the other. The anomalous diffusion exponent and the duration of the subdiffusive interval can be controlled with the Rabi frequency of the coherent coupling between the two components, and with the coupling strength of the impurity to the BEC.

The phenomenon of anomalous diffusion, i.e. when a particle does not follow Brownian dynamics, attracts a growing interest in classical and quantum physics, appearing in a plethora of systems. In classical systems, there has been a considerable effort to elucidate the properties and conditions of anomalous diffusive behavior, with a large emphasis given to the question of how this anomalous diffusion could potentially be controlled.
In quantum systems, a paradigmatic instance of a highly controlled system is that of a Bose Einstein Condensate (BEC). Furthermore, it has already been shown that BEC with tunable interactions, are promising systems to study a number of diffusion related phenomena.

In this work, we study the diffusive behavior of an impurity immersed in a coherently coupled two-component BEC. We find that the impurity superdiffuses if it couples in the same manner to both components, i.e. either attractively or repulsively to both of them. This is the same behavior as that of an impurity immersed in a single BEC. However, the impurity exhibits a transient nontrivial subdiffusive behavior if it couples attractively to one of the components and repulsively to the other. The anomalous diffusion exponent as well as the duration of the subdiffusive interval, appearing in this case, are shown to be controlled by the Rabi frequency of the coherent coupling between the two components, and by the coupling strength of the impurity to the BEC.

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