Abstract
The dynamics of a wide range of technologically important quantum systems are dominated by their interaction with just a few environmental modes. Such highly structured environments give rise to long-lived bath correlations that induce complex dynamics which are very difficult to simulate. These difficulties are further aggravated when spatial correlations between different parts of the system are important. By modeling the dynamics of a pair of two-level quantum systems in a common, structured, environment we show that a recently developed numerical approach, the time-evolving matrix product operator, is capable of accurate simulation under exactly these conditions. We find that tuning the separation to match the wavelength of the dominant environmental modes can drastically modify the system dynamics. To further explore this behavior, we show that the full dynamics of the bath can be calculated directly from those of the system, thus allowing us to develop intuition for the complex system dynamics observed.
Highlights
When a spatially extended quantum system interacts with a structured environment in which a narrow band of modes dominate, the resulting dynamics can be very complex and difficult to simulate accurately
We have shown that time-evolving matrix product operator (TEMPO) can provide accurate simulations of quantum systems in structured environments
We presented TEMPO simulations of the more complex dynamics that result from the interplay between a highly structured spectral function and spatial correlations between different parts of the system
Summary
When a spatially extended quantum system interacts with a structured environment in which a narrow band of modes dominate, the resulting dynamics can be very complex and difficult to simulate accurately Such environments can retain a memory of their interactions with the system on a time scale comparable to that on which the state of the system changes, and in the face of such memory effects standard open system techniques can fail. By assuming that the environment is uniform the coupling gi,k = gk exp(−ikri ) consists of a position independent part gk and a phase that depends on the site i This kind of model can underpin a wide range of physical systems, for example biological or molecular systems undergoing energy transport and interacting with vibrational modes [5,41], energy transfer in solid-state systems [42], superconducting qubits in microwave resonators [43], or quantum dots interacting with a micromechanical resonator [44]. The cosine term arises from the phase factors in the original coupling terms
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