Description
Collective tunnelling involves the coherent tunnelling of several strongly interacting particles, and is central to, for example, stellar nuclear fusion. However, it remains difficult to describe theoretically, particularly using standard time-dependent mean-field approaches. Mean-field models such as time-dependent Hartree-Fock replace pair-wise particle correlations with an average one-body field, and fail to predict collective tunnelling. This motivates identifying which particle correlations are essential for collective tunnelling but are not fully treated in the mean field, and how they might be reincorporated into beyond mean-field descriptions.
This project investigates the roles of entanglement and quantum magic in collective tunnelling. Entanglement characterises a many-body state’s deviation from tensor-product structure, while magic, or non-stabiliserness, measures a state’s quantum resources and is associated with classical simulation complexity. Using a two-particle, two-state toy model of interacting particles in a double-well potential, we compare exact time evolution with a time-dependent Hartree mean-field approximation. Entanglement is quantified through the entanglement power of the time-evolution operator, following [1], and magic through the magic power based on the second-order stabiliser Rényi entropy, following [2].
Exact solutions show collective tunnelling and indicate that the evolving states possess both entanglement and magic. In contrast, the corresponding mean-field evolution suppresses these correlations and does not reproduce collective tunnelling. These results indicate that entanglement and magic are expected to be important many-body correlations missing in mean-field models. Following this study we will discuss possible avenues for extending mean-field approximations for collective tunnelling.
[1] Beane et al., Phys. Rev. Lett. 122, 102001 (2019)
[2] Leone et al., Phys. Rev. Lett. 128, 050402 (2022).
| I am the presenting author | Yes |
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