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arXiv:2610.23392

Resonance crossings and diabolical points for DC electric field quantum sensors

Andrea Sacchetti

quant-phSubmitted Oct 16, 2026• Announced Oct 19, 2026• 0 citations
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Abstract

Since the 1990s, experiments on double-well heterostructures have highlighted a key phenomenon: applying an external DC electric field induces pronounced wave packet oscillations at specific field strengths. \ To gain a deeper insight into this effect, a comprehensive quantitative analysis of the properties of quantum resonances near a crossing point is required. \ This approach lays the theoretical foundation for devising a quantum sensor capable of rapidly and efficiently determining whether the strength of an external DC electric field lies within a narrow target range.

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17 pages - 5 Figures

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Since the 1990s, experiments on double-well heterostructures have highlighted a key phenomenon: applying an external DC electric field induces pronounced wave packet oscillations at specific field strengths. \ To gain a deeper insight into this effect, a comprehensive quantitative analysis of the properties of quantum resonances near a crossing point is required. \ This approach lays the theoretical foundation for devising a quantum sensor capable of rapidly and efficiently determining whether the strength of an external DC electric field lies within a narrow target range.
Abstract We propose a theoretical model for a quantum sensor that can determine in a very simple way whether the intensity of an electric field has an assigned value or not. It is based on the fact that when an exact crossing of the imaginary parts of the resonances occurs in a double-well quantum system subject to an external DC electric field, a damped beating phenomenon occurs, which is absent if there is no such a crossing. This result is then tested numerically on an explicit one-dimensional model.
While the phenomenon of the exact crossing of energy levels is a rarely occurring event, in the case of quantum resonances associated with metastable states this phenomenon is much more frequent and various scenarios can occur. When there is an exact crossing of the imaginary parts of the resonances in a two-level quantum system subject to an external DC electric field, then a damped beating phenomenon occurs, which is absent if there is no such crossing. This fact, tested numerically on an explicit one-dimensional model, suggests the possibility of designing quantum sensors to determine in a very simple way whether the external field strength has an assigned value or not.
In the case of crossings of isolated pairs of quantum resonances for double-well potentials it is possible to observe that, under appropriate conditions, the associated metastable states are equally localised on both wells. This property, together with the fact that the imaginary parts of the two resonances coincide, results in the establishment of an interference phenomenon between the two metastable states that characterises the time dynamics of certain physical observables. In this way, it is possible to lay the theoretical foundations for the design of a quantum device to assess whether or not the model’s parameters assume pre-assigned values.
The tunability of the helium-helium interaction through an external electric field is investigated. For a static external field, electric-field-induced resonances and associated electric-field-induced bound states are calculated for the $^{4}\mathrm{He}\text{\ensuremath{-}}^{4}\mathrm{He},^{3}\mathrm{He}\text{\ensuremath{-}}^{4}\mathrm{He}$, and $^{3}\mathrm{He}\text{\ensuremath{-}}^{3}\mathrm{He}$ systems. Qualitative agreement is found with the literature for the $^{3}\mathrm{He}\text{\ensuremath{-}}^{4}\mathrm{He}$ and $^{3}\mathrm{He}\text{\ensuremath{-}}^{3}\mathrm{He}$ systems [E. Nielsen, D. V. Fedorov, and A. S. Jensen, Phys. Rev. Lett. 82, 2844 (1999)]. The implications of the predicted electric-field-induced resonances for $^{4}\mathrm{He}\text{\ensuremath{-}}^{4}\mathrm{He}$ on the wave packet dynamics, initiated by intense laser pulses, are investigated. Our results are expected to guide next generation experiments.