Abstract
Quantum electrodynamics predicts the vacuum to behave as a non-linear medium, including effects such as birefringence. However, for experimentally available field strengths, this vacuum polarizability is extremely small and thus very hard to measure. In analogy to the Heisenberg limit in quantum metrology, we study the minimum requirements for such a detection in a given strong field (the pump field). Using a laser pulse as the probe field, we find that its energy must exceed a certain threshold depending on the interaction time. However, a detection at that threshold, i.e., the Heisenberg limit, requires highly non-linear measurement schemes - while for ordinary linear-optics schemes, the required energy (Poisson or shot noise limit) is much larger. Finally, we discuss several currently considered experimental scenarios from this point of view.
Highlights
Classical electrodynamics is governed by the Maxwell equations, which are linear in the absence of sources
Apart from the strength of the quantum vacuum polarizability, we find that the available interaction time and the total energy of the probe pulse play an important role
Turning the above argument around, we get a minimum energy E of the probe pulse required for detecting the vacuum polarizability δε, δμ and δΨ in a given interaction time T since the phase shift φ should not be too small in order to achieve a measurable effect
Summary
Classical electrodynamics is governed by the Maxwell equations, which are linear in the absence of sources. On the other hand, predicts deviations from this behavior: Even the quantum vacuum should be polarizable and behave as a nonlinear medium due to the coupling to the fermionic modes; see, e.g., [2,3,4,5,6,7,8,9,10,11] Since this polarizability is extremely weak for available fields, this fundamental prediction of quantum electrodynamics has not been experimentally verified yet for electromagnetic waves in vacuum (i.e., real photons). Apart from the strength of the quantum vacuum polarizability, we find that the available interaction time and the total energy of the probe pulse play an important role The independence of this limit on the concrete measurement scheme helps us to compare different experimental scenarios and to identify their advantages and drawbacks. Preconditions and limitations of this limit point toward ultimate possibilities of increasing sensitivity, even though the required experimental capabilities may be beyond present-day technology
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