Suppressed Quantum Effects of Weakly Coupled Waves

Modern precision experiments, such as axion haloscopes and gravitational wave detectors, are reaching unprecedented sensitivity. A central question is whether these experiments can demonstrate that the fields they detect are fundamentally quantized, or if their results can be fully explained by semiclassical models where a quantum detector interacts with a classical field. This paper investigates whether such "nonclassical" effects—phenomena with no classical counterpart—can be observed in these systems.

Using a combination of quantum optics and field theory, the authors model the interaction between a detector (e.g., a microwave cavity) and a weakly coupled wave (e.g., axion dark matter). They define nonclassicality through the P-function, a quasiprobability distribution where negative values indicate states that cannot be represented as a classical ensemble. The authors analyze two primary barriers: the "coarse-graining" of field modes by realistic detectors and the mathematical suppression of quantum signatures by the weak coupling constant.

The authors identify two severe, independent obstructions to detecting nonclassicality. First, detectors do not couple to fundamental field modes but rather to "effective" modes. The authors show that, due to the quantum central limit theorem, this coarse-graining process typically erases nonclassical features, rendering the effective mode a thermal Gaussian state. Second, even if a nonclassical state is prepared, the observable quantum signatures are suppressed by powers of the weak coupling efficiency (the conversion rate between the wave and the detector). Consequently, any nonclassical effect is parametrically harder to detect than the wave itself. The authors conclude that current and near-future experiments, including those targeting gravitational waves, are unable to establish the quantization of these fields.