The zero-point energy stored in the modes of an electromagnetic cavity has experimentally detectable effects, giving rise to an attractive interaction between the opposite walls, the static Casimir effect. A dynamical version of this effect was predicted to occur when the vacuum energy is changed either by moving the walls of the cavity or by changing the index of refraction, resulting in the conversion of vacuum fluctuations into real photons. Here, we demonstrate the dynamical Casimir effect using a Josephson metamaterial embedded in a microwave cavity at 5.4 GHz. We modulate the effective length of the cavity by flux-biasing the metamaterial based on superconducting quantum interference devices (SQUIDs), which results in variation of a few percentage points in the speed of light. We extract the full 4 × 4 covariance matrix of the emitted microwave radiation, demonstrating that photons at frequencies symmetrical with respect to half of the modulation frequency are generated in pairs. At large detunings of the cavity from half of the modulation frequency, we find power spectra that clearly show the theoretically predicted hallmark of the Casimir effect: a bimodal, “sparrow-tail” structure. The observed substantial photon flux cannot be assigned to parametric amplification of thermal fluctuations; its creation is a direct consequence of the noncommutativity structure of quantum field theory.
Dynamical Casimir effect in a Josephson metamaterial
it is due to the mismatch between the field modes at different times when the vacuum is perturbed fast enough.
i.e. Noncommutativity
Indeed, the input-output theory (21, 22) predicts that the field reflected by the cavity will acquire a phase that depends on the detuning with respect to the resonant frequency of the cavity. An observer somewhere along the transmission line far from the cavity would only see a change in the phase of the reflected field, which could have resulted equally well from the movement of a mirror reflecting the input field. From the point of view of this observer, the metamaterial plus cavity system is simply a phase-shifting device.
i.e. Noncommutativity
However, the quantum-mechanical prediction is different: Due to the uncertainty principle, even in the ground state, the pendulum is not truly at rest and the quantum fluctuations will be parametrically converted into real, measurable oscillations of the superconducting phase. According to the ac-Josephson relation, oscillations of the phase will produce an oscillatory voltage that will propagate as real photons in the transmission line. Hence, the Josephson metamaterial acts as an antenna broadcasting information about the local vacuum.
i.e. Noncommutatvity
When the cavity is pumped off-resonance, the spectrum splits into two well-resolved lines and their separation could be extended up to 800 MHz. In addition, we prove experimentally that the emitted radiation is strongly correlated and that it satisfies a nonseparability criterion.
2018 Ph.D. thesis on quantum entanglement in curved spacetime pdf
We show that a possible violation of the Robertson-Schr\"odinger uncertainty principle may signal the existence of a deformation of the Heisenberg-Weyl algebra. More precisely, we prove that any Gaussian in phase-space (even if it violates the Robertson-Schr\"odinger uncertainty principle) is always a quantum state of an appropriate non-commutative extension of quantum mechanics. Conversely, all canonical non-commutative extensions of quantum mechanics display states that violate the Robertson-Schr\"odinger uncertainty principle.
Chattopadhyay, P. Non-commutative space: boon or bane for quantum engines and refrigerators. Eur. Phys. J. Plus 135, 302 (2020). https://doi.org/10.1140/epjp/s13360-020-00318-7
The answer is boon - I speed-read the article.
https://journals.aps.org/prd/pdf/10.1103/PhysRevD.97.044015
So this is just as with the Music Noncommutative analysis! Fascinating.
And so when Heisenberg originally realized that quantum mechanics was Noncommutative - he could NOT accept it at first! ONly his Advisor BORN emphasized this point of the mathematics:
https://arxiv.org/ftp/arxiv/papers/1612/1612.02959.pdf
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