https://arxiv.org/ftp/arxiv/papers/2302/2302.04066.pdf
Recently conservation laws in this system have been studied [15] and it was found that energy is
not always conserved.... frequencies may be negative but
photon energies are always positive. The two expressions do not conflict if transitions are
confined to frequencies of the same sign, but if photons make a transition that flips the sign of the
frequency there is a conflict,...The presence of negative frequencies in the transmitted spectrum implies that
qubits have been formed in an essentially quantum process....Spontaneous emission can be
thought
of as emission stimulated by vacuum fluctuations and this is the
approach we take here..... the negative frequency flux will give a true
representation of the processes available to vacuum fluctuations.... the
problem of calculating the emitted spectrum of photons
is reduced to
finding the portion of the two-frequency transmission function that
mixes positive and negative frequencies....positive frequency input can
only stimulate emission at negative frequencies by the creation of
qubits, even though they may not be individually detectable. We shall
show that a substantial fraction of the input energy can be converted to
negative frequencies....negative frequencies do not show up as such in a
spectrometer, they are easily identified if the stimulating frequency
is not an integer multiple...A transluminal diffraction grating traps
and amplifies radiation at points where the local wave and grating
velocities are equal. For a simple cosine modulation of the refractive
index these points occur in pairs, one of which is such an accumulation
point for wave energy, whereas the other is the time reverse of this,
from which electromagnetic radiation is extinguished. We have
demonstrated the equivalence of these points to white and black hole event horizons respectively
and calculated the associated Hawking radiation: the photon emission that occurs when the
vacuum state is incident onto the grating....the vacuum radiation is determined by the classical amplitude for
radiation to be shifted from positive to negative frequencies (or the reverse) after transmission
through the grating.... our results are not restricted to electromagnetism and analogous phenomena should be present in pressure
acoustics
or elasticity, where material dispersion may be reduced....Although the
quantum vacuum radiation can be identified through coincidence photon
counting of oppositely circularly polarized photons, it may be
experimentally challenging to reduce the
temperature such that the
pure vacuum state is incident on the grating. Nevertheless, classical
stimulated emission experiments can reveal the same amplification
process and positive to negative frequency conversion. This makes
acoustics a promising platform for investigating these effects,
connecting to recent work demonstrating amplification of acoustic waves
through positive
to negative frequency conversion [30,31]
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