Parametric excitation of the quantum vacuum

Quantum electrodynamics is the most accurate and best tested theory in physics so far. The electromagnetic force is described by a quantum field where its interaction with charged particles like the electron is mediated by photons. Photons are excitations of the field which contains an infinite amount of continuous frequency modes. Each of the modes is a quantum harmonic oscillator and has a non-vanishing amount of energy in its ground state. This energy together with the Heisenberg uncertainty principle leads to a magnificent consequence: for a short amount of time we can borrow some energy and produce particles out of the quantum vacuum which vanish in an instant. These vacuum fluctuations are in general not directly accessible in experiments and the particles are called virtual.

Casimir Cavity
© Pascal Kobel

Since cavities enable highly sensitive measurements, they serve as a test bed for studying quantum electrodynamics. With the exclusion of non-resonant modes inside the cavity, it modifies the electromagnetic field structure. Hence, only those electromagnetic waves can enter the resonator which retrace themselves after one round trip. Thus, from the continuum of electromagnetic modes, the cavity selects an infinite set of discrete equidistantly separated modes.

If we now periodically change the cavity length, pairs of virtual photons are converted into real observable ones if the modulation frequency equals the sum of the photon frequencies. Virtual particles exert a radiation pressure force onto the oscillating mirror and damp its motion with the consequence of exciting the quantum vacuum. It is a parametric excitation, since due to the time-varying cavity length, the fundamental frequency mode is changed and thus the set of resonant frequency modes.

Since the oscillation frequency needs to be twice the photon frequency, it is impossible to perform the experiment at optical frequencies on the order of several hundred THz. However, instead of modulating the physical cavity length, we modify the optical path length by altering the speed of light periodically. Since the speed of light in materials is determined by the material’s refractive index, we can modify the fundamental frequency by modulating the refractive index. This is analogous to altering the physical cavity length. We place a nonlinear material inside a cavity and change its refractive index by illuminating the nonlinear material with two high-power lasers.

We reach intensities ten orders of magnitude larger than the intensity of the sun on a sunny day in Germany. The modulation of the fundamental frequency of the cavity leads to an excitation of the quantum vacuum. We generate pairs of photons and convert virtual pairs of photons into real, detectable ones.

Casimir Effect Scheme
© Thorsten Langerfeld
Casimir High Power Laser
© Thorsten Langerfeld


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Dr. Thorsten Langerfeld

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