Quantum Vacuum Contribution to the Momentum of Dielectric Media

Momentum transfer between matter and electromagnetic field is analyzed. The related equations of motion and conservation laws are derived using relativistic formalism. Their correspondence to various, at first sight self-contradicting, experimental data (the so-called Abraham-Minkowski controversy) is demonstrated. A new, Casimir-like, quantum phenomenon is predicted: contribution of vacuum fluctuations to the motion of dielectric liquids in crossed electric and magnetic fields. Velocities of about $50\mathrm{n}\mathrm{m}/\mathrm{s}$ can be expected due to the contribution of high frequency vacuum modes. The proposed phenomenon could be used in the future as an investigating tool for zero fluctuations. Other possible applications lie in fields of microfluidics or precise positioning of micro-objects, e.g., cold atoms or molecules.

Figure 1

Vacuum fluctuations contribute to the motion of dielectrics in crossed electric and magnetic fields. Applied fields convert matter to magnetoelectric by breaking both spatial and time symmetries. Inside a magnetoelectrics the momenta of counterpropagating vacuum modes [$k_{+}(\omega )$ and $k_{-}(\omega )$] do not eliminate each other, in contrast to the other materials. Therefore, the vacuum field gains a finite momentum each time the fields are turned on. The latter is compensated by the motion of the matter itself. The vacuum fluctuations induced flow in dielectric liquids with $v_{\mathrm{v}\mathrm{a}\mathrm{c}\mathrm{u}\mathrm{u}\mathrm{m}}\approx v_{\mathrm{c}\mathrm{l}\mathrm{a}\mathrm{s}\mathrm{s}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{l}}\approx 50\mathrm{n}\mathrm{m}/\mathrm{s}$ was predicted theoretically in external crossed electric and magnetic fields.