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In terms of a photon wave function corresponding to the (1, 0)+(0, 1) representation of the Lorentz group, the radiation and Coulomb fields within a source-free region can be described unitedly by a Lorentz-covariant Dirac-like equation. In our formalism, the relation between the positive- and negative-energy solutions of the Dirac-like equation corresponds to the duality between the electric and magnetic fields, rather than to the usual particle-antiparticle symmetry. The zitterbewegung (ZB) of photons is studied via the momentum vector of the electromagnetic field, which shows that only in the presence of virtual longitudinal and scalar photons, the ZB motion of photons can occur, and its vector property is described by the polarization vectors of the electromagnetic field.
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In quantum communications, quantum states are employed for the transmission of information between remote parties. This usually requires sharing knowledge of the measurement bases through a classical public channel in the sifting phase of the protocol. Here, we demonstrate a quantum communication scheme where the information on the bases is shared non-classically, by encoding this information in the same photons used for carrying the data. This enhanced capability is achieved by exploiting the localization of the photonic wave function, observed when the photons are prepared and measured in the same quantum basis. We experimentally implement our scheme by using a multi-mode optical fiber coupled to an adaptive optics setup. We observe a decrease in the error rate for higher dimensionality, indicating an improved resilience against noise.
Ultra-cold atoms which are subject to ultra-relativistic dynamics are investigated. By using optically induced gauge potentials we show that the dynamics of the atoms is governed by a Dirac type equation. To illustrate this we study the trembling motion of the centre of mass for an effective two level system, historically called Zitterbewegung. Its origin is described in detail, where in particular the role of the finite width of the atomic wave packets is seen to induce a damping of both the centre of mass dynamics and the dynamics of the populations of the two levels.
In term of the volume-integrated Poynting vector, we present a quantum field-theory investigation on the zitterbewegung (ZB) of photons, and show that this ZB occurs only in the presence of virtual longitudinal and scalar photons. To present a heuristic explanation for such ZB, by assuming that the space time is sufficiently close to the flat Minkowski space, we show that the gravitational interaction can result in the ZB of photons.
A neo-classical relativistic mechanics model is presented where the spin of an electron is a natural part of its space-time path. The fourth-order equation of motion corresponds to the same Lagrangian function in proper time as in special relativity except for an additional spin energy term. The total motion can be decomposed into a sum of a local circular motion giving the spin and a global motion of the spin center, each being governed by a second-order differential equation. The local spin motion corresponds to Schrodingers zitterbewegung and is a perpetual motion; it produces magnetic and electric dipoles through the Lorentz force on the electrons point charge. The global motion is sub-luminal and described by Newtons second law in proper time, the time for a clock fixed at the spin center, where the inertia to acceleration resides. The total motion occurs at the speed of light c, consistent with the eigenvalues of Diracs velocity operators having magnitude c. A spin tensor is introduced that is the angular momentum of the electrons total motion about its spin center. The fundamental equations of motion expressed using this tensor are identical to those of the Barut-Zanghi theory; they can be expressed in an equivalent form using the same operators as in Diracs theory for the electron but applied to a state function of proper time satisfying a Dirac-Schrodinger spinor equation. This state function produces a neo-classical wave function that satisfies Diracs relativistic wave equation for the free electron when the Lorentz transformation is used to express proper time in terms of an observers space-time coordinates. In summary, the theory provides a hidden-variable model for spin that leads to Diracs relativistic wave equation and explains the electrons moment coupling to an electro-magnetic field, albeit with a magnetic moment that is one half of that in Diracs theory.
We show that Bogoliubovs quasiparticle in superfluid $^3He-B$ undergoes the Zitterbewegung, as a free relativistic Diracs electron does. The expectation value of position, as well as spin, of the quasiparticle is obtained and compared with that of the Diracs electron. In particular, the Zitterbewegung of Bogoliubovs quasiparticle has a frequency approximately $10^5$ lower than that of an electron, rendering a more promising experimental observation.
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