Relativistic electron vortices

The desire to push recent experiments on electron vortices to higher energies has led to some theoretical difficulties. In particular the simple and very successful picture of phase vortices of vortex charge $\ell$ associated with $\ell\hbar$ units of orbital angular momentum per electron has been challenged by the facts that: (i) the spin and orbital angular momentum are not separately conserved for a Dirac electron, which suggests that the existence of a spin-orbit coupling will complicate matters and (ii) that the velocity of a Dirac electron is not simply the gradient of a phase as it is in the Schr\"{o}dinger theory suggesting that, perhaps, electron vortices might not exist at a fundamental level. We resolve these difficulties by showing that electron vortices do indeed exist in the relativistic theory and show that the charge of such a vortex is simply related to a conserved orbital part of the total angular momentum, closely related to the familiar situation for the orbital angular momentum of a photon

Comment on "Trouble with the Lorentz Law of Force: Incompatibility with Special Relativity and Momentum Conservation"

This editorial discusses "Trouble with the Lorentz Law of Force: Incompatibility with Special Relativity and Momentum Conservation"

Quantum state comparison and the universal-NOT operation

We show that the form of the optimal universal-NOT operation for a single qubit can be determined by considering quantum-limited state comparison. Similarly, optimal state comparison can be derived from the properties of the universal-NOT. This points to the possibility of a fundamental link between these processes

On the recoil and Doppler shifts

The recoil shift due to the finite mass of an absorbing atom is, when viewed in the right way, simply part of the total Doppler shift. This is true both in the low speed and relativistic limits and also for the reflection of light from a low-mass mirror

Asynchronous quantum key distribution on a relay network

We show how quantum key distribution on a multi-user, multi-path, network can be used to establish a key between any two end-users in an asynchronous fashion using the technique of bit-transport. By a suitable adaptation of our previous secret-sharing scheme we show that an attacker has to compromise all of the intermediate relays on the network in order to obtain the key. Thus, two end-users can establish a secret key provided they trust at least one of the network relays

Mutually unbiased measurements for high-dimensional time-bin based photonic states

The task of measuring in two mutually unbiased bases is central to many quantum information protocols, as well as being of fundamental interest. Increasingly, there is an experimental focus on generating and controlling high-dimensional photonic states. One approach is to use the arrival time of a photon, which can be split into discrete time bins. An important problem associated with such states is the difficulty in experimentally realizing a measurement that is mutually unbiased with respect to the time-of-arrival. We propose a simple and compact scheme to measure in both the time of arrival basis and a basis that is approximately mutually unbiased with respect to the arrival time.Comment: Accepted in EPL, 4.1 pages and 2 figure

Analytic stochastic treatment of a nonlinear quantum model with negative diffusion

We apply a proposal of Yuen and Tombesi, for treating stochastic problems with negative diffusion, to the analytically soluble problem of the single-mode anharmonic oscillator. We find that the associated stochastic realizations include divergent trajectories. It is possible, however, to solve the stochastic problem exactly, but the averaging must be performed with great care.Comment: Phys.Rev.

Vacuum Friction

We know that in empty space there is no preferred state of rest. This is true both in special relativity but also in Newtonian mechanics with its associated Galilean relativity. It comes as something of a surprise, therefore, to discover the existence a friction force associated with spontaneous emission. he resolution of this paradox relies on a central idea from special relativity even though our derivation of it is non-relativistic. We examine the possibility that the physics underlying this effect might be explored in an ion trap, via the observation of a superposition of different mass states.Comment: 8 pages, 2 figures. Published in Journal of Modern Optics on 14 September 2017. Version 2 with a corrected typo on page

Resolution in rotation measurements

The limiting resolution in optical interferometry is set by the number of photons used, with the functional dependence determined by the state of light that is prepared. We consider the problem of measuring the rotation of a beam of light about an optical axis and show how the limiting resolution depends on the total number of quanta of orbital angular momentum carried by the light beam.Comment: 14 page

The Röntgen interaction and forces on dipoles in time-modulated optical fields

The Röntgen term is an often neglected contribution to the interaction between an atom and an electromagnetic field in the electric dipole approximation. In this work we discuss how this interaction term leads to a difference between the kinetic and canonical momentum of an atom which, in turn, leads to surprising radiation forces acting on the atom. We use a number of examples to explore the main features of this interaction, namely forces acting against the expected dipole force or accelerations perpendicular to the beam propagation axis