Generally Applicable Holographic Torque Measurement for Optically Trapped Particles.

We present a method to measure the optical torque applied to particles of arbitrary shape such as micrometer-sized micro-organisms or cells held in an optical trap, inferred from the change of angular momentum of light induced by the particle. All torque components can be determined from a single interference pattern recorded by a camera in the back focal plane of a high-NA condenser lens provided that most of the scattered light is collected. We derive explicit expressions mapping the measured complex field in this plane to the torque components. The required phase is retrieved by an iterative algorithm, using the known position of the optical traps as constraints. The torque pertaining to individual particles is accessible, as well as separate spin or orbital parts of the total torque.

Quantum Nonlocal Aberration Cancellation.

Phase distortions, or aberrations, can negatively influence the performance of an optical imaging system. Through the use of position-momentum entangled photons, we nonlocally correct for aberrations in one photon's optical path by intentionally introducing the complementary aberrations in the optical path of the other photon. In particular, we demonstrate the simultaneous nonlocal cancellation of aberrations that are of both even and odd order in the photons' transverse degrees of freedom. We also demonstrate a potential application of this technique by nonlocally canceling the effect of defocus in a quantum imaging experiment and thereby recover the original spatial resolution.

Mechanical chiral resolution.

Mechanical interactions of chiral objects with their environment are well-established at the macroscale, like a propeller on a plane or a rudder on a boat. At the colloidal scale and smaller, however, such interactions are often not considered or deemed irrelevant due to Brownian motion. As we will show in this tutorial review, mechanical interactions do have significant effects on chiral objects at all scales, and can be induced using shearing surfaces, collisions with walls or repetitive microstructures, fluid flows, or by applying electrical or optical forces. Achieving chiral resolution by mechanical means is very promising in the field of soft matter and to industry, but has not received much attention so far.

Relativistic Electron Vortices.

The desire to push recent experiments on electron vortices to higher energies leads to some theoretical difficulties. In particular the simple and very successful picture of phase vortices of vortex charge ℓ associated with ℓℏ units of orbital angular momentum per electron is 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 Schrödinger 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.

Will a Decaying Atom Feel a Friction Force?

We show how a simple calculation leads to the surprising result that an excited two-level atom moving through a vacuum sees a tiny friction force of first order in v/c. At first sight this seems to be in obvious contradiction to other calculations showing that the interaction with the vacuum does not change the velocity of an atom. It is even more surprising that this change in the atom's momentum turns out to be a necessary result of energy and momentum conservation in special relativity.

Experimental implementation of a quantum optical state comparison amplifier.

We present an experimental demonstration of a practical nondeterministic quantum optical amplification scheme that employs two mature technologies, state comparison and photon subtraction, to achieve amplification of known sets of coherent states with high fidelity. The amplifier uses coherent states as a resource rather than single photons, which allows for a relatively simple light source, such as a diode laser, providing an increased rate of amplification. The amplifier is not restricted to low amplitude states. With respect to the two key parameters, fidelity and the amplified state production rate, we demonstrate significant improvements over previous experimental implementations, without the requirement of complex photonic components. Such a system may form the basis of trusted quantum repeaters in nonentanglement-based quantum communications systems with known phase alphabets, such as quantum key distribution or quantum digital signatures.

Optical angular momentum in a rotating frame.

It is well established that light carrying orbital angular momentum (OAM) can be used to induce a mechanical torque causing an object to spin. We consider the complementary scenario: will an observer spinning relative to the beam axis measure a change in OAM as a result of their rotational velocity? Remarkably, although a linear Doppler shift changes the linear momentum of a photon, the angular Doppler shift induces no change in the angular momentum. Further, we examine the rotational Doppler shift in frequency imparted to the incident light due to the relative motion of the beam with respect to the observer and consider what must happen to the measured wavelength if the speed of light c is to remain constant. We show specifically that the OAM of the incident beam is not affected by the rotating observer and that the measured wavelength is shifted by a factor equal and opposite to that of the frequency shift induced by the rotational Doppler effect.

Is the angular momentum of an electron conserved in a uniform magnetic field?

We show that an electron moving in a uniform magnetic field possesses a time-varying "diamagnetic" angular momentum. Surprisingly this means that the kinetic angular momentum of the electron may vary with time, despite the rotational symmetry of the system. This apparent violation of angular momentum conservation is resolved by including the angular momentum of the surrounding fields.

Optical activity in the scattering of structured light.

We observe that optical activity in light scattering can be probed using types of illuminating light other than single plane (or quasi plane) waves and that this introduces new possibilities for the study of molecules and atoms. We demonstrate this explicitly for natural Rayleigh optical activity which, we suggest, could be exploited as a new form of spectroscopy for chiral molecules through the use of illuminating light comprised of two plane waves that are counter propagating.

Molecules in the mirror: how SERS backgrounds arise from the quantum method of images.

The Raman coupling of light to molecular vibrations is strongly modified when they are placed near a plasmonic metal surface, with the appearance of a strong broad continuum background in addition to the normal surface-enhanced Raman scattering (SERS) peaks. Using a quantum method of images approach, we produce a simple but quantitative explanation of the inevitable presence of the background, due to the resistive damping of the image molecule. This model thus suggests new strategies for enhancing the SERS peak to background ratio.

Diffraction gratings for chiral molecules and their applications.

We suggest the use of certain readily producible types of light to exert a force that points in opposite directions for the enantiomers of a chiral molecule and propose multiple devices based upon this novel manifestation of optical activity: in particular, our discriminatory chiral diffraction grating; a device that could be employed, for example, to measure the enantiomeric excess of a sample of chiral molecules simply and to high precision. Our work is relevant for many types of molecules and our proposed devices may be realizable using currently existing technology.

Spatial Control of 2D Nanomaterial Electronic Properties Using Chiral Light Beams.

Single-layer two-dimensional (2D) nanomaterials exhibit physical and chemical properties which can be dynamically modulated through out-of-plane deformations. Existing methods rely on intricate micromechanical manipulations (e.g., poking, bending, rumpling), hindering their widespread technological implementation. We address this challenge by proposing an all-optical approach that decouples strain engineering from micromechanical complexities. This method leverages the forces generated by chiral light beams carrying orbital angular momentum (OAM). The inherent sense of twist of these beams enables the exertion of controlled torques on 2D monolayer materials, inducing tailored strain. This approach offers a contactless and dynamically tunable alternative to existing methods. As a proof-of-concept, we demonstrate control over the conductivity of graphene transistors using chiral light beams, showcasing the potential of this approach for manipulating properties in future electronic devices. This optical control mechanism holds promise in enabling the reconfiguration of devices through optically patterned strain. It also allows broader utilization of strain engineering in 2D nanomaterials for advanced functionalities in next-generation optoelectronic devices and sensors.

Comment on "Trouble with the Lorentz law of force: incompatibility with special relativity and momentum conservation".

A comment on the letter by M. Mansuripur, Phys. Rev. Lett. 108, 193901 (2012). The authors of the letter offer a reply.

Do waves carrying orbital angular momentum possess azimuthal linear momentum?

All beams are a superposition of plane waves, which carry linear momentum in the direction of propagation with no net azimuthal component. However, plane waves incident on a hologram can produce a vortex beam carrying orbital angular momentum that seems to require an azimuthal linear momentum, which presents a paradox. We resolve this by showing that the azimuthal momentum is not a true linear momentum but the azimuthal momentum density is a true component of the linear momentum density.

Quantum optical state comparison amplifier.

It is a fundamental principle of quantum theory that an unknown state cannot be copied or, as a consequence, an unknown optical signal cannot be amplified deterministically and perfectly. Here we describe a protocol that provides nondeterministic quantum optical amplification in the coherent state basis with high gain and high fidelity and which does not use quantum resources. The scheme is based on two mature quantum optical technologies: coherent state comparison and photon subtraction. The method compares favorably with all previous nondeterministic amplifiers in terms of fidelity and success probability.

Optical Thomas-Reiche-Kuhn sum rules.

The Thomas-Reiche-Kuhn sum rule is a fundamental consequence of the position-momentum commutation relation for an atomic electron and it provides an important constraint on the transition matrix elements for an atom. Analogously, the commutation relations for the electromagnetic field operators in a magnetodielectric medium constrain the properties of the dispersion relations for the medium through four sum rules for the allowed phase and group velocities for polaritons propagating through the medium. These rules apply to all bulk media including the metamaterials designed to provide negative refractive indices. An immediate consequence of this is that it is not possible to construct a medium in which all the polariton modes for a given wavelength lie in the negative-index region.

Influence of atmospheric turbulence on the propagation of quantum states of light using plane-wave encoding.

We consider the possibility of performing quantum key distribution (QKD) by encoding information onto individual photons using plane-wave basis states. We compare the results of this calculation to those obtained by earlier workers, who considered encoding using OAM-carrying vortex modes of the field. We find theoretically that plane-wave encoding is less strongly influenced by atmospheric turbulence than is OAM encoding, with potentially important implications for free-space quantum key distribution.

Resolution of the abraham-minkowski dilemma.

The dilemma of identifying the correct form for the momentum of light in a medium has run for a century and has been informed by many distinguished contributions, both theoretical and experimental. We show that both the Abraham and Minkowski forms of the momentum density are correct, with the former being the kinetic momentum and the latter the canonical momentum. This identification allows us to explain why the experiments supporting each of the rival momenta gave the results that they did. The inclusion of dispersion and absorption provides an interesting subtlety, but does not change our conclusion.

Angular two-photon interference and angular two-qubit states.

Using angular-position-orbital-angular-momentum entangled photons, we study angular two-photon interference in a scheme in which entangled photons are made to pass through apertures in the form of double angular slits, and using this scheme, we demonstrate an entangled two-qubit state that is based on the angular-position correlations of entangled photons. The entanglement of the two-qubit state is quantified in terms of concurrence. These results provide an additional means for preparing entangled quantum states for use in quantum information protocols.