arXiv subjects

M. Babiker

Publications and source records attributed to M. Babiker.

14 recordsLinked to original sources

arXiv2024

Reply to Comment by K. Forbes on "The super-chirality of vector twisted light" by M. Babiker, J. Yuan, K. Koksal and V. E. Lembessis; Optics Communications 554, 130185 (2024)

We respond to the recent comment in Optics Communications by Kayn Forbes on our recent Optics Communications article and we maintain that, contrary to what Forbes claims, substantial superchirality exists as a property of the $m\geq 1$ higher order Poincare modes. Forbes arguments are based on misconceptions and analytical errors, leading to erroneous results and unjustified criticism.

physics.optics↗

arXiv2019

Interference of axially-shifted Laguerre-Gaussian beams and their interaction with atoms

Counter-propagating co-axial Laguerre-Gaussian (LG) beams are considered, not in the familiar scenario where the focal planes coincide at $z=0$, but when they are separated by a finite axial distance $d$. The simplest case is where both beams are doughnut beams which have the same linear polarisation. The total fields of this system are shown to display novel amplitude and phase distributions and are shown to give rise to a ring or a finite ring lattice composed of double rings and single central ring. When the beams have slightly different frequencies the ring lattice pattern becomes a finite set of rotating Ferris wheels and the whole pattern also moves axially between the focal planes. We show that the field of such an axially shifted pair of counter-propagating LG beams generate trapping potentials due to the dipole force which can trap two-level atoms in the components of the ring lattice. We also highlight a unique feature of this system which involves the creation of a new longitudinal optical atom trapping potential due to the scattering force which arises solely when $d \ne 0$. The results are illustrated using realistic parameters which also confirm the importance of the Gouy and curvature effects in determining the ring separation both radially and axially and gives rise to the possibility of atom tunnelling between components of the double rings.

quant-ph↗

arXiv2019

Even-odd effect in higher-order holographic production of electron vortex beams with nontrivial radial structures

Structured electron beams carrying orbital angular momentum are currently of considerable interest, both from a fundamental point of view and for application in electron microscopy and spectroscopy. Until recently, most studies have focused on the azimuthal structure of electron vortex beams with well-defined orbital angular momentum. To unambiguously define real electron-beam states and realise them in the laboratory, the radial structure must also be specified. Here we use a specific set of orthonormal modes of electron (vortex) beams to describe both the radial and azimuthal structures of arbitrary electron wavefronts. The specific beam states are based on truncated Bessel beams localised within the lens aperture plane of an electron microscope. We show that their Fourier transform set of beams can be realised at the focal planes of the probe-forming lens using a binary computer generated electron hologram. Using astigmatic transformation optics, we demonstrate that the azimuthal indices of the diffracted beams scale with the order of the diffraction through phase amplification. However, their radial indices remain the same as those of the encoding beams for all the odd diffraction orders or are reduced to the zeroth order for the even-order diffracted beams. This simple even-odd rule can also be explained in terms of the phase amplification of the radial profiles. We envisage that the orthonormal cylindrical basis set of states could lead to new possibilities in phase contrast electron microscopy and spectroscopy using structured electron beams.

quant-ph↗

arXiv2017

Orbital angular momentum mode selection by rotationally symmetric superposition of chiral states with application to electron vortex beams

A general orbital angular momentum (OAM) mode selection principle is put forward involving the rotationally symmetric superposition of chiral states. This principle is not only capable of explaining the operation of spiral zone plate holograms and suggesting that naturally occurring rotationally symmetric patterns could be inadvertent sources of vortex beams, but more importantly, it enables the systematic and flexible generation of structured OAM waves in general. This is demonstrated both experimentally and theoretically in the context of electron vortex beams using rotationally symmetric binary amplitude chiral sieve masks.

quant-ph↗

arXiv2016

Robust and adjustable C-shaped vortex beams

Wavefront engineering is an important quantum technology. Here, we demonstrate the design and production of a robust C-shaped and orbital angular momentum (OAM) carrying beam in which the doughnut shaped structure contains an adjustable gap. We find that the presence of the vortex line in the core of the beam is crucial for the robustness of the C-shape against beam propagation. The topological charge of the vortex core controls mainly the size of the C, while its opening angle is controlled by the presence of vortex-anti-vortex loops. We demonstrate the generation and characterisation of C-shaped electron vortex beams, although the result is equally applicable to other quantum waves. Applications of C-shaped vortex beams include lithography, dynamical atom sorting and atomtronics.

physics.optics↗

arXiv2013

Chiral specific electron vortex beam spectroscopy

Electron vortex beams carry well-defined orbital angular momentum (OAM) about the propagation axis. Such beams are thus characterised by chirality features which make them potentially useful as probes of magnetic and other chiral materials. An analysis of the inelastic processes in which electron vortex beams interact with atoms and which involve OAM exchange is outlined, leading to the multipolar selection rules governing this chiral specific electron vortex beam spectroscopy. Our results show clearly that the selection rules are dependent on the dynamical state and location of the atoms involved. In the most favorable scenario, this form of electron spectroscopy can induce magnetic sublevel transitions which are commonly probed using circularly polarized photon beams.

quant-ph↗

arXiv2012

Interaction of electron vortices and optical vortices with matter and processes of orbital angular momentum exchange

The quantum processes involved in the interaction of matter with, separately, an electron vortex(EV) and an optical vortex (OV) are described, with matter modelled in terms of a neutral two particle atomic system, allowing for both the internal (electronic-type) motion and the gross (center of mass-type) motion of matter to be taken into account. The coupling of the atomic system to the EV is dominated by Coulomb forces, while that of the OV is taken in the $\mathbf{p}\cdot\mathbf{A}$ canonical form which couples $\mathbf{A}$, the transverse vector potential of the optical vortex, to the linear momenta of the two-particle system. An analysis of the dipole active transition matrix element is carried out in each case. The electron vortex is found to be capable of exchanging its orbital angular momentum (OAM) with both the electronic and the center of mass motions of the atomic system in an electric dipole transition. In contrast, for electric dipole transitions the optical vortex is found to be capable of exchanging OAM only with the center of mass. The predictions are discussed with reference to recent experiments on electron energy loss spectroscopy (EELS) using EVs traversing magnetised iron thin film samples and those involving OVs interacting with chiral molecules.

quant-ph↗

arXiv2011

Asymptotic quantum degeneracy at a 2D corner

In quantum mechanics, asymptotic degeneracy is often considered in the context of a particle in a symmetric double-well potential, and is the phenomenon whereby pairs of energy levels come together to form doubly degenerate levels in response to an increase in the separation, or depth of the two wells. Here we highlight a new kind of asymptotic degeneracy that can arise when a particle is bound to a surface formed by the intersection of two planes, when the intersection angle is greater than pi. To demonstrate this effect we consider the bound states of a charged particle subject its own 'image' potential in a highly polarizable wedge, as a function of the wedge opening angle.

quant-ph↗

arXiv2010

Electron scattering and capture rates in quantum wells by emission of hybrid optical phonons

Intra and intersubband scattering rates and electron capture rates are considered when mediated by hybrid optical phonons in an AlAs/GaAs/AlAs double heterostructure confined between two outer metallic barriers. In evaluating scattering rates we concentrate first on an infinite quantum well for the electrons and show that the presence of the outer metal barriers results in reductions of the intra and intersubband scattering rates due to the suppression of the interface-like modes. For a quantum well (QW) with a finite depth we find that the outer barriers are responsible for the existence of a discrete energy spectrum above the well. The electron capture process under these circumstances is defined as the electron transition from the first electron subband above the well to all possible subbands inside the well by the emission of hybrid phonons. Explicit calculations reveal that the capture rates are characterized by sharp peaks, referred to as electron resonances which arise when a new electron state is generated on increasing the quantum well width. Other sharp peaks are identified as phonon resonances and arise when the energy of the initial state differs by a phonon energy from an electron state at the bottom of a quantum well subband.

cond-mat.mes-hall↗

arXiv2006

Atomic reflection off conductor walls as a tool in cold atom traps

We explain why a system of cold $^{85}Rb$ atoms at temperatures of the order $T\approx 7.78\times 10^{-5}$ K and below, but not too low to lie in the quantum reflection regime, should be automatically repelled from the surface of a conductor without the need of an evanescent field, as in a typical atom mirror, to counteract the van der Waals attraction. The repulsive potential arises naturally outside the conductor and is effective at distances from the conductor surface of about 400nm, intermediate between the van der Waals and the Casimir-Polder regions of variation. We propose that such a field-free reflection capability should be useful as a component in cold atom traps. It should be practically free of undesirable field fluctuations and would be operative at distances for which surface roughness, dissipative effects and other finite conductivity effects should be negligibly small.

quant-ph↗

arXiv2002

Enhancement of energy relaxation rates near metal-coated dielectric cylinders

The electromagnetic modes and their field distributions are evaluated for a dielectric cylindrical structure embedded in another dielectric, with a thin metallic film at the cylinder/dielectric interface. These modes provide energy relaxation channels for excited dipole emitters located inside or outside the cylinder. Significantly, we find that the emission rate is sensitive to the magnitude of the electron density of the metallic film coating. For typical parameter values, we find large enhancements of the emission rate, which can be in excess of three orders of magnitude, relative to the case in the absence of the film, arising at specific ranges of electron density. The theory is shown to conform with known limits, including the high density (perfect conductor) limit and the large distance (unbounded bulk) limit. The implications of the predicted enhancement due to the metal coating for the purpose of guiding atoms within such microstructures are pointed out.

physics.atom-ph↗

arXiv2001

Quantum theory of spontaneous emission by real moving atoms

We outline the solution of a fundamental problem in quantum theory which has hitherto lacked a proper solution, namely finding the requisite quantum theoretical framework guaranteeing that the calculated inverse spontaneous emission rate of a moving atom, as a composite system of charged particles interacting with the Maxwell field, is slowed down exactly as in time dilation.

physics.atom-ph↗

arXiv2000

The influence of a metallic sheet on an evanescent mode atomic mirror

A theory of evanescent mode atomic mirrors utilising a metallic sheet on a dielectric substrate is described. The emphasis here is on the role of the metallic sheet and on the evaluation of atomic trajectories using the field- dipole orientation picture. At low intensity, the atomic reflection process is controlled by two separate mechanisms both of which are modified by the presence of the metallic sheet and influenced by the use of the field-dipole orientation picture. The first mechanism involves the spontaneous force which accelerates the atom parallel to the sheet plane. The second mechanism involves the combined dipole plus van der Waals force which acts to repel the atom from the surface, decelerating its motion until it attains an instantaneous halt before changing direction away from the surface at an appr opriate turning point in the trajectory. Various quantitative features arising from varying the controllable parameters of the system, including screening effects as well as desirable enhancement effects, are pointed out and discussed.

physics.optics↗

arXiv2000

Many-body theory of dilute gas condensates - derivation of a field-modified Gross-Pitaevskii equation from multipolar QED

The Hamiltonian of a moving atom in electromagnetic fields includes velocity- dependent terms. We show that the leading velocity dependence emerges systematically in the non-relativistic limit from a scheme firmly based on the relativistic invariance of the energy-momentum stress tensor of the coupled matter-fields system. We then extend the Hamiltonian to the many-body situation suitable for describing a Bose-Einstein condensate (BEC). From first principles, we use the equation of motion for the condensate wavefunction to obtain an extended version of the Gross-Pitaevskii (GP) equation and an equation for the internal states of the atoms. It is shown that laser fields modify the GP equation by inclusion of convective terms involving a Rontgen interaction plus a term coupling the centre of mass momentum to the Poynting vector. We also obtain the modified Maxwell equations for the electromagnetic fields coupled to the BEC involving the average velocity of the atoms.

cond-mat↗