Generalized coherent states

In the coherent state of the harmonic oscillator, the probability density is that of the ground state subjected to an oscillation along a classical trajectory. Senitzky and others pointed out that there are states of the harmonic oscillator corresponding to an identical oscillatory displacement of the probability density of any energy eigenstate. These generalizations of the coherent state are rarely discussed, yet they furnish an interesting set of quantum states of light that combine features of number states and coherent states. Here we give an elementary account of the quantum optics of generalized coherent states

Derivation of quantum probabilities from deterministic evolution

This is the author accepted manuscript. The final version is available from the Institute for the History of Natural Sciences, Chinese Academy of Sciences.The predictions of quantum mechanics are probabilistic. Quantum probabilities are extracted using a postulate of the theory called the Born rule, the status of which is central to the "measurement problem" of quantum mechanics. Efforts to justify the Born rule from other physical principles, and thus elucidate the measurement process, have involved lengthy statistical or information-theoretic arguments. Here we show that Bohm's deterministic formulation of quantum mechanics allows the Born rule for measurements on a single system to be derived, without any statistical assumptions. We solve a simple example where the creation of an ensemble of identical quantum states, together with position measurements on those states, are described by Bohm's quantum dynamics. The calculated measurement outcomes agree with the Born-rule probabilities, which are thus a consequence of deterministic evolution. Our results demonstrate that quantum probabilities can emerge from simple dynamical laws alone, and they support the view that there is no underlying indeterminism in quantum phenomena

Electromagnetic reflection, transmission and energy density at boundaries of nonlocal media

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.We consider a semi-infinite spatially dispersive dielectric with unequal transverse and longitudinal susceptibilities. The effect of the boundary is characterized by arbitrary reflection coefficients for polarization waves in the material that propagate to the surface. Specific values of these coefficients correspond to various additional boundary conditions (ABC) for Maxwell's equations. We derive the electromagnetic reflection and transmission coefficients at the boundary and investigate their dependence on material parameters and ABC. We also investigate the electromagnetic zero-point and thermal spectral energy density outside the dielectric. The nonlocal response removes the boundary divergence of the spectral energy density that is present in a local model. The spectral energy density shows a large dependence on the difference between the transverse and longitudinal susceptibilities, even at distances up to 10nm from the boundary

Transmutation of singularities and zeros in graded index optical instruments: a methodology for designing practical devices.

We describe a design methodology for modifying the refractive index profile of graded-index optical instruments that incorporate singularities or zeros in their refractive index. The process maintains the device performance whilst resulting in graded profiles that are all-dielectric, do not require materials with unrealistic values, and that are impedance matched to the bounding medium. This is achieved by transmuting the singularities (or zeros) using the formalism of transformation optics, but with an additional boundary condition requiring the gradient of the co-ordinate transformation be continuous. This additional boundary condition ensures that the device is impedance matched to the bounding medium when the spatially varying permittivity and permeability profiles are scaled to realizable values. We demonstrate the method in some detail for an Eaton lens, before describing the profiles for an "invisible disc" and "multipole" lenses.This work was supported by the EPSRC (UK) through the QUEST project (ref: EP/1034548/1)

Reflection and transmission in nonlocal susceptibility models with multiple resonances

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.We consider a semi-infinite dielectric with multiple spatially dispersive resonances in the susceptibility. The effect of the boundary is described by an arbitrary reflection coefficient for polarization waves in the material at the surface, with specific values corresponding to various additional boundary conditions (ABCs) for Maxwell's equations. We derive exact expressions for the electromagnetic reflection and transmission coefficients and present the results for a variety of materials with multiple exciton bands. We find an improved single-band approximation for heavy/light exciton bands and extend our model to exciton dispersion relations with linear $k$ terms which occur in uniaxial crystals. Finally, we calculate the spectral energy density of thermal and zero-point radiation for a variety of multi-resonance models and ABCs

Jarzynski equality for a gas particle driven out of equilibrium

ArticleThis version: arXiv:1404.5181v1 [cond-mat.stat-mech]. Available from ArXiv.org via the link in this record.One particle in a classical perfect gas is driven out of equilibrium by changing its mass over a short time interval. The work done on the driven particle depends on its collisions with the other particles in the gas. This model thus provides an example of a non-equilibrium process in a system (the driven particle) coupled to an environment (the rest of the gas). We calculate the work done on the driven particle and compare the results to Jarzynski's equality relating a non-equilibrium work process to an equilibrium free-energy difference. The results for this model are generalised to the case of a system that is driven in one degree of freedom while interacting with the environment through other degrees of freedom

Wave propagation in complex coordinates

ArticleWe give an interpretation for the use of complex spatial coordinates in electromagnetism, in terms of a family of closely related inhomogeneous media. Using this understanding we find that the phenomenon of reflection can be related to branch cuts in the wave that originate from poles of ϵ (z) at complex positions. Demanding that these branch cuts disappear, we derive a new large family of inhomogeneous media that are reflectionless for a single angle of incidence. Extending this property to all angles of incidence leads us to a generalized form of the Poschl Teller potentials that in general include regions of loss and gain. We conclude by analyzing our findings within the phase integral (WKB) method, and find another very large family of isotropic planar media that from one side have a transmission of unity and reflection of zero, for all angles of incidence.SARH and TGP acknowledge financial support from EPSRC program grant EP/I034548/1

Perfect transmission through disordered media

This is the author accepted manuscript. The final version is available from American Physical Society via the DOI in this record.The transmission of a wave through a randomly chosen `pile of plates' typically decreases expo- nentially with the number of plates, a phenomenon closely related to Anderson localisation. In ap- parent contradiction we construct disordered planar permittivity pro les which are complex-valued (i.e. have reactive and dissipative properties) that appear to vary randomly with position, yet are one-way re ectionless for all angles of incidence and exhibit a transmission coe cient of unity. In addition to these complex-valued 'random' planar permittivity pro les, we construct a family of real-valued, two-way re ectionless and perfectly transmitting disordered permittivity pro les that function only for a single angle of incidence and a narrow frequency range.C. G. K. acknowledges financial support from the EPSRC Centre for Doctoral Training in Electromagnetic Metamaterials Grant No. EP/L015331/1. S. A. R. H. acknowledges financial support from EPSRC program Grant No. EP/I034548/1, the Royal Society, and TATA. T. G. P. acknowledges financial support from EPSRC program Grant No. EP/I034548/1. The authors acknowledge useful discussions about localization in disordered media with J. Bertolotti

Graded index lenses for spin wave steering

This is the final version. Available from the American Physical Society via the DOI in this record. We use micromagnetic modelling to demonstrate the operation of graded index lenses designed to steer forward-volume magnetostatic spin waves by 90 and 180 degrees. The graded index profiles require the refractive index to diverge in the lens center, which, for spin waves, can be achieved by modulating the saturation magnetization or external magnetic field in a ferromagnetic film by a small amount. We also show how the 90$^\circ$ lens may be used as a beam divider. Finally, we analyse the robustness of the lenses to deviations from their ideal profiles.Royal Society (Charity)Engineering and Physical Sciences Research Council (EPSRC

A class of invisible inhomogeneous media and the control of electromagnetic waves

We propose a general method to arbitrarily manipulate an electromagnetic wave propagating in a two-dimensional medium, without introducing any scattering. This leads to a whole class of isotropic spatially varying permittivity and permeability profiles that are invisible while shaping the field magnitude and/or phase. In addition, we propose a metamaterial structure working in the infrared that demonstrates deep sub-wavelength control of the electric field amplitude and strong reduction of the scattering. This work offers an alternative strategy to achieve invisibility with isotropic materials and paves the way for tailoring the propagation of light at the nanoscal