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C. Duval

Publications and source records attributed to C. Duval.

At least 19 recordsLinked to original sources
arXiv2020

Shelving spectroscopy of the strontium intercombination line

We present a spectroscopy scheme for the 7-kHz-wide 689-nm intercombination line of strontium. We rely on shelving detection, where electrons are first excited to a metastable state by the spectroscopy laser before their state is probed using the broad transition at 461 nm. As in the similar setting of calcium beam clocks, this enhances dramatically the signal strength as compared to direct saturated fluorescence or absorption spectroscopy of the narrow line. We implement shelving spectroscopy both in directed atomic beams and hot vapor cells with isotropic atomic velocities. We measure a fractional frequency instability $\sim 2 \times 10^{-12}$ at 1 s limited by technical noise - about one order of magnitude above shot noise limitations for our experimental parameters. Our work illustrates the robustness and flexibility of a scheme that can be very easily implemented in the reference cells or ovens of most existing strontium experiments, and may find applications for low-complexity clocks.

physics.atom-ph↗
arXiv2018

Ion Traps and the Memory Effect for Periodic Gravitational Waves

The Eisenhart lift of a Paul Trap used to store ions in molecular physics is a linearly polarized periodic gravitational wave. A modified version of Dehmelt's Penning Trap is in turn related to circularly polarized periodic gravitational waves, sought for in inflationary models. Similar equations rule also the Lagrange points in Celestial Mechanics. The explanation is provided by anisotropic oscillators.

gr-qc↗
arXiv2018

Velocity Memory Effect for Polarized Gravitational Waves

Circularly polarized gravitational sandwich waves exhibit, as do their linearly polarized counterparts, the Velocity Memory Effect: freely falling test particles in the flat after-zone fly apart along straight lines with constant velocity. In the inside zone their trajectories combine oscillatory and rotational motions in a complicated way. For circularly polarized periodic gravitational waves some trajectories remain bounded, while others spiral outward. These waves admit an additional "screw" isometry beyond the usual five. The consequences of this extra symmetry are explored.

gr-qc↗
arXiv2018

Memory Effect for Impulsive Gravitational Waves

Impulsive gravitational plane waves, which have a delta-function singularity on a hypersurface, can be obtained by squeezing smooth plane gravitational waves with Gaussian profile. They exhibit (as do their smooth counterparts) the Velocity Memory Effect: after the wave has passed, particles initially at rest move apart with non vanishing constant transverse velocity. A new effect is that, unlike to the smooth case, (i) the velocities of particles originally at rest jump, (ii) the spacetime trajectories become discontinuous along the (lightlike) propagation direction of the wave.

gr-qc↗
arXiv2017

Soft Gravitons & the Memory Effect for Plane Gravitational Waves

The "gravitational memory effect" due to an exact plane wave provides us with an elementary description of the diffeomorphisms associated with soft gravitons. It is explained how the presence of the latter may be detected by observing the motion of freely falling particles or other forms of gravitational wave detection. Numerical calculations confirm the relevance of the first, second and third time integrals of the Riemann tensor pointed out earlier. Solutions for various profiles are constructed. It is also shown how to extend our treatment to Einstein-Maxwell plane waves and a midi-superspace quantization is given.

gr-qc↗
arXiv2017

Gravitational birefringence of light in Robertson-Walker cosmologies

The spacetime evolution of massless spinning particles in a Robertson-Walker background is derived using the deterministic system of equations of motion due to Papapetrou, Souriau and Saturnini. A numerical integration of this system of differential equations in the case of the standard model of cosmology is performed. The deviation of the photon worldlines from the null geodesics is of the order of the wavelength. Perturbative solutions are also worked out in a more general case. An experimental measurement of this deviation would test the acceleration of our expanding universe.

gr-qc↗
arXiv2017

The Memory Effect for Plane Gravitational Waves

We give an account of the gravitational memory effect in the presence of the exact plane wave solution of Einstein's vacuum equations. This allows an elementary but exact description of the soft gravitons and how their presence may be detected by observing the motion of freely falling particles. The theorem of Bondi and Pirani on caustics (for which we present a new proof) implies that the asymptotic relative velocity is constant but not zero, in contradiction with the permanent displacement claimed by Zel'dovich and Polnarev. A non-vanishing asymptotic relative velocity might be used to detect gravitational waves through the "velocity memory effect", considered by Braginsky, Thorne, Grishchuk, and Polnarev.

gr-qc↗
arXiv2017

Carroll symmetry of plane gravitational waves

The well-known 5-parameter isometry group of plane gravitational waves in $4$ dimensions is identified as Levy-Leblond's Carroll group in $2+1$ dimensions with no rotations. Our clue is that plane waves are Bargmann spaces into which Carroll manifolds can be embedded. We also comment on the scattering of light by a gravitational wave and calculate its electric permittivity considered as an impedance-matched metamaterial.

gr-qc↗
arXiv2017

Conformal and projective symmetries in Newtonian cosmology

Definitions of non-relativistic conformal transformations are considered both in the Newton-Cartan and in the Kaluza-Klein-type Eisenhart/Bargmann geometrical frameworks. The symmetry groups that come into play are exemplified by the cosmological, and also the Newton-Hooke solutions of Newton's gravitational field equations. It is shown, in particular, that the maximal symmetry group of the standard cosmological model is isomorphic to the 13-dimensional conformal-Newton-Cartan group whose conformal-Bargmann extension is explicitly worked out. Attention is drawn to the appearance of independent space and time dilations, in contrast with the Schr{ö}dinger group or the Conformal Galilei Algebra.

gr-qc↗
arXiv2016

Duality and helicity: a symplectic viewpoint

The theorem which says that helicity is the conserved quantity associated with the duality symmetry of the vacuum Maxwell equations is proved by viewing electromagnetism as an infinite dimensional symplectic system. In fact, it is shown that helicity is the moment map of duality acting as an $SO(2)$ group of canonical transformations on the symplectic space of all solutions of the vacuum Maxwell equations.

math-ph↗
arXiv2016

Eisenhart lifts and symmetries of time-dependent systems

Certain dissipative systems, such as Caldirola and Kannai's damped simple harmonic oscillator, may be modelled by time-dependent Lagrangian and hence time dependent Hamiltonian systems with $n$ degrees of freedom. In this paper we treat these systems, their projective and conformal symmetries as well as their quantisation from the point of view of the Eisenhart lift to a Bargmann spacetime in $n+2$ dimensions, equipped with its covariantly constant null Killing vector field. Reparametrization of the time variable corresponds to conformal rescalings of the Bargmann metric. We show how the Arnold map lifts to Bargmann spacetime. We contrast the greater generality of the Caldirola-Kannai approach with that of Arnold and Bateman. At the level of quantum mechanics, we are able to show how the relevant Schrödinger equation emerges naturally using the techniques of quantum field theory in curved spacetimes, since a covariantly constant null Killing vector field gives rise to well defined one particle Hilbert space. Time-dependent Lagrangians arise naturally also in cosmology and give rise to the phenomenon of Hubble friction. We provide an account of this for Friedmann-Lemaitre and Bianchi cosmologies and how it fits in with our previous discussion in the non-relativistic limit.

hep-th↗
arXiv2016

Helicity of spin-extended chiral particles

The helicity of a free massless relativistic particle, $χ^o={\bf s}.{\bf p}/|{\bf p}|$, is generalized, for a particle in an electromagnetic field, to $χ={\bf s}.{\bf p}/{\cal E}$, where ${\cal E}$ is the modified kinetic energy. Both $χ^o$ and $χ$ coincide and are conserved for minimal coupling (gyromagnetic ratio $g=0$) but are different and neither of them is conserved when the coupling is non-minimal, $g\neq0$, generating non-zero effective mass. For a chiral particle with $g=2$ in a constant electric field both helicities converge asymptotically to the same value. Helicity is also conserved for minimal gravitational coupling.

hep-th↗
arXiv2015

On the Schr{ö}dinger-Newton equation and its symmetries: a geometric view

The \SN (SN) equation is recast on purely geometrical grounds, namely in terms of Bargmann structures over $(\d+1)$-dimensional Newton-Cartan (NC) spacetimes. Its maximal group of invariance, which we call the SN group, is determined as the group of conformal Bargmann automorphisms that preserve the coupled Schrödinger and NC gravitational field equations. Canonical unitary representations of the SN group are worked out, helping us recover, in particular, a very specific occurrence of dilations with dynamical exponent $z=(\d+2)/3$.

math-ph↗
arXiv2015

Chiral fermions as classical massless spinning particles

Semiclassical chiral fermion models with Berry term are studied in a symplectic framework. In the free case, the system can be obtained from Souriau's model for a relativistic massless spinning particle by "enslaving" the spin. The Berry term is identified with the classical spin two-form of the latter model. The Souriau model carries a natural Poincaré symmetry that we highlight, but spin enslavement breaks the boost symmetry. However the relation between the models allows us to derive a Poincare symmetry of unconventional form for chiral fermions. Then we couple our system to an external electromagnetic field. For gyromagnetic ratio $g=0$ we get curious superluminal Hall-type motions; for $g=2$ and in a pure constant magnetic field in particular, we find instead spiraling motions.

hep-th↗
arXiv2015

Wigner-Souriau translations and Lorentz symmetry of chiral fermions

Chiral fermions can be embedded into Souriau's massless spinning particle model by "enslaving" the spin, viewed as a gauge constraint. The latter is not invariant under Lorentz boosts; spin enslavement can be restored, however, by a subsequent Wigner-Souriau (WS) translation, analogous to a compensating gauge transformation. The combined transformation is precisely the recently uncovered twisted boost, which we now extend to finite transformations. WS-translations are identified with the stability group of a motion acting on the right on the Poincare group, whereas the natural Poincare action corresponds to action on the left. The relation to non-commutative mechanics is explained.

hep-th↗
arXiv2014

Conformal Carroll groups

Conformal extensions of Levy-Leblond's Carroll group, based on geometric properties analogous to those of Newton-Cartan space-time are proposed. The extensions are labelled by an integer $k$. This framework includes and extends our recent study of the Bondi-Metzner-Sachs (BMS) and Newman-Unti (NU) groups. The relation to Conformal Galilei groups is clarified. Conformal Carroll symmetry is illustrated by "Carrollian photons". Motion both in the Newton-Cartan and Carroll spaces may be related to that of strings in the Bargmann space.

hep-th↗
arXiv2014

Conformal Carroll groups and BMS symmetry

The Bondi-Metzner-Sachs (BMS) group is shown to be the conformal extension of Levy-Leblond's "Carroll" group. Further extension to the Newman-Unti (NU) group is also discussed in the Carroll framework.

gr-qc↗