Vacuum Birefringence Research Articles

X-ray photon scattering at a focused high-intensity laser pulse

We study x-ray photon scattering in the head-on collision of an XFEL pulse and a focused high-intensity laser pulse, described as paraxial Laguerre-Gaussian beam of arbitrary mode composition. For adequately chosen relative orientations of the polarization vectors of the colliding laser fields, this gives rise to a vacuum birefringence effect manifesting itself in polarization flipped signal photons. Throughout this article the XFEL is assumed to be mildly focused to a waist larger than that of the high-intensity laser beam. As previously demonstrated for the special case of a fundamental paraxial Gaussian beam, this scenario is generically accompanied by a scattering phenomenon of x-ray energy signal photons outside the forward cone of the XFEL beam, potentially assisting the detection of the effect in experiment. Here, we study the fate of the x-ray scattering signal under exemplary deformations of the transverse focus profile of the high-intensity pump.

Characterization of the Vacuum Birefringence Polarimeter at BMV: Dynamical Cavity Mirror Birefringence

We present the current status and outlook of the optical characterization of the polarimeter at the birefringence magnetique du vide (BMV) experiment. BMV is a polarimetric search for the quantum electrodynamics predicted anisotropy of vacuum in the presence of external electromagnetic fields. The main challenge faced in this fundamental test is the measurement of polarization ellipticity on the order of $ {10^{-15}}$ induced in linearly polarized laser field per pass through a magnetic field having an amplitude and length $ {B^{2}L=100~\mathrm {T}^{2}\mathrm {m}}$ . This challenge is addressed by understanding the noise sources in precision cavity-enhanced polarimetry. In this paper, we discuss the first investigation of dynamical birefringence in the signal-enhancing cavity as a result of cavity mirror motion.

On the sensitivity of a laser heterodyne polarimeter for vacuum birefringence detection

Detecting vacuum magnetic birefringence (VMB) requires an immensely accurate, precisely calibrated experiment. We are working on a new design to detect the birefringence (BF) of individual optical components without a cavity that can also be used to measure VMB in reflection off a cavity. Our design uses two overlapping, orthogonally polarized laser beams to measure the relative phase difference between a reference path and one with rotating polarizations, which may experience oscillating phase shifts in vacuum in the presence of a magnetic field. To test the design, we developed a small-scale setup without cavities that can analyze different birefringent sources with the same principle. Our early results from testing mirrors show spatial variations in BF due to imperfect mirror coatings and show no correlation between the strength of a magnetic field applied parallel to the mirror’s surface and BF amplitude. In addition to assisting in the selection of suitable components for the final design, our laser heterodyne polarimeter (LHP) promises more sensitive results than previous experiments and may very well be the basis for the very first detection of VMB.

Probing and possible application of the QED vacuum with micro-bubble implosions induced by ultra-intense laser pulses

The interaction of micro-bubbles with ultra-intense laser pulses has been shown to generate ultra-high proton densities and correspondingly high electric fields. We investigate the possibility of using such a combination to study the fundamental physical phenomenon of vacuum polarization. With current or near-future laser systems, measurement of vacuum polarization via the bending of gamma rays that pass near imploded micro-bubbles may be possible. Since it is independent of photon energy to within the leading-order solution of the Heisenberg–Euler Lagrangian and the geometric optics approximation, the corresponding index of refraction can dominate the indices of refraction due to other effects at sufficiently high photon energies. We consider the possibility of its application to a transient gamma-ray lens.

Vacuum Birefringence in a Supercritical Magnetic Field

The birefringence effect in vacuum in strong magnetic fields has been considered. The polarization tensor in a constant external magnetic field is analyzed in the framework of quantum field theory and on the basis of the electron Green’s function calculated as the sum over the Landau levels. The case of the lowest Landau levels for photons with the energies below the electron-positron pair creation threshold is considered, and the corresponding refractive indices of the physical vacuum for anomalous and normal waves are determined.

The Role of Riemann’s Zeta Function in Mathematics and Physics †,‡

In particular, Riemann’s impact on mathematics and physics alike is demonstrated using methods originating from the theory of numbers and from quantum electrodynamics, i.e., from the behavior of an electron in a prescribed external electromagnetic field. More specifically, we employ Riemann’s zeta function to regularize the otherwise infinite results of the so-called Heisenberg–Euler Lagrangian. As a spin-off, we also calculate some integrals that are useful in mathematics and physics.

New constraints on Lorentz invariance violation with polarized gamma-ray bursts

Lorentz invariance violations (LIV) can yield vacuum birefringence, which results in an energy-dependent rotation of the polarization vector of linearly polarized emission from astrophysical sources. It is believed that if the relative rotation angle ($\Delta\Theta$) of the polarization vector of high energy photons with respect to that of low energy photons is larger than $\pi/2$, then the net polarization of the signal would be significantly depleted and could not be as high as the observed level. Hence, the measurement of high polarization implies that $\Delta\Theta$ should not be too large. In this work, we assemble recent detections of prompt emission polarization in gamma-ray bursts (GRBs), all of whom have high detection significance. Following the method shown in Lin et al. (2016), we give a detailed calculation on the polarization evolution arising from the LIV effect for each GRB, and confirm that, even if $\Delta\Theta$ is approaching to $\pi/2$, the net polarization is not severely suppressed, and more than 60\% of the initial polarization can be conserved. Applying this method to our GRB polarimetric data, we improve existing sensitivities to LIV involving photons by factors ranging from two to ten. In addition, we prove that our constraints are not greatly affected by uncertainties in the spectral parameters of GRBs.

Three-loop Euler-Heisenberg Lagrangian in 1+1 QED. Part I. Single fermion-loop part

We study the three-loop Euler-Heisenberg Lagrangian in spinor quantum electrodynamics in 1+1 dimensions. In this first part we calculate the one-fermion-loop contribution, applying both standard Feynman diagrams and the worldline formalism which leads to two different representations in terms of fourfold Schwinger-parameter integrals. Unlike the diagram calculation, the worldline approach allows one to combine the planar and the non-planar contributions to the Lagrangian. Our main interest is in the asymptotic behaviour of the weak-field expansion coefficients of this Lagrangian, for which a non-perturbative prediction has been obtained in previous work using worldline instantons and Borel analysis. We develop algorithms for the calculation of the weak-field expansion coefficients that, in principle, allow their calculation to arbitrary order. Here for the non-planar contribution we make essential use of the polynomial invariants of the dihedral group D4 in Schwinger parameter space to keep the expressions manageable. As expected on general grounds, the coefficients are of the form r1 + r2ζ3 with rational numbers r1, r2. We compute the first two coefficients analytically, and four more by numerical integration.

Coulomb's law modification driven by a logarithmic electrodynamics

We examine physical aspects for the electric version of a recently proposed logarithmic electrodynamics, for which the electric field of a point-like charge is finite at the origin. It is shown that this electrodynamics displays the vacuum birefringence phenomenon in the presence of external magnetic field. Afterwards we compute the lowest-order modification to the interaction energy by means of the gauge-invariant but path-dependent variables formalism. These are shown to result in a long-range (-type) correction, in addition to a linear and another logarithmic correction, to the Coulomb potential.

Constraints on Lorentz invariance and CPT violation using optical photometry and polarimetry of active galaxies BL Lacertae and S5 B0716+714

Various quantum gravity approaches that extend beyond the standard model predict Lorentz Invariance and Charge-Parity-Time Violation at energies approaching the Planck scale. These models frequently predict a wavelength dependent speed of light, which would result in time delays between promptly emitted photons at different energies, as well as a wavelength-dependent rotation of the plane of linear polarization for photons resulting from vacuum birefringence. Here, we describe a pilot program with an automated system of small telescopes that can simultaneously conduct high cadence optical photometry and polarimetry of Active Galactic Nuclei (AGN) in multiple passbands. We use these observations as a proof-of-principle to demonstrate how such data can be used to test various Lorentz Violation models, including special cases of the Standard Model Extension (SME). In our initial campaign with this system, the Array Photo Polarimeter, we observed two AGN sources, including BL Lacertae at redshift z = 0.069, and S5 B0716+714 at z = 0.31. We demonstrate that optical polarimetry with a broadband Luminance filter combined with simultaneous $I_c$-band observations yields SME parameter constraints that are up to ~10 and ~30 times more sensitive than with a standard $I_c$-band filter, for SME models with mass dimension d = 5 and d = 6, respectively. Using only a small system of telescopes with an effective 0.45-m aperture, we further demonstrate d = 5 constraints for individual lines of sight that are within a factor of ~1-10 in sensitivity to comparable constraints from optical polarimetry with a 3.6-m telescope. Such an approach could significantly improve existing SME constraints via a polarimetric all-sky survey of AGN with multiple 1-meter class telescopes.

Dispersive property of the quantum vacuum and the speed of light

We want to study the influence of the quantum vacuum on light propagation. At first, by working in the standard linear quantum theory of the electromagnetic fields, it is shown that the electric permittivity and the magnetic permeability of the vacuum medium are changed; but, the resulting speed of light is not modified. Then, taking into account nonlinear effects by considering the Euler–Heisenberg Lagrangian, the corresponding zero point (vacuum) energy and the resulting modification of the speed of light are found up to the first nonvanishing correction.

One-loop structure of the photon propagator in the standard model extension

We study radiative corrections on the photon propagator from the electroweak sector of the minimal Lorentz- and $CPT$-violating Standard Model Extension. We derive the most general Lorentz-violating ghost sector from BRST symmetry and renormalization theory. We introduce a Lorentz-violating nonlinear gauge that simplifies both the Higgs and gauge-sector extensions, which can be helpful in radiative corrections. At one loop, these sectors contribute to the $CPT$-even part of the photon propagator, characterized by the Riemann-type tensor $(k_F)_{\alpha\beta\mu\nu}$. We give exact results for the contributions to the SO(1,3) irreducible parts of $(k_F)_{\alpha \beta \mu \nu}$, namely, the Weyl-type tensor $(\hat{k}_F)_{\alpha \beta \mu \nu}$, the Ricci-type tensor $(k_F)_{\alpha \beta}$, and the curvature-type scalar $k_F$. In the Yukawa sector, one-loop contributions are ultraviolet finite, but most of them are unobservable due to finite renormalization. The only observable effect is a contribution proportional to $(k_F)_{\alpha \beta}$ that emerges via a dimension-6 term that is observer and gauge invariant. In the Higgs and gauge sectors, all the irreducible parts of the corresponding Riemann-type tensors receive divergent contributions, so they are observable. The only finite contribution corresponds to the dimension-6 term. We think of these contributions as radiative corrections to the renormalized tensors and assume that both effects are of the same order of magnitude to find bounds from vacuum birefringence and compare with the literature. Bounds on $(k_F)_{\alpha \beta}$ contributions, innocuous to birefringence, are also derived using limits on the renormalized tensor from Laser-Interferometer-Gravitational-Wave-Observatory data. We compare these bounds with the literature. Beta functions associated with $(\hat{k}_F)_{\alpha \beta \mu \nu}$ and $(k_F)_{\alpha \beta}$ are derived.

Vacuum Birefringence in the Fields of a Current Coil and a Guided Electromagnetic Wave

The vacuum birefringence effect in magnetic fields generated by either a laser-driven capacitor-coil generator or an electromagnetic wave in a radio frequency guide has been theoretically studied. The ellipticity acquired by a linearly polarized laser beam propagating in those fields is calculated. The obtained results are compared with the parameters of the PVLAS experiment aimed at the experimental observation of the vacuum birefringence effect in a magnetic field.

Vacuum birefringence and the Schwinger effect in (3+1) de Sitter

In de Sitter space, the current induced by an electric field in vacuum is known to feature certain peculiarities, such as infrared hyperconductivity for light bosons in weak electric fields. Moreover, negative conductivity has been claimed to occur for light bosons in moderate electric fields, and for fermions of any mass in electric fields below a certain threshold. Furthemore, in the limit of large mass and weak electric field, the current contains terms which are not exponentially suppressed, contrary to the semiclassical intuition. Here we explain these behaviors, showing that most of the reported negative conductivity is spurious. First, we show that the terms which are not exponentially suppressed follow precisely from the local Euler-Heisenberg Lagrangian (suitably generalized to curved space). Thus, such terms are unrelated to pair creation or to the transport of electric charge. Rather, they correspond to non-linearities of the electric field (responsible in particular for vacuum birefringence). The remaining contributions are exponentially suppressed and correspond to the creation of Schwinger pairs. Second, we argue that for light carriers the negative term in the regularized current does not correspond to a negative conductivity, but to the logarithmic running of the electric coupling constant, up to the high energy Hubble scale. We conclude that none of the above mentioned negative contributions can cause an instability such as the spontaneous growth of an electric field in de Sitter, at least within the weak coupling regime. Third, we provide a heuristic derivation of infrared hyperconductivity, which clarifies its possible role in magnetogenesis scenarios.

Vacuum birefringence in the head-on collision of x-ray free-electron laser and optical high-intensity laser pulses

The focus of this article is on providing compact analytical expressions for the differential number of polarization flipped signal photons constituting the signal of vacuum birefringence in the head-on collision of x-ray free electron (XFEL) and optical high-intensity laser pulses. Our results allow for unprecedented insights into the scaling of the effect with the waists and pulse durations of both laser beams, the Rayleigh range of the high-intensity beam, as well as transverse and longitudinal offsets. They account for the decay of the differential number of signal photons in the far-field as a function of the azimuthal angle measured relative to the beam axis of the probe beam in forward direction, typically neglected by conventional approximations. Moreover, they even allow us to extract an analytical expression for the angular divergence of the perpendicularly polarized signal photons. We expect our formulas to be very useful for the planning and optimization of experimental scenarios aiming at the detection of vacuum birefringence in XFEL/high-intensity laser setups, such as the one put forward at the Helmholtz International Beamline for Extreme Fields (HIBEF) at the European XFEL.

On the low-energy limit of the QED N-photon amplitudes: part 2

In recent work, Gies and Karbstein have discovered that the two-loop Euler–Heisenberg Lagrangians for scalar and spinor QED have non-vanishing reducible contributions in addition to the well-studied irreducible ones. This invalidates previous applications of those Lagrangians to the computation of the two-loop N-photon amplitudes in the low energy limit. Here we compute the corrections to those amplitudes due to the reducible contributions.

Generation of circular polarization of CMB from the Euler–Heisenberg Lagrangian

It is known that the dominated contribution of primordial anisotropies of cosmic microwave background (CMB) are linearly polarized via Compton scattering. However, circular polarization of this anisotropy has not been observed up to now, but it has not been excluded in observational evidences. Here we show that the Euler–Heisenberg effective Lagrangian can generate circular polarization in CMB. This generation is calculated by using the quantum Boltzman equation for time evolution of the Stokes parameter. Also we estimate Faraday conversion phase on the order of 10−13 due to this Lagrangian, which gives a lower bound on circular polarization of CMB.

Effective Euler–Heisenberg Lagrangians in models of QED

The main goal of this paper is a direct diagrammatic evaluation of the effective four-photon Lagrangian of the Euler–Heisenberg type for the quantum electrodynamics of massive charged vector bosons. This QED model is naturally embedded in the standard electroweak theory, and we have carried out the corresponding one-loop calculation in the unitary gauge. As far as we know, such a work has not been published before since usually the R-gauge techniques are preferred for the computation of loop Feynman diagrams. We have recovered the result obtained many years ago by Vanyashin and Terent’ev, who used a specific functional method. For completeness and for validation of our techniques, we have also redone the analogous calculations for scalar and spinor QED.

Intrinsic mirror noise in Fabry\u2013Perot based polarimeters: the case for the measurement of vacuum magnetic birefringence

Although experimental efforts have been active for about 30 years, a direct laboratory observation of vacuum magnetic birefringence, due to vacuum fluctuations, still needs confirmation: the predicted birefringence of vacuum is Delta n = 4.0times 10^{-24} @ 1 T. Key ingredients of a polarimeter for detecting such a small birefringence are a long optical path within the magnetic field and a time dependent effect. To lengthen the optical path a Fabry–Perot is generally used with a finesse ranging from {{mathscr {F}}} approx 10^4 to {{mathscr {F}}} approx 7times 10^5. Interestingly, there is a difficulty in reaching the predicted shot noise limit of such polarimeters. We have measured the ellipticity and rotation noises along with Cotton-Mouton and Faraday effects as a function of the finesse of the cavity of the PVLAS polarimeter. The observations are consistent with the idea that the cavity mirrors generate a birefringence-dominated noise whose ellipticity is amplified by the cavity itself. The optical path difference sensitivity at 10;hbox {Hz} is S_{Delta {{mathscr {D}}}}=6times 10^{-19};hbox {m}/sqrt{mathrm{Hz}}, a value which we believe is consistent with an intrinsic thermal noise in the mirror coatings. Our findings prove that the continuous efforts to increase the finesse of the cavity to improve the sensitivity has reached a limit.

Vacuum birefringence detection in all-optical scenarios

In this paper we propose an all-optical vacuum birefringence experiment and evaluate its feasibility for various scenarios. Many petawatt-class lasers became operational and many more are expected to enter operation in the near future, therefore unprecedented electromagnetic fields ($E_L\sim10^{14}-10^{15}$ V/m and intensities $I_L\sim10^{21}-10^{23}$ W/cm$^2$) will become available for experiments. In our proposal a petawatt-class laser disturbs the quantum vacuum and creates a delay in a counter-propagating probe laser beam. Placing this delayed beam in one arm of a Mach-Zehnder interferometer (MZI), allows the measurement of the vacuum refraction coefficient via a phase shift. Coherent as well as squeezed light are both considered and the minimum phase sensitivity evaluated. We show that using existing technology and with some moderately optimistic assumptions, at least part of the discussed scenarios are feasible for a vacuum birefringence detection experiment.