Subluminal Propagation Research Articles

Finite distance effects on the Hellings–Downs curve in modified gravity

There is growing interest in the overlap reduction function in pulsar timing array observations as a probe of modified gravity. However, current approximations to the Hellings–Downs curve for subluminal gravitational wave propagation, say v<1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$v<1$$\\end{document}, diverge at small angular pulsar separation. In this paper, we find that the overlap reduction function for the v<1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$v<1$$\\end{document} case is sensitive to finite distance effects. First, we show that finite distance effects introduce an effective cut-off in the spherical harmonics decomposition at ℓ∼1-v2kL\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell \\sim \\sqrt{1-v^2} \\, kL$$\\end{document}, where ℓ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell $$\\end{document} is the multipole number, k the wavenumber of the gravitational wave and L the distance to the pulsars. Then, we find that the overlap reduction function in the small angle limit approaches a value given by πkLv2(1-v2)2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pi kL\\,v^2\\,(1-v^2)^2$$\\end{document} times a normalization factor, exactly matching the value for the autocorrelation recently derived. Although we focus on the v<1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$v<1$$\\end{document} case, our formulation is valid for any value of v.

Anomalous to normal dispersion nonlinear optical dephasing switch in electromagnetically induced transparency using a Kerr effect

The atomic decoherence effect (DE) on a Kerr nonlinear (KNL) electromagnetically induced transparency (EIT)is studied in a Δ system. The DE between the ground state hyperfine levels is caused by the dephasing rate γ d which dramatically modifies the medium response. It controls the normal dispersive region which shows steep positive slopes for linear response at the line center while the nonlinear response experiences steep negative slopes for low γ d . The microwave field strength and γ d modify the nonlinear response from the anomalous dispersion to normal dispersion. The calculations show that room-temperature atoms are used to quantify the quantum interference (QI) on linear and nonlinear absorption with γ d . The EIT spectrum explores the understanding of the subluminal and superluminal wave propagation of probe signal and this study opens a new pathway for the understanding of the QI devices and their nonlinearities based on EIT.

Effects on neutrino propagation in space-time foam of D-branes revisited

Neutrinos from the cosmos have proven to be ideal for probing the nature of space-time. Previous studies on high-energy events of IceCube suggested that some of these events might be gamma-ray burst neutrinos, with their speeds varying linearly with their energy, implying also the coexistence of subluminal and superluminal propagation. However, a recent reanalysis of the data, incorporating revised directional information, reveals stronger signals that neutrinos are actually being slowed down compared to previous suggestion of neutrino speed variation. Thus, it is worth discussing its implications for the brane/string inspired framework of space-time foam, which has been used to explain previous observations. We revisit effects on neutrino propagation from specific foam models within the framework, indicating that the implied violation of Lorentz invariance could necessarily cause the neutrino to decelerate. We therefore argue that this sort of model is in agreement with the updated phenomenological indication just mentioned. An extended analysis of the revised IceCube data will further test these observations and stringy quantum gravity.

Coherent manipulation of Brewster angles and phase shifts for both left right circularly polarized beams in chiral medium

The Brewster angles and phase shift of both left right circular polarization beams of the probe field is controlled and modified in this manuscript. Subluminal and superluminal propagation of light having group indices of ±200 has been reported. The group velocities of left circularly polarized (LCP) and right circularly polarized (RCP) beam varies to ±1.5×106 m/s while, delay times varies to ±5ns. The peak values of Brewster angles of LCP and RCP beams are calculated 0.786 radian. The maximum value phase shift of LCP and RCP is reported to 31.45 radian at length L=5λ. Strong oscillation in Brewster angles and phase variations of LCP and RCP beams are investigated with azimuthal quantum number of control field and increasing length of position coordinates. The modified results of this manuscript are useful for interferometry and lasers technology.

Dispersion Relations Alone Cannot Guarantee Causality.

We show that linear superpositions of plane waves involving a single-valued, covariantly stable dispersion relation ω(k) always propagate outside the light cone unless ω(k)=a+bk. This implies that there is no notion of causality for individual dispersion relations since no mathematical condition on the function ω(k) (such as the front velocity or the asymptotic group velocity conditions) can serve as a sufficient condition for subluminal propagation in dispersive media. Instead, causality can only emerge from a careful cancellation that occurs when one superimposes all the excitation branches of a physical model. This happens automatically in local theories of matter that are covariantly stable. Hence, we find that the need for nonhydrodynamic modes in relativistic fluid mechanics is analogous to the need for antiparticles in relativistic quantum mechanics.

Controllable light group velocity in a degenerate two-level medium under the assistance of an external magnetic field

In this work, we proposed a simple model for control of subluminal and superluminal light propagation via an external magnetic field in a lambda configuration degenerate two-level atomic medium. We show that the absorption-dispersion properties and group index under the influence of the strength of coupling laser and external magnetic fields are controlled. By changing the direction and magnitude of the magnetic field, the medium switches from transparency with normal dispersion to enhanced absorption with anomalous dispersion at the line center, corresponding with the transfer from slow light to fast light. This work may provide for the application realization of magneto-optic switches and storage devices in quantum information processing.

Tunable superluminal propagation at spectral hole-burning regions in magneto-optical atomic medium

In the context of spectral hole-burning, normal dispersion with subluminal propagation is usually observed in the spectral hole-burning depth region. However, anomalous dispersion can occur in the continuous absorption peak region, which leads to superluminal light propagation. In this paper, we report an unusual behavior of dispersion at discontinued absorption kink regions. We demonstrate both normal dispersion at the kink absorption region and anomalous dispersion at the spectral hole-burning depth region. The unusual dispersion leads to a positive group index in the absorption kink region and a negative group index in the spectral hole-burning depth region. The spectral hole-burning is due to variation of magnetization rather than the molecular distribution. The outcomes of our work offer promising applications in communication technologies and storage devices.

Knob of adjusting light group velocity in an inhomogeneously broadened degenerate two-level atomic medium by a magnetic field

We proposed a simple model for investigating subluminal and superluminal light propagation via an external magnetic field in an inhomogeneously broadened degenerate two-level atomic medium. We show that a magnetic field can be utilized as a knob to control the absorption/dispersion properties and group index of the medium. By changing the magnitude and reversing the direction of the magnetic field, the positive group index is converted to the negative group index at the center of the EIT window, corresponding with the propagation of a weak light pulse from subluminal to superluminal. Moreover, the influence of the Doppler broadening effect on the group index is also included, making the results approach to actual conditions. Therefore, the suggested model may be helpful for the application realization of optical storage in quantum computers and quantum information processing.

Positivity bounds on Higgs-portal freeze-in dark matter

We consider the relic density and positivity bounds for freeze-in scalar dark matter with general Higgs-portal interactions up to dimension-8 operators. When dimension-4 and dimension-6 Higgs-portal interactions are proportional to mass squares for Higgs or scalar dark matter in certain microscopic models such as massive graviton, radion or general metric couplings with conformal and disformal modes, we can take the dimension-8 derivative Higgs-portal interactions to be dominant for determining the relic density via the 2-to-2 thermal scattering of the Higgs fields after reheating. We discuss the implications of positivity bounds for microscopic models. First, massive graviton or radion mediates attractive forces between Higgs and scalar dark matter and the resultant dimension-8 operators respect the positivity bounds. Second, the disformal couplings in the general metric allow for the subluminal propagation of graviton but violate the positivity bounds. We show that there is a wide parameter space for explaining the correct relic density from the freeze-in mechanism and the positivity bounds can curb out the dimension-8 derivative Higgs-portal interactions nontrivially in the presence of the similar dimension-8 self-interactions for Higgs and dark matter.

Sensitivity of atom based on slow light propagation and rotary photon drag: an efficient and secure model for quantum-based sensors in Internet of Things

Quantum technology has the potential to revolutionize sensors and the Internet of Things (IoT). Efficient and secure data transfer among sensors and IoT devices is a major challenge. To address this, the manuscript presents coherent manipulation of the scattering cross section and its sensitivity based on subluminal propagation and rotary photon drag, using an atomic medium with two levels coupled with a cavity. The group index of the proposed atomic medium is measured in the range of -0.1le n_gle 150 and group velocity in the range of 2times 10^6m/sle v_gle pm 2times 10^9m/s. The maximum delay time is reported to t_g=0.3mu s and rotary photon drag to theta _d=pm 5 micro radian. This effect of photon drag is used in sensing, energy harvesting, and optical switching in IoT. The scattering cross-section of 0.1times 10^{21}m^2 is reported. The scattering cross-section impacts the efficiency and reliability of quantum-based communication for IoT. The maximum cross-sectional sensitivity is measured to S_sigma =0.4times 10^{-19}m^2/n_r. The cross-sectional sensitivity potentially impacts secure communication and highly precise detection in sensors and IoT.

Bayesian evidence for spectral lag transition due to Lorentz invariance violation for 32 Fermi/GBM Gamma-ray bursts

We use the spectral lag data of 32 long GRBs detected by Fermi/GBM, which has been recently collated in Liu et al. (2022) to quantify the statistical significance of a transition in the spectral lag data based on Lorentz invariance violation (LIV) (for both sub-luminal and super-luminal propagation) using Bayesian model selection. We use two different parametric functions to model the null hypothesis of only intrinsic emission: a smooth broken power law model (SBPL) (proposed in Liu et al. (2022)) as well as a simple power law model, which has been widely used before in literature. We find that for sub-luminal propagation, when we use the SBPL model as the null hypothesis, five GRBs show “decisive evidence” based on Jeffreys' scale for linear LIV and quadratic LIV. When we use the simple power-law model as the null hypothesis, we find that 10 and 9 GRBs show Bayesian “decisive evidence” for linear and quadratic LIV, respectively. However these results should not be construed as evidence for LIV, as they would be in conflict with the most stringent upper limits. When we did a test for super-luminal LIV, we find that only four and two GRBs show Bayesian “decisive evidence” for linear and quadratic LIV, respectively, assuming a simple power law for the intrinsic emission. When we use the SBPL model, one GRB shows Bayesian “decisive evidence” for linear and quadratic LIV. This underscores the importance of adequately modeling the intrinsic emission while obtaining constraints on LIV using spectral lags, since inadequate modeling could masquerade as a signature of LIV.

Photon centroids and their subluminal propagation

We examine properties of the energy-density and photon-probability centroids of electromagnetic wavepackets in free space. In the second-order paraxial approximation, both of these centroids propagate with the same subluminal velocity because of the transverse confinement of the wavepacket and its diffraction. The tiny difference between the energy and probability centroid velocities appears only in the fourth order. We consider three types of wavepackets: Gaussian, Bessel, and non-diffracting Bessel. In all these cases, the subluminal propagation is clearly visible in the intensity distributions and can be measured experimentally in both classical-light and single-photon regimes. For Gaussian wavepackets, the half-wavelength delay is accumulated after propagation over about 12 Rayleigh lengths.

Manipulation speed of light and giant phase shifting: a new quantum-based model for improving efficiency and security of internet of things

The Internet of Things (IoT) is transitioning towards Quantum Computing soon, relying on electromagnetic waves for data transfer within circuits and between IoT devices. This paper introduces a four-level atomic medium controlled by electromagnetic fields to manipulate the speed of light, resulting in subluminal and superluminal information transfer for IoT. Subluminal propagation transmits data at an average rate, while superluminal propagation transfers data faster than conventional methods. The differentiation between these two modes of propagation is determined by the sign of the group index, which is positive for subluminal and negative for superluminal. Our proposed model reports a maximum positive and negative group index of ± 5000. This modified group velocity to become {v}_{g}=pm ,c/5000 enhances IoT information transferring in quantum-based communication. The group delay time is measured to {t}_{d}=pm 10 mu s in the medium, which increases the capacity for IoT information storage. The maximum value of normal and anomalous phase shift is reported to Phi =pm , 20000 radians at 60 cm lengths of the medium; this effect is used to divide information in sub-set that protect IoT information from different types of attacks and losses.

Normal and anomalous dispersion study on probe light propagation in the presence of structured coupling light using electromagnetically induced transparency protocol

Here, we present a study on the dispersion features obtained in an electromagnetically induced transparency (EIT) experiment using a three-level cascade configuration in an 87Rb atomic vapor medium in the presence of Laguerre–Gaussian (LG) light as a coupling. A doublet transmission structure was obtained experimentally, and dispersion spectra were extracted using transmission spectra to study the probe light behavior. Dispersive regions that exhibit normal and anomalous nature were studied considering the polarization of various orientations as a coupling light. We established that normal dispersive region shows steep positive slopes, and anomalous dispersive region shows negative slopes, which can be controlled by polarization orientations. Owing to the change in the slopes of dispersion, normal and anomalous dispersive region is observed, and spectrum shows the effects of subluminal and superluminal propagation of probe light. This work, to the best of our knowledge, is novel in the study of dispersive region arising out of double-resonance EIT transmission spectra in the presence of LG light with the l=10 and p=0 mode as a coupling light with various polarization orientations. In the discussion, we establish that single parameter θ is sufficient for identifying the orientation and ellipticity of the polarization ellipse and also determine that the polarization of coupling light acts as a tuning parameter for changing the behavior of normal and anomalous dispersive region. Slow and fast light or superluminal propagation of probe light arise as a consequence of positive or negative group index, and fast light does not violate the principle of causality. Slow and fast light have future applications in high-speed quantum information and quantum communication using EIT-based protocol.

Slow and Fast Light in Microwave Interferometers

We propose and demonstrate a method for manipulation of group velocity from slow-to-fast light (SFL) in a two-beam Mach–Zehnder interferometer in radio frequency (RF) regime. The subluminal, superluminal, and tunneling propagation regimes occur in a narrow frequency band around the resonance frequency of the interferometer where destructive interference occurs. Importantly, the group velocity at the resonance frequency can be controlled by simply adjusting the transmission magnitude of the signals from the two beams, without changing the length of the interferometer. Models that fully describe the SFL effects in the microwave interferometer system are developed and closed-form expressions for the prediction of group delays at the resonance frequency are obtained. The simple and effective method is verified through numerical calculations and experimental measurements. We also demonstrate that the proposed method applies to a microwave cavity interferometer. A proof-of-concept experiment is performed using a custom open-ended coaxial cable resonator (OE-CCR). Positive and negative group delays are experimentally measured when the resonator is set at different coupling states.

Ghost condensation and subluminal propagation on low derivative backgrounds

We show a new class of interaction terms with higher derivatives that can be added to every low derivative real scalar, such that the first order perturbations induced by the higher derivative terms on the low derivative background are ghost-free. This follows without imposing additional constraints. Furthermore, we show a related class of theories with an additional stabilizer variable and a constraint which are ghost-free without restricting to a perturbative expansion. In this case the field equation followed by the stabilizer variable may have interesting physical applications: namely, in contrast to some models with first-order derivative interactions with applications for dark energy and inflation, these constrained second-order derivative self-interactions do not necessarily affect the luminal propagation, hence, avoiding the common superluminality issues of the former.

Match Zehnder interferometry and Laguerre–Gaussian fields dependent photon drag in atomic medium

The absorption, dispersion and transmission are controlled and modified with the intensities of Laguerre–Gaussian control fields in a four level cesium atomic medium. The normal and anomalous slope of dispersion are investigated for subluminal and superluminal propagation. The maximum measured value of positive/negative group index is n g =±1×107, at which, the group velocity is ±30 ms−1. The maximum delay time between the two beams at the detector without dragging is 0.414 ns and in the presence of dragging is measured to 0.44 ns. The fractional change in delay time without and in the presence of dragging Δt F is measured to ±2%. The maximum phase shift without dragging is reported to 2.6 micro radian and in the presence of dragging is investigated to ±4 micro radian. The fractional change in phase shift is reported from −200% to 50% and may be used for gravitational waves detection and other signals identification.

Phase sensitivity by fast light propagation using compton scattering and Kerr non-linearity

We theoretically investigated the sub-luminal and super-luminal light propagation by introducing compton scattering and Kerr non-linear effects to a four level atomic system. Slow light propagation is observed at a group index of 3918 in the transparency region. The slow light propagation is tuned to fast light propagation at group index 0.2, using compton scattering angle of varphi =pi /6. The surperluminality is further enhanced with compton scattering angle at the resonance frequency. Under the Kerr nonlinearity, the slow light propagation at a group index of 3918 is enhanced to fast light propagation at group index of 2times 10^6 at the resonance frequency. The group index is reduced to 6.56281times 10^{-5} in the presence of both Kerr non-linearity and compton scattering. In the presence of compton scattering, the Phase shift at pi /2 without Kerr nonlinearity is 7times 10^{-8} radian and with Kerr nonlinearity its value is 1.7times 10^{-9} radian at resonance frequency. This demonstrate that introducing Kerr effect and compton scattering lead to significant modifications in the phase shift.

Microwave or radio-frequency controlled electromagnetically induced transparency (EIT) and related dispersion spectra in a pump-probe lasers driven multi-level [formula omitted]-type system of [formula omitted] atom

The optical responses of a pump-probe lasers driven six-level cascade (Ξ)-type system to the probe field are studied in the present work. The six-level system considered to be formed by the hyperfine energy levels of 5S12, 5P12 and 7S12 states of 87Rb atom. The main feature that makes the present light-atom interaction scheme different from the other routinely studied Ξ-type systems is the coupling of magnetic dipole allowed hyperfine ground levels by the magnetic field component of a microwave (MW) or radio-frequency (RF) field and the use of it as a control field. Probe absorption and dispersion profiles are simulated by numerically solving the corresponding optical Bloch equations (OBEs). Effects of the MW or RF field on the electromagnetically induced transparency (EIT) as well as probe absorption and related dispersion signals are examined under strong pump and different probe strength conditions. Group index (ng) of the medium is also evaluated and the effect of the MW or RF field on ng is explored. It has been found that the MW or RF field, working as a control field in the medium facilitates the enhancement of the overall absorption of the probe field in weak and moderate probe strength limits for stationary as well as for moving atoms. At higher probe strength, the MW or RF field contributes in the subluminal probe propagation through the stationary atomic medium along with a non-vanishing probe absorption at the line center.

Multifrequency Bessel beams with adjustable group velocity and longitudinal acceleration in free space

The group velocity of an optical beam in free space is usually considered to be equal to the speed of light in vacuum. However, it has been recently realized that, by structuring the beam’s angular and temporal spectra, one can achieve well pronounced and controlled subluminal and superluminal propagation. In this work, we consider multifrequency Bessel beams that are known to propagate without divergence and show a variety of possibilities to adjust the group velocity of the beam by means of designed angular dispersion. We present several examples of multifrequency Bessel beams with negative and arbitrary positive group velocities, as well as longitudinally accelerating beams and beams with periodically oscillating local group velocities. The results of these studies can be of interest to scientists working in the fields of optical beam engineering, light amplitude and intensity interferometry, ultrafast optics, and optical tweezers.