Superluminal Group Velocity Research Articles

Anomalous dispersion, superluminality, and instabilities in two-flavor theories with local non-Hermitian mass mixing

Pseudo-Hermitian field theories possess a global continuous “similarity” symmetry, interconnecting the theories with the same physical particle content and an identical mass spectrum. In their regimes with real spectra, within this family of similarity transformations, there is a map from the non-Hermitian theory to its Hermitian similarity partner. We promote the similarity transformation to a local symmetry, which requires the introduction of a new vector similarity field as a connection in the similarity space of non-Hermitian theories. In the case of non-Hermitian two-flavor scalar or fermion mixing and by virtue of a novel IR/UV mixing effect, the effect of inhomogeneous non-Hermiticity then reveals itself via anomalous dispersion, instabilities, and superluminal group velocities at very high momenta, thus setting an upper bound on the particle momentum propagating through inhomogeneous backgrounds characterized by Lagrangians with non-Hermitian mass matrices. Such a non-Hermitian extension of the Standard Model of particle physics, encoded in a weak inhomogeneity of the non-Hermitian part of the fermion mass matrix, may nevertheless provide us with a low-energy particle spectrum consistent with experimentally observed properties. Published by the American Physical Society 2024

Electromagnetic field theory in superluminal spacetime

Recently, a number of experimental observations on the superluminal group velocities of pulses propagating in dispersive media have led to reconsidering electromagnetism theory in an unconventional framework. To consider faster-than-light phenomena, it is not necessary to replace the current relativistic theory, but it is sufficient to extend it to superluminal motions in a way that preserves the principle of causality. In the present paper, a new approach to study superluminal motions is proposed, which avoids introducing unphysical complex quantities and allows for the formulation of equations that are covariant according to a hyperbolic metric. In the framework of this formalism, Maxwell equations and the single-photon wave equation are obtained through superluminal transformations of ordinary equations. It is shown that the covariant and contravariant components of the superluminal electromagnetic field determine its magnitude and direction, respectively. Furthermore, the solutions of the transformed Maxwell equations are X-shaped ways propagating in the superluminal spacetime region that is delimited by the infinite light cone and the two-sheeted hyperboloid perpendicular to it. Instead, in quantum mechanics, the covariant and contravariant components of the electromagnetic field are proportional to the right- and left-handed helicities of the single photon, respectively.

Exotic light transition between superluminal and subluminal group velocity in a [formula omitted] coupled slab waveguide

We propose a rigorous full-wave modal analysis based on the eigenmodes approach (“supermodes”), that allows the calculation of the transverse electric (TE) and transverse magnetic (TM) stationary propagation eigenmodes in a coupled PT-symmetric slab waveguide. Our findings show that the group velocity, for the fundamental TE0 supermode, passes from superluminal to subluminal speed over both sides of a critical point (CP), located near to the exceptional point (EP). We also demonstrate that the first higher-order supermode, TE1, exhibits a slow light phenomenon around the EP.

Plasma density transition-based electron injection in laser wake field acceleration driven by a flying focus laser

By using a high-intensity flying focus laser, the dephasingless [Phys. Rev. Lett. 124 134802 (2020)] or phase-locked [Nat. Photon. 14 475 (2020)] laser wakefield acceleration (LWFA) can be realized, which may overcome issues of laser diffraction, pump depletion, and electron dephasing which are always suffered in usual LWFA. The scheme thus has the potentiality to accelerate electrons to TeV energy in a single acceleration stage. However, the controlled electron injection has not been self-consistently included in such schemes. Only external injection was suggested in previous theoretical studies, which requires other accelerators and is relatively difficulty to operate. Here, we numerically study the actively controlled density transition injection in phase-locked LWFA to get appropriate density profiles for amount of electron injection. The study shows that compared with LWFA driven by lasers with fixed focus, a larger plasma density gradient is necessary. Electrons experience both transverse and longitudinal loss during acceleration due to the superluminal group velocity of the driver and the variation of the wakefield structure. Furthermore, the periodic deformation and fracture of the flying focus laser in the high-density plasma plateau make the final injected charge also depend on the beginning position of the density downramp. Our studies show a possible way for amount of electron injection in LWFA driven by flying focus lasers.

Fundamental issues with light propagation through PT -symmetric systems

We analyze the emergence of unphysical superluminal group velocities in Su-Schrieffer-Heeger (SSH) parity-time ($\mathcal{PT}$) symmetric chains, and explore the origins of such a behavior. By comparing the band structure of an infinite loss-gain SSH chain with that of a continuous realization---a one-dimensional Bragg stack governed by the Helmholtz equation---we first exclude insufficient coupling consideration in the tight-binding description as the cause of group-velocity divergence. We then focus on material dispersion, and show that indeed, restoring causality in the description of both the lossy and the gain components resolves the problem and recovers finite group velocities, whose real part can only exceed the speed of light in vacuum when accompanied by a significant imaginary part. Our analysis introduces thus the required practical limits in the performance of common $\mathcal{PT}$-symmetric systems.

Exact analytical solution of the driven qutrit in an open quantum system: V and Λ configurations

We obtain the exact analytical solution for the continuously driven qutrit in the V and Λ configurations governed by the Lindblad master equation. We calculate the linear susceptibility in each system, determining regimes of transient gain without inversion, and identify exact parameter values for superluminal, vanishing, and negative group velocity for the probe field.

Quantum coherence-assisted optical properties and drag of SPPs on quantum dots and resonantly-coupled dots-metal plasmonic interfaces via interbands tunneling and Fano resonance

Owing to their peculiar properties of great fundamental and practical implications, surface plasmons and exciton-plasmons interaction have attracted immense interest in the recent decades. In this regard, quantum dots and dots-metal waveguides and interfaces are promising candidates. In this article, we report first theoretical demonstration on the detailed optical and optotransport properties and surface plasmon polaritons (SPPs) dragging via quantum dots interbands tunneling-induced quantum coherence. For the required properties of SPPs, we proposed a resonantly coupled dots-metal plasmonic interface, which comprises of ensemble of three-level double quantum dot molecules (DQDMs) placed on the flat surface of gold thin film. For the theoretical results, we first solved analytically the density-matrix equation for the eigenvalues of the DQDMs in the Λ− type configuration. In view of the dressed-states picture, we interpreted the results further with regard to EIT (electromagnetically induced transparency), PIT (plasmonic induced transparency) and Fano interference. In particular, we elaborate on the role of interplay of the quantum dots and the coupled plasmonic resonances on the optical, optical-cum transport properties and drag of SPPs. We predict ultrafast superluminal group velocity for SPPs of the order 1.5×1010 m/s, quality factor of 38.48, confinment factor 1.52 and the optimum drag for SPPs of order 0.2 micro meter/radian.

Superluminal light group velocity in tapered optical microfibers

Superluminal light group velocity was formerly reported in anomalous dispersion, nonlinear amplification of light pulse, high-gain lasers' cavities, and waveguides. Motivated by a recent observation of light acceleration in optical microfiber [1], the possibility of attaining the light group velocity exceeds its value in vacuum is investigated. The investigation of superluminal velocity is in tapered optical microfiber that has a radius decreases with propagation axis by a factor 10-3. Our results show the possibility of attaining superluminal group velocity in this microfiber at length of about 1080µm. At this length the instantaneous acceleration of light is found to be 13×1019 m/s2 which its corresponding Unruh temperature is 0.527K.

Stability bounds on superluminal propagation in active structures

Active materials have been explored in recent years to demonstrate superluminal group velocities over relatively broad bandwidths, implying a potential path towards bold claims such as information transport beyond the speed of light, as well as antennas and metamaterial cloaks operating over very broad bandwidths. However, causality requires that no portion of an impinging pulse can pass its precursor, implying a fundamental trade-off between bandwidth, velocity and propagation distance. Here, we clarify the general nature of superluminal propagation in active structures and derive a bound on these quantities fundamentally rooted into stability considerations. By applying filter theory, we show that this bound is generally applicable to causal structures of arbitrary complexity, as it applies to each zero-pole pair describing their response. As the system complexity grows, we find that only minor improvements in superluminal bandwidth can be practically achieved. Our results provide physical insights into the limitations of superluminal structures based on active media, implying severe constraints in several recently proposed applications.

Theoretical and experimental examination of simple coaxial photonic crystals for undergraduate teaching

A study implementing a coaxial photonic crystal with a simple structure composed of only one type of coaxial cable is described. The coaxial photonic crystal consists of alternating sections of a single cable and N parallel cables, with impedances of ZH and ZH/N, respectively. The high mismatch in impedance at the interfaces enables access to a highly superluminal group velocity with few cables. An easily realizable method is also presented to measure both the amplitude of transmission and the phase of the crystal by using an oscilloscope and a function generator. The measurements were validated by an advanced vector network analyzer and matched the results of theoretical analysis based on the transfer matrix method. The experiment only requires electronic components and equipment that are typically used in undergraduate teaching laboratories.

Propagation-invariant space-time caustics of light.

Caustics are responsible for a wide range of natural phenomena, from rainbows and mirages to sparkling seas. Here, we present caustics in space-time wavepackets, a class of pulsed beams featuring strong coupling between spatial and temporal frequencies. Space-time wavepackets have attracted much attention with their propagation-invariant intensity profiles that travel at tunable superluminal and subluminal group velocities. These intensity profiles, however, have been largely restricted to an X-shape or similar pattern. We show that space-time caustics combine the propagation invariance of space-time wavepackets with the flexible design of caustics, allowing for customizable intensity patterns in space-time wavepackets. Our method directly provides the phase distribution needed to realize user-designed caustic patterns in space-time wavepackets. We show that space-time caustics can feature in a broad range of intriguing optical phenomena, including backward traveling caustics formed from purely forward propagating waves, and nondiffracting beams that evolve with time. Our findings should open the doors to an even wider range of structured light with spatiotemporal coupling.

Doppler broadening and squeezing-induced sub- and super-luminal group velocity in a driven qubit model

Doppler broadening and squeezing-induced sub- and super-luminal group velocity in a driven qubit model

Corrigendum: Conductivity-dependent absorption-free, gain-assisted superluminal propagation and rotary photon drag [Optical Materials 115 (2021) 111047

Unfortunately, some of the Figures were placed at wrong order (e.g. Figs. 1–6), in addition to the repetition of Fig. 6, in our published Article [ 1 ]. Besides correcting the order, the missing Fig. 1 (on the energy level scheme of the proposed quantum model) and Fig. 7 are added in the Corrigendum. As such, the correct orders of Figs. 1–6 in the Article should be Figs. 2–7 as in the Corrigendum. Figs. 8–9 are replaced with the correct ones. Figs. 10–12 are also correctly readjusted. Figures 13 and 14 in the Article are correct in all respects. However, description in the captions of all the Figures with the corrected order in the Article is same as in the corrigendum. The authors highly regret the inconvenience. • Study of absorption-free, gain-assisted propagation at positive and negative group velocity for positive and negative index refractive index of the conducting medium. • Phase and amplitude of conductivity influence largely the optical properties such as group index, group velocity, group delay and photon drag. • The maximum calculated values of positive and negative superluminal group velocities are of order 4 ×10 8 m/s at positive and negative group indices, respectively. • The maximum value of photon drag calculated is of order 6.4 ×10 −7 radian. • Probe detuning can be used as a tuning nob to switching the light absorption profile to the transparent window at resonance.

Conductivity-dependent absorption-free, gain-assisted superluminal propagation and rotary photon drag

Abstract Superluminal light propagation and photon drag are subjects of immense scientific interest owing to potential fundamental and technological implications in the fields of atomic and molecular physics, condensed-matter physics, quantum optics, nanoplasmonics, nanophotonics, and nanoelectronics. In this paper, we present a systematic study on the optical properties, rotary photon drag and superluminal propagation in a conducting gain medium comprising a four-level invert-N-type atomic system. In particular, to explore the nature of light propagation, as to whether subluminal or superluminal, we aim to investigate optical properties of the medium in view of the derived expression of group index, group velocity, group delay, phase delay and photon drag. Interestingly, by tuning the spectral parameters of the proposed system, we predict gain-assisted, absorption-free propagation and superluminality at positive and negative group velocity for positive and negative refractive indices of the medium, respectively. The medium, subjected to various spectral conditions, displays an interesting switching from ON-resonance single absorption peak in the probe field spectrum to an ON-resonance absorption-free region between two OFF-resonance absorption peaks to OFF-resonance gain singlet accompanied by OFF-resonance absorption peak. The maximum calculated values of positive and negative superluminal group velocities of the light pulse are of order 4 × 10 8 m / s both at positive and negative group indices, respectively. On the other hand, the maximum value of photon drag calculated is of order 6.4 × 10 − 7 radian.

On the Principle of Causality and Superluminal Signal Propagation Velocities

This paper considers the question of superluminal (or negative) group velocities of signals in dispersive media, as well as negative group delay times of signals passing through linear filters. It is shown that information can be transmitted only with the help of jumps in the time dependence of a function or its derivatives and, therefore, the information propagation velocity in any (including dispersive, absorbing, or amplifying) medium exactly coincides with the speed of light in vacuum. As for the group velocity of a wave packet, it is only the propagation velocity of its infinitely differentiable envelope, by means of which the transmission of information, strictly speaking, is impossible. Therefore, in regions with anomalous dispersion, the group velocity can be superluminal or negative without violating the “light limitation” of the theory of relativity or the principle of causality. Examples of situations in which superluminal or negative group velocity occurs are given.

Fizeau’s light birefringence dragging effect in a moving chiral medium

The Fizeau’s light birefringence dragging effect is investigated in a moving chiral medium. The effect significantly influences the subluminality, superluminality, phase shift and divergence angle between the circularly polarized birefringent modes. The maximum superluminal group velocity is measured in the range $$-4\times 10^8$$ – $$1\times 10^{10}$$ m/s. The group index and group velocity measured with phase of the control field and phase of the superposition states are in the range $$0.4\le n^{(\pm )}_g\le 0.8$$ and $$4\times 10^8$$ m/s $$\le v^{(\pm )}_g\le 8\times 10^8$$ m/s, respectively. The maximum Fizeau’s birefringence dragging coefficient is noted in the range $$-20\le F_D\le 20$$ and varies with phases of the applied fields in the range $$\pm 1$$ . The birefringent phase uncertainty between the phase shift under dragging and in the absence of the dragging effect is in the range $$0.005\le \Delta \Phi ^{(\pm )}\le 0.015$$ radian. The divergence angle between the two modes is in the range $$0.000\le \theta _d\le 0.004$$ radian. The controlled birefringence phase uncertainty may show significant applications in interferometry, velocimetry and sensitivity.

Time-domain properties of electromagnetic signals in a dynamical axion background

Electromagnetic waves in a dynamical axion background exhibit superluminal group velocities at high frequencies and instabilities at low frequencies, altering how photons propagate through space. Local disturbances propagate causally, but unlike in ordinary Maxwell theory, propagation occurs inside as well as on the lightcone. For the unstable modes, the energy density in the electromagnetic field grows exponentially along timelike displacements. In this paper we derive retarded Green functions in axion electrodynamics in various limits and study the time-domain properties of propagating signals.

Optical wave-packet with nearly-programmable group velocities

During the process of Bessel beam generation in free space, spatiotemporal optical wave-packets with tunable group velocities and accelerations can be created by deforming pulse-fronts of injected pulsed beams. So far, only one determined motion form (superluminal or luminal or subluminal for the case of group velocity; and accelerating or uniform-motion or decelerating for the case of acceleration) could be achieved in a single propagation path. Here we show that deformed pulse-fronts with well-designed axisymmetric distributions (unlike conical and spherical pulse-fronts used in previous studies) allow us to obtain nearly-programmable group velocities with several different motion forms in a single propagation path. Our simulation shows that this unusual optical wave-packet can propagate at alternating superluminal and subluminal group velocities along a straight-line trajectory with corresponding instantaneous accelerations that vary periodically between positive (acceleration) and negative (deceleration) values, almost encompassing all motion forms of the group velocity in a single propagation path. Such unusual optical wave-packets with nearly-programmable group velocities may offer new opportunities for optical and physical applications.

Off-axis optical vortices using double-Raman singlet and doublet light-matter schemes

We study the formation of off-axis optical vortices propagating inside a double-Raman gain atomic medium. The atoms interact with two weak probe fields as well as two strong pump beams which can carry orbital angular momentum (OAM). We consider a situation when only one of the strong pump lasers carries an OAM. A particular superposition of probe fields coupled to the matter is shown to form specific optical vortices with shifted axes. Such off-axis vortices can propagate inside the medium with sub- or superluminal group velocity depending on the value of the two-photon detuning. The superluminal optical vortices are associated with the amplification as the energy of pump fields is transferred to the probe fields. The position of the peripheral vortices can be manipulated by the OAM and intensity of the pump fields. We show that the exchange of optical vortices is possible between individual probe beams and the pump fields when the amplitude of the second probe field is zero at the beginning of the atomic cloud. The model is extended to a more complex double Raman doublet interacting with four pump fields. In contrast to the double-Raman-singlet, now the generation of the off-axis sub- or superluminal optical vortices is possible even for zero two-photon detuning.

Astrometric effects of gravitational wave backgrounds with nonluminal propagation speeds

A passing gravitational wave causes a deflection in the apparent astrometric positions of distant stars. The effect of the speed of the gravitational wave on this astrometric shift is discussed. A stochastic background of gravitational waves would result in a pattern of astrometric deflections which are correlated on large angular scales. These correlations are quantified and investigated for backgrounds of gravitational waves with sub- and super-luminal group velocities. The statistical properties of the correlations are depicted in two equivalent and related ways: as correlation curves and as angular power spectra. Sub-(super-)luminal gravitational wave backgrounds have the effect of enhancing (suppressing) the power in low-order angular modes. Analytical representations of the redshift-redshift and redshift-astrometry correlations are also derived. The potential for using this effect for constraining the speed of gravity is discussed.