Light Wave Packets Research Articles

A Simple Quantum Picture of the Relativistic Doppler Effect

The relativistic Doppler effect comes from the fact that observers in different inertial reference frames experience space and time differently, while the speed of light always remains the same. Consequently, a wave packet of light exhibits different frequencies, wavelengths, and amplitudes. In this paper, we present a local approach to the relativistic Doppler effect based on relativity, spatial and time translational symmetries, and energy conservation. Afterwards, we investigate the implications of the relativistic Doppler effect for the quantum state transformations of wave packets of light and show that a local photon is a local photon at the same point in the spacetime diagram in all inertial frames.

Stochastic approach to evolution of a quantum system interacting with environment in squeezed number state

We determine filtering and master equations for a quantum system interacting with wave packet of light in a continuous-mode squeezed number state. We formulate the problem of conditional evolution of a quantum system making use of model of repeated interactions and measurements. In this approach, the quantum system undergoes a sequence of interactions with an environment defined by a chain of harmonic oscillators. We assume that the environment is prepared in an entangled state being a discrete analogue of a continuous-mode squeezed number state. We present a derivation of a discrete stochastic dynamics that depends on the results of measurement performed on the field after its interaction with the system. In this paper, we consider a photon counting measurement scheme. By taking a continuous time limit, we finally obtain differential stochastic equations for the system. Analytical formulae for quantum trajectories and exclusive probability densities that allow to fully characterize the statistics of photons in the output field are given.

Frequency-domain interferometry for the determination of time delay between two extreme-ultraviolet wave packets generated by a tandem undulator

Synchrotron radiation, emitted by relativistic electrons traveling in a magnetic field, has poor temporal coherence. However, recent research has proved that time-domain interferometry experiments, which were thought to be enabled by only lasers of excellent temporal coherence, can be implemented with synchrotron radiation using a tandem undulator. The radiation generated by the tandem undulator comprises pairs of light wave packets, and the longitudinal coherence within a light wave packet pair is used to achieve time-domain interferometry. The time delay between two light wave packets, formed by a chicane for the electron trajectory, can be adjusted in the femtosecond range by a standard synchrotron technology. In this study, we show that frequency-domain spectra of the tandem undulator radiation exhibit fringe structures from which the time delay between a light wave packet pair can be determined with accuracy on the order of attoseconds. The feasibility and limitations of the frequency-domain interferometric determination of the time delay are examined.

Antichiral topological phases and protected bulk transport in dual-helix Floquet lattices

The incorporation of driven auxiliary nodes in Floquet lattices can substantially enhance their topological nature, resulting in unique nontrivial phases. Here, we develop an alternative design approach in Floquet topology by introducing a dual-helix modulation scheme that can simultaneously support a clockwise and a counterclockwise helicity in a singular unit cell. As a result, the band structure of a dual-helix configuration can parametrically deform between a conventional phase that exhibits crossed edge states and an antichiral phase with tilted unidirectional states, showcasing for the first time an antichiral phase in Floquet topological systems. An extended family of tilted and overtilted edge states is identified and topologically characterized, revealing that integer Chern and winding numbers can successfully characterize lattices that lack global topological gaps. This results in a rich dynamic response where light wave-packets can acquire different velocities at adjacent edges, and even halt or reverse their direction into unidirectional bulk channels, preserving their topological protection. To investigate these effects, we study a dual-helix photonic lattice of evanescently coupled waveguides where a nontrivial topology can now emerge on a completely stationary configuration, departing from conventional schemes that require helical variations of the lattice sites.

Generating ultrashort visible light pulses based on multidimensional solitary states in gas-filled hollow core fiber

Multidimensional solitary states (MDSS) are self-sustaining light wave packets confined in multiple dimensions in multimode fibers. In this work, we experimentally demonstrate the generation of MDSS, driven by a few hundreds of femtoseconds (fs) of long frequency doubled pulses from a Titanium:Sapphire chirped pulsed amplifier in a nitrous oxide-filled hollow core fiber (HCF). The MDSS output, resulting from intermodal interactions in a Raman-active gas-filled large core diameter HCF, features a broadband, red-shifted spectrum in the visible spectral region with a characteristic negative quadratic spectral phase. Therefore, the output with broadband spectra and negative chirp results in the generation of sub-30 fs pulses upon propagation through glass windows and a spectral filter. Backed with experimental observations and multidimensional simulations, we demonstrate that the sign of the frequency chirp of input pulses influences the spectral broadening in the HCF in the high gas-dispersion regime. We observed that the MDSS red-shifted pulses have a clean spatial profile. Therefore, the experimental requirements on the input beam size and quality to achieve a clean MDSS beam profile at the output of large core HCFs can be relaxed. Hence, this work extends the validation of the MDSS phenomenon toward the ultraviolet-visible region of the electromagnetic spectrum, thus providing an alternate source with a clean spatial beam profile for various applications in the field of ultrafast spectroscopy.

Time domain double slit interference of electron produced by XUV synchrotron radiation

We present a new realization of the time-domain double-slit experiment with photoelectrons, demonstrating that spontaneous radiation from a bunch of relativistic electrons can be used to control the quantum interference of single-particles. The double-slit arrangement is realized by a pair of light wave packets with attosecond-controlled spacing, which is naturally included in the spontaneous radiation from two undulators in series. Photoelectrons emitted from helium atoms are observed in the energy-domain under the condition of detecting them one by one, and the stochastic buildup of the quantum interference pattern on a detector plane is recorded.

Pendulum-type light beams

Nondiffracting and shape-preserving light beams have been extensively studied and were shown to exhibit intriguing wave phenomena, which led to applications including particle manipulation, curved plasma channel generation, and optical superresolution. However, these beams are generated by caustics, i.e., conical superposition of waves. As a result, they tend to propagate along a straight line or accelerate in a plane [(1 + 1)D], and tailoring their propagation trajectories in a higher dimension [(2 + 1]D] is challenging. Here we report both theoretically and experimentally a class of nondiffracting solutions to the paraxial wave equation perturbed by harmonic potential. We demonstrate that the initial wave packets of light can be engineered to accelerate along an arbitrary trajectory centered on an elliptic or a circular orbit in a (2 + 1)D configuration, while maintaining their phase and polarization structures during propagation. Such particle-like features manifested by orbital movements can be attributed to the centripetal force of the underlying potential. We name such oscillating wave packets as pendulum-type beams. We suggest the concept can be generalized to other waves such as quantum waves, matter waves, and acoustic waves, opening possibilities for the study and applications of the pendulum-type wave packet in a wide range, e.g., it may be utilized in the field of laser scanning technology.

Coherent control of atoms in the extreme ultraviolet and attosecond regime by synchrotron radiation

Control of interference between wave packets is one of the basic concepts in coherent control that enables quantum manipulation of populations and reaction pathways in matter. We have recently shown a new method to achieve coherent control in the extreme ultraviolet and attosecond regime using synchrotron radiation. This method is based on the use of longitudinal coherence of light wave packets that are naturally included in the undulator radiation. For quantum manipulation of atomic systems, wave packet interference is precisely controlled by tuning the time delay between the light wave packets. Here we show that the quantum phase controlled by the time delay can be monitored as an initial phase of the quantum beat oscillation in fluorescence decay.

Analysis of single-photon self-interference in Young’s double-slit experiments

For centuries Young’s double-slit interference continues to be a hot discussion subject about whether light is waves or particles. This work unravels the self-interference parados, and sheds light on such a concept that assumes a photon can split, self-interfere, and recombine. This work elucidates how coherent photons from a laser source could produce a double-slit interference pattern without the hypothesis of unphysical splitting and recombination of a single photon. Unlike the conventional single wave-function description for the whole ensemble of particles, we develop a pilot-wave trajectory approach to track every photon’s wave-packet propagation and calculate the evolution of the interference intensity in time. We demonstrate how wave packets and phase coherence affect the interference pattern. To resolve the century-old self-interference paradox, we show that such an hypothesis is unnecessary, and the illusion is due to the long coherence length of laser photons and overlaps of delocalized light wave packets.

Spacetime effects on wavepackets of coherent light

We investigate the interplay between gravity and the quantum coherence present in the state of a pulse of light propagating in curved spacetime. We first introduce an operational way to distinguish between the overall shift in the pulse wavepacket and its genuine deformation after propagation. We then apply our technique to quantum states of photons that are coherent in the frequency degree of freedom, as well as to states of completely incoherent light. We focus on Gaussian profiles and frequency combs and find that the quantum coherence initially present can enhance the deformation induced by propagation in a curved background. These results further supports the claim that genuine quantum features, such as quantum coherence, can be used to probe the gravitational properties of physical systems. We specialize our techniques to Earth-to-satellite communication setups, where the effects of gravity are weak but can be tested with current satellite technologies.

Locally acting mirror Hamiltonians

Photons, i.e. the basic energy quanta of monochromatic waves, are highly non-localized and occupy all available space in one dimension. This non-local property can complicate the modelling of the quantized electromagnetic field in the presence of optical elements that are local objects. Therefore, in this paper, we take an alternative approach and quantize the electromagnetic field in position space. Taking into account the negative- and the positive-frequency solutions of Maxwell's equations, we construct annihilation operators for highly localized field excitations with bosonic commutator relations. These provide natural building blocks of wave packets of light and enable us to construct locally acting interaction Hamiltonians for two-sided semi-transparent mirrors.

Discrete wavelet structure and discrete energy of classical plane light waves

We find by the wavelet transform that the classical plane light wave of linear polarization can be decomposed into a series of discrete Morlet wavelets. In the theoretical frame, the energy of the classical light wave becomes discrete; interestingly, the discretization is consistent with the energy division of P portions in Planck radiation theory, where P is an integer. It is shown that the changeable energy of a basic plane light wave packet or wave train is H 0k = np 0k ω (n = 1, 2, 3, … k = | k |), with discrete wavelet structure parameter n, wave vector k and idler frequency ω, and a constant p 0k . The wave-particle duality from the Mach--Zehnder interference of single photons is simulated by using random basic plane light wave packets.

Isolated Photonic Flatband with the Effective Magnetic Flux in a Synthetic Space Including the Frequency Dimension

AbstractExploration of the flatband in photonics is fundamentally important, aiming to control the localization of light for potential applications in optical communications. Herein, the flatband physics is studied in a synthetic space including the frequency axis of light. A ring‐resonator array is used to construct a synthetic Lieb‐type lattice, where the modulation phase distribution supports a locally non‐zero effective magnetic flux pointing into the synthetic space. It is found that the flatband is isolated from other dispersive bands and the light can still be localized even with perturbation from the group velocity dispersion of the waveguide. This work points out a route towards manipulating the localization performance of a wavepacket of light along both the spatial dimension and the frequency dimension, which holds the potential implication for controlling the storage of optical information in dispersive materials.

Actively mode tunable electromagnetically induced transparency in a polarization-dependent terahertz metamaterial

Electromagnetically induced transparency (EIT) is a quantum destructive interference phenomenon in three-level atomic systems, which can slow down the light velocity and has application prospects in information storage and processing. However, the EIT effect in atomic systems requires harsh experimental conditions. This problem can be solved by employing an EIT metamaterial, where destructive interference occurs between a bright mode and a dark mode or a quasi-dark mode, inducing a transparency window accompanied by the slow light effect. Here, we propose an actively mode tunable electromagnetically induced transparency terahertz metamaterial, which is comprised of a T-type resonator, a split-ring resonator (SRR), and coupled split-ring resonators (CSRRs). When the external electric field is vertical to the gap of the SRR (x-polarization), there is a single EIT mode accompanied by one slow light wave packet. On the other hand, when the external electric field is parallel to the gap of the SRR (y-polarization), there are two EIT modes accompanied by two slow light wave packets. Therefore, an active switch from a single EIT mode to dual EIT modes controlled by changing the polarization is demonstrated, which can find explanation from the electric field intensity distributions. This work offers a strategy to realize the mode tunable EIT, which may achieve potential applications in active filters, modulators, and slow light devices.

Subcycle squeezing of light from a time flow perspective

Light as a carrier of information and energy plays a fundamental role in both general relativity and quantum physics, linking these areas that are still not fully compliant with each other. Its quantum nature and spatio-temporal structure are exploited in many intriguing applications ranging from novel spectroscopy methods of complex many-body phenomena to quantum information processing and subwavelength lithography. Recent access to subcycle quantum features of electromagnetic radiation promises a new class of time-dependent quantum states of light. Paralleled with the developments in attosecond science, these advances motivate an urgent need for a theoretical framework that treats arbitrary wave packets of quantum light intrinsically in the time domain. Here, we formulate a consistent time domain theory of the generation and sampling of few-cycle and subcycle pulsed squeezed states, allowing for a relativistic interpretation in terms of induced changes in the local flow of time. Our theory enables the use of such states as a resource for novel ultrafast applications in quantum optics and quantum information.

Free-fall of photons in a planar optical cavity

We consider a planar optical cavity with one of its in-plane axis aligned with the Earth’s local gravity field. We examine the motion of a wavepacket of light trapped within the cavity spacer under the action of gravity. Using a general relativity framework, we find that the wavepacket initially at rest in terms of its in-plane group velocity, is subject to a non-relativistic free-fall motion of acceleration in the Earth-bound reference frame.

Bloch oscillations and resonant radiation of light propagating in arrays of nonlinear fibers with high-order dispersion

Bloch oscillations of spatio-temporal light wave packets in arrays of nonlinear fibers with high-order dispersion are studied. The light wave experiences discrete spatial diffraction along the waveguide array coordinate together with continuous temporal dispersion including higher order terms. When a gradient in the waveguide light confinement strength is considered, the wave packet features robust long-lived Bloch oscillations with temporal and spatial spreading in the presence of a Kerr nonlinearity. The effect of the spatial Bloch oscillations on the emission of the dispersive radiation by the solitary wave is studied. It is shown that Bloch oscillations result in the generation of new frequencies. The condition of resonant emission of dispersive waves is derived and it is demonstrated that it matches very well with the results of direct numerical simulations.

A solid-state single-photon filter.

A strong limitation of linear optical quantum computing is the probabilistic operation of two-quantum-bit gates based on the coalescence of indistinguishable photons. A route to deterministic operation is to exploit the single-photon nonlinearity of an atomic transition. Through engineering of the atom-photon interaction, phase shifters, photon filters and photon-photon gates have been demonstrated with natural atoms. Proofs of concept have been reported with semiconductor quantum dots, yet limited by inefficient atom-photon interfaces and dephasing. Here, we report a highly efficient single-photon filter based on a large optical nonlinearity at the single-photon level, in a near-optimal quantum-dot cavity interface. When probed with coherent light wavepackets, the device shows a record nonlinearity threshold around 0.3 ± 0.1 incident photons. We demonstrate that 80% of the directly reflected light intensity consists of a single-photon Fock state and that the two- and three-photon components are strongly suppressed compared with the single-photon one.

On spacetime structure and electrodynamics

Electrodynamics is the most tested fundamental physical theory. Relativity arose from the completion of Maxwell–Lorentz electrodynamics. Introducing the metric [Formula: see text] as gravitational potential in 1913, versed in general (coordinate-)covariant formalism in 1914 and shortly after the completion of general relativity, Einstein put the Maxwell equations in general covariant form with only the constitutive relation between the excitation and the field dependent on and connected by the metric in 1916. Further clarification and developments by Weyl in 1918, Murnaghan in 1921, Kottler in 1922 and Cartan in 1923 together with the corresponding developments in electrodynamics of continuous media by Bateman in 1910, Tamm in 1924, Laue in 1952 and Post in 1962 established the premetric formalism of electrodynamics. Since almost all phenomena electrodynamics deal with have energy scales much lower than the Higgs mass energy and intermediate boson energy, electrodynamics of continuous media should be applicable and the constitutive relation of spacetime/vacuum should be local and linear. What is the key characteristic of the spacetime/vacuum? It is the Weak Equivalence Principle I (WEP I) for photons/wave packets of light which states that the spacetime trajectory of light in a gravitational field depends only on its initial position and direction of propagation, and does not depend on its frequency (energy) and polarization, i.e. nonbirefringence of light propagation in spacetime/vacuum. With this principle it is proved by the author in 1981 in the weak field limit, and by Lammerzahl and Hehl in 2004 together with Favaro and Bergamin in 2011 without assuming the weak-field condition that the constitutive tensor must be of the core metric form with only two additional degrees of freedom — the pseudoscalar (Abelian axion or EM axion) degree of freedom and the scalar (dilaton) degree of freedom (i.e. metric with axion and dilaton). In this paper, we review this connection and the ultrahigh precision empirical tests of nonbirefringence together with present status of tests of cosmic Abelian axion and dilaton. If the stronger version of WEP is assumed, i.e. WEP II for photons (wave packets of light) which states in addition to WEP I also that the polarization state of the light would not change (e.g. no polarization rotation for linear polarized light) and no amplification/attenuation of light, then no Abelian (EM) axion and no dilaton, and we have a pure metric theory.

Dynamics of Plasmonic Stopped-Light Nanolasing and Condensation

ABSTRACTBy reducing the number of dimensions that light can propagate in from three down to two, one may gain control over the characteristics of propagation. This control can allow for “Stopped Light” (SL), where wavepackets of light are slowed down to a zero group velocity. This is achieved by designing planar metal-dielectric structures that are stacked in one dimension allowing for waveguide modes in the other two, and engineering the dispersion relation of these structures. Stopped light structures can be further optimized to reduce their dispersion and increase the number of spatial frequencies supported, which allows for confinement of electromagnetic energy over volumes smaller than the diffraction limit over fixed regions in space. If this electromagnetic energy is confined over a region that provides gain, the question arises, can amplification of this light energy occur? and indeed can a regime of lasing be entered into? We show that stopped light lasing is indeed possible, despite there being no resonant cavity in 2d to confine the light, and explore the properties of this new type of laser.