Initial Relative Phase Research Articles

Relativistic head-on collisions of U(1) gauged Q -balls

We investigate the collision dynamics of U(1) gauged Q-balls by performing high-resolution numerical simulations in axisymmetry. Focusing on the case of relativistic head-on collisions, we consider the effects of the initial velocity, relative phase, relative charge, and electromagnetic coupling strength on the outcome of the collision. We find that the collision dynamics can depend strongly on these parameters; most notably, electromagnetic effects can significantly alter the outcome of the collision when the gauge coupling is large. When the gauge coupling is small, we find that the dynamics generally resemble those of ordinary (nongauged) Q-balls. Published by the American Physical Society 2024

Quantum enhancement of qutrit dynamics of a three-level giant atom coupling to a one-dimensional waveguide

Dynamics of quantum coherence and non-Markovianity of a three-level giant atom coupling to a one-dimensional waveguide and a classical field are investigated theoretically. The time delay of the photo propagation in the waveguide is taken into account and our aim is to access the collective impact of a waveguide and classical control of the system on the time evolution of coherence and non-Markovianity. For a giant atom, we find that the various values of the accumulated phase and time delay does not make much difference for the coherence evolution but there exists non-Markovian behavior for the vast majority of the chosen parameter values. With regard to the initial relative phase, the quantum coherence takes a monotonic behavior for a small atom but decreases with oscillations for a giant atom with majority values of the initial relative phase. Quantum coherence of a small atom decreases monotonically with regardless of the Rabi frequency and the atom’s detuning to a large extent but a large Rabi frequency or a large atom’s detuning will induce non-Markovian behavior for a giant atom. With a comparative analysis, the coherence evolution is enhanced significantly in that there is non-Markovian behavior for the dynamics of quantum coherence in a much larger range of scaled time for a giant atom than that for a small atom. Our study provide clues to preserve and to enhance quantum coherence in qutrit systems.

Asymmetric solitons induced by transition and beating effects

We investigate the dynamics of beating solitons in a two-component Bose–Einstein condensate with tunable Rabi coupling strength. Our results demonstrate that the balance between transition and beating effects permits the emergence of a novel family of asymmetric solitons in the symmetric physical settings. We derive the exact analytical solutions for them, which primarily consist of one bright soliton and one dark soliton element. The analytical solutions provide us with precise balance conditions required for the formation of asymmetric solitons. We also show that the degree of asymmetry can be effectively manipulated by adjusting the background density flow of dark soliton element, initial relative phase between two soliton elements, and their width. Furthermore, we discuss the oscillation behavior of asymmetric solitons in a harmonic potential, and the interaction between them.

Effect of initial phase on the ablative Rayleigh–Taylor instability

The effect of initial perturbation phase on the ablative Rayleigh–Taylor instability is investigated by numerical simulations. We aim at the growth of harmonic amplitudes and the formation of spikes and bubbles in single- and two-mode coupling cases, respectively. In the two-mode coupling case, two kinds of simulations are performed: two modes with relatively small linear growth rate difference and two modes with relatively large linear growth rate difference. The initial relative phase between the original two modes has a significant effect on the growth of harmonic amplitudes, and in different initial relative phases, the structures of spikes and bubbles begin to show great differences in the nonlinear stage. Fortunately, the harmonic amplitudes are weakened at a specific initial relative phase. This has a certain enlightening significance for the stabilization of ablative Rayleigh–Taylor instability.

Creation of galaxy-shaped vortex relief structures in azo-polymers with petal-like beams.

We demonstrate the formation of surface relief structures in azo-polymers which exhibit multiple spiral arms, through irradiation of a rotating petal-like beam formed by the coherent superposition of Laguerre-Gaussian modes with opposite handedness. Intriguingly, the fabricated relief structures reflect full geometric parameters of the irradiated petal beam, such as handedness, topological charge, initial azimuthal phase and even ellipticity, corresponding to azimuthal and polar angles along equator and meridian planes of an orbital Poincaré sphere. The handedness, or direction of rotation, of the fabricated structures with multiple spiral arms could be controlled via the rotation and polarization directions of the irradiating laser field. This effect highlights an exotic coupling between the optical intensity gradient induced mass transport of the irradiated material and the spin angular momentum characteristics of the irradiating optical field. The azimuthal orientation of the surface relief structures could also be tuned by altering the initial relative phase between the coherently superposed Laguerre-Gaussian modes with opposite handedness, constituting the irradiating petal laser field. This work offers new insights into fundamental interactions which occur between light and matter, and we believe, will pave the way towards advanced technologies, such as ultrahigh density optical data storage.

Ultrashort pulsed neutron source driven by two counter-propagating laser pulses interacting with ultra-thin foil

Neutron production via D(d, n)<sup>3</sup>He nuclear reaction during the interaction of two counter-propagating circularly polarized laser pulses with ultra-thin deuterium target is investigated by particle-in-cell simulation and Monte Carlo method. It is found that the rotation direction and initial relative phase difference of laser electric field vector have important effects on deuterium foil compression and neutron characteristics. The reason is attributed to the net light pressure and the difference in transverse instability development. The highest neutron yield can be obtained by choosing two laser pulses with a relative phase difference of 0 and the same rotation direction of the electric field vector. When the relative phase difference is 0.5π or 1.5π and the rotation direction of electric field vector is different, the neutrons have a directional spatial distribution and the neutron yield only slightly decreases. For left-handed circularly polarized laser pulse and right-handed circularly polarized laser pulse, each with an intensity of 1.23 × 10<sup>21</sup> W/cm<sup>2</sup>, a pulse width of 33 fs and a relative phase difference of 0.5π, it is possible to produce a pulsed neutron source with a yield of 8.5 × 10<sup>4</sup> n, production rate of 1.2 × 10<sup>19</sup> n/s, pulse width of 23 fs and good forward direction as well as tunable spatial distribution. Comparing with photonuclear neutron source and beam target neutron source driven by ultraintense laser pulses, the duration of neutron source in our scheme decreases significantly, thereby possessing many potential applications such as neutron nuclear data measurement. Our scheme offers a possible method to obtain a compact neutron source with short pulse width, high production rate and good forward direction.

Impact of the wavelike nature of Proca stars on their gravitational-wave emission

We present a systematic study of the dynamics and gravitational-wave emission of head-on collisions of spinning vector boson stars, known as Proca stars. To this aim we build a catalog of about 800 numerical-relativity simulations of such systems. We find that the wavelike nature of bosonic stars has a large impact on the gravitational-wave emission. In particular, we show that the initial relative phase $\mathrm{\ensuremath{\Delta}}\ensuremath{\epsilon}={\ensuremath{\epsilon}}_{1}\ensuremath{-}{\ensuremath{\epsilon}}_{2}$ of the two complex fields forming the stars (or, equivalently, the relative phase at merger) strongly impacts both the emitted gravitational-wave energy and the corresponding mode structure. This leads to a nonmonotonic dependence of the emission on the frequency of the secondary star ${\ensuremath{\omega}}_{2}$, for fixed frequency ${\ensuremath{\omega}}_{1}$ of the primary. This phenomenology, which has not been found for the case of black-hole mergers, reflects the distinct ability of the Proca field to interact with itself in both constructive and destructive manners. We postulate this may serve as a smoking gun to shed light on the possible existence of these objects.

Persistent Nonlinear Phase-Locking and Nonmonotonic Energy Dissipation in Micromechanical Resonators.

Many nonlinear systems are described by eigenmodes with amplitude-dependent frequencies, interacting strongly whenever the frequencies become commensurate at internal resonances. Fast energy exchange via the resonances holds the key to rich dynamical behavior, such as time-varying relaxation rates and signatures of nonergodicity in thermal equilibrium, revealed in the recent experimental and theoretical studies of micro- and nanomechanical resonators. However, a universal yet intuitive physical description for these diverse and sometimes contradictory experimental observations remains elusive. Here we experimentally reveal persistent nonlinear phase-locked states occurring at internal resonances and demonstrate that they are essential for understanding the transient dynamics of nonlinear systems with coupled eigenmodes. The measured dynamics of a fully observable micromechanical resonator system are quantitatively described by the lower-frequency mode entering, maintaining, and exiting a persistent phase-locked period-tripling state generated by the nonlinear driving force exerted by the higher-frequency mode. This model describes the observed phase-locked coherence times, the direction and magnitude of the energy exchange, and the resulting nonmonotonic mode energy evolution. Depending on the initial relative phase, the system selects distinct relaxation pathways, either entering or bypassing the locked state. The described persistent phase locking is not limited to particular frequency fractions or types of nonlinearities and may advance nonlinear resonator systems engineering across physical domains, including photonics as well as nanomechanics.

Interaction between double solitons in anti-PT symmetric synthetic photonic lattices

An anti-parity-time symmetry (anti-PT symmetric) double fiber loop synthetic photonic lattice is constructed theoretically by projecting the intensity of two loops and adjusting the phase and gain/loss distribution. Numerical studies on pulse dynamics show that the trajectories of double-pulse solitons may be manipulated by tuning the initial relative phases, pulse separation, nonlinearity, and non-Hermitian characteristics of the system. Our research may provide a new way to realize logic gate devices and optical switches in optical interconnection and optical communications.

Phase-sensitive seeded modulation instability in passive fiber resonators

Modulation instability is one of the most ubiquitous phenomena in physics. Here we investigate the phase-sensitive properties of modulation instability with harmonic seeding in passive fiber resonators. Theoretical investigations based on the Lugiato−Lefever equation with time dependent pump and a three-wave truncation show that the dynamics of the system is sensitive to the relative phase between input signal, idler, and pump waves. The modulation instability gain can even vanish for a peculiar value of the initial relative phase. An advanced multi-heterodyne measurement technique had been developed to record the real time evolution, round-trip to round-trip, of the power and phase of the output cavity field to confirm these theoretical predictions.

Observation of a different type of splitting solitons induced by interaction of second order spatial solitons

In this work the behavior of the split solitons derived from the interaction between two (1 + 1)- Dimensional second-order bright spatial solitons, is numerically investigated. Each individual interaction occurs when the two second-order solitons are initially propagating in the parallel way, while the variety of relative phases and the different initial transversal separation are adjusted. When the initial separation distance is on the appropriate distance where they feel the presence of other soliton, both second-order solitons breakup into a couple of first order (fundamental) low- and high-amplitude solitons, and consequently their initial parallel path suffers a lot. Although the propagation path of high- amplitude solitons receive low effects due to interaction and consequently almost follow their initial propagation path, the propagation path of the low-amplitude solitons suffers based on their initial relative phase. The derived low-amplitude fundamental solitons interact with each other and their propagation path also, as usual of their basic interaction properties, while the high-amplitude fundamental solitons, do not show the interaction, and almost continue their own parallel paths. As the initial separation distance decreases, and almost the initial overlap occurs, the propagation paths suffer for both (high and low amplitude) fundamental solitons. Behavior of the broken solitons induced by the interaction between the second order spatial solitons are investigated by solving the Nonlinear Schrodinger equation (NLSE), and it is simulated numerically by MATLAB program by using the well-known Split-Step Fourier Transform method.

Nonlinear interactions of nearly non-dispersive equatorial shallow-water waves

Abstract This paper is concerned with nonlinear interactions of fundamental equatorial modes. In order to understand the mechanism of large-scale atmospheric motions in the near equator regime—especially the observed wavenumber-frequency spectrum—we develop novel models describing interactions among Kelvin, Yanai and Poincaré waves. Based on the methods of multiple scales and Galerkin projection, the primitive equations can be simplified to model equations which reduce the complexity and cost of computation significantly. Subsequently, the detailed numerical results indicate that wave interactions between the aforementioned modes in the non-dispersive regime depends on initial amplitude and relative phase and that the eastward Yanai wave can be generated from the second Poincaré mode. We also compare the simplified models to an advanced finite element approximation for the primitive equations. The fact that results of the latter are in good agreement, at least qualitatively, with those of the simplified models, indicates that reduced models capture most of the wave interaction mechanisms in the nearly non-dispersive regime.

Collisions of solitary waves in condensates beyond mean-field theory

Bright solitary waves in a Bose-Einstein condensate contain thousands of identical atoms held together despite their only weakly attractive contact interactions. They nonetheless behave like a compound object, staying whole in collisions, with their collision properties strongly affected by inter-soliton quantum coherence. We show that separate solitary waves decohere due to phase diffusion, dependent on their effective ambient temperature, after which their initial mean-field relative phases are no longer well defined or relevant for collisions. In this situation, collisions occur predominantly repulsively and can no longer be described within mean field theory. When considering the time-scales involved in recent solitary wave experiments where non-equilibrium phenomena play an important role, these features could explain the predominantly repulsive collision dynamics observed in most condensate soliton train experiments.

Abnormal evolutionary dynamics of erupting solitons in dissipative systems

The evolution of initial finite-energy Airy pulse pairs with different initial relative phases and time separations is numerically investigated in the erupting soliton parameter region of the cubic-quintic complex Ginzberg–Laudau equation-governed dissipative system. It shows that, before evolving to the final erupting solitons, all of the Airy pulse pairs will experience a special soliton dynamic called erupting soliton molecules that consist of two or more branches of erupting solitons. Moreover, the number and structures of the suberupting solitons will vary with different initial relative phases and time separations. Before forming the finally single erupting solitons, these suberupting solitons may merge for one moment and separate for the next. The merging or separating position as well as the erupting positions of every suberupting soliton may vary with the propagation distance. The evolutionary dynamics of the final erupting solitons also varies with different initial relative phases and time separations.

On resonant interactions of gravity‐capillary waves without energy exchange

AbstractWe consider resonant triad interactions of gravity‐capillary waves and investigate in detail special resonant triads that exchange no energy during their interactions so that the wave amplitudes remain constant in time. After writing the resonance conditions in terms of two parameters (or two angles of wave propagation), we first identify a region in the two‐dimensional parameter space, where resonant triads can be always found, and then describe the variations of resonant wavenumbers and wave frequencies over the resonance region. Using the amplitude equations recovered from a Hamiltonian formulation for water waves, it is shown that any resonant triad inside the resonance region can interact without energy exchange if the initial wave amplitudes and relative phase satisfy the two conditions for fixed point solutions of the amplitude equations. Furthermore, it is shown that the symmetric resonant triad exchanging no energy forms a transversely modulated traveling wave field, which can be considered a two‐dimensional generalization of Wilton ripples.

Adjustable Propagation Length Enhancement of the Surface Plasmon Polariton Wave via Phase Sensitive Optical Parametric Amplification

The adjustable propagation length enhancement of the surface plasmon polariton (SPP) mode under the effects of the initial relative phase (ψ0) between interacting waves in difference frequency generation (DFG) based optical parametric amplification (OPA) are numerically considered. The waveguide is a silver coated PPLN planar waveguide. Obtained results indicate ultra long propagation length for the SPP mode could be achieved via manipulation of ψ0 in exact quasi phase matching (QPM) case up to 30 mm for initial pump intensity about 66 MW/cm for degenerate DFG (dDFG). For chirped QPM by mitigating the high depletion of the pump intensity, it is possible to enhance the SPP propagation length up to 43 mm for initial pump intensity about 135 MW/cm. In this case ψ0 does not affect the SPP propagation length except around a narrow range of unsuitable phases. The unsuitable phase is frac{pi }{2} for exact QPM but is pump dependent for chirped QPM case. Using this unsuitable phase is the key parameter to the SPP propagation length enhancement via controlling ψ0. In this case with a high pump intensity, the pump and the SPP modes interact at longer distances which leads to the SPP propagation length enhancement.

Generation of single or double parallel breathing soliton pairs, bound breathing solitons, moving breathing solitons, and diverse composite breathing solitons in optical fibers.

Interactions of two truncated Airy pulses with arbitrarily initial relative phases, initial pulse intervals, and different soliton order are numerically investigated in optical fibers. When the soliton order is 1, depending on different initial pulse intervals, the initial in-phase Airy pulses may evolve to single breathing solitons, bound breathing solitons, and single parallel breathing solitons. While the out-of-phase Airy pulses may evolve to parallel or repulsive soliton pairs with breathing or weak breathing, after radiating away some dispersive waves. When the initial relative phases take arbitrary values except 0 and π, moving single breathing solitons and repulsive or parallel soliton pairs will form. Moreover, the whole temporal profiles may become asymmetric. The repulsive soliton pairs consist of two moving breathing solitons with different intensities, moving velocities, and breathing periods. The most interestingly is that, when the soliton order is larger than one, we observe double bound breathing solitons, double parallel breathing soliton pairs, and diverse composite breathing solitons which consist of two or more different breathing solitons. one can effectively manipulate and select the soliton expected and its evolution dynamics by adjusting the soliton order, initial pulse intervals, and initial relative phases.

Evolution of terahertz waves in air plasma driven by orthogonally polarized two-color pulses

We experimentally investigate the evolution of the terahertz (THz) waveform and polarization state inside the plasma filament produced by orthogonally polarized two-color pulses. We find that the variation of the THz polarization state along the plasma column is dominantly caused by the relative phase difference and spectra blue shift of the two-color field. Elliptically polarized THz radiation is generated by controlling the initial relative phase and the filament length. The result indicates the coherent control of the polarization state of the THz emission.

The Effect of Dipole-Dipole Interaction on Tripartite Entanglement in Different Cavities

The effect of dipole-dipole interaction, the initial relative phase and the coupling strength with the cavity on the dynamics of three two level atoms in the good and the bad cavity regime are investigated. It is found that the presence of strong dipole-dipole interaction not only ensures avoiding entanglement sudden death but also retains entanglement for long time. The choice of the phase in the initial state is crucial to the operational regime of the cavity. Under specific conditions, the entanglement can be frozen in time to its initial values through strong dipole-dipole interaction. This trait of tripartite entanglement may prove helpful in engineering multiparticle entanglement for the practical realization of quantum technology.

Manipulation of the stationary entanglement of three atoms coupled to a common environment

In this work, we study the dynamics of three entangled atoms coupled to a common structured reservoir. The atoms are initially prepared in different W-like states characterized by different relative phases. We examine the roles of initial relative phases on the energy transfers among the individual atoms as well as atomic entanglement dynamics. We show that the features of quantum interferences induced by initial relative phases greatly affect the energy transfers and entanglement dynamics. In particular, a suitable choice of initial phases can increase atomic stationary entanglement over their initial value. The results imply a possible control strategy for atomic entanglement dynamics.