Wave-packet Effects Research Articles

Longitudinal and Transverse Optical Beam Shifts Show Non‐separability

AbstractUnder the introduction of any tilted interface in its trajectory, an optical beam experiences polarization‐dependent deflections in the longitudinal and transverse directions with respect to the plane of incidence. The physics of such optical beam shifts are connected to profound universal wave phenomena governed by the fine interference effects of wave packets and have opened up avenues toward metrological applications. Here, the inherent non‐separability of the longitudinal and transverse optical beam shifts is revealed by considering a rather simple case of a partially reflecting Gaussian laser beam from a dielectric interface. This non‐separability appears substantially at some particular regions in the corresponding experimental parameter space. This manifests as a position–position non‐separable state of classical light field. The tunability of the related experimental parameters offers control over the degree of non‐separability. These findings are expected to be a step forward in the exploration of optical beam shifts and a number of analogous universal phenomena. The initial observation also indicates its practical impact on metrology and generation of high‐quality tunable position–position non‐separable states of classical light fields.

Neutrino decoherence and the mass hierarchy in the JUNO experiment

The finite size of a neutrino wavepacket at creation can affect its oscillation probability. Here, we consider the electron antineutrino wavepacket and decoherence in the context of the nuclear reactor based experiment JUNO. Given JUNO's high expected statistics [$\sim$100k IBD events ($\bar{\nu}_e p \rightarrow e^+ n$)], long baseline ($\sim$53\,km), and excellent energy resolution [$\sim$$0.03/\sqrt{E_{\mathrm{vis}}~\mathrm{(MeV)}}$], its sensitivity to the size of the wavepacket is expected to be quite strong. Unfortunately, this sensitivity may weaken the experiment's ability to measure the orientation of the neutrino mass hierarchy for currently allowed values of the wavepacket size. Here, we report both the JUNO experiment's ability to determine the hierarchy orientation in the presence of a finite wavepacket and its simultaneous sensitivity to size of the wavepacket and the hierarchy. We find that wavepacket effects are relevant for the hierarchy determination up to nearly two orders of magnitude above the current experimental lower limit on the size, noting that there is no theoretical consensus on the expectation of this value. We also consider the effect in the context of other aspects of JUNO's nominal three-neutrino oscillation measurement physics program and the prospect of future enhancements to sensitivity, including from precise measurements of $\Delta m^2_{3l}$ and a near detector.

Neutrino physics opportunities with the IsoDAR source at Yemilab

IsoDAR seeks to place a high-power-cyclotron and target combination, as an intense source of $\bar{\nu}_e$ at the level of $\sim 10^{23}$/year, close to a kiloton-scale neutrino detector in order to gain sensitivity to very short-baseline neutrino oscillations ($\bar{\nu}_e \rightarrow \bar{\nu}_{e}$) and perform precision tests of the weak interaction, among other physics opportunities. Recently, IsoDAR has received preliminary approval to be paired with the 2.26~kton target volume liquid scintillator detector at the Yemi Underground Laboratory (Yemilab) in Korea, at a 17~m center-to-center baseline, and cavern excavation for IsoDAR is now complete. In this paper, we present the physics capabilities of IsoDAR@Yemilab in terms of sensitivity to oscillations (via inverse beta decay, IBD; $\bar{\nu}_e+p \rightarrow e^+ + n$), including initial-state wavepacket effects, and the weak mixing angle (via elastic scattering off atomic electrons, $\bar{\nu}_e + e^- \rightarrow \bar{\nu}_e + e^-$). We also introduce a study of IsoDAR sensitivity to new particles, such as a light $X$ boson, produced in the target that decays to $\nu_e \bar \nu_e$.

Studying the neutrino wave-packet effects at medium-baseline reactor neutrino oscillation experiments and the potential benefits of an extra detector

We examine the potential of the future medium-baseline reactor neutrino oscillation (MBRO) experiments in studying neutrino wave-packet impact. In our study, we treat neutrinos as wave packets and use the corresponding neutrino flavor transition probabilities. The delocalization, separation and spreading of the wave packets lead to decoherence and dispersion effects, which modify the plane-wave neutrino oscillation pattern, by amounts that depend on the energy uncertainties in the initial neutrino wave packets. We find that MBRO experiments could be sensitive to the wave-packet impact, since the baseline is long enough and also the capability of observing small corrections to the neutrino oscillations due to excellent detector energy resolution. Besides studying the constraints on the decoherence parameter, we also examine the potential wave-packet impacts on the precision of measuring θ12 and other oscillation parameters in the future medium-baseline reactor neutrino oscillation experiments. Moreover, we also probe the potential benefits of an additional detector for studying such exotic neutrino physics.

Scalar scattering amplitude in the Gaussian wave-packet formalism

Abstract We compute an $s$-channel $2\to2$ scalar scattering $\phi\phi\to\Phi\to\phi\phi$ in the Gaussian wave-packet formalism at the tree level. We find that wave-packet effects, including shifts of the pole and the width of the propagator of $\Phi$, persist even when we do not take into account the time boundary effect for $2\to2$ proposed earlier. An interpretation of the result is that a heavy scalar $1\to2$ decay $\Phi\to\phi\phi$, taking into account the production of $\Phi$, does not exhibit the in-state time boundary effect unless we further take into account in-boundary effects for the $2\to2$ scattering. We also show various plane-wave limits.

Perturbative operator approach to high-precision light-pulse atom interferometry

Light-pulse atom interferometers are powerful quantum sensors, however, their accuracy for example in tests of the weak equivalence principle is limited by various spurious influences like magnetic stray fields or blackbody radiation. Pushing the accuracy therefore requires a detailed assessment of the size of such deleterious effects. Here, we present a systematic operator expansion to obtain phase shifts and contrast analytically in powers of the perturbation. The result can either be employed for robust straightforward order-of-magnitude estimates or for rigorous calculations. Together with general conditions for the validity of the approach, we provide a particularly useful formula for the phase including wave-packet effects.

Quantum boomeranglike effect of wave packets in random media

We unveil an original manifestation of Anderson localization for wave packets launched with a finite average velocity: after an initial ballistic motion, the center of mass of the wave packet experiences a retroreflection and slowly returns to its initial position, an effect that we dub "Quantum Boomerang" and describe numerically and analytically in dimension 1. In dimension 3, we show numerically that the quantum boomerang is a genuine signature of Anderson localization: it exists if and only if the quantum dynamics if localized.

Impact of coherence decay on wavepacket models for broadband shock-associated noise in supersonic jets

Motivated by the success of wavepackets in modelling the noise from subsonic and perfectly expanded supersonic jets, we apply the wavepacket model to imperfectly expanded supersonic jets. Recent studies with subsonic jets have demonstrated the importance of capturing the ‘jitter’ of wavepackets in order to correctly predict the intensity of far-field sound. Wavepacket jitter may be statistically represented using a two-point coherence function; accurate prediction of noise requires identification of this coherence function. Following the analysis of Cavalieri & Agarwal (J. Fluid Mech., vol. 748, 2014. pp. 399–415), we extend their methodology to model the acoustic sources of broadband shock-associated noise in imperfectly expanded supersonic jets using cross-spectral densities of the turbulent and shock-cell quantities. The aim is to determine the relationship between wavepacket coherence-decay and far-field broadband shock-associated noise, using the model as a vehicle to explore the flow mechanisms at work. Unlike the subsonic case where inclusion of coherence decay amplifies the sound pressure level over the whole acoustic spectrum, we find that it does not play such a critical role in determining the peak sound amplitude for shock-cell noise. When higher-order shock-cell modes are used to reconstruct the acoustic spectrum at higher frequencies, however, the inclusion of a jittering wavepacket is necessary. These results suggest that the requirement for coherence decay identified in prior broadband shock-associated noise (BBSAN) models is in reality the statistical signature of jittering wavepackets. The results from this modelling approach suggest that nonlinear jittering effects of wavepackets need to be included in dynamic models for broadband shock-associated noise.

Quantum mechanix plus Newtonian gravity violates the universality of free fall

Classical point particles in Newtonian gravity obey, as they do in general relativity, the universality of free fall. However, classical structured particles, (for instance with a mass quadrupole moment), need not obey the universality of free fall. Quantum mechanically, an elementary “point” particle (in the particle physics sense) can be described by a localized wave packet, for which we can define a probability quadrupole moment. This probability quadrupole can, under plausible hypotheses, affect the universality of free fall. (So point-like elementary particles, in the particle physics sense, can and indeed must nevertheless have structure in the general relativistic sense once wave packet effects are included.) This raises an important issue of principle, as possible quantum violations of the universality of free fall would fundamentally impact on our ideas of what “quantum gravity” might look like. I will present an estimate of the size of the effect, and discuss where if at all it might be measured.

INFLUENCE OF SECOND-ORDER CORRECTIONS TO THE ENERGY-DEPENDENCE OF NEUTRINO FLAVOR CONVERSION FORMULAS

We discuss the intermediate wave-packet formalism for analytically quantifying the energy dependence of the two-flavor conversion formula that is usually considered for analyzing neutrino oscillations and adjusting the focusing horn, target position and/or detector location of some flavor conversion experiments. Following a sequence of analytical approximations where we consider the second-order corrections in a power series expansion of the energy, we point out a residual time-dependent phase which, in addition to some well-known wave-packet effects, can subtly modify the oscillation parameters and limits. In the present precision era of neutrino oscillation experiments where higher precision measurements are required, we quantify some small corrections in neutrino flavor conversion formulas which lead to a modified energy-dependence for νμ ↔ νe oscillations.

Gravity wave packet effects on chemical exothermic heating in the mesopause region

Numerical simulations of the interaction of transient, dissipating gravity wave packets with the minor species involved in the OH airglow chemistry in the mesopause region reveal large wave‐driven downward fluxes of the minor species. In addition to the minor species fluctuating in response to the wave, a strong secular variation of minor species densities occurs. At 90 km altitude this secular variation becomes significant ∼80 min after the wave packet onset, and increases approximately linearly with increasing time for the following 2 hours. At later times the secular variation diminishes. Heating rates due to exothermic chemical reactions consequently exhibit a fluctuating component as well as a secular variation. When averaged over time, the net effect of each of the two waves considered is to cause large (∼22% and 37%) increases in average heating rates. This secular variation in heating rates could be more significant than the present results suggest because larger amplitude gravity waves can exist in the mesopause region.

Weakly Nonlinear Evolution of a Wave Packet in a Zonal Mixing Layer

A nonlinear integrodifferential equation governing the amplitude evolution of a wavepacket near the critical value of the beta parameter is derived. The basic velocity profile is a hyperbolic tangent shear layer and although the neutral eigensolution is regular, all higher‐order terms in the expansion of the stream function are singular at the critical point. The analysis is inviscid and in the critical layer both wave packet effects and nonlinearity are present, but the former are taken to be slightly larger. Unlike the Stuart–Watson theory, the critical layer analysis dictates the form of the amplitude equation, the outer expansion being relatively passive. A secondary instability analysis shows that the packet is unstable to sideband perturbations, but the instability is weak so its main consequence would be to produce some modulation of the packet without destroying its coherence.

Wave packet critical layers in stratified shear flows

Abstract In the inviscid theory of shear flow stability, the eigenvalue problem for a neutral or weakly amplified mode revolves around possible discontinuities in the eigenfunction as the singular critical point is crossed. Extensions of the linear normal mode approach to include nonlinearity and/or wave packets lead to amplitude evolution equations whose coefficients generally involve singular integrals. In the past, viscosity, nonlinearity or time dependence has been introduced in a critical layer centered upon the singular point to resolve these integrals. The form of the amplitude evolution equation is greatly influenced by which choice is made. In this paper, a new approach is proposed in which wave packet effects are dominant in the critical layer, and it is argued that in many applications this is the appropriate choice. The theory is applied here to two-dimensional wave propagation in stratified shear flows.

Electronic Rydberg wavepacket effects on molecular vibration

Electronic wavepacket states of molecular hydrogen are considered which represent the situation of a spectator electron orbiting a molecular core. A quantum defect theory approach is used to determine the energy level structure, wavefunctions and molecular potentials, which is valid in regions where the quantum defects approach zero. In such a region the orbital motion of the wavepacket leads to a periodic variation in the molecular vibration frequency of the order of 100 cm-1. Possible detection schemes are discussed.

Wave Packet Critical Layers in Shear Flows

In the linear inviscid theory of shear flow stability, the eigenvalue problem for a neutral or weakly amplified mode revolves around possible discontinuities in the eigenfunction as the singular critical point is crossed. Extensions of the linear normal mode approach to include nonlinearity and/or wave packets lead to amplitude evolution equations where, again, critical point singularities are an issue because the coefficients of the amplitude equations generally involve singular integrals. In the past, viscosity, nonlinearity, or time dependence has been introduced in a critical layer centered upon the singular point to resolve these integrals. The form of the amplitude evolution equation is greatly influenced by which choice is made. In this paper, a new approach is proposed in which wave packet effects are dominant in the critical layer and it is argued that in many applications this is the appropriate choice. The theory is applied to two‐dimensional wave propagation in homogeneous shear flows and also to stratified shear flows. Other generalizations are indicated.

Fundamental Interactions of Molecules (Na2, Na3) with Intense Femtosecond Laser Pulses

AbstractThe real‐time dynamics of multiphoton ionization and fragmentation of molecules Na2 and Na3 has been studied in molecular beam experiments employing ion and electron spectroscopy together with femtosecond pump‐probe techniques. Experiments with Na2 and Na3 reveal unexpected features of the dynamics of the absorption of several photons as seen in the one‐ and three‐dimensional vibrational wave packet motion in different potential surfaces and in high laser fields:In Na2 a second major resonance‐enhanced multiphoton ionization (REMPI) process is observed, involving the excitation of two electrons and subsequent electronic autoionization. The possibility of controlling a reaction by controlling the duration of propagation of a wave packet on an electronically‐excited surface is demonstrated. In high laser fields, the contributions from direct photoionization and from the second REMPI process to the total ion yield change, due to different populations in the electronic states participating in the multiphoton ionization (MPI) processes. In addition, a vibrational wave packet motion in the electronic ground state is induced through stimulated emission pumping by the pump laser. The 41Σ+g shelf state of Na2 is given as an example for performing frequency spectroscopy of high‐lying electronic states in the time domain. Pure wave packet effects, such as the spreading and the revival of a vibrational wave packet, are investigated.The three‐dimensional wave packet motion in the Na3 reflects the normal modes in the X and B states, and shows in addition the pseudorotational motion in the B state in real time.

Calculation of the relativistic Bloch correction to stopping power

Bloch's technique of joining the nonrelativistic Bethe and Bohr stopping-power expressions by taking into account wave-packet effects for close collisions is extended to the relativistic case. It is found that Bloch's nonrelativistic correction term must be modified and that charge asymmetric terms appear. Excellent agreement is observed by comparing the results of these calculations to recent data on the stopping power of relativistic heavy ions.