Distinct Wave Packets Research Articles

Properties of a Broadband Gaussian Pulse Propagating Through a Λ-type Atomic Medium at Room Temperature

Abstract In our study, we conduct a comprehensive theoretical analysis on the propagation behavior of a Gaussian pulse through a four-level Λ-type Rubidium atomic medium under room temperature conditions. Our investigation uncovers the presence of two distinct wavepackets within the medium’s transmission signal. The primary wavepacket, linked to electromagnetically induced transparency transmission, serves as the central signal in the study. Characterized by its optical beat signal utilized for fast microwave strength detection, this wavepacket demonstrates notable features such as pronounced normal dispersion and decreased group velocity. Additionally, the emergence of the Sommerfeld-Brillouin precursor as the second wavepacket further enriches our understanding of pulse dynamics in the medium. Our simulation findings reveal the potential for the optical precursor to play a dominant role in the transmission signal with the adopted methodology. Furthermore, we identify that experimental parameters like atomic density, vapor cell length, and control field intensity play crucial roles in modulating the time delay of the primary signal and the amplitude of the optical precursor.

Detection and assessment of pitting corrosion in rebars using scattering of ultrasonic guided waves

The present study aims at developing a robust non-destructive evaluation technique by using the scattering of ultrasonic guided waves for early detection and assessment of localised damage in bare rebars in the form of corrosion pits. The guided wave interaction with the pitting corrosion is numerically simulated by using finite element analysis, and the results are validated with experiments. The received signal contains several wave packets, which could be identified as various scattered modes that are generated from the edges of the corroded region. It is found that when the damage is placed at the centre of the rebar, several scattered wave modes superimpose to form two distinct wave packets in the received signal. A damage index is proposed by using these two distinct wave packets. It is shown that the proposed damage index method can be used successfully to monitor the axial extent and intensity of pitting corrosion in rebars. However, for the pitting corrosion that is situated at an arbitrary position, a different methodology, which utilises the differential time of arrival of various scattered wave modes, is proposed to identify the location of the pitting corrosion. Finally, a non-dimensional parameter, namely the scatter coefficient, is defined to analyse the energy contributions of various scatter modes. It is found that this scatter coefficient gradually increases with the mass loss and that the increment is pronounced when the corrosion pit is closer to the receiver location. The findings of the study can be used to identify the pitting corrosion in bare rebars.

Coherent states for ladder operators of general order related to exceptional orthogonal polynomials

We construct the coherent states of general order, m, for the ladder operators and , which act on rational deformations of the harmonic oscillator. The position wavefunctions of the eigenvectors involve type III Hermite exceptional orthogonal polynomials. We plot energy expectations, time-dependent position probability densities for the coherent states and for the even and odd cat states, Wigner functions, and Heisenberg uncertainty relations. We find generally non-classical behaviour, with one exception: there is a regime of large magnitude of the coherent state parameter, z, where the otherwise indistinct position probability density separates into m + 1 distinct wavepackets oscillating and colliding in the potential, forming interference fringes when they collide. The Mandel Q parameter is calculated to find sub-Poissonian statistics, another indicator of non-classical behaviour. We plot the position standard deviation and find squeezing in many of the cases. We calculate the two ‘photon’ number probability density for the output state when the m = 4, coherent states (where μ labels the lowest weight in the superposition) are placed on one arm of a beamsplitter. We find that it does not factorize, again indicating non-classical behaviour. Calculation of the linear entropy for this beamsplitter output state shows significant entanglement, another non-classical feature. We also construct linearized versions, , of the annihilation operators and their coherent states and calculate the same properties that we investigate for the coherent states. For these we find similar behaviour to the coherent states, at much smaller magnitudes of z, but comparable average energies.

Non-classical behaviour of coherent states for systems constructed using exceptional orthogonal polynomials

We construct the coherent states and Schrödinger cat states associated with new types of ladder operators for a particular case of a rationally extended harmonic oscillator involving type III Hermite exceptional orthogonal polynomials. In addition to the coherent states of the annihilation operator, c, we form the linearised version, and obtain its coherent states. We find that while the coherent states defined as eigenvectors of the annihilation operator c display only quantum behaviour, those of the linearised version, have position probability densities displaying distinct wavepackets oscillating and colliding in the potential. The collisions are certainly quantum, as interference fringes are produced, but the remaining evolution indicates a classical analogue.

Source Process of the October 2016 Tottori-Chubu Earthquake(<i>M</i>j 6.6) and Relation with Near Source Strong Motions

A source process inversion for an Mj 6.6 earthquake which occurred on October 21, 2016 in central Tottori Prefecture, was performed using near-field strong motion waveforms. The results showed that a left-lateral strike-slip component was dominant on the fault plane, the strike of which was in a NNW-SSE direction and the dip almost vertical. The moment magnitude was estimated as 6.2. A large slip area (asperity) was determined around the hypocenter, including its northern shallow part, in which the maximum slip was nearly 1.2 m. Another small asperity was estimated also near the northern edge of the fault plane. These two asperities corresponded to the two distinct wave packets observed at the stations near the source region. Furthermore, the results suggested that a discrepancy in frequency characteristics between these asperities existed, by comparing them with waveforms obtained just above the source region. We also estimated the stress drop on the fault plane by the final slip distribution, and the maximum value was about 16 MPa. This result meant that the strong ground motion excitation of this earthquake was of an average level compared to past crustal earthquakes in Japan.

Evolution of disturbance wavepackets in an oscillatory Stokes layer

AbstractNumerical simulation results are presented for the linear and nonlinear evolution of disturbances in a flat Stokes layer. The response to a spatially localised impulsive forcing is investigated and it is found that the spatial–temporal development of the flow displays an intriguing family-tree-like structure, which involves the birth of successive generations of distinct wavepacket components. It is shown that some features of this unexpected structure can be predicted using the results of a linear stability analysis based on Floquet theory.

Wavepacket models for supersonic jet noise

AbstractGudmundsson and Colonius (J. Fluid Mech., vol. 689, 2011, pp. 97–128) have recently shown that the average evolution of low-frequency, low-azimuthal modal large-scale structures in the near field of subsonic jets are remarkably well predicted as linear instability waves of the turbulent mean flow using parabolized stability equations. In this work, we extend this modelling technique to an isothermal and a moderately heated Mach 1.5 jet for which the mean flow fields are obtained from a high-fidelity large-eddy simulation database. The latter affords a rigourous and extensive validation of the model, which had only been pursued earlier with more limited experimental data. A filter based on proper orthogonal decomposition is applied to the data to extract the most energetic coherent components. These components display a distinct wavepacket character, and agree fairly well with the parabolized stability equations model predictions in terms of near-field pressure and flow velocity. We next apply a Kirchhoff surface acoustic propagation technique to the near-field pressure model and obtain an encouraging match for far-field noise levels in the peak aft direction. The results suggest that linear wavepackets in the turbulence are responsible for the loudest portion of the supersonic jet acoustic field.

Molecular Feshbach dissociation as a source for motionally entangled atoms

We describe the dissociation of a diatomic Feshbach molecule due to a time-varying external magnetic field in a realistic trap and guide setting. An analytic expression for the asymptotic state of the two ultracold atoms is derived, which can serve as a basis for the analysis of dissociation protocols to generate motionally entangled states. For instance, the gradual dissociation by sequences of magnetic field pulses may delocalize the atoms into macroscopically distinct wave packets, whose motional entanglement can be addressed interferometrically. The established relation between the applied magnetic field pulse and the generated dissociation state reveals that square-shaped magnetic field pulses minimize the momentum spread of the atoms. This is required to control the detrimental influence of dispersion in a recently proposed experiment to perform a Bell test in the motion of the two atoms [C. Gneiting and K. Hornberger, Phys. Rev. Lett. 101, 260503 (2008)].

Scattering of an attractive Bose-Einstein condensate from a barrier: Formation of quantum superposition states

Scattering in one dimension of an attractive ultracold bosonic cloud from a barrier can lead to the formation of two nonoverlapping clouds. Once formed, the clouds travel with constant velocity, in general different in magnitude from that of the incoming cloud, and do not disperse. The phenomenon and its mechanism---transformation of kinetic energy to internal energy of the scattered cloud---are obtained by solving the time-dependent many-boson Schr\"odinger equation. The analysis of the wave function shows that the object formed corresponds to a quantum superposition state of two distinct wave packets traveling through real space.

Elastic scattering losses from colliding Bose-Einstein condensates

Bragg diffraction divides a Bose-Einstein condensate into two overlapping components, moving with respect to each other with high momentum. Elastic collisions between atoms from distinct wave packets can significantly deplete the condensate. Recently, Zi\ifmmode \acute{n}\else \'{n}\fi{} et al. [Phys. Rev. Lett. 94, 200401 (2005)] introduced a model of two counterpropagating atomic Gaussian wave packets incorporating the dynamics of the incoherent scattering processes. Here we study the properties of this model in detail, including the nature of the transition from spontaneous to stimulated scattering. Within the first-order approximation, we derive analytical expressions for the density matrix and anomalous density that provide excellent insight into correlation properties of scattered atoms.

Wavepacket synthesis of far-field echoes from a ribbed cylindrical shell with hemispherical endcaps

Recent investigations concerning acoustical signal decomposition of Wigner distributions [N. C. Yen, ‘‘Wavepacket decomposition,’’ accepted for publication in J. Acoust. Soc. Am.] have motivated further investigations of echoes from more complex submerged targets. The signal decomposition method of Boudreaux-Bartels [G. F. Boudreaux-Bartel and T. W. Parks, ‘‘Wigner distribution synthesis techniques,’’ IEEE Trans. Acoust. Speech Signal Process. ASSP-34, 442–451 (1986)] is applied to monostatic echoes from a finite, ribbed cylinder with hemispherical endcaps at frequencies below ka=42. The cylinder has a length of 1 m long, a radius of 7.0 cm, and an internal rib spacing of 1 cm. Distinct wavepackets associated with Bloch waves and Bragg waves on the target are synthesized over the suitable range of monostatic target angle.

The ion cyclotron group delay for source regions near the plasmapause

Electromagnetic ion cyclotron waves are generated near the magnetic equator through an instability driven by the energetic ion temperature anisotropy. Many of these waves are observed on the ground as Pc 1 magnetic pulsations, which often exhibit a distinct wave packet structure (pearl pulsations). We use the warm dispersion relation to calculate the group delay of ion cyclotron waves from the equatorial source region near the plasmapause to the foot of the field line and compare the results to both cold theory and observations. Our results differ significantly from the cold plasma result for frequencies less than 0.85 fnof;cHe. In general we find that the presence of the ring current produces longer delays and greater wave dispersion. We model three particular ion cyclotron wave events each of which was observed simultaneously by DE 1 and the Air Force Geophysics Laboratory Magnetometer Network. Plasma data from three other instruments on DE 1 provide input parameters to the model. In two out of three cases our predicted delays agree with ground/satellite correlation delays. The third event does not agree as well with theory possibly due to the presence of a significantly greater O+ concentration during this event. The enhanced O+ concentration introduces an additional stop band below fnof;cHe along the propagation path which the linear theory is unable to model.

Characterization of the sources of VLF hiss and chorus observed on Geos 1

Ray‐tracing techniques are used to locate the apparent source regions of natural electromagnetic emissions observed on the GEOS 1 satellite and to determine the wave normal directions at this apparent source region. They are applied to VLF hiss, whose analysis in terms of the wave distribution function (WDF) has established that they often consisted of a sum of two or more very distinct wave packets at the point of observation. An example of a two‐peaked WDF chorus is also examined. A two‐dimensional ray‐tracing program is used. For the cases analyzed here, GEOS 1 data indicate that the earth's magnetic field is to be considered as dipolar, and a diffusive equilibrium model is used to describe the medium. It is shown theoretically that even if the exact location of the source region is difficult to estimate accurately, more precise information can still be obtained on the wave normal distribution at the source region. In the examples considered, it is pointed out that the VLF hiss was generated in the vicinity of the equator at high wave normal angles.