1,720,992 research outputs found
Non-inertial interpretation of the Dirac oscillator
Full text linkNon-inertial physics is seldom considered in quantum mechanics and this contrasts with the ubiquity of non-inertial reference frames. Here, we show an application to the Dirac oscillator which provides a fundamental model of relativistic quantum mechanics. The model emerges from a term linearly dependent on spatial coordinates added to the momentum of the free-particle Dirac Hamiltonian. The definition generates peculiar features (mutating vacuum energy, non-Hermitian momentum, accidental degeneracies of the spectrum, etc). We interpret these anomalies in terms of inertial effects. The demonstration is based on the decoupling of the Dirac equation from the stereographic projection that maps the 3D geometry of the dynamical problem to the complex plane. The decoupling shows that the fundamental mechanical model underpinning the Dirac oscillator reduces to the representation of the oscillator in the rotating reference frame attached to the orbital angular momentum. The resulting Coriolis-like contribution to the Hamiltonian accounts for the peculiarities of the model (mutating vacuum energy, form of the non-minimal correction to the momentum, classical intrinsic spin and gain of its quantum value, accidental degeneracies of the energy spectrum, supersymmetric potential). The suggested interpretation has an interdisciplinary character where stereographic geometry, classical physics of the Coriolis effect and quantum physics of Dirac particles contribute to the definition of one of the few exactly soluble models of relativistic quantum mechanics
Quantum states in the multipole approach to Maxwell theory of light
No full textFundamental aspects of quantum optics are reproduced within the multipole approach to Maxwell theory of light. Results are given for Fock states, vacuum field and photon statistics of chaotic and coherent light. © OSA 2015
Fourier-based approach to overcome anomalies in high-resolution spectra of vibrational CARS measurements of gases
No full textIn this work, we report on an unconventional experimental procedure useful for thermometric measurements on the basis of high-resolution vibrational coherent anti-Stokes Raman scattering (CARS) generated using conventional lasers. The high spectral dispersion of 0.02 cm-1/pixel is achieved by means of some specific spectral arrangements (single-mode pump laser and diffraction grating providing spectra at the sixth order) and is further strengthened by the use of a relay lens system mounted before the charge-coupled device camera. Surprisingly, at the high spectral dispersion of our measurements, a significant and persistent thermometric inaccuracy is observed. The effect arises from an inevitable spectral modulation of defined frequency hidden in the main CARS signal of the gas under study, and to secure a good thermometric evaluation, we describe a Fourier approach that is experimentally demonstrated for the typical nitrogen CARS spectrum measured at room temperature. Copyright © 2014 John Wiley & Sons, Ltd
Chirp effects and retrieval of Raman spectra in femtosecond stimulated Raman scattering
No full textChirp effects caused by the group delay dispersion (GDD) of optical pulses have a twofold meaning when applied to femtosecond stimulated Raman scattering (fs SRS). On the one hand, these effects are responsible for Raman mode modulation and are thus detrimental to the reconstruction of Raman spectra. On the other, they can be cleverly employed to turn GDD into an additional optical variable of great usefulness. Here, to master the whole subject, the classical approach to coherent Raman scattering is chosen for its simplicity and, with reference to a large class of measurements where electronically off-resonant Raman transitions are probed, fs SRS signals are readily found for linearly chirped Gaussian pulses that guarantee the solution to the nonlinear optical scattering problem without recourse to numerical methods. Thanks to this result, fundamental features of chirp-dependent fs SRS are explored by means of comparisons with experiments taken from the existing literature on the subject. The focus is on four fundamental manifestations of chirp dependence. They are (1) temporal resolution invariance in time modulation of Raman decay and its drift, (2) spectral focusing in Raman gain and loss, (3) line intensity modulation and Raman mode selection, and (4) single-shot time mapping of molecular dynamics. The findings of this work show that basic chirp-dependent Raman theory provides the necessary insights into the Raman phenomena appearing when chirp affects the laser pulses even in the extreme regime where the transform-limited fs pulse duration is just a few harmonic cycles of the laser fields
Sensitivity of coherent anti-Stokes Raman lineshape to time asymmetry of laser pulses
No full textWe show that coherent anti-Stokes Raman lineshapes do not follow known spectral profiles if the time asymmetry of realistic laser pulses is taken into account. Examples are given for nanosecond and picosecond laser pulses commonly employed in frequency-resolved coherent anti-Stokes Raman scattering. More remarkably, the analysis suggests an effect of line narrowing in comparison to the customary approach, based primarily on the Voigt lineshape
Time-domain coherent anti-Stokes Raman scattering in terms of the time-delayed Yuratich equation
No full textWe show that the increasingly popular nonlinear optical technique of time-domain coherent anti-Stokes Raman scattering (CARS), which is often viewed from the dynamical perspective of the semiclassical time-dependent third-order polarization, can also be studied by means of the time-delayed version of the Yuratich equation, so popular in traditional frequency-domain CARS. The method proves successful in explaining experimental results that are otherwise treated by means of numerical methods only. © 2014 Optical Society of America
Classical approach to off‐resonant Raman coherence with chirped femtosecond laser pulses
No full textRaman coherence of electronically off-resonant transitions provides a simple class of Raman techniques that, when realized with chirped femtosecond laser pulses, are commonly studied with reference to the methods of quantum mechanics. In this work, we show instead that the classical approach, when extended to chirp-dependent laser fields, is equally effective in reproducing experimental results that are particularly sensitive to the chirp carried by the laser pulses. The extension is nothing but a follow-up of the traditional model based on the driven damped harmonic oscillator, which is however known to work for transform-limited femtosecond pulses. The demonstration starts with the comparison of the time-dependent third-order polarizations for the Liouville-space wavepacket representation with the classical analog. The formal similarity between these nonlinear polarizations is further analyzed in the frequency domain to show an important difference related to the handling of the phase factor containing the carrier frequencies of the laser pulses. Finally, we simulate a couple of significant and acknowledged chirp-dependent experimental measurements in the impulsive regime of stimulated Raman scattering
“A call to action”: Schrödinger's representation of quantum mechanics via Hamilton's principle
No full textA few years ago, one of the former Editors of this journal launched "a call to action"(E. F. Taylor, Am. J. Phys. 71, 423-425 (2003)) for a revision of teaching methods in physics in order to emphasize the importance of the principle of least action. In response, we suggest the use of Hamilton's principle of stationary action to introduce the Schrödinger equation. When considering the geometric interpretation of the Hamilton-Jacobi theory, the real part of the action S defines the phase of the wave function exp (iS/ħ), and requiring the Hamilton-Jacobi wave function to obey wave-front propagation (i.e., Re(S) is a constant of the motion) yields the Schrödinger equation
Dirac equation from stereographic projection of the momentum sphere
Full text linkThe Dirac equation is commonly demonstrated under stringent hypotheses and after considerable math work made in relativistic quantum mechanics and quantum field theory. Here, a purely geometric approach free from hypotheses is suggested. The suggestion draws inspiration from the technique of stereographic projection that was developed before the quantum era to solve gyroscopic problems of classical mechanics. The projected variable is the generalized (or canonical) momentum vector. Its undetermined geometric orientations define a sphere in the momentum space and the projection onto the equatorial plane generates the Pauli matrices as soon as the conventional stereographic matrix is introduced. The associated eigenvalue problem results in the Dirac equation and the eigenvector (bispinor) has components that are related to geometric elements of the momentum space. The procedure has the advantage of revealing the correct form of the Dirac matrices without the mathematical effort that characterizes the presentation of the equation in traditional approaches. The other remarkable advantage is that, unlike the common reduction to the case of free space, the spatial inhomogeneity due to interaction potentials is included in the demonstration from the very beginning. The whole suggestion has an interdisciplinary character (relativity, complex analysis, rotation of rigid bodies, Pauli matrices) and can be useful in teaching the equation to students who lack in sufficient knowledge of quantum mechanics. Students equipped with more advanced education can benefit from the purely geometric perspective of this work if used to complement their studies about the equation
Effect of vibration–rotation coupling on simultaneous extraction of temperature and species concentration from vibrational CARS spectra of hot gases
No full textThe coupling between vibration and rotation in light molecules changes the strength of the Raman response. From this standpoint, we consider high-temperature molecular spectra obtained by means of coherent anti-Stokes Raman scattering (CARS), whose spectral intensity is useful to extract thermometric information and species concentrations for applications in combustion science. In this context and unlike other studies on the subject that are exclusively focused on thermometry, the novelty of the current work lies in the determination of the mutual relationship among the free variables adopted in the analysis of CARS spectra when these do not include the effect of the vibration-rotation coupling. The relationship emerges from the comparison to a reference made of calculated vibrational spectra of nitrogen and oxygen subject to the coupling. These spectra are then fitted by means of spectra developed under the ordinary rigid-rotor approximation that is usually adopted in any fitting procedure for such molecules. The results show that small changes of the fitted temperature correspond to larger deviations for the determination of concentrations and non-resonant background. Copyright © 2013 John Wiley & Sons, Ltd
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