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Register a new userKlein paradox for bosons, wave packets and negative tunnelling times
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We analyse a little known aspect of the Klein paradox. A Klein-Gordon boson appears to be able to cross a supercritical rectangular barrier without being reflected, while spending there a negative amount of time. The transmission mechanism is demonstrably acausal, yet an attempt to construct the corresponding causal solution of the Klein-Gordon equation fails. We relate the causal solution to a divergent multiple-reflections series, and show that the problem is remedied for a smooth barrier, where pair production at the energy equal to a half of the barriers height is enhanced yet remains finite.
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The well known Klein paradox for the relativistic Dirac wave equation consists in the computation of possible ``negative probabilities induced by certain potentials in some regimes of energy. The paradox may be resolved employing the notion of electron-positron pair production in which the number of electrons present in a process can increase. The Klein paradox also exists in Maxwells equations viewed as the wave equation for photons. In a medium containing ``inverted energy populations of excited atoms, e.g. in a LASER medium, one may again compute possible ``negative probabilities. The resolution of the electromagnetic Klein paradox is that when the atoms decay, the final state may contain more photons then were contained the initial state. The optical theorem total cross section for scattering photons from excited state atoms may then be computed as negative within a frequency band with matter induced amplification.
In this paper we examine critically and in detail some existing definitions for the tunnelling times, namely: the phase-time; the centroid-based times; the Buttiker and Landauer times; the Larmor times; the complex (path-integral and Bohm) times; the dwell time, and finally the generalized (Olkhovsky and Recami) dwell time, by adding also some numerical evaluations. Then, we pass to examine the equivalence between quantum tunnelling and photon tunnelling (evanescent waves propagation), with particular attention to tunnelling with Superluminal group-velocities (Hartman effect). At last, in an Appendix, we add a bird-eye view of all the experimental sectors of physics in which Superluminal motions seem to appear.
The classical and quantum representations of thermal equilibrium are strikingly different, even for free, non-interacting particles. While the first involves particles with well-defined positions and momenta, the second usually involves energy eigenstates that are delocalized over a confining volume. In this paper, we derive convex decompositions of the density operator for non-interacting, non-relativistic particles in thermal equilibrium that allow for a connection between these two descriptions. Associated with each element of the decomposition of the N-particle thermal state is an N-body wave function, described as a set of wave packets; the distribution of the average positions and momenta of the wave packets can be linked to the classical description of thermal equilibrium, while the different amplitudes in the wave function capture the statistics relevant for fermions or bosons.
The interaction between matter and squeezed light has mostly been treated within the approximation that the field correlation time is small. Methods for treating squeezed light with more general correlations currently involve explicitly modeling the systems producing the light. We develop a general purpose input-output theory for a particular form of narrowband squeezed light -- a squeezed wave-packet mode -- that only cares about the statistics of the squeezed field and the shape of the wave packet. This formalism allows us to derive the input-output relations and the master equation. We also consider detecting the scattered field using photon counting and homodyne measurements which necessitates the derivation of the stochastic master equation. The non Markovian nature of the field manifests itself in the master equation as a coupled hierarchy of equations. We illustrate these with consequences for the decay and resonance fluorescence of two-level atoms in the presence of such fields.
The problems of cavity atom optics in the presence of an external strong coherent field are formulated as the problems of potential scattering of doubly-dressed atomic wave packets. Two types of potentials produced by various multiphoton Raman processes in a high-finesse cavity are examined. As an application the deflection of dressed atomic wave by a cavity mode is investigated. New momentum distribution of the atoms is derived that depends from the parameters of coherent field as well as photon states in the cavity.
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