On the basis of our assumption that the Tersoff-Bayer averaging is a consequence of the nonlocal correlations inherent in the quantum potential model of Bohm we describe a situation where this potential can be "switched" on and off giving rise to Bose-Einstein and Boltzmann statistics, respectively. This would imply a change in the fringe visibility in interference experiments.
On the basis of our assumption that the Tersoff-Bayer averaging is a consequence of the nonlocal correlations inherent in the quantum potential model of Bohm we describe a situation where this potential can be "switched" on and off giving rise to Bose-Einstein and Boltzmann statistics, respectively. This would imply a change in the fringe visibility in interference experiments.
We have discovered from Michelson and Young interferometry experiments, carried out with the use of an argon laser (working at λ = 5145 Å, with intracavity etalon, cw, 1-W power) that the standard application of quantum electrodynamics (QED) to this problem is incorrect. Photons belonging to a chaotic mixture of |n〉 states behave as Bose-Einstein (BE) particles showing a large reduction of the interference-fringe visibility V ( n ¯ ) = ( I max − I min ) / ( I max + I min ) for increasing average photon number per radiation mode 〈 n 〉 = n ¯ , where I ( n ¯ ) is the photodetected intensity. This effect, never investigated or anticipated before, is a manifestation of the quantum interparticle correlations inherent BE statistics. Photons belonging to a superimposition of coherent, Glauber, |α〉 states (i.e., a laser beam) follow Maxwell-Boltzmann (MB) statistics leading to V ( n ¯ ) = 1 for any n ¯ , owing to absence of interparticie correlations.
Recently, the question of the origin of correlations in thermal light has again been debated. The alternative viewpoints suggest that (i) stimulated emission causes the correlations implied by Bose-Einstein statistics and exemplified by the Hanbury Brown-Twiss effect, or (ii) stimulated emission coherently amplifies any initial field, with no change in the nature of photon statistics, apart from the addition of, and interference with, spontaneous-emission noise. It is shown that two essentially different physical models have been considered previously, with many results being only approximate. For these models we obtain the evolution of the photon statistics by deriving exactly the generating function for the diagonal elements of the field density matrix and the quantum characteristic function. The source of Bose-Einstein correlations is seen to be merely the interference in the superposition of random independent fields from a chaotic source, spontaneous emission being one example. Extending the investigation to a nonlinear model, we show that, although there is no longer coherent amplification, it is still not correct to infer that this interaction, which produces the amplification, also leads to Bose-Einstein statistics.
We calculate the first-order interference-fringe visibilities for Mach-Zehnder interferometers in which the input beam splitting has time-varying reflection and transmission coefficients. Particular attention is given to single-photon input states, and it is shown that fringes persist in appropriate conditions even for a beam splitter that alternates between complete transmission and complete reflection. The similar behavior found for input coherent and chaotic light confirms the single-photon nature of first-order interference. The states of excitation of the internal arms of the interferometer are derived and discussed in the context of delayed-choice experiments.
Interference experiments characterized by the degree of first-order coherence (Young’s fringes, Fresnel, and Fraunhofer diffraction, etc.) have been performed with massive particles, in particular electrons and neutrons, as well as with light. Optical intensity interference or correlation experiments characterized by the degree of second-order coherence have not yet been performed with particles. The theory for such experiments shows striking differences in the behavior of electrons compared with that of light deriving from the differences in quantum statistics and charge. Photons are neutral bosons. They can be prepared in states that exhibit bunching, no bunching, or antibunching; they are unaffected by the presence of electromagnetic potentials. Electrons are charged fermions. Theory indicates that they exhibit antibunching regardless of the coherence of the source, and that their degree of second-order coherence can be influenced by electromagnetic fields through which they do not pass. A remarkable example is the Hanbury Brown-Twiss experiment with electrons that have interacted locally with the vector potential of an inaccessible magnetic field. The electron intensity correlation at two detectors is shown to be sensitive to the confined magnetic flux; experimental conditions differ considerably from those of the well-known Aharonov-Bohm effect.
The mean-field limit of a bosonic quantum many-body system is described by (mostly) nonlinear equations of motion which may exhibit chaos very much in the spirit of classical particle chaos, i.e., by an exponential separation of trajectories in Hilbert space with a rate given by a positive Lyapunov exponent $\ensuremath{\lambda}$. The question now is whether $\ensuremath{\lambda}$ imprints itself onto measurable observables of the underlying quantum many-body system even at finite particle numbers. Using a Bose-Einstein condensate expanding in a shallow potential landscape as a paradigmatic example for a bosonic quantum many-body system, we show that the system loses its coherence at an exponentially fast rate. Furthermore, we show that the rate is given by the Lyapunov exponent associated with the chaotic mean-field dynamics. Finally, we demonstrate that this chaos-induced loss of coherence imprints itself onto the visibility of interference fringes in the total density after time of flight, thus, opening the possibility to measure $\ensuremath{\lambda}$ and with it the interplay between chaos and nonequilibrium quantum matter in a real experiment.
The visibility of the density interference pattern of two Bose-Einstein condensates, which are produced in traps and overlap after the trapping potential is switched off, is investigated. Coherent wave packets are used to describe the order parameter in a second-quantization formalism. This results in a decrease of the visibility of the interference fringes with increasing time delay between the formation of the condensates and the observation of interference. In the two limiting cases of ideal and very dense gases the correlation time increases, τ →∞, and the result is identical to that obtained using an approach based on the Gross-Pitaevskii equation. Under the conditions of the experiment performed by M. R. Andrews, C. G. Townsend, H. J. Miesner et al. , Science 275 , 6367 (1997), the computed correlation time τ ≈0.2 s is much longer than the confinement time of the condensate, and it is possible to observe the predicted decrease of visibility of the interference fringes of the density of the atoms.