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.
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.
Examples of charged-particle interferometry are descibed whereby isolated magnetic fields—i.e., fields through which the particles do not pass—influence the clustering, as well as spatial distribution, of the particles. The configurations, which combine features characteristic of (i) Aharonov–Bohm and Hanbury Brown–Twiss experiments, and (ii) Aharonov–Bohm and Einstein–Podolsky–Rosen experiments, manifest simultaneously the effects of three distinct kinds of interference: (i) interference, dependent upon optical path length difference, resulting from wavelike propagation of particles; (ii) interference, dependent upon confined magnetic flux, resulting from particle charge and spatial topology; and (iii) interference, dependent upon quantum statistics, resulting from particle indistinguishability under exchange.
Since the first observation of two-point correlation effects in optical fields (Hanbury, Brown, and Twiss, 1957) there has been continuous theoretical and experimental interest in photon correlation. In this paper we examine the possibility of measuring similar effects involving massive particles. We first discuss the theory of correlations between noninteracting massive particles by using the formalism of second quantization. This theory is considerably simpler than that for light because we can treat particles in the strictly nonrelativistic limit. However, the theory provides a particularly interesting contrast with the photon case because we may choose particles that are either fermions or bosons. We then apply the theory to the case of beams of atoms and neutrons and consider the experimental parameters of existing beams. In particular, we consider the case of experiments with laser-cooled metastable helium.
The Hanbury Brown-Twiss effect is one of the celebrated phenomenologies of modern physics that accommodates equally well classical (interferences of waves) and quantum (correlations between indistinguishable particles) interpretations. The effect was discovered in the late thirties with a basic observation of Hanbury Brown that radio-pulses from two distinct antennas generate signals on the oscilloscope that wiggle similarly to the naked eye. When Hanbury Brown and his mathematician colleague Twiss took the obvious step to propose bringing the effect in the optical range, they met with considerable opposition as single-photon interferences were deemed impossible. The Hanbury Brown-Twiss effect is nowadays universally accepted and, being so fundamental, embodies many subtleties of our understanding of the wave/particle dual nature of light. Thanks to a novel experimental technique, we report here a generalized version of the Hanbury Brown-Twiss effect to include the frequency of the detected light, or, from the particle point of view, the energy of the detected photons. Our source of light is a polariton condensate, that allows high-resolution filtering of a spectrally broad source with a high degree of coherence. In addition to the known tendencies of indistinguishable photons to arrive together on the detector, we find that photons of different colors present the opposite characteristic of avoiding each others. We postulate that fermions can be similarly brought to exhibit positive (boson-like) correlations by frequency filtering.
Very much like the ubiquitous quantum interference of a single particle with itself, quantum interference of two independent, but indistinguishable, particles is also possible. This interference is a direct result of quantum exchange statistics, however, it is observed only in the joint probability to find the particles in two separated detectors. Here we report the first observation of such interference fringes between two independent and non-interacting electrons in an interferometer proposed by Yurke et al. and Samuelsson et al. Our experiment resembles the "Hanbury Brown and Twiss" (HBT) experiment, which was performed with classical waves. In the experiment, two independent and mutually incoherent electron beams were each partitioned into two trajectories. The combined four trajectories enclosed an Aharonov-Bohm (AB) flux (but not the two trajectories of a single electron). While individual currents were found to be independent of the AB flux, as expected, the cross-correlation between current fluctuations in two opposite points across the device exhibited strong AB oscillations. This is a direct signature of orbital entanglement between two electrons even though they never interact with each other.
The Hanbury Brown-Twiss effect is one of the celebrated phenomenologies of modern physics that accommodates equally well classical (interferences of waves) and quantum (correlations between indistinguishable particles) interpretations.The effect was discovered in the late thirties with a basic observation of Hanbury Brown that radio-pulses from two distinct antennas generate signals on the oscilloscope that wiggle similarly to the naked eye.When Hanbury Brown and his mathematician colleague Twiss took the obvious step to propose bringing the effect in the optical range, they met with considerable opposition as single-photon interferences were deemed impossible.The Hanbury Brown-Twiss effect is nowadays universally accepted and, being so fundamental, embodies many subtleties of our understanding of the wave/particle dual nature of light.Thanks to a novel experimental technique, we report here a generalized version of the Hanbury Brown-Twiss effect to include the frequency of the detected light, or, from the particle point of view, the energy of the detected photons.Our source of light is a polariton condensate, that allows high-resolution filtering of a spectrally broad source with a high degree of coherence.In addition to the known tendencies of indistinguishable photons to arrive together on the detector, we find that photons of different colors present the opposite characteristic of avoiding each others.We postulate that fermions can be similarly brought to exhibit positive (bosonlike) correlations by frequency filtering.
In quantum mechanics it is possible to pack an arbitrary number of bosons into the same quantum state. The maximum occupancy for fermions, however is one. Back in 1956 two British scientists, Hanbury Brown and Twiss, conducted a classic experiment that showed that photons, a type of boson, have a tendency to bunch into clusters. Their experiment comprised two light sources and two detectors set up to measure the light that was transmitted and reflected by a beam splitter at the centre of the experimental configuration (see figure a). The bunching was observed by measuring the intensity correlation between the two coherent beams of light as a function of time. Hanbury Brown and Twiss measured the likelihood of observing a fluctuation in one detector at a particular time when a signal was detected at an earlier time in the other detector. The positive correlation they found was consistent with the bunching property of bosons.