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Science

Bunches of Photons--Antibunches of Electrons

Μ. Büttiker

Published Apr 9, 1999• 10 citations
Publisher

Abstract

When a photon beam from a light source is split in two, with one part transmitted and the other reflected at a half-silvered mirror, it is found that the intensities of these beams are correlated: the photons exhibit "bunching," that is, they tend to come in clusters of identical particles occupying the same state. In contrast, electrons are expected to exhibit "antibunching" and therefore a negative intensity correlation. Büttiker (page 275) discusses two successful measurements of such antibunching of fermions in mesoscopic conductors (Henny et al., page 296, and Oliver et al., page 299) and explains why their approach is important for investigating a range of subjects from superconductivity to noise suppression in quantum computing.

DOI
10.1126/science.284.5412.275

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When a photon beam from a light source is split in two, with one part transmitted and the other reflected at a half-silvered mirror, it is found that the intensities of these beams are correlated: the photons exhibit "bunching," that is, they tend to come in clusters of identical particles occupying the same state. In contrast, electrons are expected to exhibit "antibunching" and therefore a negative intensity correlation. Büttiker (page 275) discusses two successful measurements of such antibunching of fermions in mesoscopic conductors (Henny et al., page 296, and Oliver et al., page 299) and explains why their approach is important for investigating a range of subjects from superconductivity to noise suppression in quantum computing.
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.
Addressing the feasibility of quantum communication with entangled electrons in an interacting many-body environment, we propose an interference experiment using a scattering setup with an entangler and a beam splitter. It is shown that, due to electron-electron interaction, the spin correlation of the entangled singlet and triplet states is reduced by zF2{z}_{F}^{2}zF2​ in a conductor described by Fermi liquid theory. We calculate the quasiparticle weight factor zF{z}_{F}zF​ for a two-dimensional electron system. The current noise for electronic singlet states turns out to be enhanced (bunching behavior), while it is reduced for triplet states (antibunching). Within standard scattering theory, we find that the Fano factor (noise-to-current ratio) for singlets is twice as large as for independent classical particles and is reduced to zero for triplets.
Correlations between successive detections in beams of free electrons are studied with a transmission electron microscope. For incoherent illumination of the detectors, a certain random coincidence probability is observed, indicative for uncorrelated arrival times of the electrons. When the illumination is changed from incoherent to coherent, a reduction of the random coincidence probability is observed, indicative for antibunching in the arrival times of the electrons. However, the amount of reduction is larger than the theoretically expected value calculated from the Pauli principle, forbidding more than one identical fermion to occupy the same quantum state. For a certain coherent illumination of the detectors, where we use magnetic lenses in electron microscopes for magnifications of the coherence length, we find an enhanced coincidence probability, indicative for bunching in the arrival times of the electrons. This originates from correlations in beams of free electrons due to Coulomb interactions.
Since Hanbury Brown and Twiss revealed the photon bunching effect of a thermal light source in 1956, almost all studies in correlation optics have been based on light’s intensity fluctuation, regardless of fact that the polarization fluctuation is a basic attribute of natural light. In this work, we uncover the veil of the polarization fluctuation and corresponding photon correlations by proposing a new light source model, termed pseudo-natural light, embodying both intensity and polarization fluctuations. Unexpectedly, the strong antibunching and superbunching effects can be simultaneously realized in such a new source, whose second-order correlation coefficient g ( 2 ) can be continuously modulated across 1. For the symmetric Bernoulli distribution of the polarization fluctuation, particularly, g ( 2 ) can be in principle from 0 to unlimitedly large. In pseudo-natural light, while the bunching effects of both intensity and polarization fluctuations enhance the bunching to superbunching photon correlation, the antibunching correlation of the polarization fluctuation can also be extracted through the procedure of division operation in the experiment. The antibunching effect and the combination with the bunching one will arouse new applications in quantum imaging. As heuristic examples, we carry out high-quality positive or negative ghost imaging, and devise high-efficiency polarization-sensitive and edge-enhanced imaging. This work, therefore, sheds light on the development of multiple and broad correlation functions for natural light.
Being bosons, photons like to group together, with the behavior of photon bunching described as an attribute of classical light. At the other extreme, photons emitted by a single emitter are expected to antibunch, trickling out of the emitter one at a time. Although bunching and antibunching are well established behaviors of classical and nonclassical light, respectively, the transition between the two has not been observed. It is expected that as the number of emitters is increased, a smooth transition should occur. Using a high-quality cavity into which they can place a variable number of atoms, Hennrich et al. show that they can probe the transition systematically as the number of emitters (atoms in the cavity) is gradually increased. They observe that the antibunching behavior disappears when the average number of atoms in the cavity is one, and they are able to explain the experimental data well if the emitters are assumed to form an independent ensemble. — ISO
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.