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Physica B Condensed Matter

Signs of quantum statistical effects in electron collision

R.C. Liu, Y. Yamamoto, Seigo Tarucha

Published Jun 1, 1998• 4 citations
Publisher

Abstract

A suppression of the output current noise relative to classical partition noise is observed in a ballistic electron beam splitter when the electron streams from two inputs are collided. This noise suppression reflects the quantum statistical interference between colliding identical quantum particles which underlies the Pauli exclusion principle.

DOI
10.1016/s0921-4526(98)00088-x

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A suppression of the output current noise relative to classical partition noise is observed in a ballistic electron beam splitter when the electron streams from two inputs are collided. This noise suppression reflects the quantum statistical interference between colliding identical quantum particles which underlies the Pauli exclusion principle.
Identical particles exhibit correlations even in the absence of inter-particle interaction, due to the exchange (anti)symmetry of the many-particle wavefunction. Two fermions obey the Pauli principle and anti-bunch, whereas two bosons favor bunched, doubly occupied states. Here, we show that the collective interference of three or more particles leads to much more diverse behavior than expected from the boson–fermion dichotomy known from quantum statistical mechanics. The emerging complexity of many-particle interference is tamed by a simple law for the strict suppression of events in the Bell multiport beam splitter. The law shows that counting events are governed by widely species-independent interference, such that bosons and fermions can even exhibit identical interference signatures, while their statistical character remains subordinate. Recent progress in the preparation of tailored many-particle states of bosonic and fermionic atoms promises experimental verification and applications in novel many-particle interferometers.
We report shot noise cross correlation measurements in a four terminal beam splitter configuration. By using two tunnel barriers as independent electron sources with tunable statistics and energy, we can adjust the degree of quantum interference that results when the electrons scatter at a beam splitter. Even though quantum interference is only weakly affected by noise, it can be strongly suppressed by detuning the energies of the interfering electrons. Our results illustrate the importance of indistinguishability for quantum interference, and its resilience to unsynchronized electron sources and noise.
The interference between quantum amplitude for two electrons, emitted from two source points, to be detected at two detection points, is a direct result of quantum exchange statistics. Such interference is observed in the coincidence probability, compared with that of statistically independent electrons, by computing the time correlation function from the arrival times of the electrons. When the two detectors are separated by a distance less than the coherence length, the coincidence probability is suppressed for electrons (antibunching) due to the Pauli principle, even though they do not interact with each other. However, electrons are charged particles. The Coulomb potential, which governs the scattering of one charged particle by another, is so long ranged. It is obvious that we must consider the Pauli principle and the Coulomb interactions simultaneously. This paper deals with basic experimental and theoretical investigations of the antibunching behavior of electrons in a free beam by considering the Pauli principle and the direct Coulomb interaction between two individual electrons. The experimentally found dependences are described in a model which considers the Coulomb scattering and theoretical values of correlation signals evaluated by analytical calculations agree with those determined by experiment. A study of the time correlation function from the arrival times of the electrons will lead to an understanding of the physical processes that take place in electron guns.
A partitioned system of fermions is mathematically equivalent to an assembly of two-level atoms described by spin operators. A number-phase uncertainty relation can therefore be derived to describe the noise properties of divided electrons. We examine both the number (or electron flux) and phase (or electron wave phase) decorrelation introduced by electron branching in mesoscopic circuits. Initially Poissonian, this electron number partition noise is increasingly suppressed by inelastic scattering in the transition from ballistic to dissipative electron division. Graphical results from our model show a trend from a coherent spin state in the ballistic regime toward a number-squeezed spin state in the dissipative regime, even when detrimental elastic scattering is present.
In this article, we discuss the identity and indistinguishability of quantum systems and the consequent need to introduce an extra postulate in Quantum Mechanics to correctly describe situations involving indistinguishable particles. This is, for electrons, the Pauli Exclusion Principle, or in general, the Symmetrization Postulate. Then, we introduce fermions and bosons and the distributions respectively describing their statistical behaviour in indistinguishable situations. Following that, we discuss the spin-statistics connection, as well as alternative statistics and experimental evidence for all these results, including the use of bunching and antibunching of particles emerging from a beam splitter as a signature for some bosonic or fermionic states.
Quantum interference between identical single particles reveals the intrinsic quantum statistic nature of particles, which could not be interpreted through classical physics. Here, we demonstrate quantum interference between nonidentical bosons using a generalized beam splitter based on a quantum memory. The Hong-Ou-Mandel type interference between single photons and single magnons with high visibility is demonstrated, and the crossover from the bosonic to fermionic quantum statistics is observed by tuning the beam splitter to be non-Hermitian. Moreover, multiparticle interference that simulates the behavior of three fermions by three input photons is realized. Our work extends the understanding of the quantum interference effects and demonstrates a versatile experimental platform for studying and engineering quantum statistics of particles.