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arXiv:1204.1214 · Europhysics Letters (EPL)

Bunching and anti-bunching of localised particles in disordered media

Frank Schlawin, Nicolas Cherroret, Andreas Buchleitner

Published Jul 1, 2012• 13 citations
arXivHTMLPDF

Abstract

We consider pairs of non-interacting quantum particles transmitted through a disordered medium, with emphasis on the role of their quantum statistics. It is shown that particle-number correlations measured in transmission are strikingly sensitive to the quantum nature of the particles when they undergo Anderson localisation, due to bosonic bunching and fermionic anti-bunching in the scattering channels of the medium. The case of distinguishable particles is also discussed.

DOI
10.1209/0295-5075/99/14001

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We consider pairs of non-interacting quantum particles transmitted through a disordered medium, with emphasis on the role of their quantum statistics. It is shown that particle-number correlations measured in transmission are strikingly sensitive to the quantum nature of the particles when they undergo Anderson localisation, due to bosonic bunching and fermionic anti-bunching in the scattering channels of the medium. The case of distinguishable particles is also discussed.
For a number of noninteracting identical particles entering a multichannel scatterer in various wave-packet states, we construct a generating function for the probabilities of various scattering outcomes. This is used to evaluate the mean numbers of particles, n‾m{\overline{n}}_{m}nm​, scattered into a given (mth)(m\mathrm{th})(mth) channel, single-channel statistics, and interchannel correlations. We show that for initially uncorrelated particles, indistinguishability changes single-channel statistics without altering the value of n‾m{\overline{n}}_{m}nm​. For uncorrelated bosons and fermions, bunching and antibunching behavior can be detected in the extreme-case probabilities, to have all particles scattered into the same channel, or none of particles scattered into a channel, or channels. As an example, we consider a cavity with a single long-lived resonance accessible to the particles, which allows them to ``pile up'' inside the scatterer.
Summary form only given. In 1958 P.W. Anderson predicted that the wave-function of a quantum particle can be localized in the presence of a static disordered potential [1]. This phenomenon arises from the destructive interference of waves propagating in static disordered media. As a consequence, in these conditions, particle and energy transport through a disordered medium are expected to be strongly suppressed and an initially localized wave packet does not spread out with time. In this work we experimentally study the localization properties of a pair of non-interacting particles obeying bosonic/fermionic statistics by simulating a one-dimensional QW of a two-photon polarization-entangled state in a disordered medium. Quantum walk is the quantum counterpart of classical random walk: a walker jumping between different sites of a lattice with a given probability. In the quantum case the walker is a quantum system, whose quantum properties affect the transport. When multi-particle walkers travel within the QW their bosonic or fermionic nature strongly affects the transport. Here we implement different quantum statistics by exploiting of the polarization-entangled bi-photon input state. The QW circuit has been experimentally realized by femtosecond laser writing which provides a perfect phase stability [2]. In particular, we realized an 8-step quantum walk circuit composed by an array of polarization independent beam splitters arranged in a cascade configuration of Mach-Zehnder (MZ) interferometers (see Fig.1a).
The present thesis deals with the interrelation between entanglement of identical particles and many-particle interference in multimode scattering scenarios. The processes that govern the scattering are shown to characterize the quantum correlations that result from coherent deletion of many-particle which-way information. Part I treats the constitutive situation of two identical particles which are measured by two detectors to provide a consistent definition of identical-particle entanglement. The key quantities that determine the strength and nature of correlations are diagnosed, which allows a formulation of the problem as scattering scenario. Quite counter-intuitively, the effective indistinguishability of the particles is not necessarily reflected monotonically by the strength of quantum correlations, which is explained by an interplay of the entanglement encoded in the initial state with measurement-induced correlations. The subject of Part II is the scattering of many non-interacting particles that are initially injected in an arbitrary number of modes. A comparison of bosons, fermions and distinguishable particles reveals that the dichotomy of bosons and fermions, known from the two-particle case, does, surprisingly, not prevail for many particles: A given output event can be suppressed or enhanced for bosons and fermions simultaneously. Consequently, the bunching behavior of bosons is not apparent at the level of single counting events, where dynamical many-particle interference dominates, and it is only reflected in more coarse-grained quantities that are related to the occupation statistics, for which efficient approximate treatments are derived. The general complexity of the many-particle problem is overcome for the special case of a Fourier multiport beam splitter. The exploitation of its scattering matrix’ symmetries yields a systematic event suppression law for, both, bosons and fermions, which provides a generalization of the two-photon Hong-Ou-Mandel effect to an arbitrary number of particles and modes. As a further characteristic trait of many-particle interference, the transition between indistinguishable and distinguishable particles is reflected non-monotonically by the event probabilities, which is also confirmed by an experiment that was suggested by the present work. Part III combines the formalism for identical-particle entanglement and the tools and notions developed in the context of many-particle scattering for a description of those multipartite entangled states that can be created via the scattering of many identical particles. The formalism is general enough to include virtually any possible scheme for the multipartite entanglement creation with single photons. An analytical treatment reveals fundamental constraints for the set of accessible states. In particular, an intuitive combinatorial bound for the Schmidt number of the target state follows from the finite number of combinations to distribute the particles among the output modes. Furthermore, bosons and fermions have very distinct potential for entanglement creation: Fewer states are accessible for fermions, whereas the success probability of entanglement production is strongly enhanced with respect to bosons.
We consider the situation in which the field of quantum particles such as photons (bosons) or electrons (fermions) undergoes a significant attenuation during the detection process. We characterize the second-order statistical properties of the field by the bunching for bosons and the antibunching for fermions. Bunching and antibunching effects are derived from the time intervals distributions of the random point process of detection instead of the moments of the number of particles registered in a given time interval. Fields of both beams are supposed to be in chaotic states and have second-order time correlation functions of exponential profile and of arbitrary correlation time. A test is proposed for nonclassical states: the behavior of the antibunching function is a nondecreasing function near the origin of the time axis.
Progress in the reliable preparation, coherent propagation and efficient detection of many-body states has recently brought collective quantum phenomena of many identical particles into the spotlight. This tutorial introduces the physics of many-boson and many-fermion interference required for the description of current experiments and for the understanding of novel approaches to quantum computing. The field is motivated via the two-particle case, for which the uncorrelated, classical dynamics of distinguishable particles is compared to the quantum behaviour of identical bosons and fermions. Bunching of bosons is opposed to anti-bunching of fermions, while both species constitute equivalent sources of bipartite two-level entanglement. The realms of indistinguishable and distinguishable particles are connected by a monotonic transition, on a scale defined by the coherence length of the interfering particles. As we move to larger systems, any attempt to understand many particles via the two-particle paradigm fails: In contrast to two-particle bunching and anti-bunching, the very same signatures can be exhibited by bosons and fermions, and coherent effects dominate over statistical behaviour. The simulation of many-boson interference, termed Boson-Sampling, entails a qualitatively superior computational complexity when compared to fermions. The hierarchy between bosons and fermions also characterises multipartite entanglement generation, for which bosons again clearly outmatch fermions. Finally, the quantum-to-classical transition between many indistinguishable and many distinguishable particles features non-monotonic structures. While the same physical principles govern small and large systems, the deployment of the intrinsic complexity of collective many-body interference makes more particles behave differently.