Beyond the regime of distinguishable particles, many-body quantum interferences influence quantum transport in an intricate manner.However, symmetries of the single-particle transformation matrix alleviate this complexity and even allow the analytic formulation of suppression laws, which predict final states to occur with a vanishing probability due to total destructive interference.Here we investigate the symmetries of hypercube graphs and their generalisations with arbitrary identical subgraphs on all vertices.We find that initial many-particle states, which are invariant under selfinverse symmetries of the hypercube, lead to a large number of suppressed final states.The condition for suppression is determined solely by the initial symmetry, while the fraction of suppressed states is given by the number of independent symmetries of the initial state.Our findings reveal new insights into particle statistics for ensembles of indistinguishable bosons and fermions and may represent a first step towards many-particle quantum protocols in higher-dimensional structures.
Beyond the regime of distinguishable particles, many-body quantum interferences influence quantum transport in an intricate manner.However, symmetries of the single-particle transformation matrix alleviate this complexity and even allow the analytic formulation of suppression laws, which predict final states to occur with a vanishing probability due to total destructive interference.Here we investigate the symmetries of hypercube graphs and their generalisations with arbitrary identical subgraphs on all vertices.We find that initial many-particle states, which are invariant under selfinverse symmetries of the hypercube, lead to a large number of suppressed final states.The condition for suppression is determined solely by the initial symmetry, while the fraction of suppressed states is given by the number of independent symmetries of the initial state.Our findings reveal new insights into particle statistics for ensembles of indistinguishable bosons and fermions and may represent a first step towards many-particle quantum protocols in higher-dimensional structures.
Abstract Quantum systems with many constituents give rise to a range of conceptual, analytical and computational challenges, hence, the label ‘complex systems’. In the first place, one can think of interactions, described by a many-body Hamiltonian, as the source of such complexity. However, it has gradually become clear that, even in absence of interactions, many-body systems are more than just the sum of their parts. This feature is due to many-body interference. One of the most well-known interference phenomena is the Hong–Ou–Mandel effect, where total destructive interference is observed for a pair of (non-interacting) identical photons. This two-photon interference effect can be generalised to systems of many particles which can be either fermionic or bosonic. The resulting many-particle interference goes beyond quantum statistical effects that are contained in the Bose–Einstein or Fermi–Dirac distributions, and is dynamical in nature. This Tutorial will introduce the mathematical framework for describing systems of identical particles, and explain the notion of indistinguishability. We will then focus our attention on dynamical systems of free particles and formally introduce the concept of many-particle interference. Its impact on many-particle transition probabilities is computationally challenging to evaluate, and it becomes rapidly intractable for systems with large numbers of identical particles. Hence, this Tutorial will build up towards alternative, more efficient methods for observing signatures of many-particle interference. A first type of signatures relies on the detection of a highly sensitive -but also highly fragile- processes of total destructive interference that occurs in interferometers with a high degree of symmetry. A second class of signatures is based on the statistical features that arise when we study the typical behaviour of correlations between a small number of the interferometer’s output ports. We will ultimately show how these statistical signatures of many-particle interference lead us to a statistical version of the Hong–Ou–Mandel effect. The work presented in this Tutorial was one of the four shortlisted finalists of the 2018 DPG SAMOP dissertation prize.
In a general, multimode scattering setup, we show how the permutation symmetry of a many-particle input state determines those scattering unitaries that exhibit strictly suppressed many-particle transition events. We formulate purely algebraic suppression laws that identify these events and show that the many-particle interference at their origin is robust under weak disorder and imperfect indistinguishability of the interfering particles. Finally, we demonstrate that all suppression laws so far described in the literature are embedded in the general framework that we here introduce.
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.
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.
Abstract Particle-exchange symmetry shapes the counting statistics of many-body systems by giving rise to multiple alternative evolutions whose transition amplitudes interfere. Here, we apply a Fourier transform over the symmetric group S N to the collection of N ! many-body transition amplitudes connecting two states of an N -particle system. This provides a decomposition of the counting statistics of many-body interference experiments into contributions associated with distinct irreducible exchange symmetries. As a first application of our formalism, we consider bosons or fermions which are rendered partially distinguishable from one another through unobserved degrees of freedom, and whose state is also subjected to a Fourier analysis. We thereby obtain a systematic description of partial distinguishability, which is both an important experimental noise source and a possible handle for the control of many-body interference. As a second application, we identify mechanisms responsible for completely destructive interference in many-body systems with other exchange symmetries than those of bosons or fermions. For an interferometer implementing the discrete Fourier transform unitary, we predict many instances of such suppressed transitions.
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.