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We apply the Fourier transform over the symmetric group $S_N$ to the set of multiparticle transition amplitudes arising from the permutations of $N$ identical particles. This allows us to analyse the counting statistics at the output of multiparticle and multimode interference setups in terms of contributions from irreducible symmetry types. We apply our formalism to the interference of partially distinguishable bosons and fermions, whose state can also be submitted to Fourier analysis, and to the determination of suppressed transitions for states of a given symmetry type.

We develop a statistical framework, based on a manifold learning embedding, to extract relevant features of multipartite entanglement structures of mixed quantum states from the measurable correlation data of a quantum computer. We show that the statistics of the measured correlators contains sufficient information to characterise the entanglement, and to quantify the mixedness of the state of the computer's register. The transition to the maximally mixed regime, in the embedding space, displays a sharp boundary between entangled and separable states. Away from this boundary, the multipartite entanglement structure is robust to finite noise.

Entanglement and interference are both hallmark effects of quantum physics. Particularly rich dynamics arise when multiple (at least partially) indistinguishable particles are subjected to either of these phenomena. By combining both entanglement and many-particle interference, we propose an interferometric setting through which N-particle interference can be observed, while any interference of lower orders is strictly suppressed. We experimentally demonstrate this effect in a four-photon interferometer, where the interference is nonlocal, in principle, as only pairs of photons interfere at two separate and independent beam splitters. A joint detection of all four photons identifies a high-visibility interference pattern varying as a function of their collective four-particle phase, a genuine four-body property.

We study the Hong-Ou-Mandel interference of two identical, composite particles, each formed of two bosonic or fermionic constituents, as they scatter against a potential barrier in a one-dimensional lattice. For tightly bound composites, we show that the combination of their constituents' mutual interactions and exchange symmetry gives rise to an effective nearest-neighbour interaction between composites, which induces a reduction of the interference contrast.

We describe the Hong-Ou-Mandel interference of two identical particles evolving on a one-dimensional tight-binding lattice where a potential barrier plays the role of a beam splitter. Careful consideration of the symmetries underlying the two-particle interference effect allows us to reformulate the problem in terms of ordinary wave interference in a Michelson interferometer. This approach is easily generalized to the case where the particles interact, and we compare the resulting analytical predictions for the bunching probability to numerical simulations of the two-particle dynamics.

We unveil the signature of many-body interference across dynamical regimes of the Bose-Hubbard model. Increasing the particles' indistinguishability enhances the temporal fluctuations of few-body observables, with a dramatic amplification at the onset of quantum chaos. By resolving the exchange symmetries of partially distinguishable particles, we explain this amplification as the fingerprint of the initial state's coherences in the eigenbasis., Comment: 5 pages, 2 figures + supplemental material

We show how coherences between identical constituents of a many-body quantum state can be interrogated by suitable correlation functions, and identify sufficient conditions under which low-order correlators fully characterize many-body coherences, as controlled by the constituents' mutual distinguishability. Comparison of correlators of different order detects many-body entanglement., Comment: 5 pages, 2 figures + supplemental material (1 page)

We develop a framework to systematically investigate the influence of many-particle interference on the dynamics of generic $-$ possibly interacting $-$ bosonic systems. We consider mixtures of bosons which belong to several distinguishable species, allowing us to tune the level of many-particle interference, and identify the corresponding signatures in the time-dependent expectation values of observables. Interference contributions to these expectation values can be classified based on the number of interfering particles. Interactions are shown to generate a series of additional, higher-order interference contributions. Finally, based on a decomposition of the Hilbert space of partially distinguishable bosons into irreducible representations of the unitary group, we determine some spectral characteristics of (in)distinguishability.

We formulate a general theory of wave-particle duality for many-body quantum states, which quantifies how wave- and particle-like properties balance each other. Much as in the well-understood single-particle case, which-way information -- here on the level of many-particle paths -- lends particle-character, while interference -- here due to coherent superpositions of many-particle amplitudes -- indicates wave-like properties. We analyze how many-particle which-way information, continuously tunable by the level of distinguishability of fermionic or bosonic, identical and possibly interacting particles, constrains interference contributions to many-particle observables and thus controls the quantum-to-classical transition in many-particle quantum systems. The versatility of our theoretical framework is illustrated for Hong-Ou-Mandel- and Bose-Hubbard-like exemplary settings.

Several distinct classes of unitary mode transformations have been known to exhibit the strict suppression of a large set of transmission events, as a consequence of totally destructive many-particle interference. In another work [Dittel et al., Phys. Rev. Lett. 120, 240404 (2018)] we unite these cases by identifying a general class of unitary matrices which exhibit such interferences. Here, we provide a detailed theoretical analysis that substantially expands on all aspects of this generalisation: We prove the suppression laws put forward in our other paper, establish how they interrelate with forbidden single-particle transitions, show how all suppression laws hitherto known can be retrieved from our general formalism, and discuss striking differences between bosons and fermions. Furthermore, beyond many-particle Fock states on input, we consider arbitrary pure initial states and derive suppression laws which stem from the wave function's permutation symmetry alone. Finally, we identify conditions for totally destructive interference to persist when the involved particles become partially distinguishable., Comment: 16 pages, 4 figures

In a general, multi-mode scattering setup, we show how the permutation symmetry of a many-particle input state determines those scattering unitaries which 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., Comment: 6 pages, 2 figures

The dynamics of bosons in generic multimode systems, such as Bose-Hubbard models, is not only determined by interactions among the particles, but also by their mutual indistinguishability manifested in many-particle interference. We introduce a measure of indistinguishability for Fock states of bosons whose mutual distinguishability is controlled by an internal degree of freedom. We demonstrate how this measure emerges both in the non-interacting and interacting evolution of observables. In particular, we find an unambiguous relationship between our measure and the variance of single-particle observables in the non-interacting limit. A non-vanishing interaction leads to a hierarchy of interaction-induced interference processes, such that even the expectation value of single-particle observables is influenced by the degree of indistinguishability.

We conceive an all-optical representation of the dynamics of two distinct types of interacting bosons in a double well by an array of evanescently coupled photonic waveguides. Many-particle interference effects are probed for various interaction strengths by changing the relative abundance of the particle species and can be readily identified by monitoring the propagation of the light intensity across the waveguide array. In particular, we show that finite inter-particle interaction strengths reduce the many-particle interference contrast by dephasing. A general description of the many-particle dynamics for arbitrary initial states is given in terms of two coupled spins by generalising the Schwinger representation to two particle species.

The GBAR experiment will time the free fall of cold antihydrogen atoms dropped onto an annihilation plate to test the universality of free fall on antimatter. In this contribution, we study the quantum reflection of the anti-atom resulting from the Casimir-Polder attraction to the plate. We evaluate the Casimir-Polder potential and the associated quantum reflection amplitudes and find that reflection is enhanced for weaker potentials. A Liouville transformation of the Schr\"odinger equation is used to map the quantum reflection problem onto an equivalent problem of scattering on a barrier, leading to an intuitive understanding of the phenomenon., Comment: Contribution to the Rencontres de Moriond 2015 Gravitation session

Liouville transformations of Schr\"odinger equations preserve the scattering amplitudes while changing the effective potential. We discuss the properties of these gauge transformations and introduce a special Liouville gauge which allows one to map the problem of quantum reflection of an atom on an attractive Casimir-Polder well into that of reflection on a repulsive wall. We deduce a quantitative evaluation of quantum reflection probabilities in terms of the universal probability which corresponds to the solution of the $V_4=-C_4/z^4$ far-end Casimir-Polder potential.

Liouville transformations map in a rigorous manner one Schr\"odinger equation into another, with a changed scattering potential. They are used here to transform quantum reflection of an atom on an attractive well into reflection of the atom on a repulsive wall. While the scattering properties are preserved, the corresponding semiclassical descriptions are completely different. A quantitative evaluation of quantum reflection probabilities is deduced from this method.

Different experiments are ongoing to measure the effect of gravity on cold neutral antimatter atoms such as positronium, muonium and antihydrogen. Among those, the project GBAR in CERN aims to measure precisely the gravitational fall of ultracold antihydrogen atoms. In the ultracold regime, the interaction of antihydrogen atoms with a surface is governed by the phenomenon of quantum reflection which results in bouncing of antihydrogen atoms on matter surfaces. This allows the application of a filtering scheme to increase the precision of the free fall measurement. In the ultimate limit of smallest vertical velocities, antihydrogen atoms are settled in gravitational quantum states in close analogy to ultracold neutrons (UCNs). Positronium is another neutral system involving antimatter for which free fall under gravity is currently being investigated at UCL. Building on the experimental techniques under development for the free fall measurement, gravitational quantum states could also be observed in positronium. In this contribution, we review the status of the ongoing experiments and discuss the prospects of observing gravitational quantum states of antimatter and their implications., Comment: This work reviews contributions made at the GRANIT 2014 workshop on prospects for the observation of the free fall and gravitational quantum states of antimatter

In the GBAR experiment, cold antihydrogen atoms will be left to fall on an annihilation plate with the aim of measuring the gravitational acceleration of antimatter. Here, we study the quantum reflection of these antiatoms due to the Casimir-Polder potential above the plate. We give realistic estimates of the potential and quantum reflection amplitudes, taking into account the specificities of antihydrogen and the optical properties of the plate. We find that quantum reflection is enhanced for weaker potentials, for example above thin slabs, graphene and nanoporous media., Comment: Workshop on Antimatter and Gravity Bern 2013 Proceedings

GBAR is a project aiming at measuring the free fall acceleration of gravity for antimatter, namely antihydrogen atoms ($\overline{\mathrm{H}}$). Precision of this timing experiment depends crucially on the dispersion of initial vertical velocities of the atoms as well as on the reliable control of their distribution. We propose to use a new method for shaping the distribution of vertical velocities of $\overline{\mathrm{H}}$, which improves these factors simultaneously. The method is based on quantum reflection of elastically and specularly bouncing $\overline{\mathrm{H}}$ with small initial vertical velocity on a bottom mirror disk, and absorption of atoms with large initial vertical velocities on a top rough disk. We estimate statistical and systematic uncertainties, and show that the accuracy for measuring the free fall acceleration $\overline{g}$ of $\overline{\mathrm{H}}$ could be pushed below $10^{-3}$ under realistic experimental conditions.

We investigate the formation of bound states made of two interacting atoms moving in a one dimensional (1D) quasi-periodic optical lattice. We derive the quantum phase diagram for Anderson localization of both attractively and repulsively bound pairs. We calculate the pair binding energy and show analytically that its behavior as a function of the interaction strength depends crucially on the nature -extended, multi-fractal, localized- of the single-particle atomic states. Experimental implications of our results are discussed., Comment: final revised version with more explanations, 4 pages, 3 figures