We show how robust statistical features of a many-particle quantum state's two-point correlations after transmission through a multimode random scatterer can be used as a sensitive probe of the injected particles' mutual indistinguishability. This generalizes Hong-Ou-Mandel interference as a diagnostic tool for many-particle transmission signals across multimode random scatterers. Furthermore, we show how, from such statistical features of the many-particle interference pattern, information can be deduced on the temporal structure of the many-particle input state, by inspection of the many-particle interference with an additional probe particle of tunable distinguishability.
We show how robust statistical features of a many-particle quantum state's two-point correlations after transmission through a multimode random scatterer can be used as a sensitive probe of the injected particles' mutual indistinguishability. This generalizes Hong-Ou-Mandel interference as a diagnostic tool for many-particle transmission signals across multimode random scatterers. Furthermore, we show how, from such statistical features of the many-particle interference pattern, information can be deduced on the temporal structure of the many-particle input state, by inspection of the many-particle interference with an additional probe particle of tunable distinguishability.
Boson samplers-set-ups that generate complex many-particle output states through the transmission of elementary many-particle input states across a multitude of mutually coupled modespromise the efficient quantum simulation of a classically intractable computational task, and challenge the extended Church-Turing thesis, one of the fundamental dogmas of computer science.However, as in all experimental quantum simulations of truly complex systems, one crucial problem remains: how to certify that a given experimental measurement record unambiguously results from enforcing the claimed dynamics, on bosons, fermions or distinguishable particles?Here we offer a statistical solution to the certification problem, identifying an unambiguous statistical signature of many-body quantum interference upon transmission across a multimode, random scattering device.We show that statistical analysis of only partial information on the output state allows to characterise the imparted dynamics through particle type-specific features of the emerging interference patterns.The relevant statistical quantifiers are classically computable, define a falsifiable benchmark for BosonSampling, and reveal distinctive features of many-particle quantum dynamics, which go much beyond mere bunching or anti-bunching effects.
Boson samplers-set-ups that generate complex many-particle output states through the transmission of elementary many-particle input states across a multitude of mutually coupled modes-promise the efficient quantum simulation of a classically intractable computational task, and challenge the extended Church-Turing thesis, one of the fundamental dogmas of computer science. However, as in all experimental quantum simulations of truly complex systems, one crucial problem remains: how to certify that a given experimental measurement record unambiguously results from enforcing the claimed dynamics, on bosons, fermions or distinguishable particles? Here we offer a statistical solution to the certification problem, identifying an unambiguous statistical signature of many-body quantum interference upon transmission across a multimode, random scattering device. We show that statistical analysis of only partial information on the output state allows to characterise the imparted dynamics through particle type-specific features of the emerging interference patterns. The relevant statistical quantifiers are classically computable, define a falsifiable benchmark for BosonSampling, and reveal distinctive features of many-particle quantum dynamics, which go much beyond mere bunching or anti-bunching effects.
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.
The two-photon Hong-Ou-Mandel (HOM) interference is a pure quantum effect which indicates the degree of indistinguishability of photons. The four-photon HOM interference exhibits richer dynamics in comparison to the two-photon interference and simultaneously is more sensitive to the input photon states. We demonstrate theoretically and experimentally an explicit dependency of the four-photon interference on the number of temporal modes, created in the process of parametric down-conversion. Moreover, we exploit the splitting ratio of the beam splitter to manipulate the interference between bunching and antibunching. Our results reveal that the temporal mode structure (multimodeness) of the quantum states shapes many-particle interference.
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.
The interplay between single-particle interference and quantum indistinguishability leads to signature correlations in many-body scattering. We uncover these with a semiclassical calculation of the transmission probabilities through mesoscopic cavities for systems of noninteracting particles. For chaotic cavities we provide the universal form of the first two moments of the transmission probabilities over ensembles of random unitary matrices, including weak localization and dephasing effects. If the incoming many-body state consists of two macroscopically occupied wave packets, their time delay drives a quantum-classical transition along a boundary determined by the bosonic birthday paradox. Mesoscopic chaotic scattering of Bose-Einstein condensates is, then, a realistic candidate to build a boson sampler and to observe the macroscopic Hong-Ou-Mandel effect.