Signatures of 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 manybody 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 (noninteracting) 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 manyparticle 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.

Classical and Quantum Electromagnetic Interferences: What Is the Difference?

“…Using Lorenz gauge with Φ = 0, one can represent a classical vector potential in mode space via eigenmode decomposition as A (r, t) = k φ k (r) a k e −iω k t + h.c. (27) where subscript k is the modal index; h.c. denotes Hermitian conjugate; φ k (r), ω k , a k are the k-th (traveling-wave) eigenmode, eigenfrequency, complex-valued modal amplitudes, respectively. It is to be noted that if one were to fix r and observe the field, it has a simple harmonic motion just like that of + The infinite dimensional linear vector spaces associated with such operators are generally known as Hilbert spaces.…”

“…Subsequent theoretical explanation of HOM was given in [11,[13][14][15][16]. HOM has also been studied in plasmons [17], numerically [18], in microwave [19], in atoms [20], in frequency domain [21,22], in Gaussian wave packets [23,24], with and without beam splitters [25,26], as well as in many particle systems [27]. Of interest is a paper demonstrating this effect at astronomical length scale [28].…”

Efficient verification of Boson Sampling

“…Gaussian state preparations and measurements are at the same time well understood theoretically [47], classically simulable [48], and routinely implemented at large scales experimentally [49,50,51]. However, there is no efficient verification protocol using single-mode Gaussian state preparation nor single-mode Gaussian measurements for Boson Sampling with input single photons: current methods used for the validation of Boson sampling are either not scalable or only provide partial certificates on the tested probability distribution [30,52,53,54,55,56,57].…”

Symmetry allows for distinguishability in totally destructive many-particle interference

“…These have been validated experimentally [25][26][27][28][29][30][31][32], and found a theoretical formulation [33,34] which -by algebraic considerations, hence applicable for arbitrary system sizes -anchors them to the symmetry properties of the many-particle input state and of the scattering unitary under permutations. Since symmetry considerations reduce the complexity of the general manyparticle interference problem, the experimental validation of said suppression rules was suggested as a viable certification protocol for bona-fide many-particle interference phenomena, as it directly assesses the granular features of many-particle quantum interference, in contrast, e.g., to mean-field samplers [27,30,[35][36][37].…”