Nonmonotonic quantum-to-classical transition in multiparticle interference

Abstract

Quantum-mechanical wave-particle duality implies that probability distributions for granular detection events exhibit wave-like interference. On the single-particle level, this leads to self-interference-e.g., on transit across a double slit-for photons as well as for large, massive particles, provided that no which-way information is available to any observer, even in principle. When more than one particle enters the game, their specific many-particle quantum features are manifested in correlation functions, provided the particles cannot be distinguished. We are used to believe that interference fades away monotonically with increasing distinguishability-in accord with available experimental evidence on the single-and on the many-particle level. Here, we demonstrate experimentally and theoretically that such monotonicity of the quantum-to-classical transition is the exception rather than the rule whenever more than two particles interfere. As the distinguishability of the particles is continuously increased, different numbers of particles effectively interfere, which leads to interference signals that are, in general, nonmonotonic functions of the distinguishability of the particles. This observation opens perspectives for the experimental characterization of many-particle coherence and sheds light on decoherence processes in many-particle systems.quantum interference | which-path information | quantum statistics T he double-slit-like (self-)interference of single particles has been observed for particles ranging from photons (1) to massive particles (2). It relies on the coherence of the singleparticle wave-function, which guarantees that the different pathways a particle can take to a detector-e.g., through the left or through the right slit in a double-slit experiment-remain indistinguishable.Interaction with the environment, however, may convey whichpath information to the environment, and then inevitably leads to decoherence (3, 4). Thereby, it jeopardizes the ideal interference pattern and induces the quantum-to-classical transition (5, 6). The stronger the decoherence, the weaker is the interference signal (3). Expectation values of observables therefore depend monotonically on the strength of decoherence, and a monotonic transition between quantum and classical expectation values takes place (2, 5-10).The superposition principle, which is responsible for the above self-interference effects, also applies to many-particle wave-functions, with entanglement (11) and many-particle interference (12) as immediate consequences. For the observation of the latter, the mutual indistinguishability of the particles is necessary and it entails, for instance, the Hong-Ou-Mandel (HOM) effect (13, 14): When a single photon is incident on each of the two input modes of a balanced beam splitter (BS), the two-particle Feynman paths of "both photons reflected" and "both photons transmitted" interfere destructively, leading to the strict suppression of the event with one particle per output mode.As particles turn distinguish...

Sampling of partially distinguishable bosons and the relation to the multidimensional permanent

“…This result harmonizes with the experimental data obtained in Ref. [42], which excludes a naive extrapolation of wave-particle duality to the many-body domain. The question naturally arises whether there exists a scattering setup U , a final event s and a distinguishability matrix S such that P S ( s) = 0 while P id ( s) = 0, i.e.…”

“…Alternatively, the initial many-body state can be decomposed into a sum of orthogonal terms with well-defined degrees of distinguishability, such that any two particles will either perfectly interfere or not at all [5,[41][42][43][44]. Recently, an approach based on the density-matrix formalism was proposed [18,45], on which our calculations further below are based.…”

“…[45], however, these methods are not easily scalable, but force us to establish the transition probabilities anew for each particle number. As shown in Section II B below, the orthonormalization of the single-particle mode functions [5,[41][42][43] reliably yields the desired many-particle transition probability in a scalable way, but it comes with high computational costs, interpretational issues, and without any straightforward generalization to mixed initial singleparticle states. The complicated formulation aggravates any attempt to establish the actual computational complexity of the problem.…”

“…. , |φ n } [5, [41][42][43], which ensures that k > l ⇒ φ k |φ l = 0. In particular, if the n particles only span a D < n-dimensional Hilbert space, at most D (n−D) D!…”

“…Treatments of partially distinguishable particles formulated in the pure-state formalism [5,[37][38][39][40][41][42][43][44] are not ideally suited to answer these questions, as they suffer from computational costs and interpretational problems, exposed in Section II. The many-particle scattering probability has more manageable expressions within the recently introduced density-matrix approach [45], which naturally encompasses mixed initial states.…”