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arXiv:1710.08876 · Physical Review Letters

Signatures of Indistinguishability in Bosonic Many-Body Dynamics

Tobias Brünner, Gabriel Dufour, Alberto Rodríguez, Andreas Buchleitner

Published May 22, 2018• 22 citations
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Abstract

The dynamics of bosons in generic multimode systems, such as Bose-Hubbard models, are 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 noninteracting and interacting evolution of observables. In particular, we find an unambiguous relationship between our measure and the variance of single-particle observables in the noninteracting limit. A nonvanishing 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.

DOI
10.1103/physrevlett.120.210401

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Abstract 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 show that kkk-point correlation measurements on output of a non-interacting, multimode, random unitary allow to quantify the kkk-particle coherence of N≥kN\geq kN≥k identical (bosonic or fermionic) particles. For separable many-particle input states, we establish an on average strictly monotonic relationship between such kkk-particle coherences, the interference contrast in the experimentally accessible counting statistics and the degree of the particles' mutual distinguishability, as controlled by their internal degrees of freedom. Non-separability on input can be unveiled by comparison of correlation measurements of different orders.
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.
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.
We predict a generic signature of quantum interference in many-body bosonic systems resulting in a coherent enhancement of the average return probability in Fock space. This enhancement is robust with respect to variations of external parameters even though it represents a dynamical manifestation of the delicate superposition principle in Fock space. It is a genuine quantum many-body effect that lies beyond the reach of any mean-field approach. Using a semiclassical approach based on interfering paths in Fock space, we calculate the magnitude of the backscattering peak and its dependence on gauge fields that break time-reversal invariance. We confirm our predictions by comparing them to exact quantum evolution probabilities in Bose-Hubbard models, and discuss their relevance in the context of many-body thermalization.