Observing fermionic statistics with photons in arbitrary processes

Abstract

Quantum mechanics defines two classes of particles-bosons and fermions-whose exchange statistics fundamentally dictate quantum dynamics. Here we develop a scheme that uses entanglement to directly observe the correlated detection statistics of any number of fermions in any physical process. This approach relies on sending each of the entangled particles through identical copies of the process and by controlling a single phase parameter in the entangled state, the correlated detection statistics can be continuously tuned between bosonic and fermionic statistics. We implement this scheme via two entangled photons shared across the polarisation modes of a single photonic chip to directly mimic the fermion, boson and intermediate behaviour of two-particles undergoing a continuous time quantum walk. The ability to simulate fermions with photons is likely to have applications for verifying boson scattering and for observing particle correlations in analogue simulation using any physical platform that can prepare the entangled state prescribed here.

Why a hole is like a beam splitter: A general diffraction theory for multimode quantum states of light

“…This fermion-like anti-bunching behavior has been more thoroughly investigated in Ref. [42]. We can see that for the iris of same size and placed at the same position at the beam axis, inputting indistinguishable photons always leads to a higher coincidence probability than distinguishable photons.…”

Suppression laws for multiparticle interference in Sylvester interferometers

“…Thus the inequality (17) holds asymptotically also considering (for fermions) only the fraction of events that were not already suppressed by the simple application of the Pauli principle. It is worth reminding that, besides manifesting naturally for true fermions and bosons, the effects of the statistics can be simulated by proper entangled states [27,28]. Thus, the laws here developed for the two kinds of particles hold true for the corresponding entangled states.…”

Increasing the Dimensionality of Quantum Walks Using Multiple Walkers

“…Recently there have been numerous experimental demonstrations of optical QWs [6][7][8][9][10][11][12][13]. Schreiber et al [7,10] demonstrated a highly scalable optical QW on a line, whereby a single walker, simulated by weak coherent light, was temporally encoded and the size of the walk was limited only by loss.…”

“…The work by Peruzzo et al [9] was a first step in experimentally achieving such complexity, and subsequently Refs. [11,15]. However the pressing question is to understand how this can be employed for QIP tasks [13,16,17].…”

“…This is particularly attractive to optical implementations, where directly implementing multi-walker interactions is difficult, requiring massive optical non-linearities or entangling gates [19]. In light of the experiments by Peruzzo et al [9] and Matthews et al [11] we also give consideration to entangled input states and discuss how they may, or may not, benefit experiments.…”