Particle Statistics Affects Quantum Decay and Fano Interference

Abstract

Fano resonances and bound states with energy in the continuum are ubiquitous phenomena in different areas of physics. Observations, however, have been limited so far to single-particle processes. In this work we experimentally investigate the multi-particle case and observe Fano interference in a non-interacting two-particle Fano-Anderson model by considering propagation of two-photon states in engineered photonic lattices. We demonstrate that the quantum statistics of the particles, either bosonic or fermionic, strongly affects the decay process. Remarkably, we find that the Fano resonance, when two discrete levels are coupled to a continuum, is suppressed in the fermionic case.Decay of excited states has been a topic of great interest since the early times of quantum mechanics [1] [6][7][8], and plasmonic nanostructures [9]. Fano interference is observed when different decay channels interfere, giving rise to broadening and asymmetric deformations of natural line shapes. In general, the destructive interference between different decay channels is associated to the formation of bound states in the continuum [2,10], which inhibit the complete decay of the excited state. The interplay between bound states in the continuum and Fano/Feshbach resonances has been highlighted in several works (see, for instance, [11][12][13][14]). Experimental studies on Fano resonances [4], quantum decay processes [15,16] and bound states in the continuum [17][18][19][20][21] have focused up to now on single-particle dynamics. Interestingly, recent works [22][23][24][25][26][27][28] showed that particle statistics and contact interactions can deeply modify the decay dynamics. Fermions and bosons may show very different decay behaviour, in particular in many cases fermions tend to decay faster [22][23][24]. However, no experimental observation of this phenomenon has been reported yet.In this work we investigate, experimentally, the decay process of two non-interacting particles to a common continuum, by probing an engineered photonic lattice with two-photon states. The lattice, consisting of a threedimensional array of coupled optical waveguides, is fabricated in a glass substrate by femtosecond laser micromachining [29][30][31]. While the bosonic dynamics is naturally observed for identically polarised photons, an antisymmetric polarisation-entangled state of the two photons is used to simulate the fermionic behavior [32][33][34][35][36].We focus on systems described by the Fano-Anderson [2,4] or Friedrichs-Lee Hamiltonian [37,38], which is a paradigmatic model to study quantum mechanical decay, Fano interference phenomena and bound states in the continuum [10,13,14,27]. The simplest case is provided by two discrete states coupled to a common tightbinding continuum of modes, i.e. a quantum wire [27]. In detail, we consider a system composed of two sites |1 and |2 , respectively with energy 1 and 2 , side-coupled with hopping rates κ 1 and κ 2 , to a common semi-infinite chain of coupled sites (a quantum wire), each with energy = 0 (s...

Characteristic dynamics near two coalescing eigenvalues incorporating continuum threshold effects

“…[92], the models studied in this work may not be so distant from what can be achieved in the laboratory. Along similar lines, one could also consider a many-body extension of the present work [71,72,93].…”

Bound states in the continuum

“…It has also been proposed that the light intensity may act as another tuning parameter in nonlinear materials, which may enable robust BICs 248 , tunable channel dropping 249 , light storage and release 250,251 , and frequency comb generation 252 . Finally, it was shown that particle statistics can be used to modify some properties of BICs 253 .…”

Second-order fermionic interference with independent photons

“…If photons can be employed to study the second-order interference of fermions, it will become easier to understand the second-order coherence of fermions. Entangled photon pairs have been employed to simulate the second-order interference of fermions [24][25][26][27][28][29][30]. Special attention is needed to employ entangled photon pairs to simulate the interference of fermions since only antisymmetrical state is possible [24].…”