Time evolution of decay of two identical quantum particles

García–Calderón, Gastón; Mendoza-Luna, Luis Guillermo

doi:10.1103/physreva.84.032106

Cited by 34 publications

(36 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We thus obtain the estimate 31) showing that the amplitude behaves for large times as an oscillatory function modulated by a decaying power law. Averaging over the oscillations, we obtain the following power-law decay for the mean echo:…”

Section: Asymptotic Analysis In the Long-time Regimementioning

confidence: 82%

Quantum return probability of a system of N non-interacting lattice fermions

Krapivsky¹,

Luck²,

Mallick³

2018

J. Stat. Mech.

View full text Add to dashboard Cite

Abstract. We consider N non-interacting fermions performing continuous-time quantum walks on a one-dimensional lattice. The system is launched from a most compact configuration where the fermions occupy neighboring sites. We calculate exactly the quantum return probability (sometimes referred to as the Loschmidt echo) of observing the very same compact state at a later time t. Remarkably, this probability depends on the parity of the fermion number -it decays as a power of time for even N , while for odd N it exhibits periodic oscillations modulated by a decaying power law. The exponent also slightly depends on the parity of N , and is roughly twice smaller than what it would be in the continuum limit. We also consider the same problem, and obtain similar results, in the presence of an impenetrable wall at the origin constraining the particles to remain on the positive half-line. We derive closed-form expressions for the amplitudes of the power-law decay of the return probability in all cases. The key point in the derivation is the use of Mehta integrals, which are limiting cases of the Selberg integral.

show abstract

Section: Asymptotic Analysis In the Long-time Regimementioning

confidence: 82%

Quantum return probability of a system of N non-interacting lattice fermions

Krapivsky¹,

Luck²,

Mallick³

2018

J. Stat. Mech.

View full text Add to dashboard Cite

show abstract

“…An advantage of this method is that the decay width can be accurately calculated even when the width is extremely small [31,[53][54][55]. In the time-dependent framework, on the other hand, the quantum decay of a metastable state is treated as a time-evolution of a wave packet [56][57][58][59][60][61][62]. An advantage of this method is that the decay dynamics can be intuitively understood by monitoring the time-evolution of the wave packet.…”

Section: Introductionmentioning

confidence: 99%

Role of diproton correlation in two-proton-emission decay of theBe6nucleus

2014

View full text Add to dashboard Cite

We discuss a role of diproton correlation in two-proton emission from the ground state of a proton-rich nucleus, 6 Be. Assuming the three-body structure of α + p + p configuration, we develop a time-dependent approach, in which the two-proton emission is described as a time-evolution of a three-body metastable state. With this method, the dynamics of the two-proton emission can be intuitively discussed by monitoring the time-dependence of the two-particle density distribution. With a model Hamiltonian which well reproduces the experimental two-proton decay width, we show that a strongly correlated diproton emission is a dominant process in the early stage of the two-proton emission. When the diproton correlation is absent, the sequential two-proton emission competes with the diproton emission, and the decay width is underestimated. These results suggest that the two-proton emission decays provide a good opportunity to probe the diproton correlation in proton-rich nuclei beyond the proton drip-line.

show abstract

“…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.…”

mentioning

confidence: 99%

“…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].…”

mentioning

confidence: 99%

Particle Statistics Affects Quantum Decay and Fano Interference

et al. 2015

View full text Add to dashboard Cite

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...

show abstract

Time evolution of decay of two identical quantum particles

Cited by 34 publications

References 17 publications

Quantum return probability of a system of N non-interacting lattice fermions

Quantum return probability of a system of N non-interacting lattice fermions

Role of diproton correlation in two-proton-emission decay of theBe6nucleus

Particle Statistics Affects Quantum Decay and Fano Interference

Contact Info

Product

Resources

About