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arXiv:1202.6145 · Physical Review A

Quantum correlations in continuous-time quantum walks of two indistinguishable particles

Claudia Benedetti, Fabrizio Buscemi, Paolo Bordone

Published Apr 13, 2012• 29 citations
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Abstract

We evaluate the degree of quantum correlation between two fermions (bosons) subject to continuous-time quantum walks in a one-dimensional (1D) ring lattice with periodic boundary conditions. In our approach, no particle-particle interaction is considered. We show that the interference effects due to exchange symmetry can result into the appearance of nonclassical correlations. The role played onto the appearance of quantum correlations by the quantum statistics of the particles, the boundary conditions, and the partition of the system is widely investigated. Quantum correlations have also been investigated in a model mimicking the ballistic evolution of two indistinguishable particles in a 1D continuous-space structure. Our results are consistent with recent quantum optics and electron quantum optics experiments where the showing up of two-particle nonclassical correlations has been observed even in the absence of mutual interaction between the particles.

DOI
10.1103/physreva.85.042314

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We evaluate the degree of quantum correlation between two fermions (bosons) subject to continuous-time quantum walks in a one-dimensional (1D) ring lattice with periodic boundary conditions. In our approach, no particle-particle interaction is considered. We show that the interference effects due to exchange symmetry can result into the appearance of nonclassical correlations. The role played onto the appearance of quantum correlations by the quantum statistics of the particles, the boundary conditions, and the partition of the system is widely investigated. Quantum correlations have also been investigated in a model mimicking the ballistic evolution of two indistinguishable particles in a 1D continuous-space structure. Our results are consistent with recent quantum optics and electron quantum optics experiments where the showing up of two-particle nonclassical correlations has been observed even in the absence of mutual interaction between the particles.
We investigate continuous-time quantum walks of two indistinguishable particles (bosons, fermions or hard-core bosons) in one-dimensional lattices with nearest-neighbour interactions. The two interacting particles can undergo independent- and/or co-walking dependent on both quantum statistics and interaction strength. We find that two strongly interacting particles may form a bound state and then co-walk like a single composite particle with statistics-dependent propagation speed. Such an effective single-particle picture of co-walking is analytically derived in the context of degenerate perturbation and the analytical results are well consistent with direct numerical simulation. In addition to implementing universal quantum computation and observing bound states, two-particle quantum walks offer a novel route to detecting quantum statistics. Our theoretical results can be examined in experiments of light propagations in two-dimensional waveguide arrays or spin-impurity dynamics of ultracold atoms in one-dimensional optical lattices.
We investigate continuous-time quantum walks of two indistinguishable particles [two bosons, or two fermions, or two hard-core bosons (HCBs)] in one-dimensional lattices with nearest-neighbor interactions. The results for two HCBs are consistent with the recent experimental observation of two-magnon dynamics [Fukuhara et al., Nature (London) 502, 76 (2013)]. The two interacting particles can undergo independent walking and/or co-walking depending on both quantum statistics and interaction strength. Two strongly interacting particles may form a bound state and then co-walk like a single composite particle with a statistics-dependent walk speed. Analytical solutions for the scattering and bound states, which appear in the two-particle quantum walks, are obtained by solving the eigenvalue problem in the two-particle Hilbert space. In the context of degenerate perturbation theory, an effective single-particle model for the quantum co-walking is analytically derived and the walk speed of bosons is found to be exactly three times that of fermions and HCBs. Our result paves the way for experimentally exploring quantum statistics via two-particle quantum walks.
We investigate continuous-time quantum walks of two indistinguishable anyons in one-dimensional lattices with both on-site and nearest-neighbor interactions based on the fractional Jordan-Wigner transformation. It is shown that the two-body correlations in position space are symmetric about the initial sites of two quantum walkers in the Bose limit ($\ensuremath{\chi}=0$) and Fermi limit ($\ensuremath{\chi}=1$), while in momentum space this happens only in the Bose limit. An interesting asymmetry arises in the correlation for most cases with the statistical parameter $\ensuremath{\chi}$ varying in between. It turns out that the origin of this asymmetry comes from the fractional statistics that anyons obey. On the other hand, the two-body correlations of hard-core anyons in position space show uniform behaviors from antibunching to cowalking regardless of the statistical parameter. The momentum correlations in the case of strong interaction undergo a smooth process of two stripes smoothly merging into a single one, i.e. the evolution of fermions into hard-core bosons.
A novel approach to investigate the dynamics of indistinguishable particles in non-Hermitian lattice systems is presented, allowing an efficient calculation of quantum correlations between these particles in the presence of losses. Particular attention is paid to quasi-parity-time-symmetric systems, for which we numerically analyze two-particle quantum random walks for a variety of input states. Our results show how in some scenarios coherence is lost, inducing classical random walks, while in others the characteristic signatures of bosonic and fermionic exchange symmetry prevail.
We investigate the dynamics of continuous-time two-particle quantum walks on a one-dimensional noisy lattice. Depending on the initial condition, we show how the interplay between particle indistinguishability and interaction determines distinct propagation regimes. A realistic model for the environment is considered by introducing non-Gaussian noise as time-dependent fluctuations of the tunneling amplitudes between adjacent sites. We observe that the combined effect of particle interaction and fast noise (weak coupling with the environment) provides a faster propagation compared to the noiseless case. This effect can be understood in terms of the band structure of the Hubbard model, and a detailed analysis as a function of both noise and system parameters is presented.
The time evolution of correlations for two indistinguishable free particles, in a one-dimensional lattice interacting with a quantum bath, is studied in the Born-Markov approximation. The analytical solution for the density matrix is obtained, for bosons and fermions, in the second quantization formalism. The time evolution of the negativity of indistinguishable particles is analyzed for quantum mixed states. Quantum correlations heavily depend on the selected bipartition; in return, a small difference between the statistics of the particles is noted, due to the Pauli exclusion principle. In the presence of dissipation, the negativity (a nonclassical correlation) shows a time-oscillatory behavior for a particular geometrical bipartition. The total probability of finding one particle in each subsystem is also calculated and shows consistent behavior.