We study the decoherence caused by particle interaction for a conceptually simple model, a quantum walk on a bipartite one-dimensional lattice with decay from every second site. The corresponding noninteracting (linear) system has been shown to have a topological transition described by the average displacement before decay. Here, we use this topological quantity to distinguish coherent quantum dynamics from incoherent classical dynamics caused by a breaking of the translational symmetry. Furthermore, we analyze the behavior by means of a rate equation providing a quantitative description of the incoherent nonlinear dynamics.
We study the decoherence caused by particle interaction for a conceptually simple model, a quantum walk on a bipartite one-dimensional lattice with decay from every second site. The corresponding noninteracting (linear) system has been shown to have a topological transition described by the average displacement before decay. Here, we use this topological quantity to distinguish coherent quantum dynamics from incoherent classical dynamics caused by a breaking of the translational symmetry. Furthermore, we analyze the behavior by means of a rate equation providing a quantitative description of the incoherent nonlinear dynamics.
We analyze a quantum walk on a bipartite one-dimensional lattice, in which the particle can decay whenever it visits one of the two sublattices. The corresponding non-Hermitian tight-binding problem with a complex potential for the decaying sites exhibits two different phases, distinguished by a winding number defined in terms of the Bloch eigenstates in the Brillouin zone. We find that the mean displacement of a particle initially localized on one of the nondecaying sites can be expressed in terms of the winding number, and is therefore quantized as an integer, changing from zero to one at the critical point. We show that the topological transition is relevant for a variety of experimental settings. The quantized behavior can be used to distinguish coherent from incoherent dynamics.
Decoherence is conventionally regarded as an obstacle to realizing topological quantum phases. This has motivated extensive efforts to suppress noise in candidate topological materials and devices. Here, we show that decoherence can instead induce topological phenomena. We demonstrate this in a lattice system subject to environment-induced dephasing. The noise-averaged dynamics, governed by an interacting quantum master equation, realize a topological phase characterized by a winding number and the non-Hermitian skin effect. The dynamical consequence is striking: the correlated nature of the stochastic noise yields asymmetric diffusion, whose direction is fixed by the winding number and is reversible only through a topological phase transition. This effect is induced purely by interactions, distinguishing it from previous studies of free, effectively single-particle systems. It also disappears upon postselecting measurement outcomes, confirming that it is a genuinely open-system phenomenon with no effective Hamiltonian description. Remarkably, the model remains analytically tractable. Our results establish correlated quantum noise as a route to topology in open many-body systems, beyond free-particle and non-Hermitian Hamiltonian paradigms.
Abstract Decoherence is conventionally regarded as an obstacle to realizing topological quantum phases. This has motivated extensive efforts to suppress noise in candidate topological materials and devices. Here, we show that decoherence can instead induce topological phenomena. We demonstrate this in a lattice system subject to environment-induced dephasing. The noise-averaged dynamics, governed by an interacting quantum master equation, realize a topological phase characterized by a winding number and the non-Hermitian skin effect. The dynamical consequence is striking: the correlated nature of the stochastic noise yields asymmetric diffusion, whose direction is fixed by the winding number and is reversible only through a topological phase transition. This effect is induced purely by interactions, distinguishing it from previous studies of free, effectively single-particle systems. It also disappears upon postselecting measurement outcomes, confirming that it is a genuinely open-system phenomenon with no effective Hamiltonian description. Remarkably, the model remains analytically tractable. Our results establish correlated quantum noise as a route to topology in open many-body systems, beyond free-particle and non-Hermitian Hamiltonian paradigms.
We investigate quantum dynamics of a quantum walker on a finite bipartite non-Hermitian lattice, in which the particle can leak out with certain rate whenever it visits one of the two sublattices. Quantum walker initially located on one of the non-leaky sites will finally totally disappear after a length of evolution time and the distribution of decay probability on each unit cell is obtained. In one regime, the resultant distribution shows an expected decreasing behavior as the distance from the initial site increases. However, in the other regime, we find that the resultant distribution of local decay probability is very counterintuitive, in which a relatively high population of decay probability appears on the edge unit cell which is the farthest from the starting point of the quantum walker. We then analyze the energy spectrum of the non-Hermitian lattice with pure loss, and find that the intriguing behavior of the resultant decay probability distribution is intimately related to the existence and specific property of the edge states, which are topologically protected and can be well predicted by the non-Bloch winding number. The exotic dynamics may be observed experimentally with arrays of coupled resonator optical waveguides.
In this thesis we study the propagation behavior of quantum particles which perform discrete-time quantum walks on spatial lattices.By definition, quantum walks are discrete-time evolutions such that a single time step couples only neighboring lattice sites.Additionally, we assume in this thesis that the dynamical law commutes with all translations of the spatial lattice, that is we consider translationally invariant quantum walks.The results presented in the following are separated into two parts: The first part is devoted to the study of single-particle quantum walks, and in the second part we investigate quantum walks of several particles.Single-particle quantum walks: Our aim is to study the asymptotic behavior of particles undergoing general translationally invariant quantum walks.Employing perturbation theory, we establish a direct method for computing the asymptotic distribution of the particle's position rescaled by an appropriate time-dependent factor.If the time evolution is implemented by a unitary operator commuting with all lattice translations and with empty pure point spectrum, we find linear scaling of the asymptotic position distribution.In this case, the asymptotic distribution of position divided by time is determined by the analog of the group velocity.If, on the other hand, the quantum walk is subject to decoherence, we expect that it behaves like a classical random walk.We provide explicit criteria under which this intuitive statement is true, that is, the asymptotic scaling of the particle's position distribution is that of a diffusion process.We find that the asymptotic distribution of position divided by the square root of time is a mixture of Gaussians in this case.However, we also provide examples of decoherent quantum walks which violate these criteria, and exhibit linear scaling of the asymptotic position distribution. Many-particle quantum walks:We investigate unitary quantum walks of two particles with collisional interactions.That is, the particles perform independent single-particle quantum walks if they are at distinct lattice sites, and an interaction takes place if both particles occupy the same lattice site.We prove that such quantum walks generically exhibit a molecular binding effect between the particles.More precisely, for a measurement of the particles' positions we have a bound on the probability to obtain a certain result which decays exponentially with the particles' distance.As a preparatory step for this analysis, we consider single-particle quantum walks with point defects, and provide a method to compute their eigenvalues in the spectral gap of the quantum walk without defect.We further generalize our model to arbitrary numbers of particles and study the behavior of local excitations in many-particle quantum walks.
We derive a quantum master equation which describes the dynamics of the ensemble-averaged state of homogeneous disorder models at short times, and mediates a transition from coherent superpositions into classical mixtures. While each single realization follows unitary dynamics, this decoherencelike behavior arises as a consequence of the ensemble average. The master equation manifestly reflects the translational invariance of the disorder correlations and allows us to relate the disorder-induced dynamics to a collisional decoherence process, where the disorder correlations determine the spatial decay of coherences. We apply our theory to the (one-dimensional) Anderson model.