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arXiv:1702.01902 · Physical Review A

Quantum evolution in disordered transport

Clemens Gneiting, Franco Nori

Published Aug 28, 2017• 14 citations
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Abstract

We analyze the propagation of quantum states in the presence of weak disorder. In particular, we investigate the reliable transmittance of quantum states, as potential carriers of quantum information, through disorder-perturbed waveguides. We quantify wave-packet distortion, backscattering, and disorder-induced dephasing, which all act detrimentally on transport, and identify conditions for reliable transmission. Our analysis relies on the treatment of the nonequilibrium dynamics of ensemble-averaged quantum states in terms of quantum master equations.

DOI
10.1103/physreva.96.022135

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We analyze the propagation of quantum states in the presence of weak disorder. In particular, we investigate the reliable transmittance of quantum states, as potential carriers of quantum information, through disorder-perturbed waveguides. We quantify wave-packet distortion, backscattering, and disorder-induced dephasing, which all act detrimentally on transport, and identify conditions for reliable transmission. Our analysis relies on the treatment of the nonequilibrium dynamics of ensemble-averaged quantum states in terms of quantum master equations.
We analyze the disorder-perturbed transport of quantum states in the absence of backscattering. This comprises, for instance, the propagation of edge-mode wave packets in topological insulators, or the propagation of photons in inhomogeneous media. We quantify the disorder-induced dephasing, which we show to be bound. Moreover, we identify a gap condition to remain in the backscattering-free regime despite disorder-induced momentum broadening. Our analysis comprises the full disorder-averaged quantum state, on the level of both populations and coherences, appreciating states as potential carriers of quantum information. The well-definedness of states is guaranteed by our treatment of the nonequilibrium dynamics with Lindblad master equations.
We study the disorder-perturbed transport of two noninteracting entangled particles in the absence of backscattering. This situation is, for instance, realized along edges of topological insulators. We find profoundly different responses to disorder-induced dephasing for the center-of-mass and relative coordinates: While a mirror symmetry protects even highly delocalized relative states when resonant with the symmetry condition, delocalizations in the center of mass [e.g., two-particle (N=2) N00N states] remain fully sensitive to disorder. We demonstrate the relevance of these differences to the example of interferometric entanglement detection. Our platform-independent analysis is based on the treatment of disorder-averaged quantum systems with quantum master equations.
The active harnessing of quantum resources in engineered quantum devices poses unprecedented requirements on device control. Besides the residual interaction with the environment, causing environment-induced decoherence, uncontrolled parameters in the system itself---disorder---remain as a substantial factor limiting the precision and thus the performance of devices. These perturbations may arise, for instance, due to imperfect sample production, stray fields, or finite accuracy of control electronics. Disorder-dressed quantum evolution means a unifying framework, based on quantum master equations, to analyze how these detrimental influences cause deviations from the desired system dynamics. This description may thus contribute to unveiling and mitigating disorder effects towards robust schemes. To demonstrate the broad scope of this framework, we evaluate two distinct scenarios: a central spin immersed in an isotropic spin bath and a random mass Dirac particle. In the former scenario, we demonstrate how the disorder average reflects purity oscillations, indicating the time- and state-dependent severity of the disorder impact. In the latter scenario, we discuss disorder-induced backscattering and disorder-induced Zitterbewegung as consequences of the breakup of spin-momentum locking.
Quantum transport in disordered systems poses intriguing fundamental questions about the interplay of disorder, interactions, and decoherence, with important implications for nanoscale energy transfer and quantum information transfer. Here, we investigate the emergence of multiple transport timescales in the dissipative dynamics of a spin impurity coupled to a small, spatially disordered network of spins. Using a two-dimensional tight-binding model with dipolar interactions and local dephasing, we demonstrate that geometric heterogeneity leads to hierarchical coupling strengths and pronounced separation of dynamical timescales. By analyzing different metrics for dynamics, we identify distinct relaxation timescales associated with cluster-level equilibration and global equilibration. A minimal three-site model reveals the physical origin of the longest timescale: strong internal hybridization generates an effective detuning that suppresses transfer to other weakly coupled sites, yielding a parametrically enhanced relaxation time in the weak-dephasing regime. We corroborate this picture with nonequilibrium steady-state transport calculations and simulations of disordered spin configurations, demonstrating orders-of-magnitude slowing of relaxation when hierarchical couplings are present. Our results highlight the central role of geometry and connectivity in spin networks and open quantum systems in general, and provide experimentally relevant predictions for relaxation times in small spin baths.
Quantum coherences are paramount resources for applications, such as quantum-enhanced light-harvesting or quantum computing, which are fragile against environmental noise.We here derive generalized quantum master equations using perturbation theory in order to describe the effective time evolution of finite-size quantum systems subject to static noise on all time scales.We then analyze the time evolution of the coherences under energy broadening noise in a variety of systems characterized by both short-and long-range interactions and by strongly correlated and fully uncorrelated noise -a single qubit, a lattice model with on-site disorder and a potential ladder, and a Bose-Hubbard dimer with random interaction strength-and show that couplings can partially protect the system from the ensemble-averaging induced loss of coherence.Our work suggests that suitably tuned couplings could be employed to counteract part of the dephasing detrimental to quantum applications.Conversely, tailored noise distributions can be utilized to reach target nonequilibrium quantum states.
This work is a simple example of the quantum dynamics of a particle in a disordered system in one dimension.In particular, we illustrate numerically the phenomenon of Anderson localisation of a wave packet using a basic model constructed with small random rectangular potential barriers.Also, we study the dynamics of a quantum particle in a disordered potential formed by an harmonic oscillator perturbed by random rectangular barriers.To show the effects of disorder on the dynamics of the system, we compare the time evolution of the wave function of the unperturbed harmonic oscillator with the wave function of the disordered system.We do this by taking the scalar product between the unperturbed and perturbed wave functions at each timestep for different values of the perturbation parameters affecting the disordered wave packet.