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Quantum transport enhancement by time-reversal symmetry breaking

Zoltán Zimborás, Mauro Faccin, Kadar, Z, James Daniel Whitfield, Lanyon, BP, Biamonte, J

Published Jan 1, 2012• 27 citations
OpenAlex

Abstract

Quantum mechanics still provides new unexpected effects when considering the transport of energy and information. Models of continuous time quantum walks, which implicitly use time-reversal symmetric Hamiltonians, have been intensely used to investigate the effectiveness of transport. Here we show how breaking time-reversal symmetry of the unitary dynamics in this model can enable directional control, enhancement, and suppression of quantum transport. Examples ranging from exciton transport to complex networks are presented. This opens new prospects for more efficient methods to transport energy and information.

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arXiv:1104.0596•International Journal of Quantum Information•Dec 1, 2010•1 citation
Quantum mechanics still provides new unexpected effects when considering the transport of energy and information. Models of continuous time quantum walks, which implicitly use time-reversal symmetric Hamiltonians, have been intensely used to investigate the effectiveness of transport. Here we show how breaking time-reversal symmetry of the unitary dynamics in this model can enable directional control, enhancement, and suppression of quantum transport. Examples ranging from exciton transport to complex networks are presented. This opens new prospects for more efficient methods to transport energy and information.
Quantum mechanics still provides new unexpected effects when considering the transport of energy and information. Models of continuous time quantum walks, which implicitly use time-reversal symmetric Hamiltonians, have been intensely used to investigate the effectiveness of transport. Here we show how breaking time-reversal symmetry of the unitary dynamics in this model can enable directional control, enhancement, and suppression of quantum transport. Examples ranging from exciton transport to complex networks are presented. This opens new prospects for more efficient methods to transport energy and information.
Given its importance to many other areas of physics, from condensed-matter physics to thermodynamics, time-reversal symmetry has had relatively little influence on quantum information science. Here we develop a network-based picture of time-reversal theory, classifying Hamiltonians and quantum circuits as time symmetric or not in terms of the elements and geometries of their underlying networks. Many of the typical circuits of quantum information science are found to exhibit time asymmetry. Moreover, we show that time asymmetry in circuits can be controlled using local gates only and can simulate time asymmetry in Hamiltonian evolution. We experimentally implement a fundamental example in which controlled time-reversal asymmetry in a palindromic quantum circuit leads to near-perfect transport. Our results pave the way for using time-symmetry breaking to control coherent transport and imply that time asymmetry represents an omnipresent yet poorly understood effect in quantum information science.
Abstract Understanding which physical processes are symmetric with respect to time inversion is a ubiquitous problem in physics. In quantum physics, effective gauge fields allow emulation of matter under strong magnetic fields, realizing the Harper–Hofstadter, the Haldane models, demonstrating one-way waveguides and topologically protected edge states. Central to these discoveries is the chirality induced by time-symmetry breaking. In quantum walk algorithms, recent work has discovered implications time-reversal symmetry breaking has on the transport of quantum states which has enabled a host of new experimental implementations. We provide a full topological classification of Hamiltonian operators that do not exhibit symmetry under time-reversal with respect to the induced transition probabilities between elements in a preferred site-basis, i.e. the nodes of the graph on which the walk takes place. We prove that a quantum process is necessarily time-symmetric for any choice of time-independent Hamiltonian precisely when the underlying support graph is bipartite or no Aharonov–Bohm phases are present in the gauge field. We further prove that certain bipartite graphs exhibit transition probability suppression, but not broken time-reversal symmetry. Furthermore, our development of a general framework characterizes gauge potentials on combinatorial graphs. These results and techniques fill an important missing gap in understanding the role this omnipresent effect has in quantum information and computation.
The formalism of continuous-time quantum walks on graphs has been widely used in the study of quantum transport of energy and information, as well as in the development of quantum algorithms. In experimental settings, however, there is limited control over the coupling coefficients between the different nodes of the graph (which are usually considered to be real valued), thereby restricting the types of quantum walks that can be implemented. In this paper, we apply the idea of Floquet engineering in the context of continuous-time quantum walks, i.e., we define periodically driven Hamiltonians which can be used to simulate the dynamics of certain target continuous-time quantum walks. We focus on two main applications: (i) simulating quantum walks that break time-reversal symmetry due to complex coupling coefficients and (ii) increasing the connectivity of the graph by simulating the presence of next-nearest-neighbor couplings. Our paper provides explicit simulation protocols that may be used for directing quantum transport, engineering the dispersion relation of one-dimensional quantum walks, or investigating quantum dynamics in highly connected structures.
The reduction of spatial symmetry can have qualitative effects for a given quantum system, such as splitting of energy levels that are degenerate in the unperturbed case. Can the breaking of temporal symmetry have a similar effect? Using a nonlinear quantum mechanical model to describe the effective interaction of simple, exactly solvable quantum systems with some dissipative environment, the time-symmetry-breaking effect of this interaction on the ground-state energy of these systems can be studied analytically. Also, in the case of dynamical properties such as tunnelling currents, the breaking of time-reversal symmetry can have quite unexpected effects. In general, a dissipative environment is assumed to inhibit the motion of a dynamical system, e.g., by reducing the frequency and amplitude of a harmonic oscillator. Our study shows, however, that under certain resonance-like conditions, the interaction with the environment can also create currents that are not present in the unperturbed system. These results follow directly from the analytical solutions of our model.
We study the classical and quantum transport processes on some finite networks and model them by continuous-time random walks (CTRW) and continuous-time quantum walks (CTQW), respectively. We calculate the classical and quantum transition probabilities between two nodes of the network. We numerically show that there is a high probability to find the walker at the initial node for CTQWs on the underlying networks due to the interference phenomenon, even for long times. To get global information (independent of the starting node) about the transport efficiency, we average the return probability over all nodes of the network. We apply the decay rate and the asymptotic value of the average of the return probability to evaluate the transport efficiency. Our numerical results prove that the existence of the symmetry in the underlying networks makes quantum transport less efficient than the classical one. In addition, we find that the increasing of the symmetry of these networks decreases the efficiency of quantum transport on them.