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Simulating transport through quantum networks in the presence of classical noise using cold atoms

Christopher Gill

Published Jul 1, 2017• 1 citation
OpenAlex

Abstract

In work towards the development and creation of practical quantum devices for use in quantum computing and simulation, the importance of long lived coherence is key to the advantages offered over classical systems. Isolation from environmental sources of decoherence is of integral importance to such platforms. Recent experiments of biological systems seem to indicate the existence of certain structures that utilise the decohering effects of their surrounding environments to enhance performance. In this thesis, we present a novel experimental set-up used to simulate the effect of decoherence-enhanced systems by mapping the energy level structure of laser cooled Rubidium 87 atoms interacting with electromagnetic fields to a quantum network of connected sites. Classical noise is controllably added to the states to create a tunable system to explore these effects. We present the design and implementation of the system, with results of several technical aspects, along with initial work on the effect of the applied noise on transport through the network. We present a key result that transport through the network is non-trivially enhanced by the presence of an optimum amplitude of noise, pointing to the interplay between the coherent nature of the quantum system and the decoherence provided by the noise.

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In work towards the development and creation of practical quantum devices for use in quantum computing and simulation, the importance of long lived coherence is key to the advantages offered over classical systems. Isolation from environmental sources of decoherence is of integral importance to such platforms. Recent experiments of biological systems seem to indicate the existence of certain structures that utilise the decohering effects of their surrounding environments to enhance performance. In this thesis, we present a novel experimental set-up used to simulate the effect of decoherence-enhanced systems by mapping the energy level structure of laser cooled Rubidium 87 atoms interacting with electromagnetic fields to a quantum network of connected sites. Classical noise is controllably added to the states to create a tunable system to explore these effects. We present the design and implementation of the system, with results of several technical aspects, along with initial work on the effect of the applied noise on transport through the network. We present a key result that transport through the network is non-trivially enhanced by the presence of an optimum amplitude of noise, pointing to the interplay between the coherent nature of the quantum system and the decoherence provided by the noise.
The challenge of making nano-scale quantum systems experimentally accessible is being overcome for an increasing diversity of systems by improved fabrication techniques and experimental control. Despite rapid progress, one of the main hindrances in all experiments is the difficulty of isolating the quantum system from the surrounding environment and its fluctuations. This experimental “noise” perturbs the quantum system, a process that is generally referred to as decoherence: the system slowly loses its distinguishing quantum features. In this thesis the effects of spatial correlations in the noise environment with a finite correlation length are investigated. The consequences for the experimental design of controlled quantum systems as well as the dynamics of solid state systems are presented. We utilize the Bloch-Redfield formalism, a Markovian master equation approach, which gives a close connection to the underpinning system-environment model. We show how to use this formalism to model any spatial correlation function of the noise environment. Using microscopic environmental models, several correlation functions are derived and their properties connected to the environmental parameters. Several phenomenological correlation functions are also studied and a mapping to the Lindblad master equation is presented, which provides a test of positivity for phenomenological models. For quantum transport through spin chains and networks, noise is generally detrimental. Spatial correlations however reduce the effect of dephasing noise and can reinstate the transport dynamics. The critical correlation length proves to be closely connected to the maximal packet width of one excitation in the transfer process. For dissipation noise, relaxation-free states emerge with spatial correlations. The decay of an excitation is therefore fundamentally modified into a fast decay towards an intermediate relaxation-reduced state and a subsequent decay to the ground state on a much longer time scale. In quantum metrology noise correlations have been observed in experiments with trapped ions, in which they limit the use of such experiments for metrology. Quantum advantage, i.e. a better precision scaling than the standard quantum limit has been proven impossible in the presence of uncorrelated Markovian noise only. We show that for certain optimized states the best possible quantum advantage, Heisenberg scaling, can be achieved in the presence of noise with a finite spatial decay of correlations. We furthermore identify how dephasing effects change and a topology dependence arises in strength with increasing correlation length for entangled states in a general way. Biological photosynthetic complexes have recently been found to potentially include quantum coherent dynamics, particularly in the process of transmitting an exciton from the point of creation to the reaction centre. We show how the formalism of spatially correlated decoherence adapts to this significantly different energy regime. Typical effects of decoherence in this field are presented and we show how the light-harvesting efficiency is influenced by spatial correlations in the noise. This thesis highlights the fundamental relevance of noise correlations to several fields of quantum physics and the importance of the efficient and comprehensive modelling techniques presented.
The transport of excitations governs fundamental properties of matter. Particularly rich physics emerges in the interplay between disorder and environmental noise, even in small systems such as photosynthetic biomolecules. Counterintuitively, noise can enhance coherent quantum transport, which has been proposed as a mechanism behind the high transport efficiencies observed in photosynthetic complexes. This effect has been called ``environment-assisted quantum transport''. Here, we propose a quantum simulation of the excitation transport in an open quantum network, taking advantage of the high controllability of current trapped-ion experiments. Our scheme allows for the controlled study of various different aspects of the excitation transfer, ranging from the influence of static disorder and interaction range, over the effect of Markovian and non-Markovian dephasing, to the impact of a continuous insertion of excitations. Our paper discusses experimental error sources and realistic parameters, showing that it can be implemented in state-of-the-art ion-chain experiments.
Environmental noise can enhance transport, an effect known as environmental noise-assisted quantum transport. Most theoretical studies focus on optimizing system parameters under spatially uniform system-environment coupling. Here, instead, we optimize the environmental noise itself by allowing for site-dependent dephasing. We investigate steady-state transport in one-dimensional lattices with either ramped or disordered energy landscapes, considering both short- and long-range coherent tunneling. In the absence of environmental effects, in the thermodynamic limit these systems can exhibit localization, and thus suppressed transport, arising from destructive interference. Using a Lindblad master equation framework, we implement local dephasing optimized to maximize steady-state population flux. We find that for ramp potentials, short-range tunneling favors selective dephasing on alternating sites, whereas long-range tunneling benefits from a dephasing profile that increases with distance from the injection site. In energetically disordered systems, strongly detuned sites require enhanced local dephasing under short-range tunneling to facilitate transport. In all cases, we find that site-optimized dephasing allows higher transport efficiency than uniform dephasing, and it is accompanied by increased spatial delocalization of the steady state. Our results provide microscopic insight into the interplay between coherent dynamics and environmental noise. Dephasing broadens energy levels locally, helping to overcome detuning and destructive interference. More generally, we establish spatially-structured environmental noise as a strategy for controlling both quantum transport and state coherence in open systems.
Recent advances in the spectroscopy of biomolecules have highlighted the possibility of quantum coherence playing an active role in biological energy transport. The revelation that quantum coherence can survive in the hot and wet environment of biology has generated a lively debate across both the physics and biology communities. In particular, it remains unclear to what extent non-trivial quantum effects are used in biology and what advantage, if any, they afford. We propose an analogue quantum simulator, based on currently available techniques in ultra-cold atom physics, to study a model of energy and electron transport based on the Holstein Hamiltonian. By simulating the salient aspects of a biological system in a tunable laboratory set-up, we hope to gain insight into the validity of several theoretical models of biological quantum transport in a variety of relevant parameter regimes.
Transport phenomena are fundamental in physics. They allow for information and energy to be exchanged between individual constituents of communication systems, networks or even biological entities. Environmental noise will generally hinder the efficiency of the transport process. However, and contrary to intuition, there are situations in classical systems where thermal fluctuations are actually instrumental in assisting transport phenomena. Here we show that, even at zero temperature, transport of excitations across dissipative quantum networks can be enhanced by local dephasing noise. We explain the underlying physical mechanisms behind this phenomenon and propose possible experimental demonstrations in quantum optics. Our results suggest that the presence of entanglement does not play an essential role for energy transport and may even hinder it. We argue that Nature may be routinely exploiting dephasing noise and show that the transport of excitations in simplified models of light harvesting molecules does benefit from such noise assisted processes. These results point toward the possibility for designing optimized structures for transport, for example in artificial nanostructures, assisted by noise.