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Sustaining Quantum Effects in Molecular Biology through a Multi-Layered Environment

Lester Buxton, Jim Al-Khalili, Andrea Rocco

Published Jun 14, 2020• 0 citations
Publisher

Abstract

Quantum mechanics now underpins much of physics and chemistry. In recent years, a new field has emerged: quantum biology, highlighting the fundamental problem of explaining how molecular processes within living cells exhibit quantum behaviour in such warm, wet and complex cellular environments. Making use of the so-called Caldeira-Leggett model for open quantum systems, where the quantum system of interest is linearly coupled to its external environment, modelled as a heat bath of harmonics oscillators, we study the effect of environmental noise on quantum behaviour. We present a new and novel adaptation to the Caldeira-Leggett model through the introduction of dissipation to create a more realistically modelled environment.

DOI
10.5281/zenodo.3893505

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New Journal of Physics•Nov 20, 2008•6 citations
Quantum mechanics now underpins much of physics and chemistry. In recent years, a new field has emerged: quantum biology, highlighting the fundamental problem of explaining how molecular processes within living cells exhibit quantum behaviour in such warm, wet and complex cellular environments. Making use of the so-called Caldeira-Leggett model for open quantum systems, where the quantum system of interest is linearly coupled to its external environment, modelled as a heat bath of harmonics oscillators, we study the effect of environmental noise on quantum behaviour. We present a new and novel adaptation to the Caldeira-Leggett model through the introduction of dissipation to create a more realistically modelled environment.
Open quantum systems often interact with complex, intractable quantum environments. Establishing a minimal solvable model that captures the essential effects of these environments on central quantum systems has long been of interest in physics, dating back to the origins of quantum mechanics. The Caldeira-Leggett oscillator bath model has become a prominent minimal model that effectively represents many quantum environments. However, it has been argued that this model cannot capture the main effects of spin environments on central two-level systems when the couplings between the spins and the central systems are strong. In contrast, I adopt an appropriate spectral density function for the Caldeira-Leggett model and demonstrate that it can effectively replicate the essential effects of spin environments in the regime of interest. This suggests that the class of the Caldeira-Leggett model is more universal than previously recognized.
We model a quantum system coupled to an environment of damped harmonic oscillators by following the approach of Caldeira-Leggett and adopting the Caldirola-Kanai Lagrangian for the bath oscillators. In deriving the master equation of the quantum system of interest (a particle in a general potential), we show that the potential is modified non-trivially by a new inverted harmonic oscillator term, induced by the damping of the bath oscillators. We analyze numerically the case of a particle in a double-well potential, and find that this modification changes both the rate of decoherence at short times and the well-transfer probability at longer times. We also identify a simple rescaling condition that keeps the potential fixed despite changes in the environmental damping. Here, the increase of environmental damping leads to a slowing of decoherence.
The quantum properties of a particle interacting with a dissipative environment are studied. We show the way in which different types of environments reduce quantum effects. The influence of certain environments, like that described by a Caldeira‐Leggett bath of oscillators suppress very efficiently interference processes, while the coupling to other (ohmic) environments does not modify qualitatively the main features of a free particle. Examples of physical realizations of the different environments are also given.
Quantum biology is the study of quantum effects on biochemical mechanisms and biological function. Quantum physics describes the behaviour of the nanoscale particles that make up all matter including living organisms, but it was generally believed that the ‘warm, wet and noisy environment’ in living organisms would result in decoherence making it impossible for meaningful quantum effects to occur. However, there is now a substantial body of work supporting that nature has actually adapted in such a way as to exploit quantum properties to enhance cellular functioning and is believed to have role in a diverse range of key processes in living organisms ranging from maintaining the stability of DNA to neuron function to conscious cognition; from light harvesting in photosynthesis to avian magnetic field based navigation. This review aims to summarize the various mechanisms and functions in living organisms believed to utilize quantum mechanics to purposefully and effectively enhance their performance, and to explore the potential this could hold in diagnosing and treating various medical conditions.
We calculate the reduced density matrix for a system of coupled harmonic oscillators in a bosonic heat bath using the Born-Markov approximation and show that the expectation values of position and momentum evolve like classical quantities. We consider the cases where every oscillator is coupled to its own reservoir and where all oscillators are coupled to the same heat bath, pointing out the differences between these two models. In particular, for systems coupled to a common reservoir, we present an uncommon dissipation mechanism, which disappears, when the dynamics of the system are gouverned by the low frequency modes of the environment (Caldeira-Leggett limit). We also address the interesting phenomenon of reservoir-induced interactions.
Quantum dissipation has been the object of study within the physics and chemistry communities for many years. Despite this, the field is in constant evolution, largely due to the fact that novel systems where the understanding of dissipation and dephasing processes is of crucial importance have become experimentally accessible in recent years. Among the ongoing research themes, we mention the defeat of decoherence in solid state-based quantum bits (qubits) (e.g. superconducting qubits or quantum dot based qubits), or dissipation due to non-equilibrium Fermi reservoirs, as is the case for quantum transport through meso- and nanoscale structures. A close inspection of dissipation in such systems reveals that one has to deal with 'unconventional' environments, where common assumptions of, for example, linearity of the bath and/or equilibrium reservoir have to be abandoned. Even for linear baths at equilibrium it might occur that the bath presents some internal structure, due, for example, to the presence of localized bath modes. A large part of this focus issue is devoted to topics related to the rapidly developing fields of quantum computation and information with solid state nanodevices. In these implementations, single and two-qubit gates as well as quantum information transmission takes place in the presence of broadband noise that is typically non-Markovian and nonlinear. On both the experimental and theory side, understanding and defeating such noise sources has become a crucial step towards the implementation of efficient nanodevices. On a more fundamental level, electron and spin transport through quantum dot nanostructures may suffer from 'unconventional' dissipation mechanisms such as the simultaneous presence of spin relaxation and fermionic dissipation, or may represent themselves out of equilibrium baths for nearby mesoscopic systems. Finally, although not expected from the outset, the present collection of articles has revealed that different 'unconventional' questions were still open on the standard harmonic oscillator and spin baths. This includes both fundamental issues, such as the possibility of estimating the specific heat for a free particle in the presence of dissipation, and the development of methods suitable to dealing with long range correlations at zero temperature and with quantum chaotic environments. We believe that the present focus issue on Quantum Dissipation in Unconventional Environments , although certainly not exhaustive, provides an important open-access resource that presents the latest state of the art of research in this field along its different lines. Focus on Quantum Dissipation in Unconventional Environments Contents Coherent control of an effective two-level system in a non-Markovian biomolecular environment J Eckel, J H Reina and M Thorwart Charge transfer dynamics in driven molecular ratchets: quantum Monte Carlo results and rate models L Mühlbacher and J Ankerhold Decoherence in qubits due to low-frequency noise J Bergli, Y M Galperin and B L Altshuler Dephasing by electron–electron interactions in a ballistic Mach–Zehnder interferometer Clemens Neuenhahn and Florian Marquardt Quantum frustration of dissipation by a spin bath D D Bhaktavatsala Rao, Heiner Kohler and Fernando Sols A random matrix theory of decoherence T Gorin, C Pineda, H Kohler and T H Seligman Dissipative dynamics of a biased qubit coupled to a harmonic oscillator: analytical results beyond the rotating wave approximation Johannes Hausinger and Milena Grifoni Dissipative dynamics of a two-level system resonantly coupled to a harmonic mode Frederico Brito and Amir O Caldeira Spin correlations in spin blockade Rafael Sánchez, Sigmund Kohler and Gloria Platero Landau–Zener tunnelling in dissipative circuit QED David Zueco, Peter Hänggi and Sigmund Kohler Quantum oscillations in the spin-boson model: reduced visibility from non-Markovian effects and initial entanglement F K Wilhelm Dynamics of dissipative coupled spins: decoherence, relaxation and effects of a spin-boson bath P Nägele, G Campagnano and U Weiss Spin chain model for correlated quantum channels Davide Rossini, Vittorio Giovannetti and Simone Montangero Finite quantum dissipation: the challenge of obtaining specific heat Peter Hänggi, Gert-Ludwig Ingold and Peter Talkner Dynamics of large anisotropic spin in a sub-ohmic dissipative environment close to a quantum-phase transition Frithjof B Anders Effects of low-frequency noise cross-correlations in coupled superconducting qubits A D'Arrigo, A Mastellone, E Paladino and G Falci From coherent motion to localization: dynamics of the spin-boson model at zero temperature Haobin Wang and Michael Thoss Phonon distributions of a single-bath mode coupled to a quantum dot F Cavaliere, G Piovano, E Paladino and M Sassetti