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Dissipative spin systems in non-Ohmic environments: real-time path integral Monte Carlo-simulations

Kast, Denis

Published Jan 1, 2014• 0 citations
Publisher

Abstract

In this work, I study the dynamics of spin-1/2 systems in contact with dissipative bosonic reservoirs. Investigations are motivated by recent progress in designing and controling atomic and solid state structures of growing complexity. The interplay between the bare system and the environment is of substantial importance for understanding the dynamics of such devices. Spin systems that are embedded in bosonic reservoirs are described by the famous spin-boson model and have been studied for several decades. Recent work has shown that two-level systems in contact with sub-Ohmic reservoirs are of fundamental interest in view of both theoretical considerations and their experimental relevance. This is why I focus on the dynamics of systems that couple to a sub-Ohmic environment. Additionally, impressive experimental progress in embedding quantum dots into photonic crystals encouraged me to investigate the dynamics of two-level systems coupled to surroundings with spectral gaps.

DOI
10.18725/oparu-2653

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In this work, I study the dynamics of spin-1/2 systems in contact with dissipative bosonic reservoirs. Investigations are motivated by recent progress in designing and controling atomic and solid state structures of growing complexity. The interplay between the bare system and the environment is of substantial importance for understanding the dynamics of such devices. Spin systems that are embedded in bosonic reservoirs are described by the famous spin-boson model and have been studied for several decades. Recent work has shown that two-level systems in contact with sub-Ohmic reservoirs are of fundamental interest in view of both theoretical considerations and their experimental relevance. This is why I focus on the dynamics of systems that couple to a sub-Ohmic environment. Additionally, impressive experimental progress in embedding quantum dots into photonic crystals encouraged me to investigate the dynamics of two-level systems coupled to surroundings with spectral gaps.
This thesis deals with the study of dynamical properties of out-of-equilibrium quantum systems. We introduce in particular a general class of Spin-Boson models, which describe for example light-matter interaction or dissipative phenomena. We contribute to the development of a stochastic approach to describe the spin dynamics in these models. In this context, the effect of the bosonic environment is encapsulated into additional stochastic degrees of freedom whose time-correlations are determined by spectral properties of the bosonic environment. We use this approach to study many-body phenomena such as the dissipative quantum phase transition induced by an ohmic bosonic environment. Synchronization phenomena as well as dissipative topological transitions are identified. We also progress in the study of arrays of interacting light-matter systems. These theoretical developments follow recent experimental achievements, which could ensure a quantitative study of these phenomena. This notably includes ultra-cold atoms, trapped ions and cavity and circuit electrodynamics setups. We finally investigate hybrid systems comprising electronic quantum dots coupled to electromagnetic resonators, which enable us to provide a spectroscopic analysis of many-body phenomena linked to the Kondo effect. We also introduce thermoelectric applications in these devices.
The quantum dynamics of pairs of two-level systems immersed in dissipative reservoirs with sub-Ohmic spectral distributions is studied by means of numerically exact path integral Monte Carlo methods. It is shown that this class of reservoirs, relevant for generic properties of strongly non-Markovian environments with possible realizations in solid state structures at cryogenic temperatures, supports bipartite entanglement in broad ranges of parameter space and even for broken symmetries and in the presence of thermal noise. The sensitivity of the creation of entanglement in nonequilibrium on the initial preparations of the reservoir is investigated in detail.
We study the dissipative quantum dynamics and the asymptotic behavior of a particle in a bistable potential interacting with a sub-Ohmic broadband environment. The reduced dynamics, in the intermediate to strong dissipation regime, is obtained beyond the two-level system approximation by using a real-time path integral approach. We find a crossover dynamic regime with damped intra-well oscillations and incoherent tunneling and a completely incoherent regime at strong damping. Moreover, a nonmonotonic behavior of the left/right well population difference is found as a function of the damping strength.
The dissipative quantum dynamics of a two-level system interacting with a structured reservoir consisting of a damped harmonic mode is investigated by means of the numerically exact path integral Monte Carlo method. This approach provides benchmark results in a broad range of parameter space, in particular, in those domains which are not accessible by approximate methods and alternative numerical schemes, that is, strong coupling between system and harmonic mode and from low to high temperatures. For low temperatures the numerical data are quantitatively in agreement with the noninteracting blip approximation only in the regimes of very weak and very strong coupling. It turns out that the entangled dynamics of the two-level system and the harmonic mode is relatively robust so that its signatures are observable up to relatively strong friction and high temperatures. Nonequilibrium initial preparations of the reservoir with respect to the initial state of the system give rise, for strong interactions, to a stepwise decay of the population, thus displaying coherent dynamics of the bath. The impact of an additional Ohmic bath coupled directly to the two-level system is studied as well, including the case where both reservoirs carry different temperatures.
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