The coupling of a qubit to a macroscopic reservoir plays a fundamental role in understanding the complex transition from the quantum to the classical world. Considering a harmonic environment, we use both intuitive arguments and numerical many-body quantum tomography to study the structure of the complete wavefunction arising in the strong-coupling regime, reached for intense qubit-environment interaction. The resulting strongly-correlated many-body ground state is built from quantum superpositions of adiabatic (polaron-like) and non-adiabatic (antipolaron-like) contributions from the bath of quantum oscillators. The emerging Schrödinger cat environmental wavefunctions can be described quantitatively via simple variational coherent states. In contrast to qubit-environment entanglement, we show that non-classicality and entanglement among the modes in the reservoir are crucial for the stabilization of qubit superpositions in regimes where standard theories predict an effectively classical spin.
The coupling of a qubit to a macroscopic reservoir plays a fundamental role in understanding the complex transition from the quantum to the classical world. Considering a harmonic environment, we use both intuitive arguments and numerical many-body quantum tomography to study the structure of the complete wavefunction arising in the strong-coupling regime, reached for intense qubit-environment interaction. The resulting strongly-correlated many-body ground state is built from quantum superpositions of adiabatic (polaron-like) and non-adiabatic (antipolaron-like) contributions from the bath of quantum oscillators. The emerging Schrödinger cat environmental wavefunctions can be described quantitatively via simple variational coherent states. In contrast to qubit-environment entanglement, we show that non-classicality and entanglement among the modes in the reservoir are crucial for the stabilization of qubit superpositions in regimes where standard theories predict an effectively classical spin.
"As a rule, the coupling of a quantum system to an uncontrollable thermal reservoir (a “bath”) gives rise to the system’s decoherence, i.e., the destruction of its unitary coherent evolution [1]. Not less common is the rule that the more complex the quantum system, the more detrimental are the bath effects [2]. Here we point out that the coupling of a complex quantum system to a bath may actually induce advantageous coherent dynamics. Namely, an exact solution for a quantum many-body system characterized by large angular momentum (or spin) that is coupled to a thermal bath reveals a hitherto unexplored general effect: bath-induced effectively nonlinear evolution. This evolution can drive the large-spin system into a macroscopic quantum-superposition (“Schroedinger-cat”) state [3, 4]. Such counter-intuitive bath-induced effects should be observable in various setups on long (Markovian) time scales. They change our perspective of non-classicality in open many-body quantum systems. Namely, the bath may cause rather than impede the formation of distinctly non-classical Schroedinger-cat states, despite their fragility in the presence of a bath [2, 5]."
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
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.
An understanding of strongly coupled open quantum systems is crucial for the realisation of many of today’s emerging quantum technologies. However, actually simulating a quantum system that strongly interacts, or couples, with its environment is no easy task. This thesis tackles a number of topics in the field of strongly coupled open quantum systems. Given the computational challenges of solving the full open system dynamics, we first discuss how and why a quasiclassical stochastic approach can be used to simulate the dynamics of a quantum harmonic oscillator that is strongly coupled to its environment. We build upon the established analytical agreement by implementing the quasiclassical stochastic case numerically in the SpiDy.jl Julia package. Motivated by the applications to magnetic modelling, we then solve the full open quantum systems model for a single spin coupled arbitrarily strongly to multiple heat baths. In doing so, we find that the presence of multiple baths can actually increase the system-environment entanglement in the steady state. We also compare this to a fully classical approach and find that, for isotropic environmental coupling, the environment-induced effects in the equilibrium state only appear quantum mechanically. Finally, we couple these two topics together by considering the quasiclassical stochastic simulation of a single quantum spin, helping to understand the regimes of validity beyond the linear harmonic oscillator. This is with the larger aim to eventually be able to encode quantum effects into more realistic systems, such as those that describe magnetic materials.
The focus of the study is the free quantum evolution of Duffing oscillators which are nonlinearly coupled to bosonic environments. The work evolves from a particular system of an undamped, nonlinear graphene resonator mode to a more generalized framework of oscillator modes interacting with two different configurations of bosonic environments. In a model with no dissipation, the nonlinear Duffing oscillator allows an initial coherent state to evolve into a macroscopic superposition state, a Schrödinger Cat state. By further subjecting a Duffing mode to nonlinear damping, the parity conservation due to the two-quanta system-bath exchange, brings the system to a nonclassical steady state - an equilibrium state very much different from the ground state. The quantum features of this state are analysed for temperatures above zero and in a more realistic scenario where the interplay of linear and nonlinear decay is taken into account. The scope of the study is then extended to bipartite systems of nonlinear interacting oscillators, each nonlinearly coupled to a bosonic environment. The generation of entanglement in initially separable states and entanglement's asymptotic behaviour are investigated. One of the outcomes is the Duffing nonlinearity not affecting the entanglement asymptote. Therefore, finally a bipartite system of harmonic oscillators, with nonlinear system-bath coupling is initiated with entangled, squeezed states, and the asymptotic behaviour is evaluated in the parameter space of temperature, squeezing and dissipation rate. This is done for common and individual reservoir configurations, and either zero or non-zero inter-mode coupling.
Entanglement and decoherence arguably define the central issues of concern in present day quantum information theory. Decoherence occurs when a system interacts with its environment in an irreversible way; this prevents the quantum superposition of the system + environment's wavefunction from interfering with each other. A better understanding of environment-induced destruction of coherent superposition states is needed, as well as a clear description of the degree of entanglement between the quantum system and its environment. We quantitatively establish a correspondence between entanglement, decoherence, and spin dynamics for a two-state system coupled to a bath of harmonic oscillators, resulting in the celebrated spin-boson model. Applications to solid-state and cold atomic systems are also discussed.