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Environmental effects on dynamics and topological features of quantum systems.

Loris Maria Cangemi

Published Mar 13, 2020• 0 citations
OpenAlex

Abstract

Theoretical models of quantum systems in the presence of their environment find many applications, ranging from condensed matter physics to quantum information science and quantum thermodynamics. In the field of macroscopic quantum systems, the Caldeira-Leggett model has been employed to study the effects of thermal baths on the coherence properties of superconducting qubits. However, if the quantum system of interest consists of many electrons in a solid, the role of the environment can be played by a quantum field of lattice vibrations, i.e. phonons, modeled by means of noninteracting bosons . In this work, we studied widely known models of quantum systems linearly coupled to their bosonic environment, ranging from simple driven two-level systems, i.e. qubits, to many electrons systems. Our approach has been focused on interesting model parameter ranges where well-established weak-coupling approximations fail in describing the physics involved. Indeed, these regimes are interesting and accessible to experiments. In the case of a driven qubit in contact with its environment, strong coupling effects in system-bath interactions, decoherence and crossover to totally incoherent tunneling dynamics have been studied. In addition, by considering prototypical models of fermionic systems strongly coupled to phonons on a lattice, we studied how topological features can be dramatically modified in the presence of electron-phonon interaction.

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Theoretical models of quantum systems in the presence of their environment find many applications, ranging from condensed matter physics to quantum information science and quantum thermodynamics. In the field of macroscopic quantum systems, the Caldeira-Leggett model has been employed to study the effects of thermal baths on the coherence properties of superconducting qubits. However, if the quantum system of interest consists of many electrons in a solid, the role of the environment can be played by a quantum field of lattice vibrations, i.e. phonons, modeled by means of noninteracting bosons .
In this work, we studied widely known models of quantum systems linearly coupled to their bosonic environment, ranging from simple driven two-level systems, i.e. qubits, to many electrons systems.
Our approach has been focused on interesting model parameter ranges where well-established weak-coupling approximations fail in describing the physics involved. Indeed, these regimes are interesting and accessible to experiments. In the case of a driven qubit in contact with its environment, strong coupling effects in system-bath interactions, decoherence and crossover to totally incoherent tunneling dynamics have been studied. In addition, by considering prototypical models of fermionic systems strongly coupled to phonons on a lattice, we studied how topological features can be dramatically modified in the presence of electron-phonon interaction.
We examine the effect of multilevels on decoherence and dephasing properties of a quantum system consisting of a non-ideal two level subspace, identified as the qubit and a finite set of higher energy levels above this qubit subspace. The whole system is under interaction with an environmental bath through a Caldeira-Leggett type coupling. The model interaction we use can generate nonnegligible couplings between the qubit states and the higher levels upto N∼10N\sim 10N∼10. In contrast to the pure two-level system, in a multilevel system the quantum information may leak out of the qubit subspace through nonresonant as well as resonant excitations induced by the environment. The decoherence properties of the qubit subspace is examined numerically using the master equation formalism of the system's reduced density matrix. We numerically examine the relaxation and dephasing times as the environmental frequency spectrum, the environmental temperature, and the multilevel system parameters are varied. We observe the influence of all energy scales in the noise spectrum on the short time dynamics implying the dominance of nonresonant transitions at short times. The relaxation and dephasing times calculated, strongly depend on NNN for 4<N<104< N<104<N<10 and saturate for $10
The quantum dynamics of mesoscopic or macroscopic systems is always complicated by their coupling to many `environmental' modes. At low T these environmental effects are dominated by localized modes, such as nuclear and paramagnetic spins, and defects (which also dominate the entropy and specific heat). This environment, at low energies, maps onto a `spin bath' model. This contrasts with `oscillator bath' models (originated by Feynman and Vernon) which describe delocalized environmental modes such as electrons, phonons, photons, magnons, etc. The couplings to N spin bath modes are independent of N (rather than the ~O(1/( N ) 1/2 ) dependence typical of oscillator baths), and often strong. One cannot in general map a spin bath to an oscillator bath (or vice versa); they constitute distinct `universality classes' of quantum environment. We show how the mapping to spin bath models is made, and then discuss several examples in detail, including moving particles, magnetic solitons, nanomagnets, and SQUIDs, coupled to nuclear and paramagnetic spin environments. We then focus on the `central spin' model, which couples a central two-level system to a background spin bath. It is the spin bath analogue of the famous `spin-boson' oscillator model, and describes, e.g., the tunnelling dynamics of nanoscopic and mesoscopic magnets and superconductors. We show how to average over (or `integrate out') spin bath modes, using an operator instanton technique, to find the central spin dynamics. The formal manouevres involve four separate averages - each average corresponds physically to a different `decoherence' mechanism acting on the central spin dynamics. Each environmental spin has its own topological `spin phase', which by interacting with the phase of the central system, decoheres it - this can happen even without dissipation. We give analytic results for the central spin correlation functions, under various conditions. We then describe the application of this theory to magnetic and superconducting systems. Particular attention is given to recent work on tunnelling magnetic macromolecules, where the role of the nuclear spin bath in controlling the tunnelling is very clear; we also discuss other magnetic systems in the quantum regime, and the influence of nuclear and paramagnetic spins on flux dynamics in SQUIDs. Finally, we discuss decoherence mechanisms and coherence experiments in superconductors and magnets. We show that a spin bath environment causes decoherence even in the T 0 limit. Control of this decoherence will be essential in the effort to construct `qubits' for quantum computers.
We examine the effect of multilevels on decoherence and dephasing properties of a quantum system consisting of a nonideal two level subspace, identified as the qubit, and a finite set of higher energy levels above this qubit subspace. The whole system is under interaction with an environmental bath through a Caldeira-Leggett type coupling. The model that we use is an rf-SQUID under macroscopic quantum coherence and coupled inductively to a flux noise characterized by an environmental spectrum. The model interaction can generate dipole couplings which can be appreciable between the qubit and the high levels. The decoherence properties of the qubit subspace is examined numerically using the master equation formalism of the system's reduced density matrix. We calculate the relaxation and dephasing times as the spectral parameters of the environment are varied. We observe that, these calculated time scales receive contribution from all available frequencies in the noise spectrum (even well above the system's resonant frequency scales) stressing the dominant role played by the nonresonant transitions. The relaxation and dephasing and the leakage times thus calculated, strongly depend on the appreciably interacting levels determined by the strength of the dipole coupling. Under the influence of these nonresonant and multilevel effects, the validity of the two level approximation is dictated not by the low temperature as conveniently believed, but by these multilevel dipole couplings as well as the availability of the environmental modes.
We examine the effect of multilevels on decoherence and dephasing properties of a quantum system consisting of a non-ideal two level subspace, identified as the qubit and a finite set of higher energy levels above this qubit subspace. The whole system is under interaction with an environmental bath through a Caldeira-Leggett type coupling. The model that we use is an rf-SQUID under macroscopic quantum coherence and coupled inductively to a flux noise characterized by an environmental spectrum. The model interaction can generate dipole couplings which can be appreciable for a number of high levels. The decoherence properties of the qubit subspace is examined numerically using the master equation formalism of the system’s reduced density matrix. We numerically examine the relaxation and dephasing times as the environmental frequency spectrum, and the multilevel system parameters are varied at zero temperature. We observe that, these time scales receive contribution from all available energies in the noise spectrum (even well above the system’s energy scales) stressing the dominant role played by the non-resonant (virtual) transitions. The relaxation and dephasing times calculated, strongly depend on the number of levels within the range of levels for which appreciable couplings are produced. Under the influence of these effects, we remark that the validity of the two level approximation is restricted not by the temperature but by these dipole couplings as well as the availability of the environmental modes at low temperatures. © 2005 by World Scientific Publishing Co. Pte. Ltd.
We study the decoherence dynamics of a superconducting qubit coupled to a quantum two-level system (TLS) in addition to its weak coupling to a background environment [1]. We identify two weak-coupling regimes, which differ by the relation between qubit and TLS decoherence times, and a strong coupling regime. We find expressions for the qubit decoherence rates in the weak-coupling regimes. For a weakly coupled and strongly dissipative TLS we find that the qubit dynamics is markovian, whereas for a weakly dissipative TLS the qubit dynamics shows non-markovian behavior. In the strong-coupling regime we study the driven qubit dynamics and we analyze the differences from standard Rabi-oscillations due to the coupling to the quantum TLS [2]. In doing so we identify signatures in the qubit dynamics that can be used to characterize the TLS. We also investigate the possibility of using environmental TLSs with long coherence times for quantum information processing [3]. By using the Josephson junction as a bus and the TLSs in the environment as qubits, we demonstrate that initialization, a universal set of quantum gates, and read-out of the TLSs can be implemented, even though the TLSs themselves cannot be directly accessed.
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.