We discuss the concept and realization of a heat bath in solid state quantum systems. We demonstrate that, unlike a true resistor, a finite one-dimensional Josephson junction array or analogously a transmission line with non-vanishing frequency spacing, commonly considered as a reservoir of a quantum circuit, does not strictly qualify as a Caldeira-Leggett type dissipative environment. We then consider a set of quantum two-level systems as a bath, which can be realized as a collection of qubits. We show that only a dense and wide distribution of energies of the two-level systems can secure long Poincare recurrence times characteristic of a proper heat bath. An alternative for this bath is a collection of harmonic oscillators, for instance, in the form of superconducting resonators.
We discuss the concept and realization of a heat bath in solid state quantum systems. We demonstrate that, unlike a true resistor, a finite one-dimensional Josephson junction array or analogously a transmission line with non-vanishing frequency spacing, commonly considered as a reservoir of a quantum circuit, does not strictly qualify as a Caldeira-Leggett type dissipative environment. We then consider a set of quantum two-level systems as a bath, which can be realized as a collection of qubits. We show that only a dense and wide distribution of energies of the two-level systems can secure long Poincare recurrence times characteristic of a proper heat bath. An alternative for this bath is a collection of harmonic oscillators, for instance, in the form of superconducting resonators.
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.
The quantum reservoirs commonly considered in open-quantum systems theory are those modeled by quantum harmonic oscillators, which are called bosonic reservoirs. Recently, quantum reservoirs modeled by two-level systems, the so-called fermionic reservoirs, have received attention due to their features. Given that the components of these reservoirs have a finite number of energy levels, unlike bosonic reservoirs, some studies are being carried out to explore the advantages of using this type of reservoir, especially in the operation of heat machines. In this paper, we carry out a case study of a quantum refrigerator operating in the presence of bosonic or fermionic thermal reservoirs, and we show that fermionic baths have advantages over bosonic ones.
Superconducting circuits provide a controllable and versatile platform for studying quantum phenomena and advancing quantum technologies. Josephson junctions and resonators are the central circuit elements, as they enable the realization of macroscopic quantum systems—such as qubits—that can be conveniently controlled, probed, and integrated with non-superconducting components. The implementation of a thermal reservoir through the integration of a dissipative element, such as a normal-metal resistor, offers an experimental platform for investigating quantum thermodynamics, heat management in circuits, on-chip thermal detectors, and the realization of quantum thermal machines. In this thesis, we integrate a mesoscopic normal metal and its associated thermometers as an on-chip bolometer within circuit quantum electrodynamics devices for thermal detection and quantum thermodynamics experiments. The on-chip bolometer is utilized as a sensitive and broadband thermal spectrometer to characterize the properties of a superconducting resonator and to investigate its dominant loss channels. We demonstrate the capability of our thermal detector to resolve the resonator modes over a wide frequency range extending above 20 GHz. When two thermal baths are connected through a qubit–resonator system, a quantum heat valve can be realized. This device has been demonstrated using both transmon and flux qubits. Photonic heat transport between the two baths is controlled by tuning the qubit energy via an applied static magnetic field. To model these experiments, we propose an approach based on electromagnetic simulation and microwave circuit theory, restricted to the linear-response regime. Despite this limitation, the method successfully captures the experimental observations and provides a practical tool for analysing and designing circuits for future experiments. A periodically driven qubit coupled to two unequal resonators, each terminated by a heat reservoir, enables the realization of a quantum Otto refrigerator. The use of a transmon qubit for this purpose is limited by its weak anharmonicity. We therefore explore alternative platforms for the experimental implementation of a quantum refrigerator based on charge and flux qubits, which exhibit strong anharmonicity. As an important step, we perform experiments on a driven flux qubit galvanically coupled to a resonator that is, in turn, weakly capacitively coupled to a heat reservoir. We observe interference patterns in the heat current arising from driving-induced coherence. In particular, resonance peaks in the heat transferred to the bath appear at driving frequencies that are integer fractions of the resonator frequency. These quantum features are governed by the relative phase accumulated by the qubit states under driving.
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
We describe a qubit linearly coupled to a heat bath, either directly or via a cavity. The bath is formed of oscillators with a distribution of energies and coupling strengths, both for qubit-oscillator and oscillator-oscillator interaction. A direct numerical solution of the Schrodinger equation for the full system including up to 106 oscillators in the bath and analytic solutions are given, verifying quantum decay in short time quadratic (Zeno), long time exponential and eventually power law relaxation regimes. The main new results of the paper deal with applications and implications in quantum thermodynamics setups. We start by providing a correspondence of the oscillator bath to a resistor in a circuit. With the presented techniques we can then shed light on two topical questions of open quantum systems. First, splitting a quantum to uncoupled baths is presented as an opportunity for detection of low energy photons. Second, we address quantitatively the question of separation between a quantum system and its classical environment.