Non-thermal quantum engine in transmon qubits

The design and implementation of quantum technologies necessitates the understanding of thermodynamic processes in the quantum domain. In stark contrast to macroscopic thermodynamics, at the quantum scale processes generically operate far from equilibrium and are governed by fluctuations. Thus, experimental insight and empirical findings are indispensable in developing a comprehensive framework. To this end, we theoretically propose an experimentally realistic quantum engine that uses transmon qubits as working substance. We solve the dynamics analytically and calculate its efficiency

Dissipative dynamics of a two - level system resonantly coupled to a harmonic mode

We propose an approximation scheme to describe the dynamics of the spin-boson model when the spectral density of the environment shows a peak at a characteristic frequency $\Omega$ which can be very close (or even equal) to the spin Zeeman frequency $\Delta$. Mapping the problem onto a two-state system (TSS) coupled to a harmonic oscillator (HO) with frequency $\omega_0$ we show that the representation of displaced HO states provides an appropriate basis to truncate the Hilbert space of the TSS-HO system and therefore a better picture of the system dynamics. We derive an effective Hamiltonian for the TSS-HO system, and show it furnishes a very good approximation for the system dynamics even when its two subsystems are moderately coupled. Finally, assuming the regime of weak HO-bath coupling and low temperatures, we are able to analytically evaluate the dissipative TSS dynamics.Comment: 12 pages, 2 figures; V2: Published versio

Efficient evaluation of decoherence rates in complex Josephson circuits

A complete analysis of the decoherence properties of a Josephson junction qubit is presented. The qubit is of the flux type and consists of two large loops forming a gradiometer and one small loop, and three Josephson junctions. The contributions to relaxation (T_1) and dephasing (T_\phi) arising from two different control circuits, one coupled to the small loop and one coupled to a large loop, is computed. We use a complete, quantitative description of the inductances and capacitances of the circuit. Including two stray capacitances makes the quantum mechanical modeling of the system five dimensional. We develop a general Born-Oppenheimer approximation to reduce the effective dimensionality in the calculation to one. We explore T_1 and T_\phi along an optimal line in the space of applied fluxes; along this "S line" we see significant and rapidly varying contributions to the decoherence parameters, primarily from the circuit coupling to the large loop.Comment: 16 pages, 20 figures; v2: minor revisio

A Schmidt decomposition approach to quantum thermodynamics

The development of a self-consistent thermodynamic theory of quantum systems is of fundamental importance for modern physics. Still, despite its essential role in quantum science and technology, there is no unifying formalism for characterizing the thermodynamics within general autonomous quantum systems, and many fundamental open questions remain unanswered. Along these lines, most current efforts and approaches restrict the analysis to particular scenarios of approximative descriptions and semi-classical regimes. Here we propose a novel approach to describe the thermodynamics of arbitrary bipartite autonomous quantum systems based on the well-known Schmidt decomposition. This formalism provides a simple, exact and symmetrical framework for expressing the energetics between interacting systems. We show that this procedure allows a straightforward identification of local effective operators suitable for characterizing the physical local internal energies. We also demonstrate that these quantities naturally satisfy the usual thermodynamic notion of energy additivity.Comment: 6 page

Non-Markovian incoherent quantum dynamics of a two-state system

We present a detailed study of the non-Markovian two-state system dynamics for the regime of incoherent quantum tunneling. Using perturbation theory in the system tunneling amplitude $\Delta$, and in the limit of strong system-bath coupling, we determine the short time evolution of the reduced density matrix and thereby find a general equation of motion for the non-Markovian evolution at longer times. We relate the nonlocality in time due to the non-Markovian effects with the environment characteristic response time. In addition, we study the incoherent evolution of a system with a double-well potential, where each well consists several quantized energy levels. We determine the crossover temperature to a regime where many energy levels in the wells participate in the tunneling process, and observe that the required temperature can be much smaller than the one associated with the system plasma frequency. We also discuss experimental implications of our theoretical analysis.Comment: 10 pages, published versio