Pushing the limits of the reaction-coordinate mapping

This is the author accepted manuscript. The final version is available from AIP Publishing via the DOI in this recordThe reaction-coordinate mapping is a useful technique to study complex quantum dissipative dynamics into structured environments. In essence, it aims to mimic the original problem by means of an 'augmented system', which includes a suitably chosen collective environmental coordinate---the 'reaction coordinate'. This composite then couples to a simpler 'residual reservoir' with short-lived correlations. If, in addition, the residual coupling is weak, a simple quantum master equation can be rigorously applied to the augmented system, and the solution of the original problem just follows from tracing out the reaction coordinate. But, what if the residual dissipation is strong? Here we consider an exactly solvable model for heat transport---a two-node linear "quantum wire" connecting two baths at different temperatures. We allow for a structured spectral density at the interface with one of the reservoirs and perform the reaction-coordinate mapping, writing a perturbative master equation for the augmented system. We find that: (a) strikingly, the stationary state of the original problem can be reproduced accurately by a weak-coupling treatment even when the residual dissipation on the augmented system is very strong; (b) the agreement holds throughout the entire dynamics under large residual dissipation in the overdamped regime; (c) and that such master equation can grossly overestimate the stationary heat current across the wire, even when its non-equilibrium steady state is captured faithfully. These observations can be crucial when using the reaction-coordinate mapping to study the largely unexplored strong-coupling regime in quantum thermodynamics.European Research Council (ERC)London Mathematical SocietyUS National Science Foundatio

A topologically protected quantum dynamo effect in a driven spin-boson model

We describe a quantum dynamo effect in a driven system coupled to a harmonic oscillator describing a cavity mode or to a collection of modes forming an Ohmic bosonic bath. When the system Hamiltonian changes in time, this induces a dynamical field in the bosonic modes having resonant frequencies with the driving velocity. This field opposes the change of the external driving field in a way reminiscent of the Faraday effect in electrodynamics, justifying the term `quantum dynamo effect'. For the specific situation of a periodically driven spin-$\frac{1}{2}$ on the Bloch sphere, we show that the work done by rolling the spin from north to south pole can efficiently be converted into a coherent displacement of the resonant bosonic modes, the effect thus corresponds to a work-to-work conversion and allows to interpret this transmitted energy into the bath as work. We study this effect, its performance and limitations in detail for a driven spin-$\frac{1}{2}$ in the presence of a radial magnetic field addressing a relation with topological systems through the formation of an effective charge in the core of the sphere. We show that the dynamo effect is directly related to the dynamically measured topology of this spin-$\frac{1}{2}$ and thus in the adiabatic limit provides a topologically protected method to convert driving work into a coherent field in the reservoir. The quantum dynamo model is realizable in mesoscopic and atomic systems.Comment: 27 pages, 11 figure

Internal components of continuous quantum thermal machines.

The dynamics of continuous quantum machines weakly coupled to thermal reservoirs is described by master equations when the bath temperatures are high enough. If, in addition, the bare frequency gaps are much larger than the thermal couplings, the steady state or limit cycle of the device coincides with the stationary solution of a set of balance equations. This solution can be analyzed by using Graph Theory. Within this framework, the balance equations are represented by a graph. We employ a circuit decomposition of this graph to calculate and, most importantly, interpret the stationary thermodynamic properties of different continuous devices. We show that each circuit can be associated with a thermodynamically consistent mechanism. This follows from the consistency of the corresponding master equations with the Laws of Thermodynamics for a proper definition of the energy currents. As a consequence, these circuits can be thought of as internal components of the corresponding machine. Thus, the overall steady state functioning of the device is the result of the contributions of its internal components and the interplay between them. We study two types of continuous devices. On one hand, we analyze ab- sorption machines including only thermal baths. We show here that not only the total number of constituents circuits affects the device performance, but also the specific structure of the graph containing these circuits. Crucially, we find that the device connectivity has a major role in the design of optimal absorption machines. On the other hand, we consider periodically driven devices with a cyclic pattern of transitions. These machines are connected to thermal baths and also to a sinusoidal laser field. We study both the strong and the weak driving limits by using Global and Local master equa- tions respectively. We compare these approaches with the Redfield master equation. A circuit decomposition can be used to describe the stationary thermodynamic quantities in both limits. Interestingly, given an arbitrary basis, the device needs coherences to operate in the weak driving limit. How- ever, an incoherent stochastic-thermodynamic model may replicate the same stationary functioning. We conclude that the steady state thermodynamic operation in all the models under consideration can be described without invoking any quantum feature. Along these lines, the graph approach may be useful for identify- ing genuinely quantum effects in other continuous machines. For example, devices with non-cyclic pattern of transitions and degenerate states

Quantum Thermal Machine as a Thermometer

We propose the use of a quantum thermal machine for low-temperature thermometry. A hot thermal reservoir coupled to the machine allows for simultaneously cooling the sample while determining its temperature without knowing the model-dependent coupling constants. In its most simple form, the proposed scheme works for all thermal machines which perform at Otto efficiency and can reach Carnot efficiency. We consider a circuit QED implementation which allows for precise thermometry down to $\sim$15 mK with realistic parameters. Based on the quantum Fisher information, this is close to the optimal achievable performance. This implementation demonstrates that our proposal is particularly promising in systems where thermalization between different components of an experimental setup cannot be guaranteed.Comment: Main text: 5 pages, 4 figures; Supplement: 5 page