Shortcuts to adiabaticity from linear response theory

A shortcut to adiabaticity is a finite-time process that produces the same final state as would result from infinitely slow driving. We show that such shortcuts can be found for weak perturbations from linear response theory. With the help of phenomenological response functions a simple expression for the excess work is found -- quantifying the nonequilibrium excitations. For two specific examples, the quantum parametric oscillator and the spin-1/2 in a time-dependent magnetic field, we show that finite-time zeros of the excess work indicate the existence of shortcuts. Finally, we propose a degenerate family of protocols, which facilitate shortcuts to adiabaticity for specific and very short driving times.Comment: 9 pages, 8 figure; published versio

Precision thermometry and the quantum speed limit

We assess precision thermometry for an arbitrary single quantum system. For a d-dimensional harmonic system we show that the gap sets a single temperature that can be optimally estimated. Furthermore, we establish a simple linear relationship between the gap and this temperature, and show that the precision exhibits a quadratic relationship. We extend our analysis to explore systems with arbitrary spectra, showing that exploiting anharmonicity and degeneracy can greatly enhance the precision of thermometry. Finally, we critically assess the dynamical features of two thermometry protocols for a two level system. By calculating the quantum speed limit we find that, despite the gap fixing a preferred temperature to probe, there is no evidence of this emerging in the dynamical features

Thermodynamic control -- an old paradigm with new applications

Tremendous research efforts have been invested in exploring and designing so-called shortcuts to adiabaticity. These are finite-time processes that produce the same final states that would result from infinitely slow driving. Most of these techniques rely on auxiliary fields and quantum control techniques, which makes them rather costly to implement. In this Perspective we outline an alternative paradigm for optimal control that has proven powerful in a wide variety of situations ranging from heat engines over chemical reactions to quantum dynamics -- thermodynamic control. Focusing on only a few, selected milestones we seek to provide a pedagogical entry point into this powerful and versatile framework.Comment: 7 pages, 1 figure; Short review paper intended as Perspective in EPL (Europhys. Lett

Holevo's bound from a general quantum fluctuation theorem

We give a novel derivation of Holevo's bound using an important result from nonequilibrium statistical physics, the fluctuation theorem. To do so we develop a general formalism of quantum fluctuation theorems for two-time measurements, which explicitly accounts for the back action of quantum measurements as well as possibly non-unitary time evolution. For a specific choice of observables this fluctuation theorem yields a measurement-dependent correction to the Holevo bound, leading to a tighter inequality. We conclude by analyzing equality conditions for the improved bound.Comment: 5 page

Single ion heat engine with maximum efficiency at maximum power

We propose an experimental scheme to realize a nano heat engine with a single ion. An Otto cycle may be implemented by confining the ion in a linear Paul trap with tapered geometry and coupling it to engineered laser reservoirs. The quantum efficiency at maximum power is analytically determined in various regimes. Moreover, Monte Carlo simulations of the engine are performed that demonstrate its feasibility and its ability to operate at maximum efficiency of 30% under realistic conditions.Comment: 5 pages, 3 figure

Shortcuts in Stochastic Systems and Control of Biophysical Processes

The biochemical reaction networks that regulate living systems are all stochastic to varying degrees. The resulting randomness affects biological outcomes at multiple scales, from the functional states of single proteins in a cell to the evolutionary trajectory of whole populations. Controlling how the distribution of these outcomes changes over time-via external interventions like time-varying concentrations of chemical species-is a complex challenge. In this work, we show how counterdiabatic (CD) driving, first developed to control quantum systems, provides a versatile tool for steering biological processes. We develop a practical graph-theoretic framework for CD driving in discrete-state continuous-time Markov networks. Though CD driving is limited to target trajectories that are instantaneous stationary states, we show how to generalize the approach to allow for nonstationary targets and local control-where only a subset of system states is targeted. The latter is particularly useful for biological implementations where there may be only a small number of available external control knobs, insufficient for global control. We derive simple graphical criteria for when local versus global control is possible. Finally, we illustrate the formalism with global control of a genetic regulatory switch and local control in chaperone-assisted protein folding. The derived control protocols in the chaperone system closely resemble natural control strategies seen in experimental measurements of heat shock response in yeast and E. coli