We report the experimental realization of a single-atom heat engine. An ion is confined in a linear Paul trap with tapered geometry and driven thermally by coupling it alternately to hot and cold reservoirs. The output power of the engine is used to drive a harmonic oscillation. From direct measurements of the ion dynamics, we determine the thermodynamic cycles for various temperature differences of the reservoirs. We use these cycles to evaluate power P and efficiency η of the engine, obtaining up to P = 342 yJ and η = 2.8 , consistent with analytical estimations. Our results demonstrate that thermal machines can be reduced to the ultimate limit of single atoms.Heat engines have played a central role in our modern society since the industrial revolution. Converting thermal energy into mechanical work, they are ubiquitously employed to generate motion, from cars to airplanes [1]. The working fluid of a macroscopic engine typically contains of the order of 10 24 particles. In the last decade, dramatic experimental progress has lead to the miniaturization of thermal machines down to the microscale, using microelectromechanical [2], piezoresistive [3] and cold atom [4] systems, as well as single colloidal particles [5,6] and single molecules [7]. In his 1959 talk "There is plenty of room at the bottom", Richard Feynman already envisioned tiny motors working at the atomic level [8]. However, to date no such device has been built.Here we report the realization of a single-atom heat engine whose working agent is an ion, held within a modified linear Paul trap. We use laser cooling and electric field noise to engineer cold and hot reservoirs. We further employ fast thermometry methods to determine the temperature of the ion [9]. The thermodynamic cycle of the engine is established for various temperature differences of the reservoirs, from which we deduce work and heat, and thus power output and efficiency. We additionally show that the work produced by the engine can be effectively stored and used to drive an oscillator against friction. Our device demonstrates the working principles of a thermodynamic heat engine with a working agent reduced to the ultimate single particle limit, thus fulfilling Feynman's dream.Trapped ions offer an exceptional degree of preparation, control and measurement of their parameters, allowing for ground state cooling [10] and coupling to engineered reservoirs [11]. Owing to their unique properties, they have recently become invaluable tools for the investigation of quantum thermodynamics [12][13][14][15][16][17]. They additionally provide an ideal setup to operate and characterize a single particle heat engine.In our experiment, a single 40 Ca + ion is trapped in a linear Paul trap with a funnel-shaped electrode geometry, as shown in Fig. 1a [15]. The electrodes are driven symmetrically at a radio-frequency voltage of 830 V pp at 21 MHz, resulting in a tapered harmonic pseudopotential [10] of the form U = (m/2) i ω 2 i i 2 , where m is the atomic mass and i ∈ {x, y} denote the trap axes as...

We consider a quantum Otto cycle for a time-dependent harmonic oscillator coupled to a squeezed thermal reservoir. We show that the efficiency at maximum power increases with the degree of squeezing, surpassing the standard Carnot limit and approaching unity exponentially for large squeezing parameters. We further propose an experimental scheme to implement such a model system by using a single trapped ion in a linear Paul trap with special geometry. Our analytical investigations are supported by Monte Carlo simulations that demonstrate the feasibility of our proposal. For realistic trap parameters, an increase of the efficiency at maximum power of up to a factor of 4 is reached, largely exceeding the Carnot bound.

We propose an experimental scheme to realize a nanoheat 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 a maximum efficiency of 30% under realistic conditions.

We consider quantum heat engines that operate between nonequilibrium stationary reservoirs. We evaluate their maximum efficiency from the positivity of the entropy production and show that it can be expressed in terms of an effective temperature that depends on the nature of the reservoirs. We further compute the efficiency at maximum power for different kinds of engineered reservoirs and derive a nonequilibrium generalization of the Clausius statement of the second law.PACS numbers: 05.30.-d, 03.65.-w Engines are devices that convert various forms of energy into useful mechanical work and motion. In thermodynamics, two different kinds of machines can be distinguished. On the one hand, there are heat engines that operate between two reservoirs at different temperatures, such as internal combustion engines [1,2]. On the other hand, there are molecular motors that are driven from equilibrium by varying external parameters, while in contact with a single isothermal reservoir [3,4]. The latter describe biological motor proteins as well as artificial nanomachines [5,6]. An essential characteristic of any machine is its efficiency defined as the ratio of work output to energy input. Whereas for heat engines the efficiency is limited by the Carnot formula, η c = 1 − T 1 /T 2 , where T 1 and T 2 are the temperatures of the two thermal reservoirs (T 1 < T 2 ), it can reach unity for molecular motors [7][8][9][10]. Maximum efficiency usually corresponds to quasistatic conditions, and therefore to zero power. A practically more relevant quantity is thus the efficiency at maximum power which for heat engines is given by η c /2 for small temperature differences [11][12][13]. For molecular motors, the efficiency at maximum power can reach the thermodynamic limit 1 for strong driving [14,15].Heat engines are usually assumed to be in contact with two equilibrium reservoirs. In this paper, we investigate the more general case where the engine runs between stationary nonequilibrium reservoirs. In a sense, this situation interpolates between traditional heat engines and molecular motors. Indeed, the efficiency of these heat engines may be larger than the Carnot efficiency and they may operate isothermally. Our study is motivated by the recent advent of reservoir engineering techniques in quantum optical systems, such as ion traps [16,17], microwave cavities [18,19], optical lattices [20,21] and optomechanical systems [22], that enable the preparation of nonthermal environments. In addition, theoretical studies have shown in individual cases that the efficiency of heat engines coupled to nonthermal quantum coherent [23] or quantum correlated [24] reservoirs may sometimes exceed the Carnot value. The two fundamental questions that we here address are therefore: i) what is the maximum (universal) efficiency that may be reached, and ii) under what conditions is this efficiency larger than the standard Carnot limit? In the following, we consider a quantum heat engine coupled to general stationary nonthermal reservoirs. It will be con...

We consider a paradigmatic quantum harmonic Otto engine operating in finite time. We investigate its performance when shortcut-to-adiabaticity techniques are used to speed up its cycle. We compute efficiency and power by taking the energetic cost of the shortcut driving explicitly into account. We analyze in detail three different shortcut methods, counterdiabatic driving, local counterdiabatic driving and inverse engineering. We demonstrate that all three lead to a simultaneous increase of efficiency and power for fast cycles, thus outperforming traditional heat engines.