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 report on the observation of ultralong range interactions in a gas of cold Rubidium Rydberg atoms. The van-der-Waals interaction between a pair of Rydberg atoms separated as far as 100,000 Bohr radii features two important effects: Spectral broadening of the resonance lines and suppression of excitation with increasing density. The density dependence of these effects is investigated in detail for the S-and P-Rydberg states with main quantum numbers n ∼ 60 and n ∼ 80 excited by narrow-band continuous-wave laser light. The density-dependent suppression of excitation can be interpreted as the onset of an interaction-induced local blockade.PACS numbers: 32.80. Rm,32.80.Pj,34.20.Cf,03.67.Lx With the advances in laser cooling and trapping, new perspectives for the investigation of Rydberg atoms [1] have been opening. When cooled to very low temperatures, the core motion can be neglected for the timescales of excitation ("frozen Rydberg gas"). Unexpected effects have been discovered, such as the many-body diffusion of excitation [2,3], the population of high-angularmomentum states through free charges [4], or the spontaneous formation and recombination of ultracold plasmas [5,6]. Other fascinating features of cold, interacting Rydberg atoms have been proposed but not been observed so far, e.g. the creation of ultralong range molecules [7,8], whereas molecular crossover resonances have already been found experimentally [9]. One outstanding property of Rydberg atoms is their high polarizability, caused by the large distance between the outer electron and the core. This leads to strong electric field sensitivity and strong long-range dipole-dipole and vander-Waals (vdW) interactions are expected. First indications of interaction effects between Rydberg gases at high densities have been found in an atomic beam experiment [10] and, more recently, collisional evidence for ultralong range interactions in a cold Rydberg gas has been reported [11]. In a frozen gas these interactions make Rydberg atoms possible candidates for quantum information processing [12,13]. One promising approach is based on the concept of a dipole blockade [13], i.e. the inhibition of multiple Rydberg excitations in a confined volume due to interaction-induced energy shifts.In this Letter we report on experimental evidence for ultralong range interactions in a frozen Rydberg gas and we present high-resolution spectroscopic signatures of these interactions. citation from a cold gas [14]. Different to these findings, our experiment makes use of a tunable narrow-bandwidth continuous-wave (cw) laser for Rydberg excitation and thus allows for high-resolution spectroscopy of the resonance lines. By varying the density of Rydberg atoms in a controlled way, the influence of interactions on the strength and the shape of these lines is investigated in detail. Signatures of ultralong range interactions appear as spectral broadening of the excitation lines and saturation of the resonance peak height, the latter being an indication of the dipole blockade.To re...

We realize fast transport of ions in a segmented micro-structured Paul trap. The ion is shuttled over a distance of more than 10 4 times its groundstate wavefunction size during only 5 motional cycles of the trap (280 µm in 3.6 µs). Starting from a ground-state-cooled ion, we find an optimized transport such that the energy increase is as low as 0.10±0.01 motional quanta. In addition, we demonstrate that quantum information stored in a spin-motion entangled state is preserved throughout the transport. Shuttling operations are concatenated, as a proof-of-principle for the shuttling-based architecture to scalable ion trap quantum computing. . Scalable information processing in a multiplexed ion trap can be accomplished by having fixed processing sites where logic operations are performed, and ion qubits will be moved in and out of these regions by shuttling operations. The duration of such shuttling has to be much faster than the relevant decoherence times [4]. Furthermore, it is desirable to reduce the total time consumption of all relevant operations, where shuttling will contribute a considerable amount [5], and aim for the performance of the naturally fast solid state architectures [6]. So far, ion shuttling in a multiplexed trap has been demonstrated together with additional sympathetic cooling [7], and in the adiabatic regime, where the transient displacement of the ion is smaller than the size of the its wavepacket [8,9]. Transport of neutral atoms have also been performed using magnetic [10] or optical [11] techniques.Because quantum gate operations require ions close to the motional ground state and fast transport inherently creates motional excitation, the challenge is to develop transport protocols that guarantee sufficiency small energy transfer. In this work we demonstrate shuttling operations that are highly non-adiabatic while the final state of the ion is close to the motional groundstate. We also show that quantum information stored in both the motional and the spin degree of freedom is preserved through the shuttling.During a shuttling operation, the ion motion in the harmonic trapping potential is excited when the acceleration is sufficiently strong. This motional excitation is a harmonic oscillation, characterized by a well defined phase, thus allowing it to be canceled out by proper management of the forces involved during or after the transport. We experimentally demonstrate two methods of canceling the acquired motional excitation. One method uses two shuttles, where the transport to the destination generates the same net momentum transfer as the transport back, but is applied 180 • out of phase with respect to the secular oscillation of the ion (Fig. 1b). We refer to this as the pairwise energy-neutral transport. For the second scheme, the self-neutral transport we apply a sharp counter-"kick" to the ion at the end of a single transport operation, stopping its motion (Fig. 1c). This case of single-sided transport allows even faster shuttling and can be sequentially repeated since it is ener...

We have calculated the long-range interaction potential curves of highly excited Rydberg atom pairs for the combinations Li–Li, Na–Na, K–K, Rb–Rb and Cs–Cs in a perturbative approach. The dispersion C-coefficients are determined for all symmetries of molecular states that correlate to the ns–ns, np–np and nd–nd asymptotes. Fitted parameters are given for the scaling of the C-coefficients as a function of the principal quantum number n for all homonuclear pairs of alkali metal atoms.

Traversal of a symmetry-breaking phase transition at finite rates can lead to causally separated regions with incompatible symmetries and the formation of defects at their boundaries, which has a crucial role in quantum and statistical mechanics, cosmology and condensed matter physics. This mechanism is conjectured to follow universal scaling laws prescribed by the Kibble-Zurek mechanism. Here we determine the scaling law for defect formation in a crystal of 16 laser-cooled trapped ions, which are conducive to the precise control of structural phases and the detection of defects. The experiment reveals an exponential scaling of defect formation g b , where g is the rate of traversal of the critical point and b ¼ 2.68 ± 0.06. This supports the prediction of b ¼ 8/3E2.67 for finite inhomogeneous systems. Our result demonstrates that the scaling laws also apply in the mesoscopic regime and emphasizes the potential for further tests of non-equilibrium thermodynamics with ion crystals.

Trapped, laser-cooled atoms and ions are quantum systems which can be experimentally controlled with an as yet unmatched degree of precision. Due to the control of the motion and the internal degrees of freedom, these quantum systems can be adequately described by a well known Hamiltonian. In this colloquium, we present powerful numerical tools for the optimization of the external control of the motional and internal states of trapped neutral atoms, explicitly applied to the case of trapped laser-cooled ions in a segmented ion-trap. We then delve into solving inverse problems, when optimizing trapping potentials for ions. Our presentation is complemented by a quantum mechanical treatment of the wavepacket dynamics of a trapped ion. Efficient numerical solvers for both time-independent and time-dependent problems are provided. Shaping the motional wavefunctions and optimizing a quantum gate is realized by the application of quantum optimal control techniques. The numerical methods presented can also be used to gain an intuitive understanding of quantum experiments with trapped ions by performing virtual simulated experiments on a personal computer. Code and executables are supplied as supplementary online material 1 .