The Jarzynski equality relates the free-energy di erence between two equilibrium states to the work done on a system through far-from-equilibrium processes-a milestone that builds on the pioneering work of Clausius and Kelvin. Although experimental tests of the equality have been performed in the classical regime, the quantum Jarzynski equality has not yet been fully verified owing to experimental challenges in measuring work and work distributions in a quantum system. Here, we report an experimental test of the quantum Jarzynski equality with a single 171 Yb + ion trapped in a harmonic potential. We perform projective measurements to obtain phonon distributions of the initial thermal state. We then apply a laser-induced force to the projected energy eigenstate and find transition probabilities to final energy eigenstates after the work is done. By varying the speed with which we apply the force from the equilibrium to the far-from-equilibrium regime, we verify the quantum Jarzynski equality in an isolated system. T here is increasing interest in non-equilibrium dynamics at the microscopic scale, crossing over quantum physics, thermodynamics and information theory as the experimental control and technology at such a scale have been developing rapidly. Most of the principles in non-equilibrium processes are represented in the form of inequalities, as seen in the example of the maximum work principle, W − F ≥ 0, where the average work W is equal to the free-energy difference F only in the case of the equilibrium process. In close-to-equilibrium processes, the fluctuation-dissipation theorem is valid and connects the average dissipated energy W diss ≡ W − F and the fluctuation of the system σ 2 /2k B T . Here σ is the standard deviation of the work distribution, T is the initial temperature of the system in thermal equilibrium and k B is the Boltzmann constant. Beyond the nearequilibrium regime, no exact results were known until Jarzynski found a remarkable equality 1 that relates the free-energy difference to the exponential average of the work done on the system:The Jarzynski equality (1) is satisfied irrespective of the protocols of varying parameters of the system even when the driving is arbitrarily far from equilibrium. The relation enables us to experimentally determine F of a system by repeatedly performing work at any speed. Experimental tests of the classical Jarzynski equality and its relation to the Crooks fluctuation theorem 2 have been successfully performed in various systems 3-12 .In classical systems, work can be obtained by measuring the force and the displacement, and then integrating the force over the displacement during the driving process. In the quantum regime, however, as a result of Heisenberg's uncertainty principle, we cannot determine the position and the momentum simultaneously-thus invalidating the concepts of force and displacement. Instead of measuring these classical observables, it is necessary to carry out projective measurements over the energy eigenstates to determine the work d...
[1] Reference evapotranspiration (RET), an indicator of atmospheric evaporating capability over a hypothetical reference surface, was calculated using the PenmanMonteith method for 75 stations across the Qinghai-Tibetan Plateau between 1971 and 2004. Generally, both annual and seasonal RET decreased for most part of the plateau during the study period. Multivariate linear models were used to determine the contributions of climate factors to RET change, including air temperature, air humidity, solar radiation, and wind speed. Spatial differences in the causes of RET change were detected by K-means clustering analysis. It indicates that wind speed predominated the changes of RET almost throughout the year, especially in the north of the study region, whereas radiation was the leading factor in the southeast, especially during the summertime. Although the recent warming trend over the plateau would have increased RET, the combined effect of the reduced wind speed and shortened sunshine duration negated the effect of rising temperature and caused RET to decrease in general. The significant decrease in surface wind speed corresponded to the decreasing trends of upper-air zonal wind and the decline of pressure gradient, possibly as a result of the recent warming.
Entanglement is an important evidence that a quantum device can potentially solve problems intractable for classical computers. In this paper, we prepare connected graph states involving 8 to 16 qubits on ibmqx5, a 16-qubit superconducting quantum processor accessible via IBM cloud, using low-depth circuits. We demonstrate that the prepared state is fully entangled, i.e. the state is inseparable with respect to any fixed partition.
A system consisting of two single-mode cavities spatially separated and connected by an optical fiber and multiple two-level atoms trapped in the cavities is considered. If the atoms resonantly and collectively interact with the local cavity fields but there is no direct interaction between the atoms, we show that an ideal quantum state transfer and highly reliable quantum swap, entangling, and controlled-Z gates can be deterministically realized between the distant cavities. We find that the operation of state transfer and swap, entangling, and controlled-Z gates can be greatly speeded up as number of the atoms in the cavities increases. We also notice that the effects of spontaneous emission of atoms and photon leakage out of cavity on the quantum processes can also be greatly diminished in the multiatom case.
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