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Register a new userPower fluctuations in a finite-time quantum Carnot engine
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Stability is an important property of small thermal machines with fluctuating power output. We here consider a finite-time quantum Carnot engine based on a degenerate multilevel system and study the influence of its finite Hilbert space structure on its stability. We optimize in particular its relative work fluctuations with respect to level degeneracy and level number. We find that its optimal performance may surpass those of nondegenerate two-level engines or harmonic oscillator motors. Our results show how to realize high-performance, high-stability cyclic quantum heat engines.
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The Carnot cycle imposes a fundamental upper limit to the efficiency of a macroscopic motor operating between two thermal baths. However, this bound needs to be reinterpreted at microscopic scales, where molecular bio-motors and some artificial micro-engines operate. As described by stochastic thermodynamics, energy transfers in microscopic systems are random and thermal fluctuations induce transient decreases of entropy, allowing for possible violations of the Carnot limit. Despite its potential relevance for the development of a thermodynamics of small systems, an experimental study of microscopic Carnot engines is still lacking. Here we report on an experimental realization of a Carnot engine with a single optically trapped Brownian particle as working substance. We present an exhaustive study of the energetics of the engine and analyze the fluctuations of the finite-time efficiency, showing that the Carnot bound can be surpassed for a small number of non-equilibrium cycles. As its macroscopic counterpart, the energetics of our Carnot device exhibits basic properties that one would expect to observe in any microscopic energy transducer operating with baths at different temperatures. Our results characterize the sources of irreversibility in the engine and the statistical properties of the efficiency -an insight that could inspire novel strategies in the design of efficient nano-motors.
In finite-time quantum heat engines, some work is consumed to drive a working fluid accompanying coherence, which is called `friction. To understand the role of friction in quantum thermodynamics, we present a couple of finite-time quantum Otto cycles with two different baths: Agarwal versus Lindbladian. We solve them exactly and compare the performance of the Agarwal engine with that of the Lindbladian engine. In particular, we find remarkable and counterintuitive results that the performance of the Agarwal engine due to friction can be much higher than that in the quasistatic limit with the Otto efficiency, and the power of the Lindbladian engine can be nonzero in the short-time limit. Based on additional numerical calculations of these outcomes, we discuss possible origins of such differences between two engines and reveal them. Our results imply that even with an equilibrium bath, a nonequilibrium working fluid brings on the higher performance than what an equilibrium working fluid does.
We derive the general probability distribution function of stochastic work for quantum Otto engines in which both the isochoric and driving processes are irreversible due to finite time duration. The time-dependent power fluctuations, average power, and thermodynamic efficiency are explicitly obtained for a complete cycle operating with an analytically solvable two-level system. We show that, there is a trade-off between efficiency (or power) and power fluctuations.
We study the possibility of achieving the Carnot efficiency in a finite-power underdamped Brownian Carnot cycle. Recently, it was reported that the Carnot efficiency is achievable in a general class of finite-power Carnot cycles in the vanishing limit of the relaxation times. Thus, it may be interesting to clarify how the efficiency and power depend on the relaxation times by using a specific model. By evaluating the heat-leakage effect intrinsic in the underdamped dynamics with the instantaneous adiabatic processes, we demonstrate that the compatibility of the Carnot efficiency and finite power is achieved in the vanishing limit of the relaxation times in the small temperature-difference regime. Furthermore, we show that this result is consistent with a trade-off relation between power and efficiency by explicitly deriving the relation of our cycle in terms of the relaxation times.
How long does it take a quantum particle to return to its origin? As shown previously under repeated projective measurements aimed to detect the return, the closed cycle yields a geometrical phase which shows that the average first detected return time is quantized. For critical sampling times or when parameters of the Hamiltonian are tuned this winding number is modified. These discontinuous transitions exhibit gigantic fluctuations of the return time. While the general formalism of this problem was studied at length, the magnitude of the fluctuations, which is quantitatively essential, remains poorly characterized. Here, we derive explicit expressions for the variance of the return time, for quantum walks in finite Hilbert space. A classification scheme of the diverging variance is presented, for four different physical effects: the Zeno regime, when the overlap of an energy eigenstate and the detected state is small and when two or three phases of the problem merge. These scenarios present distinct physical effects which can be analyzed with the fluctuations of return times investigated here, leading to a topology-dependent time-energy uncertainty principle.
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