Performance of a quantum heat engine at strong reservoir coupling

Newman, David S.; Mintert, Florian; Nazir, Ahsan

doi:10.1103/physreve.95.032139

Cited by 172 publications

(173 citation statements)

References 62 publications

(105 reference statements)

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“…A clear decrease in performance can be seen as the coupling increases for both, heat engine and refrigerator. This is consistent with performance results obtained for the quantum Otto cycle [38] and a continuously coupled but not driven three-level heat engine [37]. We also see that, as the coupling decreases, the maximum in efficiency η for the heat engine approaches the border between the white and red region, where the power goes to zero (see figure 2).…”

Section: Performancesupporting

confidence: 90%

“…In terms of efficiency, both the refrigerator and the heat engine showed a monotonic decrease of performance as a function of the coupling strength. Similar performance results for non periodically driven systems were observed in [37,38] and higher efficiency in the weak coupling but non-Markovian regime was observed in [37]. Nonetheless, as it was the case here, these results were focused on particular models, and the general question of whether strong coupling and non-Markovian effects are (un)favorable for the performance of quantum thermal machines is still open.…”

Section: Discussionsupporting

confidence: 79%

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From quantum heat engines to laser cooling: Floquet theory beyond the Born–Markov approximation

et al. 2018

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We combine the formalisms of Floquet theory and full counting statistics with a Markovian embedding strategy to access the dynamics and thermodynamics of a periodically driven thermal machine beyond the conventional Born-Markov approximation. The working medium is a two-level system and we drive the tunneling as well as the coupling to one bath with the same period. We identify four different operating regimes of our machine which include a heat engine and a refrigerator. As the coupling strength with one bath is increased, the refrigerator regime disappears, the heat engine regime narrows and their efficiency and coefficient of performance decrease. Furthermore, our model can reproduce the setup of laser cooling of trapped ions in a specific parameter limit. [35,36], redefined system-reservoir partitions (collective coordinate (CC) mappings) [37-41], a quantum absorption refrigerator [42], quenched thermodynamic protocols [43,44] and the derivation of an exact expression for the entropy production of a finite arbitrary system in contact with one or several thermal reservoirs [45], but none of which were applied to periodically driven machines so far. Exceptions are [46] and [47]. In [46] a polaron transformation and Floquet theory were used to include arbitrary strong coupling effects but only as long as the rotating wave approximation for the system Hamiltonian and the Markovian approximation for the reservoir hold. In [47] a periodically driven three-level heat engine was studied using the numerical method of hierarchy of equations of motion, an approach that is based in a decomposition of the bath correlation function rather than an explicit representation of the bath. For this reason, access to more general, thermodynamically relevant thermal transport properties requires a tailored solution [48].However, none of the aforementioned methods was successfully applied to the combinations of problems we want to tackle: a driven system coupled to multiple heat reservoirs with a possibly strong, driven and non-Markovian coupling. To achieve this we combine three methods: a CC mapping [49,50], Floquet theory for open systems [14,21] and full counting statistics [51]. This novel and unique combination provides access to steady state thermodynamics lifting the restriction of common assumptions such as a very fast driving, Markovian and weakly coupled reservoirs, and the secular approximation. First, in the CC mapping, we identify a collective degree of freedom in the reservoir, sometimes referred to as reaction coordinate [52] that is responsible for the strong coupling and non-Markovian effects. Second, using Floquet theory, we derive a master equation for the original system plus CC and apply full counting statistics methods to obtain the change in energy of the reservoirs unambiguously. This strategy allows us to perform a consistent thermodynamic analysis of periodically driven thermal machines. Furthermore, it also allows us to accurately treat periodic time dependencies in the interaction between system and res...

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Section: Performancesupporting

confidence: 90%

Section: Discussionsupporting

confidence: 79%

From quantum heat engines to laser cooling: Floquet theory beyond the Born–Markov approximation

et al. 2018

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“…In contrast, small systems may strongly couple to their environment, in the sense that the interaction energy between the system and the bath is comparable to the frequencies of the isolated system. While quantum thermodynamical machines were traditionally analyzed under a strict weak-coupling assumption, it is now recognized that to properly characterize the performance of quantum engines, one must develop methods that are not limited in this respect [21][22][23][24][25][26][27][28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

Quantum energy exchange and refrigeration: a full-counting statistics approach

Friedman¹,

Agarwalla²,

Segal³

2018

New J. Phys.

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We formulate a full-counting statistics description to study energy exchange in multi-terminal junctions. Our approach applies to quantum systems that are coupled either additively or nonadditively (cooperatively) to multiple reservoirs. We derive a Markovian Redfield-type equation for the counting-field dependent reduced density operator. Under the secular approximation, we confirm that the cumulant generating function satisfies the heat exchange fluctuation theorem. Our treatment thus respects the second law of thermodynamics. We exemplify our formalism on a multi-terminal two-level quantum system, and apply it to realize the smallest quantum absorption refrigerator, operating through engineered reservoirs, and achievable only through a cooperative bath interaction model. of the current and subsequent suppression with increasing interaction strength, appears once the system-bath interaction energy becomes comparable to the system's natural frequencies.Physically, strong system-bath interactions are responsible for three-phonon (and more) scattering contributions to thermal transport problems, beyond the weak-coupling resonant term. Alternatively, rather than focusing on the distinction between strong and weak-coupling, one may classify system-bath interaction operators based on whether they are additive or non-additive in the different reservoirs. These two classes of models, additive and non-additive, realize distinctive energy transport characteristics and refrigeration as we show in this work.An autonomous absorption refrigerator transfers thermal energy from a cold bath to a hot bath without an input power by using thermal energy provided from a so-called work reservoir. In a recent study [41], we demonstrated that the smallest system, a qubit, is incapable of operating as a quantum absorption refrigerator (QAR) when the baths are coupled weakly-additively to the system. However, we demonstrated that by coupling the system in a non-additive manner to three heat baths, which are spectrally structured, a cooling function was achieved. Moreover, we showed that the system reached the Carnot bound when the reservoirs were characterized by a single frequency component. This study thus clearly illustrates that non-additive models can bring in a new function, which is missing in additive scenarios. On the other hand, as was pointed out in [41] and illustrated earlier on in [35,36,38], the dynamics of non-additive models can be treated with standard kinetic quantum master equations (QMEs), albeit with a non-additive, baths-cooperative dissipator.The objective of this paper is to present a rigorous, thermodynamically consistent formalism for the calculation of energy exchange (current and cumulants) in additive and non-additive interaction models, thus develop the groundwork of the qubit-QAR presented in [41]. Our formalism utilizes a full-counting statistics (FCS) approach that provides cumulants of energy exchange to all orders [26,[42][43][44][45]. In this method, rather than focusing directly on the averaged heat...

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“…One may also ask whether the interference between the reservoirs is manifested in the fluctuations of the energy and particle currents. Finally, the framework presented herein appears to be an ideal setting to explore strong-coupling effects in thermodynamics [80][81][82][83][84][85], since system-environment correlations in both equilibrium and far-fromequilibrium states may be taken into account.…”

Section: Resultsmentioning

confidence: 99%

Non-additive dissipation in open quantum networks out of equilibrium

2018

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We theoretically study a simple non-equilibrium quantum network whose dynamics can be expressed and exactly solved in terms of a time-local master equation. Specifically, we consider a pair of coupled fermionic modes, each one locally exchanging energy and particles with an independent, macroscopic thermal reservoir. We show that the generator of the asymptotic master equation is not additive, i.e. it cannot be expressed as a sum of contributions describing the action of each reservoir alone. Instead, we identify an additional interference term that generates coherences in the energy eigenbasis, associated with the current of conserved particles flowing in the steady state. Notably, non-additivity arises even for wide-band reservoirs coupled arbitrarily weakly to the system. Our results shed light on the non-trivial interplay between multiple thermal noise sources in modular open quantum systems.

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Performance of a quantum heat engine at strong reservoir coupling

Cited by 172 publications

References 62 publications

From quantum heat engines to laser cooling: Floquet theory beyond the Born–Markov approximation

From quantum heat engines to laser cooling: Floquet theory beyond the Born–Markov approximation

Quantum energy exchange and refrigeration: a full-counting statistics approach

Non-additive dissipation in open quantum networks out of equilibrium

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