Refrigeration beyond weak internal coupling

Seah, Stella; Nimmrichter, Stefan; Scarani, Valerio

doi:10.1103/physreve.98.012131

Cited by 52 publications

(69 citation statements)

References 47 publications

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“…While the first distinction arises from the type of coupling considered in the system-reservoir interaction the second distinguishes between the different approximations leading to a final form of the master equation which depends on the magnitude of the inter-system coupling. For example, the Lindbladians obtained in equation (4) with the operators in equation (5) are fundamentally different from the ones obtained for the case of separate reservoirs under the global approach [31,35].…”

Section: Master Equation In the Local Approachmentioning

confidence: 75%

“…Henceforth, another figure of merit to characterize the performance of the refrigerator is the COP at maximum cooling power, which we denote by h * . This quantity has been extensively studied within the global approach in [31,35], and shown to be bounded by a fraction of h C only depending on the dimensionality of the cold reservoir [31,32].…”

Section: Characterization Of the Performancementioning

confidence: 99%

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Boosting the performance of small autonomous refrigerators via common environmental effects

et al. 2019

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We explore the possibility of enhancing the performance of small thermal machines by the presence of common noise sources. In particular, we study a prototypical model for an autonomous quantum refrigerator comprised by three qubits coupled to thermal reservoirs at different temperatures. Our results show that engineering the coupling to the reservoirs to act as common environments lead to relevant improvements in the performance. The enhancements arrive to almost double the cooling power of the original fridge without compromising its efficiency. The greater enhancements are obtained when the refrigerator may benefit from the presence of a decoherence-free subspace. The influence of coherent effects in the dissipation due to one-and two-spin correlated processes is also examined by comparison with an equivalent incoherent yet correlated model of dissipation.

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Section: Master Equation In the Local Approachmentioning

confidence: 75%

Section: Characterization Of the Performancementioning

confidence: 99%

Boosting the performance of small autonomous refrigerators via common environmental effects

et al. 2019

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“…The origin of these effects, as shown in [75], lies in the fact that the heat fluxes become of the same order of magnitude as the neglected nonlocal terms They thus suggest to use the GME to fix such thermodynamic anomalies. These findings generated a considerable stream of investigations on the comparison between global and LMEs [49,52,53,61,[76][77][78][79][80][81][82] as well as clever possible alternatives [83,84].Recent results indicate, however, that it is possible to construct a consistent thermodynamic framework for LMEs, resolving these seeming contradictions. First and foremost, it is important to mention that, unlike Redfield equations, LMEs are in Lindblad form and therefore generate completely positive trace preserving (CPTP) maps.…”

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confidence: 99%

Reconciliation of quantum local master equations with thermodynamics

et al. 2018

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The study of open quantum systems often relies on approximate master equations derived under the assumptions of weak coupling to the environment. However when the system is made of several interacting subsystems such a derivation is in many cases very hard. An alternative method, employed especially in the modeling of transport in mesoscopic systems, consists in using local master equations (LMEs) containing Lindblad operators acting locally only on the corresponding subsystem. It has been shown that this approach however generates inconsistencies with the laws of thermodynamics. In this paper we demonstrate that using a microscopic model of LMEs based on repeated collisions all thermodynamic inconsistencies can be resolved by correctly taking into account the breaking of global detailed balance related to the work cost of maintaining the collisions. We provide examples based on a chain of quantum harmonic oscillators whose ends are connected to thermal reservoirs at different temperatures. We prove that this system behaves precisely as a quantum heat engine or refrigerator, with properties that are fully consistent with basic thermodynamics. derivations are in general quite involved since they require knowledge of the full set of eigenvalues and eigenvectors of the system's Hamiltonian, something which quickly becomes prohibitive when the number of subsystems increases. Moreover, depending on the approximations employed, one may also arrive at equations which do not generate completely positive maps (the so-called Redfield equations [50]), or equations which contain unphysical heat currents [54]. For these reasons, microscopic derivations of master equations for systems connected to multiple environments still continues, nowadays, to be a topic of great interest.An alternative, more heuristic, approach consists in deriving a master equation for the individual subsystems, neglecting the interaction with the remaining subsystems. The resulting master equation will then contain only local jump operators describing exchanges between the environment E i and its corresponding subsystem S i . Such equations, which we shall henceforth refer to as LMEs (also frequently called boundarydriven master equations), are typically accurate when the dissipation rates are larger than the interaction between subsystems. Due to their computational simplicity, they have been extensively employed over the last two decades in the study of transport in non-equilibrium quantum systems [55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72][73].It turns out, however, that the nonlocal terms neglected in the LME may still lead to non-thermal steadystates [74] and play a significant role if the heat exchanges are small, even for weakly interacting parts. As a consequence, it has been found that LMEs may lead to apparent thermodynamic inconsistencies, as pointed out recently by Levy and Kosloff [75]. They have shown that the LME for two coupled quantum harmonic oscillators (QHO) may predict currents from a cold to a hot ther...

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“…More precisely, this assertion is due to a restrictive consideration of the global master equation as limited by a full secular approximation, which also the authors recognize as responsible for the breakdown of the master equation. In [27] the possibility for a partial secular approximation is also suggested in order to cure such deficiency, and many other papers have pointed out why the full secular approximation may not be valid in some parameters ranges of different scenarios [25,34,56,64,69,70]. In the following, we therefore analyze in detail both local and global approach and show that the partial secular approximation allows to derive a global master equation that never leads to unphysical results, given that in the limit l  0 it coincides with the local master equation.…”

Section: Local Versus Global: An In-depth Discussionmentioning

confidence: 99%

“…In the master equation, the absence of counter-rotating terms eliminates all the 'double emission' or 'double absorption' jump operators, namely s w  ( ) j z III in equation (C.2). Without these terms important effects do not arise, such as stationary entanglement [23], or are not properly described, as the refrigerator performance analyzed in [70]. (20), where with abuse of notation α=c 1 =c 2 =c.…”

Section: A2 Further Qubit-qubit Couplingsmentioning

confidence: 99%

Local versus global master equation with common and separate baths: superiority of the global approach in partial secular approximation

et al. 2019

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Open systems of coupled qubits are ubiquitous in quantum physics. Finding a suitable master equation to describe their dynamics is therefore a crucial task that must be addressed with utmost attention. In the recent past, many efforts have been made toward the possibility of employing local master equations, which compute the interaction with the environment neglecting the direct coupling between the qubits, and for this reason may be easier to solve. Here, we provide a detailed derivation of the Markovian master equation for two coupled qubits interacting with common and separate baths, considering pure dephasing as well as dissipation. Then, we explore the differences between the local and global master equation, showing that they intrinsically depend on the way we apply the secular approximation. Our results prove that the global approach with partial secular approximation always provides the most accurate choice for the master equation when Born-Markov approximations hold, even for small inter-system coupling constants. Using different master equations we compute the stationary heat current between two separate baths, the entanglement dynamics generated by a common bath, and the emergence of spontaneous synchronization, showing the importance of the accurate choice of approach.the case for most of the applications of the two-qubit problem, we will consider memory-less reservoirs, that is to say, we will study a Markovian master equation.Our detailed derivation allows us to establish the validity of the so-called local approach for the master equation in comparison with a global one in a rather general setting. The global approach arises naturally when deriving the master equation from a microscopic model considering the full system Hamiltonian, i.e. in presence of interactions between its subsystems (here the two qubits), while the local one follows from the approximation which neglects these interactions. Recently, the problem of characterizing the range of applicability of the local rather than global master equation has received much interest [25][26][27][28][29], mostly related to the consistency of this decription in quantum thermodynamics. It is our aim to show here that an accurate application of the secular approximation in the global approach always leads to a correct Markovian master equation, independently of the value of the coupling constant between the subsystems. The deep interconnection between a correct application of the secular approximation and the local versus global issue is discussed starting from the first principles of the derivation of the master equation. Deviations from the most accurate (global partial secular) approximation are illustrated by looking at the open system dynamics as well as the steady state. Moreover, we observe how the steady state heat current, the entanglement dynamics and the presence of quantum beats or quantum synchronization vary when using distinct master equations, so as to corroborate the validity (or inaccuracy) of each approach according to physical con...

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Refrigeration beyond weak internal coupling

Cited by 52 publications

References 47 publications

Boosting the performance of small autonomous refrigerators via common environmental effects

Boosting the performance of small autonomous refrigerators via common environmental effects

Reconciliation of quantum local master equations with thermodynamics

Local versus global master equation with common and separate baths: superiority of the global approach in partial secular approximation

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