Dissipative effects on a generation scheme of a W state in an array of coupled Josephson junctions

Migliore, Rosanna; Scala, M.; Napoli, A.; Yuasa, Kazuya; Nakazato, Hiromichi; Messina, A.

doi:10.1088/0953-4075/44/7/075503

Cited by 14 publications

(19 citation statements)

References 44 publications

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“…Since the global approach describes equilibrium situations accurately (see below), while the local in some cases does not, there has been incentive to use the global approach out of equilibrium as well. Furthermore, the local approach is often believed to be more phenomenological in nature [13,14,19,28,57] and it was even argued that it is unphysical in certain regimes [27,58,59].…”

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confidence: 99%

Markovian master equations for quantum thermal machines: local versus global approach

et al. 2017

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The study of quantum thermal machines, and more generally of open quantum systems, often relies on master equations. Two approaches are mainly followed. On the one hand, there is the widely used, but often criticized, local approach, where machine sub-systems locally couple to thermal baths. On the other hand, in the more established global approach, thermal baths couple to global degrees of freedom of the machine. There has been debate as to which of these two conceptually different approaches should be used in situations out of thermal equilibrium. Here we compare the local and global approaches against an exact solution for a particular class of thermal machines. We consider thermodynamically relevant observables, such as heat currents, as well as the quantum state of the machine. Our results show that the use of a local master equation is generally well justified. In particular, for weak inter-system coupling, the local approach agrees with the exact solution, whereas the global approach fails for non-equilibrium situations. For intermediate coupling, the local and the global approach both agree with the exact solution and for strong coupling, the global approach is preferable. These results are backed by detailed derivations of the regimes of validity for the respective approaches.or more concretely of an electrical current [34,[42][43][44], the refrigeration of a quantum degree of freedom [45][46][47][48][49][50], the creation of entanglement [51][52][53], the determination of low temperatures [54], or the design of thermal transistors [55] and autonomous quantum clocks [56].The standard description of these systems crucially relies on Markovian master equations to predict the relevant observables, such as heat currents and power. Two main approaches are followed in the literature. The first is a local approach, where the thermal baths couple locally to sub-systems of the machine. The second is a global approach, where thermal baths couple to the global eigenmodes of the machine. As the two approaches are conceptually different, there has been considerable debate about which one should be used in order to accurately describe thermal machines, and more generally out-of-equilibrium systems. Since the global approach describes equilibrium situations accurately (see below), while the local in some cases does not, there has been incentive to use the global approach out of equilibrium as well. Furthermore, the local approach is often believed to be more phenomenological in nature [13,14,19,28,57] and it was even argued that it is unphysical in certain regimes [27,58,59].The goal of the present work is to discuss these questions in depth. We will consider a system for which the full unitary dynamics of the machine and the thermal baths can be solved exactly. This allows us to evaluate the performance of local and global master equations for the machine against the exact dynamics. In addition, we give detailed derivations of the local and the global approaches and discuss the involved approximations. Specifically, ...

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confidence: 99%

Markovian master equations for quantum thermal machines: local versus global approach

et al. 2017

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“…In a similar way, from (44), one obtains that the only contributing transition amplitudes associated to the right bath are…”

Section: Coupling To External Bathsmentioning

confidence: 79%

Exact steady state of the open XX-spin chain: entanglement and transport properties

Benatti,

Floreanini,

Memarzadeh

2021

Preprint

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We study the reduced dynamics of open quantum spin chains of arbitrary length N with nearest neighbour XX interactions, immersed within an external constant magnetic field along the z direction, whose end spins are weakly coupled to heat baths at different temperatures, via energy preserving couplings. We find the analytic expression of the unique stationary state of the master equation obtained in the so-called global approach based on the spectralization of the full chain Hamiltonian. Hinging upon the explicit stationary state, we reveal the presence of sink and source terms in the spin-flow continuity equation and compare their behaviour with that of the stationary heat flow. Moreover, we also obtain analytic expressions for the steady state two-spin reduced density matrices and for their concurrence. We then set up an algorithm suited to compute the stationary bipartite entanglement along the chain and to study its dependence on the Hamiltonian parameters and on the bath temperatures.

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“…Twenty years later, Cresser observed the failure of the local approach to describe a lossy Jaynes-Cummings model [49], terming 'phenomenological master equation' what it is nowadays usually called 'local master equation'. Quite the same issue has been addressed in some more recent papers [50,51], extending the analysis to three coupled Josephson junctions [52] or coupled harmonic oscillators [34], while the 3-level atom has been investigated in [53]. Some comments about the validity of the local approach to describe energy transport in chains of harmonic oscillators or spins appear in [54][55][56].…”

Section: Local Versus Global: An In-depth Discussionmentioning

confidence: 93%

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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Dissipative effects on a generation scheme of a W state in an array of coupled Josephson junctions

Cited by 14 publications

References 44 publications

Markovian master equations for quantum thermal machines: local versus global approach

Markovian master equations for quantum thermal machines: local versus global approach

Exact steady state of the open XX-spin chain: entanglement and transport properties

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

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