Lindblad model of quantum Brownian motion

Lampo, Aniello; Lim, Soon Hoe; Wehr, Jan; Massignan, Pietro; Lewenstein, Maciej

doi:10.1103/physreva.94.042123

Cited by 22 publications

(27 citation statements)

References 54 publications

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“…Their master equation is exact and completely positive: unlike CL, HPZ do not perform any approximation, and the bath correlation function they consider has the general form (7)- (8).…”

Section: Dissipation In the CL Modelmentioning

confidence: 99%

Dissipation in the Caldeira-Leggett model

Ferialdi

2017

Phys. Rev. A

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Caldeira and Leggett (CL) in a seminal paper derived a master equation describing Markovian Quantum Brownian motion. Such an equation suffered of not being completely positive, and many efforts have been made to solve this issue. We show that, when a careful mathematical analysis is performed, the model considered by CL leads to a non dissipative master equation. We argue that the correct way to understand the master equation derived in the CL regime is to consider it non-Markovian. Moreover, we show that if one wants to provide a microscopic description of Quantum Brownian motion with the CL model, one always needs to consider a non-Markovian dynamics. We conclude that dissipation is a genuinely non-Markovian feature

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“…Their master equation is exact and completely positive: unlike CL, HPZ do not perform any approximation, and the bath correlation function they consider has the general form (7)- (8).…”

Section: Dissipation In the CL Modelmentioning

confidence: 99%

Dissipation in the Caldeira-Leggett model

Ferialdi

2017

Phys. Rev. A

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“…There is a number of existing techniques aimed at dealing with the QBM model with this kind of non-linearity. For instance, one could recall the master equation treatment in the Born-Markov regime in [73], or in the Lindblad framework [74].…”

Section: Hamiltonianmentioning

confidence: 99%

Non-Markovian polaron dynamics in a trapped Bose-Einstein condensate

et al. 2018

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We study the dynamics of an impurity embedded in a trapped Bose-Einstein condensate, i.e. the Bose polaron problem. This problem is treated by recalling open quantum systems techniques: the impurity corresponds to a particle performing quantum Brownian motion, while the excitation modes of the gas play the role of the environment. It is crucial that the model considers a parabolic trapping potential to resemble the experimental conditions. Thus, we detail here how the formal derivation changes due to the gas trap, in comparison to the homogeneous gas. More importantly, we elucidate all aspects in which the gas trap plays a relevant role, with an emphasis in the enhancement of the non-Markovian character of the dynamics. We first find that the presence of a gas trap leads to a new form of the bath-impurity coupling constant and a larger degree in the super-ohmicity of the spectral density. We then solve the quantum Langevin equation to derive the position and momentum variances of the impurity, where the former is a measurable quantity. For the particular case of an untrapped impurity, the asymptotic behaviour of this quantity is found to be motion superdiffusive. When the impurity is trapped, we find position squeezing, casting the system suitable for implementing quantum metrology and sensing protocols. We detail how both super-diffusion and squeezing can be enhanced or inhibited by tuning the Bose-Einstein condensate trap frequency. Compared to the homogeneous gas case, the form of the bath-impurity coupling constant changes, and this is manifested as a different dependence of the system dynamics on the past history. To quantify this, we introduce several techniques to compare the different amount of memory effects arising in the homogeneous and inhomogeneous gas. We find that it is higher in the second case. This analysis paves the way to the study of non-Markovianity in ultracold gases, and the possibility to exploit such a property in the realization of new quantum devices. arXiv:1803.08946v2 [cond-mat.quant-gas]

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“…Its properties have been investigated as a function of λ. Setting λ = μ cancels the squeezing term completely, while λ = 0 (providing a partial cancellation) gives additional flexibility to add desirable properties to the master equation, such as reasonable low T behavior [21,24]. This does, however, sacrifice translational invariance [19] and Ehrenfest [23].…”

Section: The Open Quantum Systemmentioning

confidence: 99%

“…As Eq. (6) is a nonrotating wave (NRW) equation, to assume Lindblad form [19], both of the following adjustments are required: some terms that present in the form of a unitary evolution must be combined with H S to produce an effective Hamiltonian and some new terms must be added to the dissipator [24,35]. At the end of this process, Eq.…”

Section: An Example Anharmonic Potential-the Squidmentioning

confidence: 99%

“…H δ is routinely canceled by introducing an identical counterterm, i.e., by settingĤ LS =Ĥ δ , while the impact ofĤ XP has previously been discussed in terms of frequency shifts and squeezing [30,32], and in other contexts too [19,21,[21][22][23][24][25][26]29]; however, it has also been the source of some debate as discussed in the Introduction: arranging for a counterterm inĤ LS allows the master equation to display additional properties [21], while such cancellation does come at the cost of sacrificing translational invariance [19] and Ehrenfest [23].…”

Section: The Effective Hamiltonianmentioning

confidence: 99%

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Open quantum systems, effective Hamiltonians, and device characterization

2017

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High fidelity models, which are able to both support accurate device characterization and correctly account for environmental effects, are crucial to the engineering of scalable quantum technologies. As it ensures positivity of the density matrix, one preferred model of open systems describes the dynamics with a master equation in Lindblad form. In practice, Linblad operators are rarely derived from first principles, and often a particular form of annihilator is assumed. This results in dynamical models that miss those additional terms which must generally be added for the master equation to assume the Lindblad form, together with the other concomitant terms that must be assimilated into an effective Hamiltonian to produce the correct free evolution. In first principles derivations, such additional terms are often canceled (or countered), frequently in a somewhat ad hoc manner, leading to a number of competing models. Whilst the implications of this paper are quite general, to illustrate the point we focus here on an example anharmonic system; specifically that of a superconducting quantum interference device (SQUID) coupled to an Ohmic bath. The resulting master equation implies that the environment has a significant impact on the system's energy; we discuss the prospect of keeping or canceling this impact and note that, for the SQUID, monitoring the magnetic susceptibility under control of the capacitive coupling strength and the externally applied flux results in experimentally measurable differences between a number of these models. In particular, one should be able to determine whether a squeezing term of the formXP +PX should be present in the effective Hamiltonian or not. If model generation is not performed correctly, device characterization will be prone to systemic errors.

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Lindblad model of quantum Brownian motion

Cited by 22 publications

References 54 publications

Dissipation in the Caldeira-Leggett model

Dissipation in the Caldeira-Leggett model

Non-Markovian polaron dynamics in a trapped Bose-Einstein condensate

Open quantum systems, effective Hamiltonians, and device characterization

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