Markovian quantum master equation beyond adiabatic regime

We study the quantum speed limit for open quantum systems described by the Lindblad master equation. The obtained inequality shows a trade-off relation between the operation time and the physical quantities such as the energy fluctuation and the entropy production. We further identify a quantity characterizing the speed of the state transformation, which appears only when we consider the open system dynamics in the quantum regime. When the thermal relaxation is dominant compared to the unitary dynamics of the system, we show that this quantity is approximated by the energy fluctuation of the counter-diabatic Hamiltonian which is used as a control field in the shortcuts to adiabaticity protocol. We discuss the physical meaning of the obtained quantum speed limit and try to give better intuition about the speed in open quantum systems. t .

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“…We consider an externally driven system interacting with the heat bath, described by the following Lindblad type master equation [27][28][29]…”

Section: Lindblad Master Equationmentioning

confidence: 99%

Speed limit for open quantum systems

2019

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“…4 we show the time dependence Q LZ (t) calculated by numerical solution of Eq. (17) for particular value G ω = 0.6, when the Bessel function J 0 (4G/ω) turns to zero. We see that, for this coupling, Q LZ (t) does not change with time in a certain domain around t = 0 suggesting that the effective gap is zero.…”

Section: Fast Oscillatormentioning

confidence: 95%

Landau-Zener transition in a two-level system coupled to a single highly excited oscillator

Malla

Raǐkh

2018

Phys. Rev. B

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Two-level system strongly coupled to a single resonator mode (harmonic oscillator) is a paradigmatic model in many subfields of physics. We study theoretically the Landau-Zener transition in this model. Analytical solution for the transition probability is possible when the oscillator is highly excited, i.e. at high temperatures. Then the relative change of the excitation level of the oscillator in the course of the transition is small. The physical picture of the transition in the presence of coupling to the oscillator becomes transparent in the limiting cases of slow and fast oscillator. Slow oscillator effectively renormalizes the drive velocity. As a result, the transition probability either increases or decreases depending on the oscillator phase. The net effect is, however, the suppression of the transition probability. On the contrary, fast oscillator renormalizes the matrix element of the transition rather than the drive velocity. This renormalization makes the transition probability a non-monotonic function of the coupling amplitude.

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“…As a final remark, note that by assuming L t (ω β (H t )) = 0 we are neglecting non-adiabatic contributions to L t , which is justified whenever the bath dynamics are fast compared to the driving rate of the system Hamiltonian [28][29][30]. For slow driving of H t , we can assume that the state is always close to the equilibrium one: ρ t = ω β (H t ) + δω t .…”

Section: Metric Structure In Open Quantum Systemsmentioning

confidence: 99%

Thermodynamic length in open quantum systems

Scandi

Perarnau-Llobet

2019

Quantum

122

120

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The dissipation generated during a quasistatic thermodynamic process can be characterised by introducing a metric on the space of Gibbs states, in such a way that minimally-dissipating protocols correspond to geodesic trajectories. Here, we show how to generalize this approach to open quantum systems by finding the thermodynamic metric associated to a given Lindblad master equation. The obtained metric can be understood as a perturbation over the background geometry of equilibrium Gibbs states, which is induced by the Kubo-Mori-Bogoliubov (KMB) inner product. We illustrate this construction on two paradigmatic examples: an Ising chain and a two-level system interacting with a bosonic bath with different spectral densities.arXiv:1810.05583v3 [quant-ph]

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Markovian quantum master equation beyond adiabatic regime

Cited by 46 publications

References 59 publications

Speed limit for open quantum systems

Speed limit for open quantum systems

Landau-Zener transition in a two-level system coupled to a single highly excited oscillator

Thermodynamic length in open quantum systems

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