Driven Open Quantum Systems and Floquet Stroboscopic Dynamics

Restrepo, Sebastian; Cerrillo, Javier; Bastidas, V. M.; Angelakis, Dimitris G.; Brandes, Tobias

doi:10.1103/physrevlett.117.250401

Cited by 71 publications

(57 citation statements)

References 47 publications

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“…To access the dynamics or study thermal transport in periodically driven systems beyond the Born-Markov approximation, more sophisticated methods must be used such as stochastic Liouville-von Neumann equations [32], perturbative high-frequency expansions [33] or influence functional integral methods [34]. Their thermodynamic interpretation, however, is not always clear.…”

Section: Introductionmentioning

confidence: 99%

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: Introductionmentioning

confidence: 99%

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

et al. 2018

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“…The integrable model of the parametrically driven oscillator (1) features an unusually simple quasienergy spectrum (6) in its stability regime. Combined with a system-bath coupling of the natural form (7) it gives rise to a merely tridiagonal Floquet transition matrix (8) and therefore leads to the expression (17) which allows one to discuss the effect of the environment on the quasistationary state in an exceptionally transparent manner.…”

Section: Discussionmentioning

confidence: 99%

Floquet-state cooling

Diermann

Holthaus

2019

Sci Rep

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We demonstrate that a periodically driven quantum system can adopt a quasistationary state which is effectively much colder than a thermal reservoir it is coupled to, in the sense that certain Floquet states of the driven-dissipative system can carry much higher population than the ground state of the corresponding undriven system in thermal equilibrium. This is made possible by a rich Fourier spectrum of the system’s Floquet transition matrix elements, the components of which are addressed individually by a suitably peaked reservoir density of states. The effect is expected to be important for driven solid-state systems interacting with a phonon bath predominantly at well-defined frequencies.

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“…In addition, non-Markovian behavior has been explored in the context of photonic systems with structured reservoirs [14] that even allow one to inhibit spontaneous emission of an atom embedded in a photonic crystal [15]. In some situations where the reservoir is structured or under the effect of an external drive, the open-system approach is inadequate to describe the dynamics of the system and it is suitable to study the combined dynamics of the system and the environment as in [16]. Besides the theoretical investigations, there are experimental realizations of non-Markovian dynamics in all-optical setups [17], trapped ions [18,19], and optomechanical systems [20], to mention but a few.…”

Section: Introductionmentioning

confidence: 99%

“…Time dependent LOs appear when the system is driven externally or due to time-dependent damping rates. For a long time, the theoretical understanding of time dependent LOs has been an open problem [16,[25][26][27]. These kind of LOs lead to time-local (timeconvolutionless) master equations, which can be non-Markovian when the damping rates become negative at certain times [28,29].…”

Section: Introductionmentioning

confidence: 99%

Floquet stroboscopic divisibility in non-Markovian dynamics

et al. 2018

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We provide a general description of a time-local master equation for a system coupled to a non-Markovian reservoir based on Floquet theory. This allows us to have a divisible dynamical map at discrete times, which we refer to as Floquet stroboscopic divisibility. We illustrate the theory by considering a harmonic oscillator coupled to both non-Markovian and Markovian baths. Our findings provide us with a theory for the exact calculation of spectral properties of time-local non-Markovian Liouvillian operators, and might shed light on the nature and existence of the steady state in non-Markovian dynamics.

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Driven Open Quantum Systems and Floquet Stroboscopic Dynamics

Cited by 71 publications

References 47 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

Floquet-state cooling

Floquet stroboscopic divisibility in non-Markovian dynamics

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