Nonadiabatic effects in periodically driven dissipative open quantum systems

Reimer, Viktor; Pedersen, Kim G. L.; Tanger, Niklas; Pletyukhov, Mikhail; Gritsev, Vladimir

doi:10.1103/physreva.97.043851

Cited by 14 publications

(11 citation statements)

References 42 publications

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“…This is familiar, e.g., from Green's function techniques 44,77,[108][109][110][111] used extensively in electron transport theory or input-output formalisms in quantum optics [74][75][76]112 . Often, the approach is used in conjunction with various approximations and/or limits 75,113,114 . However, in this case we can follow it through exactly due to the wideband-limit 44 .…”

Section: Equation Of Motion Approachmentioning

confidence: 99%

Five approaches to exact open-system dynamics: Complete positivity, divisibility, and time-dependent observables

Reimer

Wegewijs

Nestmann

et al. 2019

The Journal of Chemical Physics

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To extend the classical concept of Markovianity to an open quantum system, different notions of the divisibility of its dynamics have been introduced. Here we analyze this issue by five complementary approaches: equations of motion, real-time diagrammatics, Kraus-operator sums, as well as time-local (TCL) and nonlocal (Nakajima-Zwanzig) quantum master equations. As a case study featuring several types of divisible dynamics, we examine in detail an exactly solvable noninteracting fermionic resonant level coupled arbitrarily strongly to a fermionic bath at arbitrary temperature in the wideband limit. In particular, the impact of divisibility on the time-dependence of the observable level occupation is investigated and compared with typical Markovian approximations. We find that the loss of semigroup-divisibility is accompanied by a prominent reentrant behavior: Counter to intuition, the level occupation may temporarily increase significantly in order to reach a stationary state with smaller occupation, implying a reversal of the measurable transport current. In contrast, the loss of the so-called completely-positive divisibility is more subtly signaled by the prohibition of such current reversals in specific time-intervals. Experimentally, it can be detected in the family of transient currents obtained by varying the initial occupation. To quantify the nonzero footprint left by the system in its effective environment, we determine the exact time-dependent state of the latter as well as related information measures such as entropy, exchange entropy and coherent information.

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Section: Equation Of Motion Approachmentioning

confidence: 99%

Five approaches to exact open-system dynamics: Complete positivity, divisibility, and time-dependent observables

Reimer

Wegewijs

Nestmann

et al. 2019

The Journal of Chemical Physics

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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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“…Markovian master equations in Lindblad form find widespread use in quantum optics, where the time-local form of the equation results from a separation of scales between the typical time scale of the system's evolution and the much shorter coherence time of the bath which induces dissipation in the system. Similarly, the FLE (29) is local in driving cycles, i.e., the state of the system ρ n+1 after n + 1 cycles depends only on the state ρ n after n cycles and not on ρ n with n < n. This is due to our assumption that fluctuations of the stochastic drive are uncorrelated between different driving cycles, which is analogous to the Markovian baths encountered in the quantum optics context [18]. Finally, we note that while here we found the FLE equation in the limit of weak noise, it is not guaranteed that the generator of the Floquet superoperator is of Lindblad form [19].…”

Section: Weak Noise: Discrete-time Floquet-lindblad Equationmentioning

confidence: 95%

Statistical periodicity in driven quantum systems: General formalism and application to noisy Floquet topological chains

et al. 2018

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Much recent experimental effort has focused on the realization of exotic quantum states and dynamics predicted to occur in periodically driven systems. But how robust are the sought-after features, such as Floquet topological surface states, against unavoidable imperfections in the periodic driving? In this work, we address this question in a broader context and study the dynamics of quantum systems subject to noise with periodically recurring statistics. We show that the stroboscopic time evolution of such systems is described by a noise-averaged Floquet superoperator. The eigenvectors and -values of this superoperator generalize the familiar concepts of Floquet states and quasienergies and allow us to describe decoherence due to noise efficiently. Applying the general formalism to the example of a noisy Floquet topological chain, we re-derive and corroborate our recent findings on the noise-induced decay of topologically protected end states. These results follow directly from an expansion of the end state in eigenvectors of the Floquet superoperator.

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Nonadiabatic effects in periodically driven dissipative open quantum systems

Cited by 14 publications

References 42 publications

Five approaches to exact open-system dynamics: Complete positivity, divisibility, and time-dependent observables

Five approaches to exact open-system dynamics: Complete positivity, divisibility, and time-dependent observables

Floquet-state cooling

Statistical periodicity in driven quantum systems: General formalism and application to noisy Floquet topological chains

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