Electron pumping in the strong coupling and non-Markovian regime: A reaction coordinate mapping approach

Abstract

We study electron pumping in the strong coupling and non-Markovian regime. Our model is a single quantum dot with periodically modulated energy and tunnelling amplitudes. We identify four parameters to control the direction of the current: the driving phase, the coupling strength, the driving frequency and the location of the maxima of the spectral density. In the high-frequency regime, we use a Markovian embedding strategy to map our model to three serial quantum dots weakly coupled to the reservoirs allowing us to use a Floquet master equation. We observe a rectification effect of the pumped charge that is exclusive to the non-Markovian character of our model. In the low-frequency regime, we apply an additional transformation to see our model as three independent transport channels. With the use of full counting statistics, we study charge fluctuations and validate that our model behaves as a single electron source. arXiv:1905.00581v1 [quant-ph] 2 May 2019 t k,R (t) t k,L (t) u,R (t)

Accurate Truncations of Chain Mapping Models for Open Quantum Systems

“…In Figure 5a, we show the population dynamics of an initially excited quantum emitter with the same frequency as before, ω e = 3.6 eV, and different chains with smoothly increasing absorption. In particular, we here choose α = 0.02 and β = 0.1 and show results for the combinations (N C , N d ) = (30,8), (25,7), (15,5).…”

“…In particular, such approaches often are based on the general idea of enlarging the system by including one (or several) “reaction modes” of the environment within it in such a way that these modes contain the “memory” of the bath, and are then in turn coupled to a new residual bath that ideally has little or no memory. Among these approaches are the pseudomode method [ 22 , 23 , 24 , 25 ], effective Lindblad master equation procedure [ 26 ], and reaction coordinate mappings [ 27 , 28 , 29 , 30 ]. In such a mapping, an orthogonal transformation is applied on the bath modes such that the interaction between the system and the full environment is captured by a single mode, which itself interacts with the residual bath ( Figure 1 b).…”

Measurability of nonequilibrium thermodynamics in terms of the Hamiltonian of mean force

“…It nevertheless has its limitations. Most importantly, it does not extend to the experimentally relevant situation of multiple heat baths, where only a few formally exact results are known [29,30,35] and a couple of promising theoretical tools, restricted to particular models, were devised [7,21,23,[44][45][46][47][48][49][50][56][57][58][59][64][65][66][67][68][69][70][71][72][73][74][75].…”

“…[11] was that the so-defined thermodynamic quantities F CG S (t ), U CG S (t ), and S CG S (t ) capture the full nonequilibrium thermodynamics of the weakly coupled open system S = S ⊗ R in the limit where the remaining degrees of freedom R are fast and can be adiabatically eliminated, i.e., whenever they can be approximated to be in a conditional equilibrium state. Even beyond that limit, so-called Markovian embedding strategies can be used to study the thermodynamics of strongly coupled open quantum systems [7,[44][45][46][47][48][49][50].…”

Nonadiabaticity in Quantum Pumping Phenomena under Relaxation

“…We can find recent extensions of the treatments with full counting statistics into the strong system-environment coupling for heat transfer [ 64 ] and electron pumping [ 65 ]. The essential idea to go beyond the weak coupling is to use the similarity (unitary) transformations: the polaron transformation (the reaction coordinate mapping) is used in the former (latter) studies, respectively.…”