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Gernot Schaller

Publications and source records attributed to Gernot Schaller.

At least 37 records · Page 2Linked to original sources

Thermodynamics of the Coarse-Graining Master Equation

We study the coarse-graining approach to derive a generator for the evolution of an open quantum system over a finite time interval. The approach does not require a secular approximation but nevertheless generally leads to a Lindblad-Gorini-Kossakowski-Sudarshan generator. By combining the formalism with Full Counting Statistics, we can demonstrate a consistent thermodynamic framework, once the switching work required for the coupling and decoupling with the reservoir is included. Particularly, we can write the second law in standard form, with the only difference that heat currents must be defined with respect to the reservoir. We exemplify our findings with simple but pedagogical examples.

cond-mat.stat-mech↗

Polaron-transformed dissipative Lipkin-Meshkov-Glick Model

We investigate the Lipkin-Meshkov-Glick model coupled to a thermal bath. Since the isolated model itself exhibits a quantum phase transition, we explore the critical signatures of the open system. Starting from a system-reservoir interaction written in positive definite form, we find that the position of the critical point remains unchanged, in contrast to the popular mean-field prediction. Technically, we employ the polaron transform to be able to study the full crossover regime from the normal to the symmetry-broken phase, which allows us to investigate the fate of quantum-critical points subject to dissipative environments. The signatures of the phase transition are reflected in observables like stationary mode occupation or waiting-time distributions.

quant-ph↗

Stochastic thermodynamics of an electron-spin-resonance quantum dot system

We present a stochastic thermodynamics analysis of an electron-spin-resonance pumped quantum dot device in the Coulomb-blocked regime, where a pure spin current is generated without an accompanying net charge current. Based on a generalized quantum master equation beyond secular approximation, quantum coherences are accounted for in terms of an effective average spin in the Floquet basis. Elegantly, this effective spin undergoes a precession about an effective magnetic field, which originates from the non-secular treatment and energy renormalization. It is shown that the interaction between effective spin and effective magnetic field may have the dominant roles to play in both energy transport and irreversible entropy production. In the stationary limit, the energy and entropy balance relations are also established based on the theory of counting statistics.

cond-mat.stat-mech↗

Collective performance of a finite-time quantum Otto cycle

We study the finite-time effects in a quantum Otto cycle where a collective spin system is used as the working fluid. Starting from a simple one-qubit system we analyze the transition to the limit cycle in the case of a finite-time thermalization. If the system consists of a large sample of independent qubits interacting coherently with the heat bath, the superradiant equilibration is observed. We show that this phenomenon can boost the power of the engine. Mutual interaction of qubits in the working fluid is modeled by the Lipkin-Meshkov-Glick Hamiltonian. We demonstrate that in this case the quantum phase transitions for the ground and excited states may have a strong negative effect on the performance of the machine. Reversely, by analyzing the work output we can distinguish between the operational regimes with and without a phase transition.

quant-ph↗

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

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.

quant-ph↗

Cooperative efficiency boost for quantum heat engines

The power and efficiency of many-body heat engines can be boosted by performing cooperative non-adiabatic operations in contrast to the commonly used adiabatic implementations. Here, the key property relies on the fact that non-adiabaticity is required in order to allow for cooperative effects, that can use the thermodynamic resources only present in the collective non-passive state of a many-body system. In particular, we consider the efficiency of an Otto cycle, which increases with the number of copies used and reaches a many-body bound, which we discuss analytically.

quant-ph↗

Transmission from reverse reaction coordinate mappings

We point out that the transport properties of non-interacting fermionic chains tunnel-coupled to two reservoirs at their ends can be mapped to those of a single quantum dot that is tunnel-coupled to two transformed reservoirs. The parameters of the chain are mapped to additional structure in the spectral densities of the transformed reservoirs. For example, this enables the calculation of the transmission of quantum dot chains by evaluating the known transmission of a single quantum dot together with structured spectral densities. We exemplify this analytically for short chains, which allows to optimize the transmission. In addition, we also demonstrate that the mapping can be performed numerically by computing the transmission of a Su-Schrieffer-Heeger chain.

cond-mat.stat-mech↗

Thermoelectric performance of topological boundary modes

We investigate quantum transport and thermoelectrical properties of a finite-size Su-Schrieffer-Heeger model, a paradigmatic model for a one-dimensional topological insulator, which displays topologically protected edge states. By coupling the model to two fermionic reservoirs at its ends, we can explore the non-equilibrium dynamics of the system. Investigating the energy-resolved transmission, the current and the noise, we find that these observables can be used to detect the topologically non-trivial phase. With specific parameters and asymmetric reservoir coupling strengths, we show that we can dissipatively prepare the edge states as stationary states of a non-equilibrium configuration. In addition, we point out that the edge states can be exploited to design a refrigerator driven by chemical work or a heat engine driven by a thermal gradient, respectively. These thermal devices do not require asymmetric couplings and are topologically protected against symmetry-preserving perturbations. Their maximum efficiencies significantly exceed that of a single quantum dot device at comparable coupling strengths.

cond-mat.stat-mech↗

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

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.

quant-ph↗

The reaction coordinate mapping in quantum thermodynamics

We present an overview of the reaction coordinate approach to handling strong system-reservoir interactions in quantum thermodynamics. This technique is based on incorporating a collective degree of freedom of the reservoir (the reaction coordinate) into an enlarged system Hamiltonian (the supersystem), which is then treated explicitly. The remaining residual reservoir degrees of freedom are traced out in the usual perturbative manner. The resulting description accurately accounts for strong system-reservoir coupling and/or non-Markovian effects over a wide range of parameters, including regimes in which there is a substantial generation of system-reservoir correlations. We discuss applications to both discrete stroke and continuously operating heat engines, as well as perspectives for additional developments. In particular, we find narrow regimes where strong coupling is not detrimental to the performance of continuously operating heat engines.

quant-ph↗

An electronic Maxwell demon in the coherent strong-coupling regime

We consider a feedback control loop rectifying particle transport through a single quantum dot that is coupled to two electronic leads. While monitoring the occupation of the dot, we apply conditional control operations by changing the tunneling rates between the dots and its reservoirs, which can be interpreted as the action of a Maxwell demon opening or closing a shutter. This can generate a current at equilibrium or even against a potential bias, producing electric power from information. While this interpretation is well-explored in the weak-coupling limit, we can address the strong-coupling regime with a fermionic reaction-coordinate mapping, which maps the system into a serial triple quantum dot coupled to two leads. There, we find that a continuous projective measurement of the central dot would lead to a complete suppression of electronic transport due to the quantum Zeno effect. In contrast, a microscopic model for the quantum point contact detector implements a weak measurement, which allows for closure of the control loop without inducing transport blockade. In the weak-coupling regime between the central dot and its leads, the energy flows associated with the feedback loop are negligible, and the information gained in the measurement induces a bound for the generated electric power. In contrast, in the strong coupling limit, the protocol may require more energy for opening and closing the shutter than electric power produced, such that the device is no longer information-dominated and can thus not be interpreted as a Maxwell demon.

cond-mat.stat-mech↗

Fermionic reaction coordinates and their application to an autonomous Maxwell demon in the strong coupling regime

We establish a theoretical method which goes beyond the weak coupling and Markovian approximations while remaining intuitive, using a quantum master equation in a larger Hilbert space. The method is applicable to all impurity Hamiltonians tunnel-coupled to one (or multiple) baths of free fermions. The accuracy of the method is in principle not limited by the system-bath coupling strength, but rather by the shape of the spectral density and it is especially suited to study situations far away from the wide-band limit. In analogy to the bosonic case, we call it the fermionic reaction coordinate mapping. As an application we consider a thermoelectric device made of two Coulomb-coupled quantum dots. We pay particular attention to the regime where this device operates as an autonomous Maxwell demon shoveling electrons against the voltage bias thanks to information. Contrary to previous studies we do not rely on a Markovian weak coupling description. Our numerical findings reveal that in the regime of strong coupling and non-Markovianity, the Maxwell demon is often doomed to disappear except in a narrow parameter regime of small power output.

quant-ph↗

Wiseman-Milburn Control for the Lipkin-Meshkov-Glick Model

We apply a measurement-based closed-loop control scheme to the dissipative Lipkin-Meshkov-Glick model. Specifically, we use the Wiseman-Milburn feedback master equation to control its quantum phase transition.For the steady state properties of the Lipkin-Meshkov-Glick system under feedback we show that the considered control scheme changes the critical point of the phase transition. Finite-size corrections blur these signatures in operator expectation values but entanglement measures such as concurrence can be used to locate the transition point more precisely. We find that with feedback, the position of the critical point can be shifted to smaller spin-spin interactions, which is potentially useful for setups with limited control on these.

quant-ph↗

Qubit absorption refrigerator at strong coupling

We demonstrate that a quantum absorption refrigerator can be realized from the smallest quantum system, a qubit, by coupling it in a non-additive (strong) manner to three heat baths. This function is un-attainable for the qubit model under the weak system-bath coupling limit, when the dissipation is additive. In an optimal design, the reservoirs are engineered and characterized by a single frequency component. We obtain then closed expressions for the cooling window and refrigeration efficiency, as well as bounds for the maximal cooling efficiency and the efficiency at maximal power. Our results agree with macroscopic designs and with three-level models for quantum absorption refrigerators, which are based on the weak system-bath coupling assumption. Beyond the optimal limit, we show with analytic calculations and numerical simulations that the cooling efficiency varies in a non-universal manner with model parameters. Our work demonstrates that strongly-coupled quantum machines can exhibit function that is un-attainable under the weak system-bath coupling assumption.

cond-mat.mes-hall↗

Initial System-Environment Correlations via the Transfer Tensor Method

Open quantum systems exhibiting initial system-environment correlations are notoriously difficult to simulate. We point out that given a sufficiently long sample of the exact short-time evolution of the open system dynamics, one may employ transfer tensors for the further propagation of the reduced open system state. This approach is numerically advantageous and allows for the simulation of quantum correlation functions in hardly accessible regimes. We benchmark this approach against analytically exact solutions and exemplify it with the calculation of emission spectra of multichromophoric systems as well as for the reverse temperature estimation from simulated spectroscopic data. Finally, we employ our approach for the detection of spectral signatures of electromagnetically-induced transparency in open three-level systems.

quant-ph↗

Nonadiabatic dynamics of the excited states for the Lipkin-Meshkov-Glick model

We theoretically investigate the impact of the excited state quantum phase transition on the adiabatic dynamics for the Lipkin-Meshkov-Glick model. Using a time dependent protocol, we continuously change a model parameter and then discuss the scaling properties of the system especially close to the excited state quantum phase transition where we find that these depend on the energy eigenstate. On top, we show that the mean-field dynamics with the time dependent protocol gives the correct scaling and expectation values in the thermodynamic limit even for the excited states.

cond-mat.quant-gas↗

Interplay of different environments in open quantum systems: Breakdown of the additive approximation

We analyze an open quantum system under the influence of more than one environment: a dephasing bath and a probability-absorbing bath that represents a decay channel, as encountered in many models of quantum networks. In our case, dephasing is modeled by random fluctuations of the site energies, while the absorbing bath is modeled with an external lead attached to the system. We analyze under which conditions the effects of the two baths can enter additively the quantum master equation. When such additivity is legitimate, the reduced master equation corresponds to the evolution generated by an effective non-Hermitian Hamiltonian and a Haken-Strobl dephasing super-operator. We find that the additive decomposition is a good approximation when the strength of dephasing is small compared to the bandwidth of the probability-absorbing bath.

cond-mat.mes-hall↗

Quantum and Information Thermodynamics: A Unifying Framework based on Repeated Interactions

We expand the standard thermodynamic framework of a system coupled to a thermal reservoir by considering a stream of independently prepared units repeatedly put into contact with the system. These units can be in any nonequilibrium state and interact with the system with an arbitrary strength and duration. We show that this stream constitutes an effective resource of nonequilibrium free energy and identify the conditions under which it behaves as a heat, work or information reservoir. We also show that this setup provides a natural framework to analyze information erasure ("Landauer's principle") and feedback controlled systems ("Maxwell's demon"). In the limit of a short system-unit interaction time, we further demonstrate that this setup can be used to provide a thermodynamically sound interpretation to many effective master equations. We discuss how non-autonomously driven systems, micromasers, lasing without inversion, and the electronic Maxwell demon, can be thermodynamically analyzed within our framework. While the present framework accounts for quantum features (e.g. squeezing, entanglement, coherence), we also show that quantum resources do not offer any advantage compared to classical ones in terms of the maximum extractable work.

quant-ph↗