arXiv subjects

Gernot Schaller

Publications and source records attributed to Gernot Schaller.

At least 55 records · Page 3Linked to original sources

arXiv2016

Feedback-charging a metallic island

We consider electronic transport through a single-electron quantum dot that is tunnel-coupled to an electronic lead and a metallic island. A background reservoir keeps the metallic island at a thermal state with the ambient temperature, while the charge accumulated on the island is reflected in a time-dependent chemical potential. Without feedback, a current would flow through the system until the chemical potentials of island and lead are equilibrated. A feedback loop can be implemented by a quantum point contact detecting the dot state, classical processing of the result and appropriate feedback actions on the electronic tunneling rates taken, with the objective to direct the current in a preferred direction. Since we directly take the detector counting statistics into account, this automatically includes measurement errors in the description. When mainly the rates are modified but hardly any energy is exchanged with the system, this feedback loop effectively implements a Maxwell demon, capable of transporting electrons against an electric bias and thereby charging the metallic island. Once the feedback protocol is stopped, the metallic island simply discharges. We find that a quantitative detector model may be useful for a realistic statistical description of feedback loops.

cond-mat.mes-hall↗

arXiv2016

Quantum Thermodynamics with Degenerate Eigenstate Coherences

We establish quantum thermodynamics for open quantum systems weakly coupled to their reservoirs when the system exhibits degeneracies. The first and second law of thermodynamics are derived, as well as a finite-time fluctuation theorem for mechanical work and energy and matter currents. Using a double quantum dot junction model, local eigenbasis coherences are shown to play a crucial role on thermodynamics and on the electron counting statistics.

cond-mat.stat-mech↗

arXiv2016

Collective couplings: rectification and supertransmittance

We investigate heat transport between two thermal reservoirs that are coupled via a large spin composed of N identical two level systems. One coupling implements the dissipative Dicke super- radiance. The other coupling is locally of the pure-dephasing type and requires to go beyond the standard weak-coupling limit by employing a Bogoliubov mapping in the corresponding reservoir. After the mapping, the large spin is coupled to a collective mode with the original pure-dephasing interaction, but the collective mode is dissipatively coupled to the residual oscillators. Treating the large spin and the collective mode as the system, a standard master equation approach is now able to capture the energy transfer between the two reservoirs. Assuming fast relaxation of the collective mode, we derive a coarse-grained rate equation for the large spin only and discuss how the original Dicke superradiance is affected by the presence of the additional reservoir. Our main finding is a cooperatively enhanced rectification effect due to the interplay of supertransmittant heat currents (scaling quadratically with $N$) and the asymmetric coupling to both reservoirs. For large $N$, the system can thus significantly amplify current asymmetries under bias reversal, functioning as a heat diode. We also briefly discuss the case when the couplings of the collective spin are locally dissipative, showing that the heat-diode effect is still present.

cond-mat.mes-hall↗

arXiv2016

Nonequilibrium thermodynamics in the strong coupling and non-Markovian regime based on a reaction coordinate mapping

We propose a method to study the thermodynamic behaviour of small systems beyond the weak coupling and Markovian approximation, which is different in spirit from conventional approaches. The idea is to redefine the system and environment such that the effective, redefined system is again coupled weakly to Markovian residual baths and thus, allows to derive a consistent thermodynamic framework for this new system-environment partition. To achieve this goal we make use of the reaction coordinate mapping, which is a general method in the sense that it can be applied to an arbitrary (quantum or classical and even time-dependent) system coupled linearly to an arbitrary number of harmonic oscillator reservoirs. The core of the method relies on an appropriate identification of a part of the environment (the reaction coordinate), which is subsequently included as a part of the system. We demonstrate the power of this concept by showing that non-Markovian effects can significantly enhance the steady state efficiency of a three-level-maser heat engine, even in the regime of weak system-bath coupling. Furthermore, we show for a single electron transistor coupled to vibrations that our method allows one to justify master equations derived in a polaron transformed reference frame.

quant-ph↗

arXiv2016

Duality in spin systems via the $SU(4)$ algebra

We provide several examples and an intuitive diagrammatic representation demonstrating the use of two-qubit unitary transformations for mapping coupled spin Hamiltonians to simpler ones and vice versa. The corresponding dualities may be exploited to identify phase transition points or to aid the diagonalization of such Hamiltonians. For example, our method shows that a suitable one-parameter family of coupled Hamiltonians whose ground states transform from an initially factorizing state to a final cluster state on a lattice of arbitrary dimension is dual to a family of trivial decoupled Hamiltonians containing local on-site terms only. As a consequence, the minimum enery gap (which determines the adiabatic run-time) does not scale with system size, which facilitates an efficient and simple adiabatic preparation of e.g. the two-dimensional cluster state used for measurement-based quantum computation.

quant-ph↗

arXiv2015

Thermodynamics of stochastic Turing machines

In analogy to Brownian computers we explicitly show how to construct stochastic models, which mimic the behaviour of a general purpose computer (a Turing machine). Our models are discrete state systems obeying a Markovian master equation, which are logically reversible and have a well-defined and consistent thermodynamic interpretation. The resulting master equation, which describes a simple one-step process on an enormously large state space, allows us to thoroughly investigate the thermodynamics of computation for this situation. Especially, in the stationary regime we can well approximate the master equation by a simple Fokker-Planck equation in one dimension. We then show that the entropy production rate at steady state can be made arbitrarily small, but the total (integrated) entropy production is finite and grows logarithmically with the number of computational steps.

cond-mat.stat-mech↗

arXiv2015

Controlling the stability of steady states in continuous variable quantum systems

For the paradigmatic case of the damped quantum harmonic oscillator we present two measurement-based feedback schemes to control the stability of its fixed point. The first scheme feeds back a Pyragas-like time-delayed reference signal and the second uses a predetermined instead of time-delayed reference signal. We show that both schemes can reverse the effect of the damping by turning the stable fixed point into an unstable one. Finally, by taking the classical limit $\hbar\rightarrow0$ we explicitly distinguish between inherent quantum effects and effects, which would be also present in a classical noisy feedback loop. In particular, we point out that the correct description of a classical particle conditioned on a noisy measurement record is given by a non-linear stochastic Fokker-Planck equation and not a Langevin equation, which has observable consequences on average as soon as feedback is considered.

quant-ph↗

arXiv2015

Steady-state thermodynamics of non-interacting transport beyond weak coupling

We investigate the thermodynamics of simple (non-interacting) transport models beyond the scope of weak coupling. For a single fermionic or bosonic level -- tunnel-coupled to two reservoirs -- exact expressions for the stationary matter and energy current are derived from the solutions of the Heisenberg equations of motion. The positivity of the steady-state entropy production rate is demonstrated explicitly. Finally, for a configuration in which particles are pumped upwards in chemical potential by a downward temperature gradient, we demonstrate that the thermodynamic efficiency of this process decreases when the coupling strength between system and reservoirs is increased, as a direct consequence of the loss of a tight coupling between energy and matter currents.

cond-mat.stat-mech↗

arXiv2015

Thermodynamics of the polaron master equation at finite bias

We study coherent transport through a double quantum dot. Its two electronic leads induce electronic matter and energy transport and a phonon reservoir contributes further energy exchanges. By treating the system-lead couplings perturbatively, whereas the coupling to vibrations is treated non-perturbatively in a polaron-transformed frame, we derive a thermodynamic consistent low-dimensional master equation. When the number of phonon modes is finite, a Markovian description is only possible when these couple symmetrically to both quantum dots. For a continuum of phonon modes however, also asymmetric couplings can be described with a Markovian master equation. We compute the electronic current and dephasing rate. The electronic current enables transport spectroscopy of the phonon frequency and displays signatures of Franck-Condon blockade. For infinite external bias but finite tunneling bandwidths, we find oscillations in the current as a function of the internal bias due to the electron-phonon coupling. Furthermore, we derive the full fluctuation theorem and show its identity to the entropy production in the system.

cond-mat.stat-mech↗

arXiv2014

Relaxation Dynamics of Meso-Reservoirs

We study the phenomenology of maximum-entropy meso-reservoirs, where we assume that their local thermal equilibrium state changes consistently with the heat transferred between the meso-reservoirs. Depending on heat and matter carrying capacities, the chemical potentials and temperatures are allowed to vary in time, and using global conservation relations we solve their evolution equations. We compare two-terminal transport between bosonic and fermionic meso-reservoirs via systems that tightly couple energy and matter currents and systems that do not. For bosonic reservoirs we observe the temporary formation of a Bose-Einstein condensate in one of the meso-reservoirs from an initial nonequilibrium setup.

cond-mat.mes-hall↗

arXiv2014

The Second Laws for an Information driven Current through a Spin Valve

We propose a physically realizable Maxwell's demon device using a spin valve interacting unitarily for a short time with electrons placed on a tape of quantum dots, which is thermodynamically equivalent to the device introduced by Mandal and Jarzynski [PNAS 109, 11641 (2012)]. The model is exactly solvable and we show that it can be equivalently interpreted as a Brownian ratchet demon. We then consider a measurement based discrete feedback scheme, which produces identical system dynamics, but possesses a different second law inequality. We show that the second law for discrete feedback control can provide a smaller, equal or larger bound on the maximum extractable work as compared to the second law involving the tape of bits. Finally, we derive an effective master equation governing the system evolution for Poisson distributed bits on the tape (or measurement times respectively) and we show that its associated entropy production rate contains the same physical statement as the second law involving the tape of bits.

cond-mat.stat-mech↗

arXiv2014

Nonequilibrium relaxation transport of ultracold atoms

We analyze the equilibration process between two either fermionic or bosonic reservoirs containing ultracold atoms with a fixed total number of particles that are weakly connected via a few-level quantum system. We allow for both the temperatures and particle densities of the reservoirs to evolve in time. Subsequently, linearizing the resulting equations enables us to characterize the equilibration process and its time scales in terms of equilibrium reservoir properties and linear-response transport coefficients. Additionally, we investigate the use of such a device as particle transistor or particle capacitor and analyze its efficiency.

cond-mat.quant-gas↗

arXiv2014

Transport as a sensitive indicator of quantum criticality

We consider bosonic transport through one-dimensional spin systems. Transport is induced by coupling the spin systems to bosonic reservoirs kept at different temperatures. In the limit of weak-coupling between spins and bosons we apply the quantum-optical master equation to calculate the energy transmitted from source to drain reservoirs. At large thermal bias, we find that the current for longitudinal transport becomes independent of the chain length and is also not drastically affected by the presence of disorder. In contrast, at small temperatures, the current scales inversely with the chain length and is further suppressed in presence of disorder. We also find that the critical behaviour of the ground state is mapped to critical behaviour of the current -- even in configurations with infinite thermal bias.

cond-mat.stat-mech↗

arXiv2014

Probing nonlinear adiabatic paths with a universal integrator

We apply a flexible numerical integrator to the simulation of adiabatic quantum computation with nonlinear paths. We find that a nonlinear path may significantly improve the performance of adiabatic algorithms versus the conventional straight-line interpolations. The employed integrator is suitable for solving the time-dependent Schrödinger equation for any qubit Hamiltonian. Its flexible storage format significantly reduces cost for storage and matrix-vector multiplication in comparison to common sparse matrix schemes.

quant-ph↗

arXiv2014

Transport with ultracold atoms at constant density

We investigate the transport through a few-level quantum system described by a Markovian master equation with temperature- and particle-density dependent chemical potentials. From the corresponding Onsager relations we extract linear response transport coefficients in analogy to the electronic conductance, thermal conductance and thermopower. Considering ideal Fermi and Bose gas reservoirs we observe steady-state currents against the thermal bias as a result of the non-linearities introduced by the constraint of a constant particle density in the reservoirs. Most importantly, we find signatures of the on-set of Bose-Einstein condensation in the transport coefficients.

cond-mat.quant-gas↗

arXiv2013

Thermodynamics of Quantum-Jump-Conditioned Feedback Control

We consider open quantum systems weakly coupled to thermal reservoirs and subjected to quantum feedback operations triggered with or without delay by monitored quantum jumps. We establish a thermodynamic description of such system and analyze how the first and second law of thermodynamics are modified by the feedback. We apply our formalism to study the efficiency of a qubit subjected to a quantum feedback control and operating as a heat pump between two reservoirs. We also demonstrate that quantum feedbacks can be used to stabilize coherences in nonequilibrium stationary states which in some cases may even become pure quantum states.

cond-mat.stat-mech↗

arXiv2013

Effective fluctuation theorems for electron transport in a double quantum dot coupled to a quantum point contact

A theoretical study is reported of electron transport at finite temperature in a double quantum dot (DQD) capacitively coupled to a quantum point contact (QPC). Starting from a Hamiltonian model, a master equation is obtained for the stochastic process taking place in the DQD while the QPC is at or away from equilibrium, allowing us to study the backaction of the QPC onto the DQD. The QPC is treated non-perturbatively in our analysis. Effective fluctuation theorems are established for the full counting statistics of the DQD current under different limiting conditions. These fluctuation theorems hold with respect to an effective affinity characterizing the nonequilibrium environment of the DQD and differing from the applied voltage if the QPC is out of equilibrium. The effective affinity may even change its sign if the Coulomb drag of the QPC reverses the DQD current. The thermodynamic implications of the effective fluctuation theorems are discussed.

cond-mat.mes-hall↗

arXiv2013

Single electron transistor strongly coupled to vibrations: Counting Statistics and Fluctuation Theorem

Using a simple quantum master equation approach, we calculate the Full Counting Statistics of a single electron transistor strongly coupled to vibrations. The Full Counting Statistics contains both the statistics of integrated particle and energy currents associated to the transferred electrons and phonons. A universal as well as an effective fluctuation theorem are derived for the general case where the various reservoir temperatures and chemical potentials are different. The first relates to the entropy production generated in the junction while the second reveals internal information of the system. The model recovers Franck-Condon blockade and potential applications to non-invasive molecular spectroscopy are discussed.

cond-mat.stat-mech↗