Patrick P. Hofer

Markovian master equations for quantum thermal machines: local versus global approach

The study of quantum thermal machines, and more generally of open quantum systems, often relies on master equations. Two approaches are mainly followed. On the one hand, there is the widely used, but often criticized, local approach, where machine sub-systems locally couple to thermal baths. On the other hand, in the more established global approach, thermal baths couple to global degrees of freedom of the machine. There has been debate as to which of these two conceptually different approaches should be used in situations out of thermal equilibrium. Here we compare the local and global approaches against an exact solution for a particular class of thermal machines. We consider thermodynamically relevant observables, such as heat currents, as well as the quantum state of the machine. Our results show that the use of a local master equation is generally well justified. In particular, for weak inter-system coupling, the local approach agrees with the exact solution, whereas the global approach fails for non-equilibrium situations. For intermediate coupling, the local and the global approach both agree with the exact solution and for strong coupling, the global approach is preferable. These results are backed by detailed derivations of the regimes of validity for the respective approaches. (Less)

Emission of time-bin entangled particles into helical edge states

We propose a single-particle source which emits into the helical edge states of a two-dimensional quantum spin Hall insulator. Without breaking time-reversal symmetry, this source acts like a pair of noiseless single-electron emitters which each inject separately into a chiral edge state. By locally breaking time-reversal symmetry, the source becomes a proper single-particle emitter which exhibits shot noise. Due to its intrinsic helicity, this system can be used to produce time-bin entangled pairs of electrons in a controlled manner. The noise created by the source contains information on the emitted wave packets and is proportional to the concurrence of the emitted state.

Autonomous quantum refrigerator in a circuit QED architecture based on a Josephson junction

An implementation of a small quantum absorption refrigerator in a circuit QED architecture is proposed. The setup consists of three harmonic oscillators coupled to a Josephson junction. The refrigerator is autonomous in the sense that it does not require any external control for cooling, but only thermal contact between the oscillators and heat baths at different temperatures. In addition, the setup features a built-in switch, which allows the cooling to be turned on and off. If timing control is available, this enables the possibility for coherence-enhanced cooling. Finally, we show that significant cooling can be achieved with experimentally realistic parameters and that our setup should be within reach of current technology.

Quantum heat engine based on photon-assisted Cooper pair tunneling

We propose and analyze a simple mesoscopic quantum heat engine that exhibits both high power and high efficiency. The system consists of a biased Josephson junction coupled to two microwave cavities, with each cavity coupled to a thermal bath. Resonant Cooper pair tunneling occurs with the exchange of photons between cavities, and a temperature difference between the baths can naturally lead to a current against the voltage, and hence work. As a consequence of the unique properties of Cooper-pair tunneling, the heat current is completely separated from the charge current. This combined with the strong energy selectivity of the process leads to an extremely high efficiency.

Electron waiting times in coherent conductors are correlated

We evaluate the joint distributions of electron waiting times in coherent conductors described by scattering theory. Successive electron waiting times in a single-channel conductor are found to be correlated due to the fermionic statistics encoded in the many-body state. Our formalism allows us also to investigate the waiting times between charge transfer events in different outgoing channels. As an application we consider a quantum point contact in a chiral setup with one or both input channels biased by either a static or a time-dependent periodic voltage described by Floquet theory. The theoretical framework developed here can be applied to a variety of scattering problems and can in a straightforward manner be extended to joint distributions of several electron waiting times. (Less)

Quantum Thermal Machine as a Thermometer

We propose the use of a quantum thermal machine for low-temperature thermometry. A hot thermal reservoir coupled to the machine allows for simultaneously cooling the sample while determining its temperature without knowing the model-dependent coupling constants. In its most simple form, the proposed scheme works for all thermal machines that perform at Otto efficiency and can reach Carnot efficiency. We consider a circuit QED implementation that allows for precise thermometry down to ∼15  mK with realistic parameters. Based on the quantum Fisher information, this is close to the optimal achievable performance. This implementation demonstrates that our proposal is particularly promising in systems where thermalization between different components of an experimental setup cannot be guaranteed.

Quantum heat engines based on electronic Mach-Zehnder interferometers

We theoretically investigate the thermoelectric properties of heat engines based on Mach-Zehnder interferometers. The energy dependence of the transmission amplitudes in such setups arises from a difference in the interferometer arm lengths. Any thermoelectric response is thus of purely quantum-mechanical origin. In addition to an experimentally established three-terminal setup, we also consider a two-terminal geometry as well as a four-terminal setup consisting of two interferometers. We find that Mach-Zehnder interferometers can be used as powerful and efficient heat engines which perform well under realistic conditions.

Electron waiting times for the mesoscopic capacitor

We evaluate the distribution of waiting times between electrons emitted by a driven mesoscopic capacitor. Based on a wave packet approach we obtain analytic expressions for the electronic waiting time distribution and the joint distribution of subsequent waiting times. These semi-classical results are compared to a full quantum treatment based on Floquet scattering theory and good agreement is found in the appropriate parameter ranges. Our results provide an intuitive picture of the electronic emissions from the driven mesoscopic capacitor and may be tested in future experiments.

Single-electron entanglement and nonlocality

Motivated by recent progress in electron quantum optics, we revisit the question of single-electron entanglement, specifically whether the state of a single electron in a superposition of two separate spatial modes should be considered entangled. We first discuss a gedanken experiment with single-electron sources and detectors, and demonstrate deterministic (i. e. without post-selection) Bell inequality violation. This implies that the single-electron state is indeed entangled and, furthermore, nonlocal. We then present an experimental scheme where single-electron entanglement can be observed via measurements of the average currents and zero-frequency current cross-correlators in an electronic Hanbury Brown-Twiss interferometer driven by Lorentzian voltage pulses. We show that single-electron entanglement is detectable under realistic operating conditions. Our work settles the question of single-electron entanglement and opens promising perspectives for future experiments.

Mach-Zehnder interferometry with periodic voltage pulses

We investigate theoretically a Mach-Zehnder interferometer driven by a time-dependent voltage. Motivated by recent experiments, we focus on a train of Lorentzian voltage pulses which we compare to a sinusoidal and a constant voltage. We discuss the visibilities of Aharonov-Bohm oscillations in the current and in the noise. For the current, we find a strikingly different behavior in the driven as compared to the static case for voltage pulses containing multiple charges. For pulses containing fractional charges, we find a universality at path-length differences equal to multiples of the spacing between the voltage pulses. These observations can be explained by the electronic energy distribution of the driven contact. In the noise oscillations, we find additional features which are characteristic to time-dependent transport. Finite electronic temperatures are found to have a qualitatively different influence on the current and the noise. (Less)