Requisite ingredients for thermal rectification

Approaching the perfect diode limit through a nonlinear interface

We consider a system formed by two different segments of particles, coupled to thermal baths, one at each end, modeled by Langevin thermostats. The particles in each segment interact harmonically and are subject to an on-site potential for which three different types are considered, namely, harmonic, ϕ^{4}, and Frenkel-Kontorova. The two segments are nonlinearly coupled, between interfacial particles, by means of a power-law potential with exponent μ, which we vary, scanning from subharmonic to superharmonic potentials, up to the infinite-square-well limit (μ→∞). Thermal rectification is investigated by integrating the equations of motion and computing the heat fluxes. As a measure of rectification, we use the difference of the currents, resulting from the interchange of the baths, divided by their average (all quantities taken in absolute value). We find that rectification can be optimized by a given value of μ that depends on the bath temperatures and details of the chains. But, regardless of the type of on-site potential considered, the interfacial potential that produces maximal rectification approaches the infinite square well (μ→∞) when reducing the average temperature of the baths. Our analysis of thermal rectification focuses on this regime, for which we complement numerical results with heuristic considerations.

Heat rectification, heat fluxes, and spectral matching

Heat rectifiers would facilitate energy management operations such as cooling or energy harvesting, but devices of practical interest are still missing. Understanding heat rectification at a fundamental level is key to helping us find or design such devices. The match or mismatch of the phonon band spectrum of device segments for forward or reverse temperature bias of the thermal baths at device boundaries was proposed as the mechanism behind rectification. However, no explicit theoretical relation derived from first principles had been found so far between heat fluxes and spectral matching. We study heat rectification in a minimalistic chain of two coupled ions. The fluxes and rectification can be calculated analytically. We propose a definition of the matching that sets an upper bound for the heat flux. In a regime where the device rectifies optimally, matching and flux ratios for forward and reverse configurations are found to be proportional. The results can be extended to a system of N particles in arbitrary traps with nearest-neighbor linear interactions.

Heat current magnification in classical and quantum spin networks

We investigate heat current magnification (CM) due to asymmetry in the number of spins in two-branched classical as well as quantum spin systems that are kept between two heat baths at different temperatures. We study the classical Ising-like spin models using Q2R and Creutz cellular automaton dynamics. We show that just the difference in the number of spins is not enough and some other source of asymmetry like unequal spin-spin interaction strengths in the upper and lower branches is required for heat CM. We also provide a suitable physical motivation for CM along with ways to control and manipulate it. We then extend this study to a quantum system with modified Heisenberg XXZ interaction and preserved magnetization. Interestingly, in this case, just the asymmetry in the number of spins in the branches is enough to achieve heat CM. We observe that the onset of CM is accompanied by a dip in the total heat current flowing through the system. We then discuss how the observed CM characteristics can be attributed to the intersection of nondegenerate energy levels, population inversion, and atypical magnetization trends as a function of the asymmetry parameter in the Heisenberg XXZ Hamiltonian. Finally we use the concept of ergotropy to support our findings.

Heat flux in chains of nonlocally coupled harmonic oscillators: Mean-field limit

We consider one-dimensional systems of all-to-all harmonically coupled particles with arbitrary masses, subject to two Langevin thermal baths. The couplings correspond to the mean-field limit of long-range interactions. Additionally, the particles can be subject to a harmonic on-site potential to break momentum conservation. Using the nonequilibrium Green's operator formalism, we calculate the transmittance, the heat flow, and local temperatures for arbitrary configurations of masses. For identical masses, we show analytically that the heat flux decays with the system size N as 1/N regardless of the conservation or not of the momentum and of the introduction or not of a Kac factor. These results describe, in good agreement, the thermal behavior of systems with small heterogeneity in the masses.

Heat rectification by two qubits coupled with Dzyaloshinskii-Moriya interaction

We investigate heat rectification in a two-qubit system coupled via the Dzyaloshinskii-Moriya (DM) interaction. We derive analytical expressions for heat currents and thermal rectification and provide possible physical mechanisms behind the observed results. We show that the anisotropy of DM interaction in itself is insufficient for heat rectification, and some other form of asymmetry is needed. We employ off-resonant qubits as the source of this asymmetry. We find the regime of parameters for higher rectification factors by examining the analytical expressions of rectification obtained from a global master equation solution. In addition, it is shown that the direction and quality of rectification can be controlled via various system parameters. Furthermore, we compare the influence of different orientations of the DM field anisotropy on the performance of heat rectification. Finally, we investigate the possible interplay between quantum correlations and the performance of the quantum thermal rectifier. We find that asymmetry in the coherences is a fundamental resource for the performance of the quantum thermal rectifier.

Analytical results for a minimalist thermal diode

We consider a system consisting of two interacting classical particles, each one subject to an on-site potential and to a Langevin thermal bath. We analytically calculate the heat current that can be established through the system when the bath temperatures are different, for weak nonlinear forces. We explore the conditions under which the diode effect emerges when inverting the temperature difference. Despite the simplicity of this two-particle diode, an intricate dependence on the system parameters is put in evidence. Moreover, behaviors reported for long chains of particles can be extracted, for instance, the dependence of the flux with the interfacial stiffness and type of forces present, as well as the dependencies on the temperature required for rectification. These analytical results can be a tool to foresee the distinct role that diverse types of nonlinearity and asymmetry play in thermal conduction and rectification.

Harmonic chains and the thermal diode effect

Harmonic oscillator chains connecting two harmonic reservoirs at different constant temperatures cannot act as thermal diodes, irrespective of structural asymmetry. However, here we prove that perfectly harmonic junctions can rectify heat once the reservoirs (described by white Langevin noise) are placed under temperature gradients, which are asymmetric at the two sides, an effect that we term "temperature-gradient harmonic oscillator diodes." This nonlinear diode effect results from the additional constraint-the imposed thermal gradient at the boundaries. We demonstrate the rectification behavior based on the exact analytical formulation of steady-state heat transport in harmonic systems coupled to Langevin baths, which can describe quantum and classical transport, both regimes realizing the diode effect under the involved boundary conditions. Our study shows that asymmetric harmonic systems, such as room-temperature hydrocarbon molecules with varying side groups and end groups, or a linear lattice of trapped ions may rectify heat by going beyond simple boundary conditions.

Heat rectification with a minimal model of two harmonic oscillators

We study heat rectification in a minimalistic model composed of two unequal atoms subjected to linear forces and in contact with effective Langevin baths induced by Doppler lasers. Analytic expressions of the heat currents in the steady state are spelled out. Asymmetric heat transport is found in this linear system if both the bath temperatures and the temperature-dependent bath-system couplings are exchanged. The model can be realized with two ions in either common or individual traps. This physical setting allows for a natural temperature dependence of the coupling to the baths. We also explore the parameter space of the model to optimize asymmetric heat current and find conditions for maximal rectification. High rectification corresponds to a good match of the power spectra of the ions for forward temperature bias and mismatch for reverse bias, which may be understood by the behavior of dissipative normal modes.

Perturbation theory of thermal rectification

In this paper, a perturbation theory of thermal rectification is developed for a thermal system where an effective thermal conductivity throughout the system can be identified and changes smoothly and slightly. This theory provides an analytical formula of the thermal rectification ratio with rigorous mathematical derivations and physical assumptions. The physical meanings and limitations of the present theory are discussed in detail. Furthermore, a physical relationship among the thermal rectification, system length, temperature difference, and thermal conductivity is built. It reveals the linear relationship between the thermal rectification ratio and temperature difference. Also, the size dependence of the thermal rectification relies on the specific form of the thermal conductivity. In addition, several previous experimental and numerical observations are well explained by this theory.

High-heat-flux rectification due to a localized thermal diode

A theoretical implementation of a localized thermal diode with a rectification factor greater than 10^{6} is demonstrated. In reverse thermal bias, extremely low thermal conductivity is achieved through phononic Rayleigh scattering from a finite-depth defect. In forward bias, the diode oscillator escapes the defect and thermal conductivity becomes up to four orders of magnitude higher. The setup provides a minimal model of a localized thermal diode between two identical oscillator chains and opens up a pathway for thermal diode implementations.

Controlling Quantum Transport via Dissipation Engineering

Inspired by the microscopic control over dissipative processes in quantum optics and cold atoms, we develop an open-system framework to study dissipative control of transport in strongly interacting fermionic systems, relevant for both solid-state and cold-atom experiments. We show how subgap currents exhibiting multiple Andreev reflections-the stimulated transport of electrons in the presence of Cooper pairs-can be controlled via engineering of superconducting leads or superfluid atomic gases. Our approach incorporates dissipation within the channel, which is naturally occurring and can be engineered in cold gas experiments. This opens opportunities for engineering many phenomena with transport in strongly interacting systems. As examples, we consider particle loss and dephasing, and note different behavior for currents with different microscopic origin. We also show how to induce nonreciprocal electron and Cooper-pair currents.

Asymmetric heat transport in ion crystals

We numerically demonstrate heat rectification for linear chains of ions in trap lattices with graded trapping frequencies, in contact with thermal baths implemented by optical molasses. To calculate the local temperatures and heat currents we find the stationary state by solving a system of algebraic equations. This approach is much faster than the usual method that integrates the dynamical equations of the system and averages over noise realizations.