Heat flow through the quantum heat valve coupled to ohmic baths via a master equation approach

Abstract

We provide a theoretical model for the non-equilibrium steady state heat flow through a quantum heat valve. The model is based on a master equation approach, where the partial secular approximation has been carefully performed in order to obtain accurate results. Our study assumes an ohmic spectral density for the two thermal baths of the model. This is in contrast with previous treatments of the quantum heat valve, where the baths have been assumed as being structured with a peaked spectral density near the resonance frequency of the resonator. These studies have also taken the resonator to be a part of the open quantum system of interest, which results in double counting of the resonator, as the latter appears both in the spectral density of the bath and as a part of the open system. Although this model accounts for the observations in a satisfactory way, it raises issues regarding its physical interpretation. Our method solves this conceptual problem. We apply it to describe an experiment on a quantum heat valve, showing that it successfully captures the experimental results and improves upon the previous theoretical model, which suffered from the resonator double-counting issue. Our findings confirm that the careful application of the master equation approach, in particular when it comes to the secular approximation, is a useful tool for explaining realistic experimental setups.

Figures (3)

• Figure 1: Top: Circuit diagram for the quantum heat valve comprised of a resonator-qubit-resonator system coupled to two resistors on either side. Bottom: An abstraction of the circuit diagram showing the effective nearest-neighbour couplings and the additional direct phenomenological resonator-resonator coupling not mediated by the qubit. The weak coupling strength $\alpha \ll 1$ of the baths is a dimensionless quantity.
• Figure 2: The numerically fitted theoretical model (dashed blue line), from Ref. Ronzani2018, is compared against the the master equation approach with partial secular approximation (solid orange line) and the experimental data (solid green line). We see that the model in Ronzani2018 matches the experimental data well but fails, to some extent, to capture the correct curvature of the data around half and integer flux. This behaviour is improved in the global ME PSA approach. On the bottom figure the mismatch between the experimental data and both models is plotted. The parameters shared by both models are $\Omega_\text{L} = \Omega_\text{R} = 2\pi\cdot5.3122\,\text{GHz}\,, E_\text{C}/\Omega_\text{L} = 0.15\,, d = 0.385\,, T_\text{L} = 308\,\text{mK}\,,T_\text{R} = 100\,\text{mK}$. Additionally, the model from Ronzani2018 uses $Q = 20\,, g/\Omega_\text{L} = 0.0171\,, g_{12}/\Omega_\text{L} = -0.0217\,,E_{\text{J}0}/\Omega_\text{L} = 27.54$, while the global ME PSA approach uses $g/\Omega_\text{L} = 0.015\,, g_{12}/\Omega_\text{L} = 0.007\,, E_{\text{J}0}/\Omega_\text{L} = 28.75$ and $\alpha^{(L)} = \alpha^{(R)} = 0.04$. Moreover, in the global ME PSA approach we have set the cutoff frequency to $\omega_\text{c}/\Omega_\text{L} = 50$, the partial secular approximation cutoff $C_\text{PSA} = 100$ and the resonators have been truncated to three levels.
• Figure 3: Non-equilibrium steady state heat flow computed using the unified master equation approach and comparison with experimental data. We can see that also the unified approach is able to capture the experimental behaviour very well, essentially numerically overlapping the more conventional global ME PSA approach from Fig. \ref{['fig:QHV_og_heatflow_model']}. The parameters used in the unified approach are the same as in Fig. \ref{['fig:QHV_og_heatflow_model']} for the global ME PSA approach.