[Paper Review] Heat rectification by two qubits coupled with Dzyaloshinskii-Moriya interaction

Vipul Upadhyay, Muhammad Tahir Naseem+2 more|arXiv (Cornell University)|Jan 1, 2021

Quantum and electron transport phenomena78 references35 citations

TL;DR

This paper proposes a quantum thermal rectifier using two spin-1/2 qubits coupled via Dzyaloshinskii-Moriya (DM) interaction, demonstrating that DM interaction alone is insufficient for heat rectification due to its inherent antisymmetry. By introducing off-resonant qubits to break symmetry, the system achieves significant thermal rectification, with rectification factors enhanced by tuning DM anisotropy and qubit detuning, and coherence asymmetry identified as a key resource for rectification performance.

ABSTRACT

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.

Motivation & Objective

• To investigate whether Dzyaloshinskii-Moriya (DM) interaction alone can induce thermal rectification in a two-qubit system.
• To identify the necessary asymmetries beyond DM interaction for achieving measurable heat rectification.
• To analytically derive heat current and rectification factor using a global master equation approach.
• To explore the influence of DM field anisotropy direction and system parameters on rectification efficiency.
• To examine the role of quantum correlations, particularly coherence asymmetry, in enabling thermal rectification.

Proposed method

• Modeling a two-qubit system with DM interaction via the Hamiltonian HDM = g(σ̂xLσ̂yR − σ̂yLσ̂xR), with on-site magnetic fields ωL and ωR.
• Using the spin-boson model to describe local coupling of each qubit to its own thermal bath at different temperatures.
• Deriving the open quantum system dynamics using the Born-Markov and secular approximations to obtain a global master equation.
• Solving the master equation analytically to compute steady-state heat currents and rectification factor.
• Employing the global master equation solution to derive analytical expressions for heat current and rectification factor as functions of system parameters.
• Analyzing the role of coherence asymmetry and quantum correlations in rectification performance through steady-state density matrix analysis.

Experimental results

Research questions

• RQ1 Is the antisymmetry of the Dzyaloshinskii-Moriya interaction sufficient to generate thermal rectification in a two-qubit system?
• RQ2 What additional asymmetry mechanisms are required to achieve significant heat rectification when DM interaction is the only coupling?
• RQ3 How do the orientation and anisotropy of the DM field affect the rectification factor and heat current?
• RQ4 Can coherence asymmetry serve as a fundamental resource for thermal rectification in this system?
• RQ5 What parameter regimes maximize the rectification factor in the presence of off-resonant qubits and DM coupling?

Key findings

• The Dzyaloshinskii-Moriya interaction alone is insufficient for heat rectification due to its antisymmetric nature, requiring additional asymmetry.
• Off-resonant qubits provide the necessary asymmetry to enable high rectification factors, with optimal performance observed at specific detuning and coupling strengths.
• The rectification factor reaches values up to approximately 0.8 in favorable parameter regimes, with maximum enhancement near resonant conditions and strong DM coupling.
• The direction of the DM field anisotropy significantly influences rectification efficiency, with z-direction alignment yielding the most favorable results.
• Asymmetry in the coherences of the steady-state density matrix is identified as a fundamental resource for rectification, independent of population imbalance.
• The analytical solution of the global master equation reveals that rectification arises from non-equilibrium quantum coherence dynamics, not just population gradients.