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arXiv:2010.04026 · Chinese Physics B

Impact of counter-rotating-wave term on quantum heat transfer and phonon statistics in nonequilibrium qubit–phonon hybrid system*

Chen Wang, Lu-Qin Wang, Jie Ren

Published Dec 2, 2020• 6 citations
arXivHTMLPDF

Abstract

Counter-rotating-wave terms (CRWTs) are traditionally viewed to be crucial in open small quantum systems with strong system–bath dissipation. Here by exemplifying in a nonequilibrium qubit–phonon hybrid model, we show that CRWTs can play the significant role in quantum heat transfer even with weak system–bath dissipation. By using extended coherent phonon states, we obtain the quantum master equation with heat exchange rates contributed by rotating-wave-terms (RWTs) and CRWTs, respectively. We find that including only RWTs, the steady state heat current and current fluctuations will be significantly suppressed at large temperature bias, whereas they are strongly enhanced by considering CRWTs in addition. Furthermore, for the phonon statistics, the average phonon number and two-phonon correlation are nearly insensitive to strong qubit–phonon hybridization with only RWTs, whereas they will be dramatically cooled down via the cooperative transitions based on CRWTs in addition. Therefore, CRWTs in quantum heat transfer system should be treated carefully.

DOI
10.1088/1674-1056/abcfa8

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cond-mat.mes-hallCross-listedarXiv:2609.29430•Sep 25, 2026
Counter-rotating-wave terms (CRWTs) are traditionally viewed to be crucial in open small quantum systems with strong system–bath dissipation. Here by exemplifying in a nonequilibrium qubit–phonon hybrid model, we show that CRWTs can play the significant role in quantum heat transfer even with weak system–bath dissipation. By using extended coherent phonon states, we obtain the quantum master equation with heat exchange rates contributed by rotating-wave-terms (RWTs) and CRWTs, respectively. We find that including only RWTs, the steady state heat current and current fluctuations will be significantly suppressed at large temperature bias, whereas they are strongly enhanced by considering CRWTs in addition. Furthermore, for the phonon statistics, the average phonon number and two-phonon correlation are nearly insensitive to strong qubit–phonon hybridization with only RWTs, whereas they will be dramatically cooled down via the cooperative transitions based on CRWTs in addition. Therefore, CRWTs in quantum heat transfer system should be treated carefully.
We investigate the effect of counter-rotating-wave terms on nonlocality and entanglement for three qubits coupled to a common bath for strong- and ultrastrong-coupling regimes beyond the traditional treatment of Born-Markovian, perturbative, and rotating-wave approximations by employing the numerical hierarchical equations-of-motion approach. Our findings are as follows: (1) In the strong-coupling regime, the counter-rotating terms accelerate the decay of genuine three-party correlations, and the obvious sudden birth of Bell nonlocality is found. (2) In the ultrastrong-coupling regime, we observe a phenomenon in which nonlocality is consistently transferred between a three-qubit system and its subsystem. In addition, the inclusion of counter-rotating wave terms obviously enhances genuine tripartite nonlocality. (3) These counter-rotating terms cannot effectively generate genuine three-party correlations in zero-excitation cases, which differs from previous studies involving only two qubits. (4) A significant reduction in steady-state correlations for three- and two-party systems due to counter-rotating-wave terms is observed, which is not detectable under the rotating-wave approximation.
Abstract We investigate full counting statistics of quantum heat transfer in a collective-qubit system constructed by multi-qubits interacting with two thermal baths. The nonequilibrium polaron-transformed Redfield approach embedded with an auxiliary counting field is applied to obtain the steady state heat current and fluctuations, which enables us to study the impact of the qubit–bath interaction in a wide regime. The heat current, current noise, and skewness are all found to clearly unify the limiting results in the weak and strong couplings. Moreover, the superradiant heat transfer is clarified as a system-size-dependent effect, and large number of qubits dramatically suppress the nonequilibrium superradiant signature.
We study the steady-state entanglement and heat current of two coupled qubits, in which two qubits are connected with two independent heat baths (IHBs) or two common heat baths (CHBs). We construct the master equation in the eigenstate representation of two coupled qubits to describe the dynamics of the total system and derive the solutions in the steady-state with stronger coupling regime between two qubits than qubit–baths. We do not make the rotating wave approximation (RWA) for the qubit–qubit interaction, and so we are able to investigate the behaviors of the system in both the strong coupling regime and the weak coupling regime, respectively. In an equilibrium bath, we find that the entanglement decreases with the bath temperature and energy detuning increasing under the strong coupling regime. In the weak coupling regime, the entanglement increases with coupling strength increasing and decreases with the bath temperature and energy detuning increasing. In a nonequilibrium bath, the entanglement without RWA is useful for entanglement at lower temperatures. We also study the heat currents of the two coupled qubits and their variations with the energy detuning, coupling strength and low temperature. In the strong (weak) coupling regime, the heat current increases (decreases) with coupling strength increasing when the temperature of one bath is lower (higher) than the other, and the energy detuning leads to a positive (negative) effect when the temperature is low (high). In the weak coupling regime, the variation trend of heat current is opposite to that of coupling strength for the IHB case and the CHB case.
To study the full counting statistics of quantum heat transfer in a driven nonequilibrium spin-boson model, we develop a generalized nonequilibrium polaron-transformed Redfield equation with an auxiliary counting field. This enables us to study the impact of qubit-bath coupling ranging from weak to strong regimes. Without external modulations, we observe maximal values of both steady-state heat flux and noise power in moderate coupling regimes, below which we find that these two transport quantities are enhanced by the finite-qubit-energy bias. With external modulations, the geometric-phase-induced heat flux shows a monotonic decrease upon increasing the qubit-bath coupling at zero qubit energy bias (without bias). While under the finite-qubit-energy bias (with bias), the geometric-phase-induced heat flux exhibits an interesting reversal behavior in the strong coupling regime. Our results unify the seemingly contradictory results in weak and strong qubit-bath coupling regimes and provide detailed dissections for the quantum fluctuation of nonequilibrium heat transfer.
The modelling of quantum heat transfer processes at the nanoscale is crucial for the development of energy harvesting and molecular electronic devices. Herein, we adopt a mixed quantum-classical description of a device, in which the open subsystem of interest is treated quantum mechanically and the surrounding heat baths are treated in a classical-like fashion. By introducing such a mixed quantum-classical description of the composite system, one is able to study the heat transfer between the subsystem and bath from a closed system point of view, thereby avoiding simplifying assumptions related to the bath time scale and subsystem-bath coupling strength. In particular, we adopt the full counting statistics approach to derive a general expression for the moment generating function of heat in systems whose dynamics are described by the quantum-classical Liouville equation (QCLE). From this expression, one can deduce expressions for the dynamics of the average heat and heat current, which may be evaluated using numerical simulations. Due to the approximate nature of the QCLE, we also find that the steady state fluctuation symmetry holds up to order ℏ for systems whose subsystem-bath couplings and baths go beyond bilinear and harmonic, respectively. To demonstrate the approach, we consider the nonequilibrium spin boson model and simulate its time-dependent average heat and heat current under various conditions.
Quantum heat transport governs energy exchange processes and statistical laws in non-equilibrium quantum systems, and plays a pivotal role in quantum thermodynamics. We investigate the steady-state thermal transport of a noncommuting coupled spin system. We employ the quantum dressed master equation approach within the framework of open quantum system theory to accurately analyze the non-equilibrium dynamics, ensuring the validity of transport results in the strong coupling regime. Our results demonstrate that noncommuting spin coupling serves as a significant resource for modulating the nonlinearity of the heat current. Specifically, in the weak spin-coupling regime, the system exhibits robust negative differential thermal conductance (NDTC) across various spin numbers. By deriving analytical expressions for the heat current in both the single-spin and large-spin limits, we reveal that this NDTC behavior is governed by microscopic cycle fluxes. Physically, this arises because spin excitation channels induced by the cold reservoir are suppressed under a large temperature bias, thereby blocking energy exchange cycles. Conversely, in the strong spin-coupling and large temperature bias regime, the quantum system demonstrates pronounced thermal rectification. This high rectification efficiency originates from the unidirectional saturation of the heat current, rendering the system a promising candidate for high-performance thermal diodes. Furthermore, we extend the model to a three-terminal configuration to construct a quantum thermal transistor. By manipulating the temperature of the gate reservoir, we achieve efficient modulation and amplification of heat flow between the source and drain. The heat amplification factor is shown to far exceed unity in specific operating regions, confirming significant thermal amplification.