We explore nonequilibrium quantum heat transport in nonlinear bosonic systems in the presence of a non-Kerr-type interaction governed by hyperparametric oscillation due to two-photon hopping between the two cavities. We estimate the thermodynamic response analytically by constructing the su(2) algebra of the nonlinear Hamiltonian and predict that the system exhibits a negative excitation mode. Consequently, this specific form of interaction enables the cooling of the system by inducing a ground-state transition when the number of particles increases, even though the interaction strength is small. We demonstrate a transition of the heat current numerically in the presence of symmetric coupling between the system and the bath and show long relaxation times in the cooling phase. We compare with the Kerr-type Bose-Hubbard form of interaction induced via cross-phase modulation, which does not exhibit any such transition. We further compute the nonequilibrium heat current in the presence of two baths at different temperatures and observe that the cooling effect for the non-Kerr-type interaction persists. Our findings may help in the manipulation of quantum states using the system's interactions to induce cooling.
We explore nonequilibrium quantum heat transport in nonlinear bosonic systems in the presence of a non-Kerr-type interaction governed by hyperparametric oscillation due to two-photon hopping between the two cavities. We estimate the thermodynamic response analytically by constructing the su(2) algebra of the nonlinear Hamiltonian and predict that the system exhibits a negative excitation mode. Consequently, this specific form of interaction enables the cooling of the system by inducing a ground-state transition when the number of particles increases, even though the interaction strength is small. We demonstrate a transition of the heat current numerically in the presence of symmetric coupling between the system and the bath and show long relaxation times in the cooling phase. We compare with the Kerr-type Bose-Hubbard form of interaction induced via cross-phase modulation, which does not exhibit any such transition. We further compute the nonequilibrium heat current in the presence of two baths at different temperatures and observe that the cooling effect for the non-Kerr-type interaction persists. Our findings may help in the manipulation of quantum states using the system's interactions to induce cooling.
Quantum heat transport is considered as an indispensable branch of quantum thermodynamics to potentially improve performance of thermodynamic devices. We theoretically propose a dissipative qubit-photon system composed of multiple coupled resonators interacting with a single two-level qubit, to explore the steady-state heat transport by tuning both the inter-resonator photon hopping and the qubit-photon coupling. Specifically in the three-mode case, the dramatic enhancement and suppression of the heat current into the central resonator can be modulated by the corresponding frequency, compared to the currents into two edge resonators. Moreover, fruitful cycle current components are unraveled at weak qubit-photon coupling, which are crucial to exhibit the nonmonotonic feature with increase of the reservoir temperature bias. In the one-dimensional case under the mean-field framework, the influence of the photon hopping on heat transport is analyzed. The steady-state heat current is comparatively enhanced to the single-mode limit at weak qubit-photon coupling, stemming from the nonvanishing mean-field photon excitation parameter and the additional cycle current component. We hope these obtained results may have possible applications in quantum thermodynamic manipulation and energy harvesting.
We investigate the transport properties of an anharmonic oscillator, modeled by a single-site Bose-Hubbard model, coupled to two different thermal baths using the numerically exact thermofield based chain-mapping matrix product states (TCMPS) approach. We compare the effectiveness of TCMPS to probe the nonequilibrium dynamics of strongly interacting system irrespective of the system-bath coupling against the global master equation approach in Gorini-Kossakowski-Sudarshan-Lindblad form. We discuss the effect of on-site interactions, temperature bias as well as the system-bath couplings on the steady-state transport properties. Last, we also show evidence of non-Markovian dynamics by studying the nonmonotonicity of the time evolution of the trace distance between two different initial states.
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.
We study the self-contained three-qubit quantum refrigerator, with a three-body interaction enabling cooling of the target qubit, in presence of baths composed of anharmonic quantum oscillators with Kerr-type nonlinearity. We show that such baths, locally connected to the three qubits, opens up the opportunity to implement superior steady-state cooling compared to using harmonic oscillator baths, aiding in access to the free energy required for empowering the refrigerator function autonomously. We find that in spite of providing significant primacy in steady-state cooling, such anharmonic baths do not impart much edge over using harmonic oscillator baths if one targets transient cooling. However, we gain access to steady-state cooling in the parameter region where only transient cooling could be achieved by using harmonic baths. Subsequently, we also study the scaling of steady-state cooling advantage and the minimum attainable temperature for varying levels of anharmonicity present in the bath oscillators. Finally, we analyse heat currents and coefficients of performance of quantum refrigerators using bath modes involving Kerr-type nonlinearity, and present a comparison with the case of using bosonic baths made of simple harmonic oscillators. On the way, we derive the decay rates in the Gorini-Kossakowski-Sudarshan-Lindblad quantum master equation for Kerr-type anharmonic oscillator baths.
Quantum thermal transport and two-photon statistics serve as two representative nonequilibrium features in circuit quantum electrodynamics (cQED) systems. Here we investigate quantum heat flow and two-photon correlation function at steady state in a composite qubit-resonator model, where one qubit shows both transverse and longitudinal couplings to a single-mode optical resonator. With weak qubit-resonator interaction, we unravel two microscopic transport pictures, i.e., cotunneling and cyclic heat exchange processes corresponding to transverse and longitudinal couplings, respectively. The nonmonotonic behavior of the heat current is exhibited by tuning the temperature bias with the weak longitudinal coupling. At strong qubit-resonator coupling, the heat current also exhibits a nonmonotonic feature by increasing qubit-resonator coupling strength, which tightly relies on the scattering processes between the qubit and the corresponding thermal bath. Furthermore, the longitudinal coupling is preferred to enhance heat current in the strong qubit-resonator coupling regime. For two-photon correlation function, it exhibits an antibunching-to-bunching transition by tuning the composite angle, which is mainly dominated by the modulation of the energy gap between the first and the second excited eigenstates. Our results are expected to deepen the understanding of nonequilibrium thermal transport and nonclassical photon radiation based on the cQED platform.
We consider a system consisting of two interacting qubits that are individually coupled to separate heat baths at different temperatures. The quantum effects in heat transport are investigated in a numerically rigorous manner with a hierarchial equations of motion (HEOM) approach for non-perturbative and non-Markovian system-bath coupling cases under non-equilibrium steady-state conditions. For a weak interqubit interaction, the total system is regarded as two individually thermostatted systems, whereas for a strong interqubit interaction, the two-qubit system is regarded as a single system coupled to two baths. The roles of quantum coherence (or entanglement) between the two qubits (q-q coherence) and between the qubit and bath (q-b coherence) are studied through the heat current calculated for various strengths of the system-bath coupling and interqubit coupling for high and low temperatures. The same current is also studied using the time convolutionless (TCL) Redfield equation and using an expression derived from the Fermi golden rule (FGR). We find that the HEOM results exhibit turnover behavior of the heat current as a function of the system-bath coupling strength for all values of the interqubit coupling strength, while the results obtained with the TCL and FGR approaches do not exhibit such behavior, because they do not possess the capability of treating the q-b and q-q coherences. The maximum current is obtained in the case that the q-q coherence and q-b coherence are balanced in such a manner that coherence of the entire heat transport process is realized. We also find that the heat current does not follow Fourier's law when the temperature difference is very large, due to the non-perturbative system-bath interactions.