Quantum thermalization of two coupled two-level systems in eigenstate and bare-state representations

Abstract

We study analytically the quantum thermalization of two coupled two-level systems (TLSs), which are connected with either two independent heat baths (IHBs) or a common heat bath (CHB). We understand the quantum thermalization in eigenstate and bare-state representations when the coupling between the two TLSs is stronger and weaker than the TLS-bath couplings, respectively. In the IHB case, we find that when the two IHBs have the same temperatures, the two coupled TLSs in eigenstate representation can be thermalized with the same temperature as those of the IHBs. However, in the case of two IHBs at different temperatures, just when the energy detuning between the two TLSs satisfies a special condition, the two coupled TLSs in eigenstate representation can be thermalized with an immediate temperature between those of the two IHBs. In bare-state representation, we find a counterintuitive phenomenon that, under some conditions, the temperature of the TLS connected with the high-temperature bath is lower than that of the other TLS, which is connected with the low-temperature bath. In the CHB case, the coupled TLSs in eigenstate representation can be thermalized with the same temperature as that of the CHB in nonresonant cases. In bare-state representation, the TLS with a larger energy separation can be thermalized to a thermal equilibrium with a lower temperature. In the resonant case, we find a phenomenon of anti-thermalization. We also study the steady-state entanglement between the two TLSs in both the IHB and CHB cases.

Steady quantum coherence in non-equilibrium environment

“…In these cases, if the coupling coefficients g i,k = g i,|k| only depend on the amplitude |k|, i.e., only depend on ω k equivalently, the relation (B.3) still holds, and we still have γ 11 (ω)γ 22 (ω) = |γ 12 (ω)| 2 , as used in many literatures [35].…”

Steady-state entanglement and coherence of two coupled qubits in equilibrium and nonequilibrium environments

“…The eigen-energies and the corresponding eigen-states of the Hamiltonian for the coupled qubit system H s are obtained as follows [17]: where δ = ω 1 + ω 2 , ∆ = ω 1 − ω 2 , Ω = √ ∆ 2 + λ 2 is the Rabi frequency, and θ ∈ [0, π] is the mixing angle defined by tan θ = λ/∆. In the symmetric qubit case ∆ = ω 1 − ω 2 = 0, we have θ = π/2.…”

“…It can be shown that in the eigen-state representation, the coherence at the equilibrium steady state vanishes, i.e., ρ 34 = ρ 43 = 0, in agreement with decoherence. The populations can be found to be [17]…”

Asymmetric coupling between two quantum emitters

“…The theory has a wide variety of applications, with similar formalisms being used to describe superconducting qubits [46], atomic and molecular spectroscopy [47,48], plasmonic dimers [49], and waveguides [50,51]. The utility of the theory has allowed for a range of phenomena to be investigated, including entanglement [52][53][54][55][56][57], decoherence [58], quantum processing [59], and coherent energy transfer [60,61].…”