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 antithermalization. We also study the steady-state entanglement between the two TLSs in both the IHB and CHB cases.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 antithermalization. We also study the steady-state entanglement between the two TLSs in both the IHB and CHB cases.

arXiv:1007.4296Physical Review AMay 10, 201139 citations

Two-Photon Scattering in One Dimension by Localized Two-Level System

Tao Shi, C. P. Sun

We study two-photon scattering in a one-dimensional coupled resonator arrays (CRA) by a two-level system (TLS), which is localized as a quantum controller. The $S$ -matrix is analytically calculated for various two-photon scattering processes by TLS, e.g., one photon is confined by TLS to form a bound state while the other is in the scattering state. It is discovered from the poles of the $S$ -matrix that there exist two kinds of three-body bound states for describing two bound photons localized around TLS.We study two-photon scattering in a one-dimensional coupled resonator arrays (CRA) by a two-level system (TLS), which is localized as a quantum controller. The $S$-matrix is analytically calculated for various two-photon scattering processes by TLS, e.g., one photon is confined by TLS to form a bound state while the other is in the scattering state. It is discovered from the poles of the $S$-matrix that there exist two kinds of three-body bound states for describing two bound photons localized around TLS.

arXiv:0907.2776Jul 16, 20096 citations

Two State Systems

WORLD SCIENTIFIC eBooksApr 29, 20140 citations

Nonequilibrium dynamics of two-level systems directly after cryogenic alternating bias

Vito Iaia, E. S. Joseph, Soohyun Im +10 more

Two-level systems (TLSs) are a dominant decoherence mechanism in superconducting qubits, microwave kinetic inductance detectors, and quantum dots. TLSs are tunneling states commonly found in amorphous materials and interfaces, which interact electromechanically, leading to energy loss. Fluctuations in the frequency of the TLSs are a significant problem for qubit operation and force recalibration every few hours. In this study, we probe the effect of alternating bias at cryogenic temperatures on TLSs in a purpose-built LC oscillator. When an alternating bias is applied, the steady-state spectra of the TLSs disappear. Spectroscopy reveals transient behavior, in which the TLS frequency fluctuates on the order of minutes. Thermal cycling above 10 K reverses these effects, restoring the TLS spectrum to its original state. Importantly, the intrinsic loss tangent of the LC oscillator remains unchanged before and after the application of the alternating bias. We propose that the disappearance of the steady-state spectrum is caused by nonequilibrium energy buildup from strain in the oxide film introduced by the pulsed voltage-bias sequence. Understanding this nonequilibrium energy could shed light on TLS fluctuations and reduce the calibration requirements for qubits.Two-level systems (TLSs) are a dominant decoherence mechanism in superconducting qubits, microwave kinetic inductance detectors, and quantum dots. TLSs are tunneling states commonly found in amorphous materials and interfaces, which interact electromechanically, leading to energy loss. Fluctuations in the frequency of the TLSs are a significant problem for qubit operation and force recalibration every few hours. In this study, we probe the effect of alternating bias at cryogenic temperatures on TLSs in a purpose-built LC oscillator. When an alternating bias is applied, the steady-state spectra of the TLSs disappear. Spectroscopy reveals transient behavior, in which the TLS frequency fluctuates on the order of minutes. Thermal cycling above 10 K reverses these effects, restoring the TLS spectrum to its original state. Importantly, the intrinsic loss tangent of the LC oscillator remains unchanged before and after the application of the alternating bias. We propose that the disappearance of the steady-state spectrum is caused by nonequilibrium energy buildup from strain in the oxide film introduced by the pulsed voltage-bias sequence. Understanding this nonequilibrium energy could shed light on TLS fluctuations and reduce the calibration requirements for qubits.

arXiv:2509.19223Physical Review AppliedApr 27, 20261 citation

Two-State Systems

Jean-Louis Basdevant

Graduate texts in physicsJan 1, 20164 citations

We study two-photon scattering in a one-dimensional coupled resonator arrays (CRA) by a two-level system (TLS), which is localized as a quantum controller. The

S

-matrix is analytically calculated for various two-photon scattering processes by TLS, e.g., one photon is confined by TLS to form a bound state while the other is in the scattering state. It is discovered from the poles of the

S

-matrix that there exist two kinds of three-body bound states for describing two bound photons localized around TLS.