Modeling Energy Relaxation via Quantum Thermalization: A Superconducting Qubit Coupled to a Many-Body TLS System

Abstract

While two-level systems (TLS) in superconducting qubits are known to introduce phonon-mediated energy dissipation channels, many-body TLS systems themselves can also act as a distinct dissipation channel whose effect on qubit energy relaxation remains to be explored. In this work, we model and numerically simulate the irreversible thermalization-driven energy relaxation of a superconducting qubit coupled to a many-body TLS system. Our numerical results show that thermalization suppresses coherent energy exchange between the qubit and TLS, resulting in exponential energy decay. The relaxation times scale as $T_1, T_2 \propto J^{-2}$, where $J$ denotes the qubit-TLS coupling strength. Moreover, $T_1$ is significantly affected by the internal coupling strength of the TLS system, the TLS frequency fluctuation rate, and the number of thermally excited TLS. This work provides a quantum thermalization perspective for understanding qubit energy relaxation and decoherence, with potential implications for decoherence scenarios in other open quantum systems.

Figures (4)

• Figure 1: Many-Body TLS Model and Full Forward-Time Information Erasure Sequence (FFTIE). (a) Coupled superconducting qubit-TLS network. The black circle (dashed box) represents the qubit, and the gold circles represent TLS. Solid lines denote near-resonant TLS-TLS couplings; the dashed line denotes weak near-resonant qubit-TLS coupling. The ghosting effect illustrates TLS with distinct frequencies, with spheres of different colors representing their excited states. (b) One-dimensional chain used for numerical simulations. (c) Full forward-time information erasure sequence (FFTIE) employed in the numerical simulations.
• Figure 2: Coherent Qubit-TLS Chain Energy Exchange. Time evolution of the qubit occupation $\langle \hat{n}_q \rangle$ for many-body TLS chain lengths $L_{\mathrm{TLS}} = 6$ and $7$, starting from different initial states $|\phi(0)\rangle_{q,\mathrm{TLS}}$.
• Figure 3: Exponential Energy Relaxation and Dephasing Induced by Thermalization. (a) and (b) Time evolution of the qubit's occupation $\langle \hat{n}_q \rangle$ and coherence $\sqrt{\langle \hat{\sigma}_x \rangle^2 + \langle \hat{\sigma}_y \rangle^2}$ for $J_{q,\tau}=0.01$, with initial states $|1\rangle$ and $(|0\rangle+|1\rangle)/\sqrt{2}$, respectively. Solid blue (orange) lines represent averages over 10 trajectories, shaded regions indicate standard deviations, and thin light lines show individual trajectories. (c) Time evolution of $\langle \hat{n}_q \rangle$ for $J_{q,\tau}=0.1$ (initial state $|1\rangle$). The solid green line represents the average over 10 trajectories, the shaded region indicates the standard deviation, and the thin light lines show individual trajectories. (d) and (e) Time evolution of $\langle \hat{n}_q \rangle$ and $\sqrt{\langle \hat{\sigma}_x \rangle^2 + \langle \hat{\sigma}_y \rangle^2}$ for $J_{q,\tau}=0.01, 0.008, 0.006, 0.004, 0.002$, with initial states $|1\rangle$ and $(|0\rangle+|1\rangle)/\sqrt{2}$, respectively. Solid lines are exponential fits, and dashed lines represent the averaged raw data (each average containing 10 trajectories). (f) Extracted $T_1$ and $T_2$ values as functions of $J_{q,\tau}$. The dashed lines are fits to the data, with error bars derived from the fitting uncertainties of $T_1$ and $T_2$ in panels (d) and (e).
• Figure 4: Qubit Energy Relaxation Under Different Many-Body TLS Parameters. (a) Average $T_1$ over 5 trajectories for varying $J_{\tau},J_{\upsilon}$. Other parameters as in Fig. \ref{['fig3']}(a). (b) Average $T_1$ over 5 trajectories for different $t_H$. Other parameters as in Fig. \ref{['fig3']}(a). (c) Average $T_1$ over 5 trajectories (dashed) with exponential fits (solid). Parameters as in Fig. \ref{['fig3']}(d), but with initial TLS state $|0\rangle_{\tau}|1\rangle_{\upsilon}$ (single $\upsilon$-excitation).