Two-Level Systems (TLSs)

• Two-Level Systems (TLSs) are quantum entities characterized by two discrete energy levels and modeled via double-well potentials.
• They cause decoherence in superconducting qubits by absorbing energy through electric dipole interactions, reducing relaxation times.
• Experimental techniques using resonators enable precise measurement of TLS parameters, facilitating engineered improvements in superconducting materials.

In condensed matter physics, two-level systems (TLSs) are quantum entities characterized by two discrete energy levels. They are vital for understanding the low-temperature properties of amorphous solids but present significant challenges in settings such as superconducting quantum circuits. TLSs are typically modeled as defects or impurities that can occupy one of two configurations, often visualized as being in a double-well potential.

1. Theoretical Background and Modeling

TLSs can be described by Hamiltonians representing the asymmetry energy $\varepsilon$ between two potential wells and a tunneling energy $\Delta_0$: $$H_{\text{TLS}} = \frac{\varepsilon}{2}\sigma_z + \frac{\Delta_0}{2}\sigma_x,$$ where $\sigma_z$ and $\sigma_x$ are Pauli matrices representing the TLS states. The energy splitting between the levels is given by $E = \sqrt{\Delta_0^2 + \varepsilon^2}$, and the TLS interacts with external fields through its electric dipole moment.

2. Impact on Superconducting Qubits

TLSs are a major source of decoherence and noise in superconducting qubits. The primary coupling mechanism is through electric fields, where TLSs resonant with the qubit's frequency can absorb energy, reducing the qubit's relaxation time $T_1$. Studies like those in superconducting qubits (Thorbeck et al., 2022) have demonstrated that ionizing radiation can lead to TLS scrambling, where a radiation event causes abrupt frequency shifts in multiple TLSs, impacting qubit performance unpredictably.

3. Phonon and Acoustic Interactions

TLSs interact with phonons, mediating effective interactions among them that contribute to the glassy behavior of amorphous materials. The strength and nature of these interactions depend on the symmetry of the TLSs: inversion asymmetric TLSs (S-TLSs) and symmetric ones ($\tau$-TLSs) (Churkin et al., 2013). These interactions are responsible for the universal low-temperature properties of disordered materials, such as the plateau in thermal conductivity and internal friction.

4. Experimental Techniques for TLS Characterization

In superconducting circuits, TLSs can be characterized using transmission-line resonators (Brehm et al., 2017) and quantum sensors (Bilmes et al., 2020). These setups exploit the strong coupling between TLSs and the electromagnetic fields in superconducting devices, allowing detailed measurements of TLS parameters such as energy spacings, coupling strengths, and interactions with strain and electric fields.

5. Many-body and Localization Effects

TLSs are shown to induce many-body localization (MBL) effects in glasses (Artiaco et al., 2020). The disorder from TLSs results in a breakdown of ergodicity, leading to localization of energy and non-thermal behavior. The interaction effects between TLSs contribute to slow relaxation dynamics characteristic of MBL.

6. Applications and Engineering Superconductivity

TLSs can be engineered to modify the superconducting properties of materials (Heath et al., 27 Oct 2025). By adjusting the density and distribution of TLSs, it's possible to enhance or suppress the critical temperature $T_c$ and the superconducting gap. This tuning can provide new pathways for designing high-$T_c$ superconductors by manipulating defects and impurities in the material.

Conclusion

TLSs present both challenges and opportunities in the world of quantum materials and devices. Understanding their dynamics, interactions, and the effects on superconducting systems is crucial for improving the performance and reliability of technologies such as quantum computers and sensors. Continued research and advanced spectroscopic techniques will further illuminate the role of TLSs, enabling better control and utilization of these ubiquitous quantum systems.