Two-Level Systems with a Time-Dependent Interaction

Sebastian Zanker, Michael Marthaler, Gerd Schön

It is frequently observed that even at very low temperatures, the number of quasiparticles in superconducting materials is higher than predicted by standard BCS theory. These quasiparticles can interact with two-level systems, such as superconducting qubits or two-level systems (TLS) in the amorphous oxide layer of a Josephson junction. This interaction leads to decay and decoherence of the TLS, with specific results, such as time dependence, depending on the distribution of quasiparticles and the form of interaction. We study the resulting decay laws for different experimentally relevant protocols.

Yoni Shalibo, Yaara Rofe, David Shwa +4 more

We measure the lifetime (T₁) and coherence (T₂) of two-level defect states (TLSs) in the insulating barrier of a Josephson phase qubit and compare to the interaction strength between the two systems. We find for the average decay times a power-law dependence on the corresponding interaction strengths, whereas for the average coherence times we find an optimum at intermediate coupling strengths. We explain both the lifetime and the coherence results using the standard TLS model, including dipole radiation by phonons and anticorrelated dependence of the energy parameters on environmental fluctuations.

Tuguldur Begzjav, Hichem Eleuch

One of the most powerful and potentially useful methods of time-dependent matrix differential equations is the Magnus expansion. In this work, we applied the Magnus expansion for Schrödinger and master equations of a dissipative two-level system interacting with a time-dependent π pulse. Two different models of dissipative two-level systems are considered, namely (i) the system decays from two considered levels into some other levels with given decay rates; (ii) the system decays from its excited level to its ground level. The obtained approximate solutions of a time dynamics by the first-order Magnus expansion are well consistent with the results of numerical calculations obtained by the fourth-order Runge-Kutta method.

J. Aliaga, J. L. Gruver, Araceli N. Proto