Decoherence spectroscopy with individual two-level tunneling defects

Abstract

Recent progress with microfabricated quantum devices has revealed that an ubiquitous source of noise originates in tunneling material defects that give rise to a sparse bath of parasitic two-level systems (TLSs). For superconducting qubits, TLSs residing on electrode surfaces and in tunnel junctions account for a major part of decoherence and thus pose a serious roadblock to the realization of solid-state quantum processors. Here, we utilize a superconducting qubit to explore the quantum state evolution of coherently operated TLSs in order to shed new light on their individual properties and environmental interactions. We identify a frequency-dependence of TLS energy relaxation rates that can be explained by a coupling to phononic modes rather than by anticipated mutual TLS interactions. Most investigated TLSs are found to be free of pure dephasing at their energy degeneracy points, around which their Ramsey and spin-echo dephasing rates scale linearly and quadratically with asymmetry energy, respectively. We provide an explanation based on the standard tunneling model, and identify interaction with incoherent low-frequency (thermal) TLSs as the major mechanism of the pure dephasing in coherent high-frequency TLS.

Rabi noise spectroscopy of individual two-level tunneling defects

“…As a result, close to the symmetry point ε = 0 (thus cos θ 1) one may assume X cos θ Ω R . We therefore expand In contrast to the Ramsey dephasing, 17,19 which is caused by individual thermal TLSs, the last term of Eq. (8) shows that the second-order contribution to the Rabi dephasing is due to pairs of thermal TLSs.…”

“…Using standard estimations within the STM, one expects the relaxation rates Γ 1 of thermal TLSs (at T = 35 mK) to be smaller than 10 ms −1 . 17,19 Consequently, these fluctuators are in the regime Γ 1 Ω R , Γ Echo and thus give rise to quasistatic noise, for whichX is constant during each run of the experiment but fluctuates between different runs. These fluctuators will not contribute to Γ ν and Γ Echo .…”

“…However, since a product of two RTPs with flipping rates γ 1 and γ 2 is also a RTP with flipping rate γ 1 + γ 2 , the second-order contribution to the Rabi dephasing is essentially similar to the Ramsey dephasing. 17,19 The decay law due to this low-frequency noise is…”

“…1. At each strain value, standard microwave pulse sequences are applied 17 to measure the energy relaxation rate Γ 1 and the dephasing rates of Rabi oscillations and echo signals, Γ Rabi and Γ Echo , of the probed TLS (bottom row of Fig. 1).…”

“…This effective coupling was utilized to directly control the quantum state of individual TLSs by coherent resonant microwave driving. 16 Previously, 17 we measured the Ramsey (free induction decay) and spin-echo pure dephasing rates of individual TLSs in a phase qubit as a function of their asymmetry energy, which was tuned by an applied strain via a piezo actuator. 18 Since the mutual longitudinal coupling between TLSs is proportional to the product of their asymmetry energies, strain-tuning allows one to gradually increase the longitudinal coupling of a single probed TLS to a bath of other TLSs and study its dephasing rates as a function of this coupling.…”