Landau-Zener population control and dipole measurement of a two-level-system bath

Abstract

Tunneling two level systems (TLS), present in dielectrics at low temperatures, have been recently studied for fundamental understanding and superconducting device development. According to a recent theory by Burin et al., the TLS bath of any amorphous dielectric experiences a distribution of Landau-Zener transitions if exposed to simultaneous fields. In this experiment we measure amorphous insulating films at millikelvin temperatures with a microwave field and a swept electric field bias using a superconducting resonator. We find that the maximum dielectric loss per microwave photon with the simultaneous fields is approximately the same as that in the equilibrium state, in agreement with the generic material theory. In addition, we find that the loss depends on the fields in a way which allows for the separate extraction of the TLS bath dipole moment and density of states. This method allows for the study of the TLS dipole moment in a diverse set of disordered films, and provides a technique for continuously inverting their population.In quantum computing, two-level systems (TLS) in dielectrics have been found to function as an environmental bath for superconducting quantum elements 1-4 and as quantum memory bits in a hybrid quantum computer 5 . The environmental impact of the deleterious bath has led to improved materials 6-8 for superconducting qubits. In recent qubit designs 9,10 the geometrical architecture allows only for a small amount of electrical energy storage in the deleterious amorphous metal oxides. Over four decades ago, a now standard model of TLS was introduced which describes charged nanoscale systems moving independently in a distribution of double well potentials, presumably created by undercoordinated bonds 11,12 . Recent measurements of individual TLSs under application of a strain field are in agreement with this model 13 . Although the TLS effects are generally known, the precise identity of the atomic defects or bonds that comprise the TLS and dipole moments from a given material are generally not known [14][15][16] . Furthermore, it was found that the sudden application of strain or electric fields can result in an immediate change in the TLS density, followed by a slow glassy relaxation to the equilibrium state 17-19 , possibly caused by weak TLS-TLS interactions 20,21 .In the case of resonant microwave measurements, the loss tangent is proportional to the weighted TLS densitythe TLS density times the dipole moment squared. Experiments on individual TLS provide important quantum properties 5,22-24 , but have previously been restricted to an alumina tunneling barrier and must characterize many TLS, one at a time, in order to extract an average dipole moment of the film. The Landau-Zener effect has been used to study a wide variety of qubit systems, including superconducting circuits 25-27 , silicon-dopants 28 , and quantum dots 29 . A recent theory using this effect predicts that TLS can be characterized using the quantum dynamics created by two simultaneous fields 30 . Experimental real...

Low-temperature1/fnoise in microwave dielectric constant of amorphous dielectrics in Josephson qubits

“…To characterize this dependence we evaluated the integral in Eq. (18) numerically, assuming a constant dipole moment p = 5 D and TLS relaxation rate parameter A = 10 8 s −1 K −3 [7,17,25]. The TLS dipole moment is chosen as 5 D following the earlier estimates for aluminum oxide and silicon nitride glasses used in previous noise measurements [7,17], though it may be smaller in other glasses [24].…”

“…The pure linear regime takes place for F ac ≪ F 1 , where F 1 is the non-linear absorption threshold defined by the condition pF 1 T 1 T 2 / ≈ 1 [19]. At T < 0.1 K both relaxation times are of the order of 1 µs and one can estimate the critical field using the typical TLS dipole moment p ∼ 5 D [25] as…”

“…(6) and Refs. [25,26]) is much larger than the field oscillation period, i.e. ωT 1 ≫ 1, and the TLS contribution to the dielectric constant is of resonant nature [19].…”

“…This time is defined by τ Similarly to the previous section and to other works [7,25], we assume a single value p for the magnitude of TLS dipole moment, as well as for the relaxation parameter A (A e ). Other assumptions (e.g., Gaussian distribution) lead to similar results and the present uncertainty of available experimental data [16] (see Figs.…”

“…Loss tangent measurements with a time-varying bias similar to Ref. [25] can help to extract these parameters separately. The non-linear threshold at the number of photons n ∼ c −2 ≈ 10 is quite typical for the microwave cavities under consideration (cf.…”