
Physics and Dynamics of TLS


Chair morning talks: Moshe Schechter

09:15  10:00

Georg Weiss
(Karlsruhe Institute of Technology)
Dielectric measurements of the dynamics of atomic tunneling systems in thinfilm AlOx
Dielectric measurements of the dynamics of atomic tunneling systems in thinfilm AlOx
S. Meißner, A. Seiler, G. Weiss
Karlsruher Institut für Technologie, Karlsruhe, Germany
Josephson junctions made from Al/AlOx/Al film sandwiches are the central elements of superconducting quantum circuits. As all disordered solids, the noncrystalline AlOx contains atomic twolevel tunneling systems (TS) which play an inglorious role in dephasing the quantum states of the circuit under consideration. Interaction is mainly caused by the electric dipole moment of the tunneling group of atoms coupling strongly to electric fields of the circuit. Here, we present a broadband study ranging from kHz to GHz frequencies of the dynamics of TS contained in thinfilm disordered AlOx. The TS ́ density of states is probed at kHz frequencies by capacitance measurements as well as in the GHz range by tracking the resonance frequencies of superconducting microstrip resonators with embedded plate capacitors. Due to the homogeneous electric field concentrated in the dielectric AlOx the influence of native oxide on top of the Al structures is negligible. The large bandwidth of the excitation frequencies allows us allows us to verify general predictions of the standard tunneling model. Our measured data, however, is more consistent with an increasing density of TS with increasing energy. Moreover, the low frequency measurements surprisingly show an influence of a magnetic field applied to the plate capacitors. The influence is attributed to the interaction between TS and quasi particles in the superconducting state of the Al electrodes and conduction electrons in the normal state, respectively.

10:00  10:30

Coffee break

10:30  11:15

Jared Cole
(RMIT University)
Microscopic models of TLS, atomic structure and phonons
Recently, individual control and addressing of TLS have allowed detailed studies of the temperature and strain dependence of TLS decoherence. The interaction of TLS with phonons within the material is typically considered an important decoherence mechanism which has been studied in depth for ensembles of TLS within the framework of the standard tunnelling model (STM). More recently the interplay of two classes of TLS has been proposed as an argument for the near universal behaviour observed in amorphous materials. These two classes are distinguished by the extent to which they couple to the phonon field, one relatively weakly due to symmetry, the other more strongly. An alternative model considers the possibility that single electrons which are ‘dressed’ by the phonon field result in an effective candidate for TLS.
Given the importance of understanding the interaction between TLS and phonons, raises the question, what are limits of what we can determine about TLS simply by measuring the phonon response? To answer this question requires careful consideration of the input parameters to the STM, its microscopic justification and the influence of geometry on the phonon response.

11:15  12:00

Martin Cyster
(RMIT University)
Simulation of the fabrication and electronic properties of Al/AlOx/Al Josephson junctions
To fabricate superconducting qubits of consistent quality, it is important to be able to reproducibly manufacture junctions with identical resistances (and critical currents). Experimental investigations of Al/AlOx/Al Josephson junctions have found a Gaussian distribution of barrier thicknesses exists within individual devices [1]. The thickness variation causes subsequent variations in current density, where the thinnest regions dominate transport. Other aspects of the microscopic structure of the barrier have been considered as candidates for twolevel systems (TLS) [2]. It is therefore important to understand the atomic structure of the amorphous barrier oxides, their interface with the aluminium electrodes, and the connection between the atomic structure and device performance.
The aluminiumoxide is often formed using a lowpressure oxidation of the aluminium surface. In some simulations heightened pressures and temperatures are used to accelerate the oxidation dynamics [3]. In contrast we consider simulating the oxidation directly by adding individual oxygen atoms (or molecules) to the aluminium surface in an iterative procedure. This allows us to capture the low pressures used in fabrication in our model. With this approach we are able to reproduce minutes of real time oxidation by only simulating the interactions between the new oxygen atom and the surface while assuming that the system evolves minimally between deposition events.
The electronic properties of the device are strongly dependent on the morphology of the barrier, both at the interfaces of the superconducting leads and within the metal oxide itself. In spite of this, the transport of charge through these devices is usually modelled with a simplified onedimensional potential which “averages out” the effects of material defects inside the junction [4]. We calculate the I–V response and normal state resistances of atomistic junction models with the nonequilibrium Green’s functions formalism (NEGF). This calculation incorporates the full detail of the threedimensional structure in the barrier.
The effect of varying the thickness, stoichiometry and oxide density on the resistance of the tunnelling barrier is also investigated. Our electronic transport model reproduces the expected exponential dependence on barrier thickness and predicts an exponential dependence the oxide density. The endtoend modelling approach we apply provides insight into how the junction structure at a microscopic level relates to the electronic properties of the device.

[1] L. J. Zeng et al., “Direct observation of the thickness distribution of ultra thin AlOx barriers in Al/AlOx/Al Josephson junctions”, Journal of Physics D: Applied Physics, 48(39), pp. 395308, 2015.
[2] Müller, C., Cole, J. H., & Lisenfeld, J. (2017). “Towards understanding twolevelsystems in amorphous solids  Insights from quantum devices”, pp. 1–30. arXiV:1705.01108
[3] T. Campbell et al., “Oxidation of aluminium nanoclusters”, Physical Review B, 71(20), pp. 205413 (2005).
[4] W. F. Brinkman, R. C. Dynes, and J. M. Rowell, “Tunneling conductance of asymmetrical barriers”, Journal of Applied Physics, 41(5), pp. 1915, 1970.

12:00  13:00

Lunch break

13:00  14:00

Discussions


Chair afternoon talks: Kevin Osborn

14:00  14:45

Alexander Burin
(Tulane University)
Theory of nonlinear absorption by interacting twolevel systems
Here we treat the spectral diffusion of two level system (TLS) energies explicitly using the generalized master equation formalism to describe the nonlinear absorption. The proposed theory predicts that the linear absorption regime holds while a TLS Rabi frequency is smaller than their phase decoherence rate. At higher external fields, a nonlinear absorption regime is found with the loss tangent inversely proportional to the intensity of the field while at highest intensities the earlier predicted "noninteracting" behavior is restored.

14:45  15:30

Shlomi Matityahu
(Ben Gurion University of the Negev)
Dynamical decoupling of twolevel systems by coherent multiple LandauZener transitions
In this talk I will discuss a theoretical and experimental study of the dielectric loss of superconducting resonators in the presence of a periodic bias field. This field slowly changes the energy bias of tunneling twolevel systems (TLSs), and sweeps them through resonance with the resonator. The dynamics of each transition is of the LandauZener type. To obtain the dielectric loss, we calculate the fullcounting statistics of the number of photons absorbed by a single TLS. At low and intermediate sweep rates, the theory and the experimental data reproduce previous studies [1,2], showing an increasing loss with increasing sweep rate, followed by a universal plateau. This behavior corresponds to the regime of strong TLS relaxation between consecutive transitions, which can thus be considered independent [1,2]. In our study we explore a regime of high sweep rates, larger than the TLS relaxation rate, for which the coherent evolution during several LandauZener transitions has to be considered. We show that due to
interference effects, the resonator loss decreases again in this regime. In contrast to the low dielectric loss at zero sweep rate, arising from saturation of photon absorption by TLSs, the low loss in the high sweep
rate regime is a consequence of a reduced photon absorption probability due to the coherent evolution of the TLS state over many LandauZener transitions. The possibility to extend this physics in order to dynamically decouple TLSs from a qubit will be discussed.
1. M. S. Khalil, S. Gladchenko, M. J. A. Stoutimore, F. C.
Wellstood, A. L. Burin, and K. D. Osborn, Phys. Rev. B
90, 100201(R) (2014).
2. A. L. Burin, M. S. Khalil, and K. D. Osborn, Phys. Rev.
Lett. 110, 157002 (2013).

15:30  16:00

Andreas Fleischmann
(Heidelberg University)
Nuclear spin driven dynamics in nonequilibrium disordered quantum systems
The investigation of nonequilibrium disordered quantum systems with novel experimental techniques have resulted in fundamentally new insights of their dynamics. In particular, the importance of nuclear spins as surprisingly active degrees of freedom at ultralow temperatures has been revealed in recent measurements on amorphous solids. These new findings are of high relevance to many quantum devices, like quantum dots, qubits, SQUIDs, nanomechanical systems and quantum limited amplifiers. We present the experimental evidence for a nuclear spin driven dynamics in nonequilibrium disordered quantum systems and discuss a possible theoretical framework for such a mechanism.

16:00  16:30

Coffee break


Chair late afternoon talks: Yuri Galperin

16:30  17:00

Vassiliy Lubchenko
(University of Houston)
Lowtemperature anomalies in disordered solids: a cold case of contested relics?
Amorphous solids manifest puzzling effects of mysterious degrees of freedom that give rise to a heat capacity and phonon scattering in great excess over what would be expected for a solid that has a unique vibrational ground state. Of particular conceptual importance is the apparent near universality of phonon scattering in amorphous solids made by quenching a liquid. To rationalise this universality, scalefree scenarios have been proposed that either hinge on there being longrange interactions between bare structural degrees of freedom or that invoke longrange criticality stemming from the emergence of marginally stable vibrational modes. In a contrasting, local scenario, the puzzling lowtemperature degrees of freedom are, instead, weaklyinteracting, strongly anharmonic degrees of freedom each of which involves the motion of a few hundred particles. In this scenario, the universality of phonon scattering comes about because the characteristic energy scale of the local anharmonic resonances and the strength of their interaction with phonons are both set by the glass transition temperature $T_g$, while their concentration is set by the cooperativity size $\xi$ for dynamics at $T_g$. The nanoscopic length $\xi$ is manifested in vibrational excitations of the spatial boundary of the resonances, which underlie the socalled Boson peak, and very deep, topological midgap electronic states in glassy semiconductors, which are implicated in a number of strange optoelectronic phenomena in amorphous chalcogenides. I discuss the merits of the above scenarios when confronted with experimental data.

17:00  17:30

Daniel Kaplan
(Weizmann Institute of Science)
Microscopic realization of the two TLS model
Recently, there's renewed interest in the two TLS model as an explanation for the phenomena observed in experiments (M Schechter et al, 2018).
We propose a new realization of the twoTLS model, based on abinitio calculation and realistic interpretation of what is the mechanism generating the two TLSs (inversion symmetry breaking), as well as an actual simulation of the tunneling entity.
We answer the question of "what tunnels" (Anderson et al, 1972), and suggest what (probable) tunneling systems may be found in real systems.


Chair discussions: Clare Yu

17:30  19:00

Discussions

19:00  20:00

Dinner

20:00  21:00

Informal discussions
