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arXiv:1510.05538

Random Nonlinear Infinite-Level-System Model for Amorphous Solid Phonon Echo and Saturation Phenomena

Zhou, Di, Anthony J. Leggett

Published Oct 19, 2015• 2 citations
arXivHTMLPDF

Abstract

The first two successful predictions for amorphous solid experiments by tunneling-two-level-system (TTLS) was phonon echo and saturation phenomena. In this paper by generalizing TTLS to infinite-level-system model with certain randomness and nonlinearity, we prove that phonon echo is a stimulated emission process. The classical infinite-level-system (taking $\hbar\to 0$ limit) cannot find saturation effect, while quantum infinite-level-system can find it with certain nonlinearity assumed. We also prove that without randomness or nonlinearity neither phonon echo nor saturation exists in arbitrary infinite-level-system.

DOI
10.48550/arxiv.1510.05538

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The first two successful predictions for amorphous solid experiments by tunneling-two-level-system (TTLS) was phonon echo and saturation phenomena. In this paper by generalizing TTLS to infinite-level-system model with certain randomness and nonlinearity, we prove that phonon echo is a stimulated emission process. The classical infinite-level-system (taking ℏ→0\hbar\to 0ℏ→0 limit) cannot find saturation effect, while quantum infinite-level-system can find it with certain nonlinearity assumed. We also prove that without randomness or nonlinearity neither phonon echo nor saturation exists in arbitrary infinite-level-system.
While two-level systems (TLSs) are ubiqitous in solid state systems, microscopic understanding of their nature remains an outstanding problem. Conflicting phenomenological models are used to describe TLSs in seemingly similar materials when probed with different experimental techniques. Specifically, bulk measurements in amorphous solids have been interpreted using the model of a tunneling atom or group of atoms, whereas TLSs observed in the insulating barriers of Josephson junction qubits have been understood in terms of tunneling of individual electrons. Motivated by recent experiments studying TLSs in Josephson junctions, especially the effects of elastic strain on TLS properties, we analyze the interaction of the electronic TLS with phonons. We demonstrate that strong polaronic effects lead to dramatic changes in TLS properties. Our model gives a quantitative understanding of the TLS relaxation and dephasing as probed in Josephson junction qubits, while providing an alternative interpretation of bulk experiments. We demonstrate that a model of polaron dressed electronic TLS leads to estimates for the density and distribution of parameters of TLSs consistent with bulk experiments in amorphous solids. This model explains such surprising observations of recent experiments as the existence of minima in the energy of some TLSs as a function of strain and makes concrete predictions for the character of TLS dephasing near such minima. We argue that better understanding of the microscopic nature of TLSs can be used to improve properties of quantum devices, from an enhancement of relaxation time of TLSs to creating new types of strongly interacting optomechanical systems.
A model consisting of a distribution of three-level systems (defects or ionic impurities) in a lattice characterized by a given phonon spectrum is considered in detail. Equations determining the temporal behavior of such a system in an electromagnetic field are analyzed. A steady-state solution describing three-level saturation in the system is achieved. The possibility of the stimulated emission of phonons is considered. It is shown that laserlike self-excitation of phonons cannot be realized, though phonon flux enhancement may be achieved provided certain conditions are fulfilled.
In the last two decades the dynamics of glasses has been a field of great interest. In order to explain the dynamical properties of glasses the two-level-system model has been proposed. In this model an atom, or group of atoms, can access two potential minima separated by a barrier. Phonon-assisted-tunneling between the two minima of this asymmetric double well potential represents a jump between two different local glass structures. These double well potentials are referred to as two-level-systems (TLS). In the standard TLS-model the potentials do not change in time. The intrinsic disorder of the glass provides a wide range of asymmetries and a broad distribution of transition rates. Consequently the dynamics of the glass takes place over a broad range of time scales.
Amorphous solids show surprisingly universal behaviour at low temperatures. The prevailing wisdom is that this can be explained by the existence of two-state defects within the material. The so-called standard tunneling model has become the established framework to explain these results, yet it still leaves the central question essentially unanswered-what are these two-level defects (TLS)? This question has recently taken on a new urgency with the rise of superconducting circuits in quantum computing, circuit quantum electrodynamics, magnetometry, electrometry and metrology. Superconducting circuits made from aluminium or niobium are fundamentally limited by losses due to TLS within the amorphous oxide layers encasing them. On the other hand, these circuits also provide a novel and effective method for studying the very defects which limit their operation. We can now go beyond ensemble measurements and probe individual defects-observing the quantum nature of their dynamics and studying their formation, their behaviour as a function of applied field, strain, temperature and other properties. This article reviews the plethora of recent experimental results in this area and discusses the various theoretical models which have been used to describe the observations. In doing so, it summarises the current approaches to solving this fundamentally important problem in solid-state physics.
Quantum two-level systems (TLSs) intrinsic to glasses induce decoherence in many modern quantum devices, such as superconducting qubits. Although the low-temperature physics of these TLSs is usually well-explained by a phenomenological standard tunneling model of independent TLSs, the nature of these TLSs, as well as their behavior out of equilibrium and at high energies above 1 K, remain inconclusive. Here we measure the non-equilibrium dielectric loss of TLSs in amorphous silicon using a superconducting resonator, where energies of TLSs are varied in time using a swept electric field. Our results show the existence of two distinct ensembles of TLSs, interacting weakly and strongly with phonons, where the latter also possesses anomalously large electric dipole moment. These results may shed new light on the low temperature characteristics of amorphous solids, and hold implications to experiments and applications in quantum devices using time-varying electric fields.
Noise within solid-state systems at low temperatures can typically be traced back to material defects. In amorphous materials, these defects are broadly described by the tunneling two-level systems (TLSs) model. TLS have recently taken on further relevance in quantum computing because they dominate the coherence limit of superconducting quantum circuits. Efforts to mitigate TLS impacts have thus far focused on circuit design, material selection, and surface treatments. Our work takes an approach that directly modifies TLS properties. This is achieved by creating an acoustic bandgap that suppresses all microwave-frequency phonons around the operating frequency of a transmon qubit. For embedded TLS strongly coupled to the transmon qubit, we measure a pronounced increase in relaxation time by two orders of magnitude, with the longestT1time exceeding 5 milliseconds. Our work opens avenues for studying the physics of highly coherent TLS and methods for mitigating noise within solid-state quantum devices.