Spectroscopic shifts as a signature of many-body localization phase transition in a one-dimensional transmon array

Abstract. Many-body localization is a phase of matter, which can occur in systems with strong disorder and interactions. One of the main characteristics of the many-body localized phase is that it cannot thermalize because localization slows or stops the propagation of information inside the system. Here, we study many-body localization in a one-dimensional transmon qubit array theoretically and numerically. Differing from frequently used approaches to many-body localization, we study the dynamical phase transition between a thermalized phase and the many-body localized phase by using a numerical method that is based on Fermi’s golden rule. This method makes it possible to distinguish the thermalized phase from the many-body localized phase and allows one to estimate how much disorder is required for the many-body localization phase transition. The distinction between the phases is made by a “soft” gap which appears at the zero-frequency and is known as a universal sign of localization. Unlike many other methods, which are used to recognize the many-body localized phase, the method in question can be easily applied to experiments. In the system that we have chosen the transmon qubits are capacitively coupled to each other, and the system is driven by a harmonic external magnetic flux that induces transitions between the energy eigenstates of the system. We calculated the numerical results for a system with eight transmon qubits, and to make calculations simpler, we assumed that the temperature of the system is infinite. The size of the system is limited by the computational expensiveness of our method. Somewhat surprisingly, the most laborious part of the calculations proved to be the Fermi’s golden rule, which is used to calculate the transition rate spectrum. The results show that the method in question can distinguish the many-body localized phase if the strength of disorder in the system is large, but near the many-body localized phase transition, it is challenging to observe the difference between the thermalized phase and the many-body localized phase. We calculated the transition rate spectra using different values of on-site interaction strength. The results show us that the disorder strength needed for the phase transition is smaller if the on-site interaction strength is weak or very strong. Lastly, we demonstrated the many-body localization phase transition by calculating the energy eigenstates as a function of disorder strength and observing how strongly the eigenenergies repel each other. This method proved to be relatively imprecise to specify the critical disorder strength needed for the many-body localized phase. However, one can clearly notice that the repulsion between energy levels grows weaker as the disorder strength grows stronger

Multimode physics of the unimon circuit

We consider a superconducting half-wavelength resonator that is grounded at its both ends and contains a single Josephson junction. Previously this circuit was considered as a unimon qubit in the single-mode approximation where dc-phase-biasing the junction to $\pi$ leads to increased anharmonicity and 99.9% experimentally observed single-qubit gate fidelity. Inspired by the promising first experimental results, we develop here a theoretical and numerical model for the detailed understanding of the multimode physics of the unimon circuit. To this end, first, we consider the high-frequency modes of the unimon circuit and find that even though these modes are at their ground state, they imply a significant renormalization to the Josephson energy. We introduce an efficient method how the relevant modes can be fully taken into account and show that unexcited high-lying modes lead to corrections in the qubit energy and anharmonicity. Interestingly, provided that the junction is offset from the middle of the circuit, we find strong cross-Kerr coupling strengths between a few low-lying modes. This observation paves the way for the utilization of the multimode structure, for example, as several qubits embedded into a single unimon circuit

Analysis of nonlinear dynamics in a classical transmon circuit

The focus of this thesis is on classical dynamics of a transmon qubit. First, we introduce the basic concepts of the classical circuit analysis and use this knowledge to derive the Lagrangians and Hamiltonians of an LC circuit, a Cooper-pair box, and ultimately we derive Hamiltonian for a transmon qubit. The transmon Hamiltonian is used to derive the equations of motion and also the meaning of these equations is discussed. Finally, the thesis is ended with some numerical results for the transmon equations of motion with a brief interpretation included

Neutron monitor count rate increase as a proxy for dose rate assessment at aviation altitudes during GLEs

Radiation exposure due to cosmic rays, specifically at cruising aviation altitudes, is an important topic in the field of space weather. While the effect of galactic cosmic rays can be easily assessed on the basis of recent models, estimate of the dose rate during strong solar particle events is rather complicated and time consuming. Here we compute the maximum effective dose rates at a typical commercial flight altitude of 35 kft (≈11 000 m above sea level) during ground level enhancement events, where the necessary information, namely derived energy/rigidity spectra of solar energetic particles, is available. The computations are carried out using different reconstructions of the solar proton spectra, available in bibliographic sources, leading to multiple results for some events. The computations were performed employing a recent model for effective dose and/or ambient dose equivalent due to cosmic ray particles. A conservative approach for the computation was assumed. A highly significant correlation between the maximum effective dose rate and peak NM count rate increase during ground level enhancement events is derived. Hence, we propose to use the peak NM count rate increase as a proxy in order to assess the peak effective dose rate at flight altitude during strong solar particle events using the real time records of the worldwide global neutron monitor network

Neutron monitor count rate increase as a proxy for dose rate assessment at aviation altitudes during GLEs

Abstract Radiation exposure due to cosmic rays, specifically at cruising aviation altitudes, is an important topic in the field of space weather. While the effect of galactic cosmic rays can be easily assessed on the basis of recent models, estimate of the dose rate during strong solar particle events is rather complicated and time consuming. Here we compute the maximum effective dose rates at a typical commercial flight altitude of 35 kft (≈11 000 m above sea level) during ground level enhancement events, where the necessary information, namely derived energy/rigidity spectra of solar energetic particles, is available. The computations are carried out using different reconstructions of the solar proton spectra, available in bibliographic sources, leading to multiple results for some events. The computations were performed employing a recent model for effective dose and/or ambient dose equivalent due to cosmic ray particles. A conservative approach for the computation was assumed. A highly significant correlation between the maximum effective dose rate and peak NM count rate increase during ground level enhancement events is derived. Hence, we propose to use the peak NM count rate increase as a proxy in order to assess the peak effective dose rate at flight altitude during strong solar particle events using the real time records of the worldwide global neutron monitor network