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We characterize the avoided crossings in a two-parameter, time-periodic system which has been the basis for a wide variety of experiments. By studying these avoided crossings in the near-integrable regime, we are able to determine scaling laws for the dependence of their characteristic features on the non-integrability parameter. As an application of these results, the influence of avoided crossings on dynamical tunneling is described and applied to the recent realization of multiple-state tunneling in an experimental system.
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We study time-optimal protocols for controlling quantum systems which show several avoided level crossings in their energy spectrum. The structure of the spectrum allows us to generate a robust guess which is time-optimal at each crossing. We correct the field applying optimal control techniques in order to find the minimal evolution or quantum speed limit (QSL) time. We investigate its dependence as a function of the system parameters and show that it gets proportionally smaller to the well-known two-level case as the dimension of the system increases. Working at the QSL, we study the control fields derived from the optimization procedure, and show that they present a very simple shape, which can be described by a few parameters. Based on this result, we propose a simple expression for the control field, and show that the full time-evolution of the control problem can be analytically solved.
Axion haloscope detectors require high-$Q$ cavities with tunable TM$_{010}$ modes whose resonant electric field occupies as much of the full volume of the cavity as possible. An analytical study of the effects of longitudinal symmetry breaking within microwave cavities was conducted to better understand the mode structure. The study revealed longitudinal symmetry breaking of the cavities was the mechanism for avoided mode crossings (AMC) in cylindrical microwave cavities. The results showed the size of the gaps in the search frequency spectrum due to an AMC was roughly proportional to the magnitude of symmetry breaking for small perturbations.
Cavity optomechanics offers powerful methods for controlling optical fields and mechanical motion. A number of proposals have predicted that this control can be extended considerably in devices where multiple cavity modes couple to each other via the motion of a single mechanical oscillator. Here we study the dynamical properties of such a multimode optomechanical device, in which the coupling between cavity modes results from mechanically-induced avoided crossings in the cavitys spectrum. Near the avoided crossings we find that the optical spring shows distinct features that arise from the interaction between cavity modes. Precisely at an avoided crossing, we show that the particular form of the optical spring provides a classical analog of a quantum-nondemolition measurement of the intracavity photon number. The mechanical oscillators Brownian motion, an important source of noise in these measurements, is minimized by operating the device at cryogenic temperature (500 mK).
Optically addressable paramagnetic defects in wide-band-gap semiconductors are promising platforms for quantum communications and sensing. The presence of avoided crossings between the electronic levels of these defects can substantially alter their quantum dynamics and be both detrimental and beneficial for quantum information applications. Avoided crossings give rise to clock transitions, which can significantly improve protection from magnetic noise and favorably increase coherence time. However, the reduced coupling between electronic and nuclear spins at an avoided crossing may be detrimental to applications where nuclear spins act as quantum memories. Here we present a combined theoretical and experimental study of the quantum dynamics of paramagnetic defects interacting with a nuclear spin bath at avoided crossings. We develop a computational approach based on a generalization of the cluster expansion technique, which can account for processes beyond pure dephasing and describe the dynamics of any solid-state spin-qubits near avoided crossings. Using this approach and experimental validation, we determine the change in nature and source of noise at avoided crossings for divacancies in SiC. We find that we can condition the clock transition of the divacancies in SiC on multiple adjacent nuclear spins states. In our experiments, we demonstrate that one can suppress the effects of fluctuating charge impurities with depletion techniques, leading to an increased coherence time at clock transition, limited purely by magnetic noise. Combined with ab-initio predictions of spin Hamiltonian parameters, the proposed theoretical approach paves the way to designing the coherence properties of spin qubits from first principles.
The relation between the Shannon entropy and avoided crossings is investigated in dielectric microcavities. The Shannon entropy of probability density for eigenfunctions in an open elliptic billiard as well as a closed quadrupole billiard increases as the center of avoided crossing is approached. These results are opposite to those of atomic physics for electrons. It is found that the collective Lamb shift of the open quantum system and the symmetry breaking in the closed chaotic quantum system give equivalent effects to the Shannon entropy.
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