Quantum systems under frequency modulation.

We review the physical phenomena that arise when quantum mechanical energy levels are modulated in time. The dynamics resulting from changes in the transition frequency is a problem studied since the early days of quantum mechanics. It has been of constant interest both experimentally and theoretically since, with the simple two-state model providing an inexhaustible source of novel concepts. When the transition frequency of a quantum system is modulated, several phenomena can be observed, such as Landau-Zener-Stückelberg-Majorana interference, motional averaging and narrowing, and the formation of dressed states with the appearance of sidebands in the spectrum. Adiabatic changes result in the accumulation of geometric phases, which can be used to create topological states. In recent years, an exquisite experimental control in the time domain was gained through the parameters entering the Hamiltonian, and high-fidelity readout schemes allowed the state of the system to be monitored non-destructively. These developments were made in the field of quantum devices, especially in superconducting qubits, as a well as in atomic physics, in particular in ultracold gases. As a result of these advances, it became possible to demonstrate many of the fundamental effects that arise in a quantum system when its transition frequencies are modulated. The purpose of this review is to present some of these developments, from two-state atoms and harmonic oscillators to multilevel and many-particle systems.

Motional averaging in a superconducting qubit.

Superconducting circuits with Josephson junctions are promising candidates for developing future quantum technologies. Of particular interest is to use these circuits to study effects that typically occur in complex condensed-matter systems. Here we employ a superconducting quantum bit--a transmon--to perform an analogue simulation of motional averaging, a phenomenon initially observed in nuclear magnetic resonance spectroscopy. By modulating the flux bias of a transmon with controllable pseudo-random telegraph noise we create a stochastic jump of its energy level separation between two discrete values. When the jumping is faster than a dynamical threshold set by the frequency displacement of the levels, the initially separate spectral lines merge into a single, narrow, motional-averaged line. With sinusoidal modulation a complex pattern of additional sidebands is observed. We show that the modulated system remains quantum coherent, with modified transition frequencies, Rabi couplings, and dephasing rates. These results represent the first steps towards more advanced quantum simulations using artificial atoms.