Quantum systems under frequency modulation

M. P. Silveri, J. A. Tuorila, E.V. Thuneberg, G. S. Paraoanu

Research output: Contribution to journalReview ArticleScientificpeer-review

51 Citations (Scopus)


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.

Original languageEnglish
Article number056002
Pages (from-to)1-39
JournalReports on Progress in Physics
Issue number5
Publication statusPublished - 5 Apr 2017
MoE publication typeA2 Review article in a scientific journal


  • artificial gauge fields
  • frequency modulation
  • Landau-Zener-Stückelberg-Majorana interference
  • motional averaging and narrowing
  • quantum control
  • superconducting qubits
  • topological phases and transitions

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