# Rabi and Josephson Oscillations

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The dynamics of two coupled quantum anharmonic oscillators is a fundamental problem in quantum physics that applies to a number of different physical systems. These include light-matter interaction (polaritons), as well as macroscopic systems defined by an order parameter, such as superconductors, superfluids, Bose–Einstein condensates in traps, and so on. In the latter case, there are three regimes, depending on the ratio of the magnitudes of interactions and coupling , following the classification of Leggett. He describes the problem as "the dynamics of * *bosons restricted to occupy the same two-dimensional single-particle Hilbert space'' [1]. These regimes are, respectively,

Contributed by: Amir Rahmani and Fabrice P. Laussy (April 2016)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Snapshot 1: A case of self-trapping. Due to very large interactions, , the system remains trapped in one mode (red) rather than Rabi-oscillating between them (blue).

Snapshot 2: In the presence of detuning, the trajectory of the noninteracting system (blue) may resemble that of a self-trapped system. In red, the trajectory on the Bloch sphere in the interacting case (red) is seen to deviate strongly from a circle.

Snapshot 3: Detuning makes the Josephson dynamics less robust. Here, the system is in the Rabi regime, as shown by the stability analysis (three centers for the fixed points).

[1] A. J. Leggett, "Bose-Einstein Condensation in the Alkali Gases: Some Fundamental Concepts," *Review of Modern Physics*, 73(307), 2001. doi:10.1103/RevModPhys.73.307.

[2] N. S. Voronova, A. A. Elistratov, and Yu. E. Lozovik, "Detuning-Controlled Internal Oscillations in an Exciton-Polariton Condensate," *Physical Review Letters*, 115(186402), 2015. doi:10.1103/PhysRevLett.115.186402.

[3] A. Rahmani and F. P. Laussy, "Polaritonic Rabi and Josephson Oscillations," arxiv.org/abs/1603.05971.

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