Altering Quantum Hall ferromagnetism with cavity fields
Luis Brey
Ceren B. Dag,1, 2, 3, Luis Brey,4 Ganpathy Murthy,2, 5 and H.A. Fertig1, 2
1Department of Physics, Indiana University, Bloomington, Indiana 47405, USA
2Quantum Science and Engineering Center, Indiana University, Bloomington, Indiana 47405, USA
3Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
4Instituto de Ciencia de Materiales de Madrid (CSIC), Cantoblanco, 28049 Madrid, Spain
5Department of Physics and Astronomy, University of Kentucky, Lexington, KY 40506, USA
We study the collective mode spectrum of a two-component quantum Hall system at filling factor ν = 1, when the system is immersed in a quantum cavity hosting a quantized electromagnetic mode of frequency ω0. The latter is assumed to be much smaller than the cyclotron frequency ωc such that projection to the lowest Landau level is justified. We analytically show and numerically confirm that the many-body electronic system is completely decoupled from the cavity in the many-body ground state when the cavity field is uniform. Hence, the electronic ground state remains to be a SU(2) Quantum Hall ferromagnet (QHF) while the cavity remains to be in vacuum. In contrast, upon introducing a linearly varying cavity field, many-body ground state develops an instability as a function of light-matter interaction ceasing to be a SU(2) ferromagnet after a critical light-matter interaction. Hence, intriguingly, both the cavity and the material alter each others’ properties, although the many-body ground state remains to be separable (unentangled) between the electronic and photonic degrees of freedom. We characterize the quantum phases of this cavity material system: (i) vacuum dressed QHF in sufficiently low light-matter coupling and (ii) breakdown of QHF leading to a cascade of first order phase transitions between states of nonuniform electronic density, as the light-matter coupling increases.