Hofstadter butterfly in a cavity-induced dynamic synthetic magnetic field

Abstract

Energy bands of electrons in a square lattice potential threaded by a uniform magnetic field exhibit a fractal structure known as the Hofstadter butterfly. Here we study a Fermi gas in a 2D optical lattice within a linear cavity with a tilt along the cavity axis. The hopping along the cavity axis is only induced by resonant Raman scattering of transverse pump light into a standing wave cavity mode. Choosing a suitable pump geometry allows to realize the Hofstadter-Harper model with a cavity-induced dynamical synthetic magnetic field, which appears at the onset of the superradiant phase transition. The dynamical nature of this cavity-induced synthetic magnetic field arises from the delicate interplay between collective superradiant scattering and the underlying fractal band structure. Using a sixth-order expansion of the free energy as function of the order parameter and by numerical simulations we show that at low magnetic fluxes the superradiant ordering phase transition is first order, while it becomes second order for higher flux. The dynamic nature of the magnetic field induces a non-trivial deformation of the Hofstadter butterfly in the superradiant phase. At strong pump far above the self-ordering threshold we recover the Hofstadter butterfly one would obtain in a static magnetic field.

Open Quantum System Simulation of Faraday’s Induction Law via Dynamical Instabilities

“…Among alternative approaches to induce dynamical gauge potentials, quantum-gas-cavity-QED setups stand out owing to the intrinsic dynamical nature of cavity fields [15,16]. Many interesting phenomena have been predicted to arise in systems with cavity-induced dynamical gauge potential, from the dynamical appearance of a vector potential at the onset of superradiance [17,18] to a dissipation-induced dynamical Peierls phase [19] and the Meissner-like expulsion of a magnetic field [20]. The prediction of cavity-induced dynamic spin-orbit coupling [21][22][23][24][25][26][27][28] and its recent realization [29] has opened a new avenue for engineering dynamical gauge potentials alongside free-space schemes and experiments [30].…”

“…A dynamic gauge potential appears at the onset of the superradiant photon scattering from two transverse pump lasers into two cavity modes owing to dissipationinduced phase shifts of cavity photons. In contrast to previous works [17][18][19], we take into account the optomechanical back-action of the atomic dynamics, leading to an average-density-dependent dynamical magnetic flux when the optomechanical back-action shifts significantly the cavity resonances and consequently the dissipationinduced photonic phases. The system exhibits three steady states: Photon-balanced Meissner (PB-M) and vortex (PB-V) states and a photon-imbalanced biased ladder (PI-BL) phase.…”

Superradiant phase transition with cavity-assisted dynamical spin-orbit coupling

“…The dynamical SOC effects induced by superrandiance opens a new way to quantum simulation in nonequilibrium systems. It has a wide application in the exploring the novel topological states in dynamical systems [34][35][36][37]; the combination of the cavity-assisted SOC and the atomic interaction induces many interesting quantum phenomena in dynamic many-body systems [38][39][40][41]; the dissipation of the cavity photons can also be utilized to explore the properties of open quantum systems [42][43][44][45]. All these applications can be discussed in the future works and we hope the methods and results in this work can give some help to the following researches in this area.…”

Bosonic Hofstadter butterflies in synthetic antiferromagnetic patterns

“…Duncan et al [11] researched topological modes in quasicrystals and observed HBs as well. The authors of [12] gave an account of HB in square lattices with a synthetic magnetic field modified by external pump. Hafezi et al designed the artificial gauge field in the square lattice of microring resonators connected by the waveguides.…”