Modulation instability in the nonlinear Schrödinger equation with a synthetic magnetic field: gauge matters

Abstract

We theoretically investigate the phenomenon of modulation instability for systems obeying nonlinear Schrödinger equation, which are under the influence of an external homogeneous synthetic magnetic field. For an initial condition, the instability is detected numerically by comparing dynamics with and without a small initial perturbation; the perturbations are characterized in a standard fashion by wavevectors in momentum space. We demonstrate that the region of (in)stability in momentum space, as well as time-evolution in real space, for identical initial conditions, depend on the choice of the gauge (i.e., vector potential) used to describe the homogeneous synthetic magnetic field. This superficially appears as if the gauge invariance is broken, but this is not true. When the system is evolved from an identical initial condition in two different gauges, it is equivalent to suddenly turning on the synthetic magnetic field at $t=0$. This gives rise, via Faraday's law, to an initial instantaneous kick of a synthetic electric field to the wavepacket, which can differ for gauges yielding an identical uniform magnetic field at $t>0$.

References in corpus (36)

• Feshbach Resonances in Ultracold Gases
• Topological Photonics
• Topological Photonics
• Photonic Floquet Topological Insulators
• Experimental realisation of the topological Haldane model
• Artificial gauge potentials for neutral atoms
• Vortex formation in a stirred Bose-Einstein condensate
• Imaging topological edge states in silicon photonics
• Robust optical delay lines via topological protection
• Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices
• Synthetic magnetic fields for ultracold neutral atoms
• Light-induced gauge fields for ultracold atoms
• Realizing the Harper Hamiltonian with Laser-Assisted Tunneling in Optical Lattices
• Lasing in topological edge states of a 1D lattice
• Topological Bands for Ultracold Atoms
• Tunable gauge potential for neutral and spinless particles in driven lattices
• Strain-induced pseudomagnetic field and Landau levels in photonic structures
• Edge Solitons in Nonlinear Photonic Topological Insulators
• Modulational instability in cigar shaped Bose-Einstein condensates in optical lattices
• Dynamical Superfluid-Insulator Transition in a Chain of Weakly Coupled Bose-Einstein Condensates
• Modulation Instability and Pattern Formation in Spatially Incoherent Light Beams
• Artificial Gauge Field for Photons in Coupled Cavity Arrays
• Formation of matter-wave soliton trains by modulational instability
• Self-induced topological transitions and edge states supported by nonlinear staggered potentials
• Superfluid current disruption in a chain of weakly coupled Bose-Einstein Condensates
• On the modulational stability of Gross-Pitaevskii type equations in 1+1 dimensions
• Observation and control of nonlinear electromagnetic topological edge states
• Synthesis and Observation of Non-Abelian Gauge Fields in Real Space
• Topologically Enhanced Harmonic Generation in a Nonlinear Transmission Line Metamaterial
• Observation of a Modulational Instability in Bose-Einstein condensates
• Topological edge states and gap solitons in the nonlinear Dirac model
• Chirality of topological gap solitons in bosonic dimer chains
• Interacting quantum fluid in a polariton topological insulator
• Effective magnetic fields for photons in waveguide and coupled resonator lattices
• Gauge matters: Observing the vortex-nucleation transition in a Bose condensate
• The Harper-Hofstadter Hamiltonian and conical diffraction in photonic lattices with grating assisted tunneling

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• Probing band topology using modulational instability
• Robust and Ultrafast State Preparation by Ramping Artificial Gauge Potentials