On quantum time crystals and interacting gauge theories in atomic Bose-Einstein condensates

We study the dynamics of a Bose-Einstein condensate trapped circumferentially on a ring, and which is governed by an interacting gauge theory. We show that the associated density-dependent gauge potential and concomitant current nonlinearity permits a ground state in the form of a rotating chiral bright soliton. This chiral soliton is constrained to move in one direction by virtue of the current nonlinearity, and represents a time crystal in the same vein as Wilczek's original proposal.Comment: New version with general improvements and correction

Experimental Tests of the New Paradigm for Laser Filamentation in Gases

Since their discovery in the mid-1990s, ultrafast laser filaments in gases have been described as products of a dynamic balance between Kerr self-focusing and defocusing by free electric charges that are generated via multi-photon ionization on the beam axis. This established paradigm has been recently challenged by a suggestion that the Kerr effect saturates and even changes sign at high intensity of light, and that this sign reversal, not free-charge defocusing, is the dominant mechanism responsible for the extended propagation of laser filaments. We report qualitative tests of the new theory based on electrical and optical measurements of plasma density in femtosecond laser filaments in air and argon. Our results consistently support the established paradigm.Comment: 4 pages, 4 figure

Fundamental properties of beam-splitters in classical and quantum optics

A lossless beam-splitter has certain (complex-valued) probability amplitudes for sending an incoming photon into one of two possible directions. We use elementary laws of classical and quantum optics to obtain general relations among the magnitudes and phases of these probability amplitudes. Proceeding to examine a pair of (nearly) single-mode wavepackets in the number-states |n1> and |n2> that simultaneously arrive at the splitter's input ports, we find the distribution of photon-number states at the output ports using an argument inspired by Feynman's scattering analysis of indistinguishable Bose particles. The result thus obtained coincides with that of the standard quantum-optical treatment of beam-splitters via annihilation and creation operators a and a{\dag}. A simple application of the Feynman method provides a form of justification for the Bose enhancement implicit in the well-known formulas a|n>=sqrt(n)|n-1> and a{\dag}|n>=sqrt(n+1)|n+1>.Comment: 13 pages, 2 figures, 22 equations, 18 references and endnote