Simulation of time-crystal-like behavior for a few-boson chiral soliton model in a ring

We present numerical simulations for a chiral soliton model with N=2,3 bosons in a ring, which is a few-particle version of our previous mean-field model for a quantum time crystal. Following Syrwid, Kosior, and Sacha (SKS), the notion is that a precise position measurement of one particle can lead to spontaneous formation of a bright soliton that in a time crystal should rotate intact for at least a few revolutions around the ring. In their work SKS found spontaneous formation of a soliton due to the position measurement, but quantum fluctuations cause the soliton to subsequently decay before it has a chance to perform even one revolution of the ring. Based on this, they concluded that time-crystal dynamics are impossible for Wilczek's model of a bright soliton in a ring. In contrast, for our few-boson chiral soliton model, allowing for imprecise (weak) measurements of the particle position, we show that time-crystal-like behavior is possible, allowing for several revolutions of the spontaneously formed soliton around the ring.