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The ability for real-time control of topological defects can open up prospects for dynamical manipulation of macroscopic properties of solids. A sub-category of these defects, formed by particle dislocations, can be effectively described using the Frenkel-Kontorova chain, which characterizes the dynamics of these particles in a periodic lattice potential. This model is known to host solitons, which are the topological defects of the system and are linked to structural transitions in the chain. This work addresses three key questions: Firstly, we investigate how imperfections present in concrete implementations of the model affect the properties of topological defects. Secondly, we explore how solitons can be injected after the rapid change in lattice potential or nucleated due to quantum fluctuations. Finally, we analyze the propagation and scattering of solitons, examining the role of quantum fluctuations and imperfections in influencing these processes. Furthermore, we address the experimental implementation of the Frenkel-Kontorova model. Focusing on the trapped ion quantum simulator, we set the stage for controllable dynamics of topological excitations and their observation in this platform., Comment: 18+1 pages, 15 figures; an extension of our previous work arXiv:2210.14904

Exploring operational regimes of many-body cavity QED with multi-level atoms remains an exciting research frontier for their enhanced storage capabilities of intra-level quantum correlations. In this work, we consider an experimentally feasible many-body cavity QED model describing a four-level system, where each of those levels is formed from a combination of different spin and momentum states of ultra-cold atoms in a cavity. The resulting model comprises a pair of Dicke Hamiltonians constructed from pseudo-spin operators, effectively capturing two intertwined superradiant phase transitions. The phase diagram reveals regions featuring weak and strong entangled states of spin and momentum atomic degrees of freedom. These states exhibit different dynamical responses, ranging from slow to fast relaxation, with the added option of persistent entanglement temporal oscillations. We discuss the role of cavity losses in steering the system's dynamics into such entangled states and propose a readout scheme that leverages different light polarizations within the cavity. Our work paves the way to connect the rich variety of non-equilibrium phase transitions that occur in many-body cavity QED to the buildup of quantum correlations in systems with multi-level atom descriptions., Comment: 13+12 pages, 8+2 figures

Topological defects have strong impact on both elastic and inelastic properties of materials. In this article, we investigate the possibility to controllably inject topological defects in quantum simulators of solid state lattice structures. We investigate the quench dynamics of a Frenkel-Kontorova chain, which is used to model discommensurations of particles in cold atoms and trapped ionic crystals. The interplay between an external periodic potential and the inter-particle interaction makes lattice discommensurations, the topological defects of the model, energetically favorable and can tune a commensurate-incommensurate structural transition. Our key finding is that a quench from the commensurate to incommensurate phase causes a controllable injection of topological defects at periodic time intervals. We employ this mechanism to generate quantum states which are a superposition of lattice structures with and without topological defects. We conclude by presenting concrete perspectives for the observation and control of topological defects in trapped ion experiments., Comment: 7 pages,4 figures

We introduce a quantum optics platform featuring the minimal ingredients for the description of a spintronically pumped magnon condensate, which we use to promote driven-dissipative phase transitions in the context of spintronics. We consider a Dicke model weakly coupled to an out-of-equilibrium bath with a tunable spin accumulation. The latter is pumped incoherently in a fashion reminiscent of experiments with magnet-metal heterostructures. The core of our analysis is the emergence of a hybrid lasing-superradiant regime that does not take place in an ordinary pumped Dicke spin ensemble, and which can be traced back to the spintronics pumping scheme. We interpret the resultant non-equilibrium phase diagram from both a quantum optics and a spintronics standpoint, supplying a conceptual bridge between the two fields. The outreach of our results concern dynamical control in magnon condensates and frequency-dependent gain media in quantum optics., Comment: 13 pages, 10 figures