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arXiv:2207.01650 · Physical Review A

Crystalline phases of laser-driven dipolar Bose-Einstein condensates

Chinmayee Mishra, Stefan Ostermann, Farokh Mivehvar, B. Prasanna Venkatesh

Published Feb 16, 2023• 6 citations
arXivHTMLPDF

Abstract

Although crystallization is a ubiquitous phenomenon in nature, crystal formation and melting still remain fascinating processes with several open questions yet to be addressed. In this work we study the emergent crystallization of a laser-driven dipolar Bose-Einstein condensate due to the interplay between long-range magnetic and effectively infinite-range light-induced interactions. The competition between these two interactions results in a collective excitation spectrum with two-roton minima that introduce two different length scales at which crystalline order can emerge. In addition to the formation of regular crystals with simple periodic patterns due to the softening of one of the rotons, we find that both rotons can also soften simultaneously, resulting in the formation of exotic, complex periodic, or aperiodic density patterns. We also demonstrate dynamic state-preparation schemes for achieving all the crystalline ground states found for experimentally relevant and feasible parameter regimes.

DOI
10.1103/physreva.107.023312

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Although crystallization is a ubiquitous phenomenon in nature, crystal formation and melting still remain fascinating processes with several open questions yet to be addressed. In this work we study the emergent crystallization of a laser-driven dipolar Bose-Einstein condensate due to the interplay between long-range magnetic and effectively infinite-range light-induced interactions. The competition between these two interactions results in a collective excitation spectrum with two-roton minima that introduce two different length scales at which crystalline order can emerge. In addition to the formation of regular crystals with simple periodic patterns due to the softening of one of the rotons, we find that both rotons can also soften simultaneously, resulting in the formation of exotic, complex periodic, or aperiodic density patterns. We also demonstrate dynamic state-preparation schemes for achieving all the crystalline ground states found for experimentally relevant and feasible parameter regimes.
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The complex dynamical phases of quantum systems are dictated by atomic interactions that usually evoke an emergent periodic order. Here, we study a quantum many-body system with two competing and substantially different long-range interaction potentials where the dynamical instability towards density order can give way to a disordered amorphous solid, which exhibits local density modulations but no long-range periodic order. We consider a two-dimensional Bose-Einstein condensate in the Rydberg-dressing regime coupled to an optical standing wave resonator. The dynamic pattern formation in this system is governed by the competition between the two involved interaction potentials: repulsive soft-core interactions arising due to Rydberg dressing and infinite-range sign changing interactions induced by the cavity photons. The amorphous phase is found when the two interaction potentials introduce incommensurate length scales. The dynamic formation of this peculiar phase can be attributed to frustration induced by the two competing interaction energies and length scales.
Quasicrystals emerge from competing interactions with incommensurate characteristic length scales that inhibit translational periodicity. Here, we show that such multiscale interactions can be realized in a dipolar Bose-Einstein condensate through the interplay between intrinsic dipole-dipole interactions and photon-mediated interactions generated by coupling to an excited-state manifold together with a suitably engineered optical feedback. This interplay gives rise to two pronounced roton instabilities in the Bogoliubov excitation spectrum, leading to a rich ground-state phase diagram including dodecagonal quasicrystals with twelvefold rotational symmetry for experimentally realistic parameters. We further propose a protocol to access these quasicrystals dynamically and develop a general numerical framework for calculating their collective excitation spectra.
Abstract The dominance of interactions over kinetic energy lies at the heart of strongly correlated quantum matter, from fractional quantum Hall liquids, to atoms in optical lattices and twisted bilayer graphene. Crystalline phases often compete with correlated quantum liquids, and transitions between them occur when the energy cost of forming a density wave approaches zero. A prime example occurs for electrons in high magnetic fields, where the instability of quantum Hall liquids towards a Wigner crystal is heralded by a roton-like softening of density modulations at the magnetic length. Remarkably, interacting bosons in a gauge field are also expected to form analogous liquid and crystalline states. However, combining interactions with strong synthetic magnetic fields has been a challenge for experiments on bosonic quantum gases. Here, we study the purely interaction-driven dynamics of a Landau gauge Bose-Einstein condensate in and near the lowest Landau level. We observe a spontaneous crystallization driven by condensation of magneto-rotons, excitations visible as density modulations at the magnetic length. Increasing the cloud density smoothly connects this behaviour to a quantum version of the Kelvin-Helmholtz hydrodynamic instability, driven by the sheared internal flow profile of the rapidly rotating condensate. At long times the condensate self-organizes into a persistent array of droplets, separated by vortex streets, which are stabilized by a balance of interactions and effective magnetic forces.
We show that metastable phases of an antiferromagnetic spin-1 condensate in a simple model with pure contact interactions can exhibit a rotonlike minimum in the excitation spectrum. The introduction of a magnetic field gives rise to the instability of roton modes, which can lead to spontaneous emergence of regular periodic, polygonal, polyhedral, or crystalline patterns, as shown in numerical simulations within the truncated Wigner approximation. An explanation of the occurrence of rotonlike instability is given based on the energy and spin conservation laws.
We theoretically investigate optically controlled pattern formation in a Rydberg-dressed Bose-Einstein condensate by employing two-frequency modulation of the control laser field. This approach enables direct and periodic tuning of the long-range nonlocal interactions in time, thereby intrinsically modulating the system's nonlinearity. A Floquet analysis reveals parametric resonances that simultaneously excite roton and Faraday instabilities (RI and FI), identifying distinct regimes of pure RI, pure FI, and a joint RI-FI phase. Direct numerical simulations confirm the emergence of novel Faraday patterns, which are selected by the relative amplitude and frequency ratio of the modulation. Our results establish a theoretical framework for studying nonlinear dynamics in driven nonlocal quantum fluids, providing a phase diagram that may serve as a benchmark for future experiments in Rydberg-dressed systems.