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arXiv:0902.3969 · Physical Review A

Faraday patterns in two-dimensional dipolar Bose-Einstein condensates

Rejish Nath, Luis Santos

Published Mar 29, 2010• 56 citations
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Abstract

We analyze the physics of Faraday patterns in dipolar Bose-Einstein condensates. Faraday patterns can be induced in Bose-Einstein condensates by a periodic modulation of the system nonlinearity. We show that these patterns are remarkably different in dipolar gases with a roton-maxon excitation spectrum. Whereas for nondipolar gases the pattern size decreases monotonously with the driving frequency, patterns in dipolar gases present, even for shallow roton minima, a highly nontrivial frequency dependence characterized by abrupt pattern size transitions, which are especially pronounced when the dipolar interaction is modulated. Faraday patterns constitute, hence, an excellent tool for revealing the onset of the roton minimum, a key feature of dipolar gases.

DOI
10.1103/physreva.81.033626

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We analyze the physics of Faraday patterns in dipolar Bose-Einstein condensates. Faraday patterns can be induced in Bose-Einstein condensates by a periodic modulation of the system nonlinearity. We show that these patterns are remarkably different in dipolar gases with a roton-maxon excitation spectrum. Whereas for nondipolar gases the pattern size decreases monotonously with the driving frequency, patterns in dipolar gases present, even for shallow roton minima, a highly nontrivial frequency dependence characterized by abrupt pattern size transitions, which are especially pronounced when the dipolar interaction is modulated. Faraday patterns constitute, hence, an excellent tool for revealing the onset of the roton minimum, a key feature of dipolar gases.
We study Faraday patterns in quasi-one-dimensional dipolar Bose-Einstein condensates with parametrically driven dipolar interactions. We show that in the presence of a roton minimum in the excitation spectrum, the emergent Faraday waves differ substantially in two- and one-dimensional geometries, providing a clear example of the key role of confinement dimensionality in dipolar gases. Moreover, Faraday patterns constitute an excellent tool to study nonlocal effects in polar gases, as we illustrate with two parallel quasi-one-dimensional dipolar condensates. Nonlocal interactions between the condensates give rise to an excitation spectrum characterized by symmetric and antisymmetric modes, even in the absence of hopping. We show that this feature, absent in nondipolar gases, results in a critical driving frequency at which a marked transition occurs between correlated and anticorrelated Faraday patterns in the two condensates. Interestingly, at this critical frequency, the emergent Faraday pattern stems from a spontaneous symmetry-breaking mechanism.
Dipolar Bose-Einstein condensates (dBECs) exhibit a plethora of physics phenomena, from supersolidity to the rotonlike minimum in the elementary excitation spectrum. In this work we first demonstrate the existence of axis-symmetric solitary waves in (quasi-)two-dimensional dBECs: these localized excitations are characterized by quantized vortex dipoles that continuously transit to vortex-free density depletions. We then show how the presence of the roton minimum fundamentally alters the fate of such solutions when approaching Landau’s critical speed: when propagating along the polarization direction where the roton minimum occurs, the solitary wave transits into roton excitations rather than into phonons as for standard contact-interaction BECs. This finding suggests that Feynman’s hypothesis, conjectured for 3D superfluid liquid helium regarding the creation of rotons as fading vortex excitations, is valid in the context of 2D dBECs.
Dipolar Bose-Einstein condensates (dBECs) exhibit a plethora of physics phenomena, from supersolidity to the rotonlike minimum in the elementary excitation spectrum. In this work we first demonstrate the existence of axis-symmetric solitary waves in (quasi-)two-dimensional dBECs: these localized excitations are characterized by quantized vortex dipoles that continuously transit to vortex-free density depletions. We then show how the presence of the roton minimum fundamentally alters the fate of such solutions when approaching Landau's critical speed: when propagating along the polarization direction where the roton minimum occurs, the solitary wave transits into roton excitations rather than into phonons as for standard contact-interaction BECs. This finding suggests that Feynman's hypothesis, conjectured for 3D superfluid liquid helium regarding the creation of rotons as fading vortex excitations, is valid in the context of 2D dBECs.
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.
We study the effects of quasiparticle interactions in a quasi-two-dimensional (quasi-2D), zero-temperature Bose-Einstein condensate of dipolar atoms, which can exhibit a roton-maxon feature in its quasiparticle spectrum. Our focus is the Beliaev damping process, in which a quasiparticle collides with the condensate and resonantly decays into a pair of quasiparticles. Remarkably, the rate for this process exhibits a highly nontrivial dependence on the quasiparticle momentum and the dipolar interaction strength. For weak interactions, low-energy phonons experience no damping, and higher-energy quasiparticles undergo anomalously weak damping. In contrast, the Beliaev damping rates become anomalously large for stronger dipolar interactions, as rotons become energetically accessible as final states. When the dipoles are tilted off the axis of symmetry, the damping rates acquire an anisotropic character. Surprisingly, this anisotropy does not simply track the anisotropy of the dipolar interactions, rather, the mechanisms for damping are qualitatively modified in the anisotropic case. Our study reveals the unconventional nature of Beliaev damping in dipolar condensates, and has important implications for ongoing studies of equilibrium and nonequilibrium dynamics in these systems. Further, our results are relevant for other 2D superfluids with roton excitations, including spin-orbit-coupled Bose gases, magnon condensates, and 4He^{4}\mathrm{He}4He films.
Excitation of Faraday patterns in the weak confinement space of low-dimensional Bose-Einstein condensates (BEC) by a periodic modulation of the trap frequency, ${\ensuremath{\Omega}}_{\text{tight}}$, in the tight confinement space is shown. For slow modulation the low-dimensional dynamics of the BEC in the weak confinement space is described by a Gross-Pitaevskii equation with time modulated nonlinearity coefficient. For increasing modulation frequencies a noticeable reduction of the pattern formation threshold is observed near $2{\ensuremath{\Omega}}_{\text{tight}}$, which is related to the parametric excitation of the internal breathing mode in the tight confinement space. These predictions could be relevant for the experimental excitation of Faraday patterns in BEC.