Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1207.1999 · Physical Review A

Faraday patterns in coupled one-dimensional dipolar condensates

Kazimierz Łakomy, Rejish Nath, Luis Santos

Published Aug 17, 2012• 34 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.86.023620

Related papers

Faraday patterns in two-dimensional dipolar Bose-Einstein condensates

Rejish Nath, Luis Santos

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.

arXiv:0902.3969•Physical Review A•Mar 29, 2010•56 citations

Faraday patterns, spin textures, spin-spin correlations, and competing instabilities in a driven spin-1 antiferromagnetic Bose-Einstein condensate

Vaishakh Kargudri, Sandra M. Jose, Rejish Nath

We study the formation of transient Faraday patterns and spin textures in driven quasi-one-dimensional and quasi-two-dimensional spin-1 Bose-Einstein condensates under the periodic modulation of $s$-wave scattering lengths $a_0$ and $a_2$, starting from the anti-ferromagnetic phase. This phase is characterized by a Bogoliubov spectrum consisting of three modes: one mode is gapped, while the other two are gapless. When $a_0$ is modulated and half of the modulation frequency lies below the gapped mode, density and spin Faraday patterns emerge. In that case, in quasi-one-dimension, the spin texture is characterized by periodic domains of opposite $z$-polarizations. When driven above the gap, the spin texture is characterized by random orientations of spin vectors along the condensate axis. Qualitatively new features appear in the driven quasi-two-dimensional condensate. For instance, when driven above the gap, the spin textures are characterized by anomalous vortices and antivortices that do not exhibit phase winding in individual magnetic components. Below the gap, the spin texture exhibits irregular ferromagnetic patches with opposite polarizations. The spatial spin-spin correlations in quasi-one-dimension exhibit a Gaussian envelope, whereas they possess a Bessel function dependence in quasi-two-dimension. Under the $a_2$-modulation, the density patterns dominate irrespective of the driving frequency, unless the spin-dependent interaction strength is sufficiently smaller than that of the spin-independent interaction. The intriguing scenario of competing instability can emerge when both scattering lengths are simultaneously modulated. Finally, we show that the competing instabilities result in a complex relationship between the population transfer and the strength of the quadratic Zeeman field, while keeping all other parameters constant.

arXiv:2510.08087•Physical Review A•Dec 18, 2025•2 citations

Faraday pattern formation in dipolar superfluid and supersolid quantum gases

Sumit Semwal, Shawan Kumar Jha, G. Bougas +2 more

We investigate Faraday instabilities in three-dimensional parametrically driven trapped dipolar quantum gases within the framework of the extended Gross-Pitaevskii equation. In the superfluid regime, periodic modulation of the short-range interactions induces the resonant excitation of discrete polygonal surface modes displaying sub-harmonic response. The resonance frequencies and the parametric windows of instability are accurately captured by an appropriate Mathieu equation, further corroborating our simulations. It is also shown that dipolar interactions in superfluids shift the resonance frequencies to lower values compared to their non-dipolar counterparts. Near the superfluid-to-supersolid transition, intrinsic density undulations associated with the softened roton mode accelerate pattern formation, yielding hybrid surface and bulk excitations. The bulk patterns prevail deeper in the supersolid regime, emerging from droplet collisions with the superfluid background. Our results reveal a crossover from surface collective modes to hybrid surface-bulk excitations and demonstrate how parametric driving dictates pattern formation in long-range interacting quantum fluids.

arXiv:2608.03553•Aug 4, 2026•0 citations

Faraday and Resonant Waves in Dipolar Cigar-Shaped Bose-Einstein Condensates

D. Vudragović, Antun Balaž

Faraday and resonant density waves emerge in Bose-Einstein condensates as a result of harmonic driving of the system. They represent nonlinear excitations and are generated due to the interaction-induced coupling of collective oscillation modes and the existence of parametric resonances. Using a mean-field variational and a full numerical approach, we studied density waves in dipolar condensates at zero temperature, where breaking of the symmetry due to anisotropy of the dipole-dipole interaction (DDI) plays an important role. We derived variational equations of motion for the dynamics of a driven dipolar system and identify the most unstable modes that correspond to the Faraday and resonant waves. Based on this, we derived the analytical expressions for spatial periods of both types of density waves as functions of the contact and the DDI strength. We compared the obtained variational results with the results of extensive numerical simulations that solve the dipolar Gross-Pitaevskii equation in 3D, and found a very good agreement.

arXiv:1909.04637•Symmetry•Sep 1, 2019•11 citations

Pattern formation in driven condensates

Ivana Vasić, D. Vudragović, Mihaela Carina Raportaru +1 more

The onset of pattern formation in a spatially homogeneous system subjected to external driving is an important topic in various scientific fields. A celebrated classical example is the Faraday instability, where a vertically oscillated fluid surface undergoes a parametric resonance, giving rise to standing waves that self-organize into regular spatial patterns. Bose-Einstein condensates (BECs) provide an ideal quantum-mechanical platform for studying pattern-forming mechanisms due to their exceptional degree of experimental control. As a compressible state of quantum matter, a condensate responds sensitively to external perturbations, including time-periodic modulation of interactions, trapping potentials, or external fields. These features make BECs particularly well suited for exploring driven nonequilibrium phases and pattern formation. In this chapter, we review the remarkable progress achieved in this field over the past two decades. We begin with the first theoretical proposal predicting parametric instabilities and emergent Faraday waves in driven condensates. We then discuss key experimental and theoretical breakthroughs that confirmed these predictions and refined the understanding of the underlying mechanisms. This line of research has culminated in the recent observation of a stabilized square lattice pattern in a periodically driven BEC confined in a two-dimensional geometry. This driven superfluid state with superposed density modulation was shown to exhibit some features of a supersolid state.

arXiv:2603.11870•Mar 12, 2026•0 citations

Generation of density waves in dipolar quantum gases by time-periodic modulation of atomic interactions

B Kh Turmanov, Bakhtiyor B. Baizakov, F. Kh. Abdullaev

We study the emergence of density waves in quasi-one-dimensional dipolar Bose-Einstein condensates (BECs) when the strength of dipole-dipole atomic interactions is periodically varied in time. The proposed theoretical model based on the evolution of small perturbations of the background density allows one to calculate the instability growth rate for an arbitrary set of input parameters, thereby identifying instability regions with respect to density waves. We find that among other modes of the system the roton mode is most effectively excited due to a significant contribution of subharmonics of the excitation frequency. The frequency of temporal oscillations of emerging density waves coincides with half of the driving frequency, which is the hallmark of the parametric resonance and is characteristic of Faraday waves. The possibility to create density waves in dipolar BECs, which can persist after emergence, is demonstrated. The existence of a standing-wave solution of the nonlocal Gross-Pitaevskii equation is revealed from numerical simulations. The effect of three-body atomic interactions, which is relevant to condensates with increased density, upon the properties of emerging waves is analyzed too. Significant modification of the condensate's excitation spectrum owing to three-body effects is shown.

arXiv:1911.10870•Physical Review A•May 11, 2020•10 citations
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.
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 the formation of transient Faraday patterns and spin textures in driven quasi-one-dimensional and quasi-two-dimensional spin-1 Bose-Einstein condensates under the periodic modulation of sss-wave scattering lengths a0a_0a0​ and a2a_2a2​, starting from the anti-ferromagnetic phase. This phase is characterized by a Bogoliubov spectrum consisting of three modes: one mode is gapped, while the other two are gapless. When a0a_0a0​ is modulated and half of the modulation frequency lies below the gapped mode, density and spin Faraday patterns emerge. In that case, in quasi-one-dimension, the spin texture is characterized by periodic domains of opposite zzz-polarizations. When driven above the gap, the spin texture is characterized by random orientations of spin vectors along the condensate axis. Qualitatively new features appear in the driven quasi-two-dimensional condensate. For instance, when driven above the gap, the spin textures are characterized by anomalous vortices and antivortices that do not exhibit phase winding in individual magnetic components. Below the gap, the spin texture exhibits irregular ferromagnetic patches with opposite polarizations. The spatial spin-spin correlations in quasi-one-dimension exhibit a Gaussian envelope, whereas they possess a Bessel function dependence in quasi-two-dimension. Under the a2a_2a2​-modulation, the density patterns dominate irrespective of the driving frequency, unless the spin-dependent interaction strength is sufficiently smaller than that of the spin-independent interaction. The intriguing scenario of competing instability can emerge when both scattering lengths are simultaneously modulated. Finally, we show that the competing instabilities result in a complex relationship between the population transfer and the strength of the quadratic Zeeman field, while keeping all other parameters constant.
We investigate Faraday instabilities in three-dimensional parametrically driven trapped dipolar quantum gases within the framework of the extended Gross-Pitaevskii equation. In the superfluid regime, periodic modulation of the short-range interactions induces the resonant excitation of discrete polygonal surface modes displaying sub-harmonic response. The resonance frequencies and the parametric windows of instability are accurately captured by an appropriate Mathieu equation, further corroborating our simulations. It is also shown that dipolar interactions in superfluids shift the resonance frequencies to lower values compared to their non-dipolar counterparts. Near the superfluid-to-supersolid transition, intrinsic density undulations associated with the softened roton mode accelerate pattern formation, yielding hybrid surface and bulk excitations. The bulk patterns prevail deeper in the supersolid regime, emerging from droplet collisions with the superfluid background. Our results reveal a crossover from surface collective modes to hybrid surface-bulk excitations and demonstrate how parametric driving dictates pattern formation in long-range interacting quantum fluids.
Faraday and resonant density waves emerge in Bose-Einstein condensates as a result of harmonic driving of the system. They represent nonlinear excitations and are generated due to the interaction-induced coupling of collective oscillation modes and the existence of parametric resonances. Using a mean-field variational and a full numerical approach, we studied density waves in dipolar condensates at zero temperature, where breaking of the symmetry due to anisotropy of the dipole-dipole interaction (DDI) plays an important role. We derived variational equations of motion for the dynamics of a driven dipolar system and identify the most unstable modes that correspond to the Faraday and resonant waves. Based on this, we derived the analytical expressions for spatial periods of both types of density waves as functions of the contact and the DDI strength. We compared the obtained variational results with the results of extensive numerical simulations that solve the dipolar Gross-Pitaevskii equation in 3D, and found a very good agreement.
The onset of pattern formation in a spatially homogeneous system subjected to external driving is an important topic in various scientific fields. A celebrated classical example is the Faraday instability, where a vertically oscillated fluid surface undergoes a parametric resonance, giving rise to standing waves that self-organize into regular spatial patterns. Bose-Einstein condensates (BECs) provide an ideal quantum-mechanical platform for studying pattern-forming mechanisms due to their exceptional degree of experimental control. As a compressible state of quantum matter, a condensate responds sensitively to external perturbations, including time-periodic modulation of interactions, trapping potentials, or external fields. These features make BECs particularly well suited for exploring driven nonequilibrium phases and pattern formation. In this chapter, we review the remarkable progress achieved in this field over the past two decades. We begin with the first theoretical proposal predicting parametric instabilities and emergent Faraday waves in driven condensates. We then discuss key experimental and theoretical breakthroughs that confirmed these predictions and refined the understanding of the underlying mechanisms. This line of research has culminated in the recent observation of a stabilized square lattice pattern in a periodically driven BEC confined in a two-dimensional geometry. This driven superfluid state with superposed density modulation was shown to exhibit some features of a supersolid state.
We study the emergence of density waves in quasi-one-dimensional dipolar Bose-Einstein condensates (BECs) when the strength of dipole-dipole atomic interactions is periodically varied in time. The proposed theoretical model based on the evolution of small perturbations of the background density allows one to calculate the instability growth rate for an arbitrary set of input parameters, thereby identifying instability regions with respect to density waves. We find that among other modes of the system the roton mode is most effectively excited due to a significant contribution of subharmonics of the excitation frequency. The frequency of temporal oscillations of emerging density waves coincides with half of the driving frequency, which is the hallmark of the parametric resonance and is characteristic of Faraday waves. The possibility to create density waves in dipolar BECs, which can persist after emergence, is demonstrated. The existence of a standing-wave solution of the nonlocal Gross-Pitaevskii equation is revealed from numerical simulations. The effect of three-body atomic interactions, which is relevant to condensates with increased density, upon the properties of emerging waves is analyzed too. Significant modification of the condensate's excitation spectrum owing to three-body effects is shown.