Geometric resonances in Bose–Einstein condensates with two- and three-body interactions

Al-Jibbouri, Hamid; Vidanović, Ivana; Balaž, Antun; Pelster, Axel

doi:10.1088/0953-4075/46/6/065303

Cited by 42 publications

(44 citation statements)

References 105 publications

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“…In addition to parametrically forced systems, many physical systems naturally exhibit collective oscillations that may lead to a so-called geometric-type of parametric instability (GPI). Both Faraday-like and geometric instabilities can be found, for instance, in Bose-Einstein condensates, where they can be induced either by the harmonic modulation of the nonlinear interaction [8][9][10], or by the profile of the trapping potential [9], respectively.…”

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confidence: 99%

Observation of Geometric Parametric Instability Induced by the Periodic Spatial Self-Imaging of Multimode Waves

et al. 2016

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Spatiotemporal mode coupling in highly multimode physical systems permits new routes for exploring complex instabilities and forming coherent wave structures. We present here the first experimental demonstration of multiple geometric parametric instability sidebands, generated in the frequency domain through resonant space-time coupling, owing to the natural periodic spatial self-imaging of a multimode quasi-continuous-wave beam in a standard graded-index multimode fiber. The input beam was launched in the fiber by means of an amplified microchip laser emitting sub-ns pulses at 1064 nm. The experimentally observed frequency spacing among sidebands agrees well with analytical predictions and numerical simulations. The first-order peaks are located at the considerably large detuning of 123.5 THz from the pump. These results open the remarkable possibility to convert a near-infrared laser directly into a broad spectral range spanning visible and infrared wavelengths, by means of a single resonant parametric nonlinear effect occurring in the normal dispersion regime. As further evidence of our strong space-time coupling regime, we observed the striking effect that all of the different sideband peaks were carried by a well-defined and stable bell-shaped spatial profile.

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confidence: 99%

Observation of Geometric Parametric Instability Induced by the Periodic Spatial Self-Imaging of Multimode Waves

et al. 2016

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“…From our numerical simulations, in the presence of three-body interaction, a strong dipolar BEC develops discrete droplet structures, which is in good agreement with the experiment. The three-body interaction in a BEC has been studied theoretically [30][31][32][33][34] and observed in the recent experiment [35]. Additionally, three-body interaction can stablize the supersolid states in two-dimensional dipolar bosons [36].…”

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confidence: 99%

Droplet formation in a Bose-Einstein condensate with strong dipole-dipole interaction

Saito

2016

Phys. Rev. A

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Motivated by the recent experiment [H. Kadau et al., arXiv:1508.05007 (2015], we study roton instability and droplet formation in a Bose-Einstein condensate of 164 Dy atoms with strong magnetic dipole-dipole interaction. We numerically solve the cubic-quintic Gross-Pitaevskii equation with dipole-dipole interaction, and show that the three-body interaction plays a significant role in the formation of droplet patterns. We numerically demonstrate the formation of droplet patterns and crystalline structures, decay of droplets, and hysteresis behavior, which are in good agreement with the experiment. Our numerical simulations provide the first prediction on the values of the three-body interaction in a 164 Dy Bose-Einstein condensate. We also predict that the droplets remain stable during the time-of-flight expansion. From our results, further experiments investigating the three-body interaction in dipolar quantum gases are required. Dipolar Bose-Einstein condensates (BECs) of atoms with large magnetic dipole moments, such as chromium [1], dysprosium [2], and erbium [3], are systems in which the longrange and anisotropic dipole-dipole interaction strongly affects their static and dynamic properties. The researches on such a dipolar system both in theories and in experiments are driven by the search for new novel phases in condensed matter physics. Structured ground states and roton excitation spectrum in a pancake-shaped trap have been studied [4][5][6][7][8][9][10]. Anisotropic expansion [11] and collapsing instability [12][13][14] have been observed in a chromium BEC. Increasing attention has also been focusing on bright solitons [15,16], anisotropic superfluidity [17,18], Faraday patterns [19], and multicomponent BECs [20][21][22][23]. A binary BEC with a strong dipole-dipole interaction exhibits instability and forms patterns similar to those in magnetic liquids, such as hexagonal, soliton-like, and labyrinthine patterns [20]. Droplet formation has also been investigated in dipolar atomic systems [24,25].In the recent experiment reported in Ref.[26], interactioninduced periodic patterns spontaneously formed in a BEC of dysprosium atoms. By using Feshbach resonance to control the ratio between the s-wave and dipole-dipole interactions, they observed discrete droplet patterns arranged in a long-lived triangular lattice. This result indicates possibility that the system possesses a stable periodic state with matterwave coherence, which is therefore a candidate of supersolidity [27][28][29]. Before exploring this possiblity, a theoretical understanding of the experimental results in Ref.[26] is required.In this Rapid Communication, we propose a theoretical model to explain the experimental results in Ref. [26]. One finds that the standard mean-field Gross-Pitaevskii model with dipole-dipole interaction cannot reproduce the experimental results; the strong Roton instability is always followed by the d-wave dipolar collapse, which hinders the droplet formation. To circumvent this problem, we propose to include the th...

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“…Although this represents a tremendous simplification of the description of BEC dynamics, it has turned out to capture the essential physics. For instance, even inherent nonlinear phenomena such as parametric and geometric resonances could successively be described within this variational approach [12,13,17]. Surprisingly, for a period modulation of the s-wave scattering length around a relatively strong background value, it has turned out that the variational equations for the BEC widths coincide quantitatively even for long propagation times with the condensate widths determined from solving the GP equation [17].…”

Section: Variational Approachmentioning

confidence: 99%

“…(13) From the corresponding Euler-Lagrange equations we obtain the equations of motion for all variational parameters. The phases α ρ,z and β ρ,z can be expressed explicitly in terms of first derivatives of the widths u ρ , u z , and the center-of-mass coordinate z 0 according to…”

Section: Variational Approachmentioning

confidence: 99%

Breakdown of the Kohn theorem near a Feshbach resonance in a magnetic trap

Al-Jibbouri

Pelster

2013

Phys. Rev. A

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We study the collective excitation frequencies of a harmonically trapped 85 Rb Bose-Einstein condensate (BEC) in the vicinity of a Feshbach resonance. To this end, we solve the underlying Gross-Pitaevskii (GP) equation by using a Gaussian variational approach and obtain the coupled set of ordinary differential equations for the widths and the center of mass of the condensate. A linearization shows that the dipole-mode frequency decreases when the bias magnetic field approaches the Feshbach resonance, so the Kohn theorem is violated.

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Geometric resonances in Bose–Einstein condensates with two- and three-body interactions

Cited by 42 publications

References 105 publications

Observation of Geometric Parametric Instability Induced by the Periodic Spatial Self-Imaging of Multimode Waves

Observation of Geometric Parametric Instability Induced by the Periodic Spatial Self-Imaging of Multimode Waves

Droplet formation in a Bose-Einstein condensate with strong dipole-dipole interaction

Breakdown of the Kohn theorem near a Feshbach resonance in a magnetic trap

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