Observation of Quantum Droplets in a Strongly Dipolar Bose Gas

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Observation of Quantum Droplets in a Strongly Dipolar Bose Gas

Igor Ferrier-Barbut, Holger Kadau, Matthias Schmitt, Matthias Wenzel, and Tilman Pfau

Phys. Rev. Lett. 116, 215301 – Published 23 May 2016

See Viewpoint: An Arrested Implosion

Abstract

Quantum fluctuations are the origin of genuine quantum many-body effects, and can be neglected in classical mean-field phenomena. Here, we report on the observation of stable quantum droplets containing $\sim 800$ atoms that are expected to collapse at the mean-field level due to the essentially attractive interaction. By systematic measurements on individual droplets we demonstrate quantitatively that quantum fluctuations mechanically stabilize them against the mean-field collapse. We observe in addition the interference of several droplets indicating that this stable many-body state is phase coherent.

Received 13 January 2016

DOI:https://doi.org/10.1103/PhysRevLett.116.215301

Physics Subject Headings (PhySH)

Quantum statistical mechanics

Bose gases Dipolar gases

Cooling & trapping

Condensed Matter, Materials & Applied PhysicsAtomic, Molecular & Optical

Viewpoint

An Arrested Implosion

Published 23 May 2016

The collapse of a trapped ultracold magnetic gas is arrested by quantum fluctuations, creating quantum droplets of superfluid atoms.

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Authors & Affiliations

Igor Ferrier-Barbut, Holger Kadau, Matthias Schmitt, Matthias Wenzel, and Tilman Pfau

5. Physikalisches Institut and Center for Integrated Quantum Science and Technology, Universität Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany

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Issue

Vol. 116, Iss. 21 — 27 May 2016

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Images

Figure 1
Quantum droplets of a dipolar Bose gas in a waveguide. (a) Schematic representation of the droplets in the waveguide; the elongation along $z$ is represented; their separation $d$ is indicated. (b) Examples of in situ optical density (OD) images after release in the waveguide at the magnetic field $B_{1} = 6.656 (10) G$ . Images taken at times $t_{WG} = 0$ , 5, 10, 15, 20 ms (top to bottom). The OD is normalized to the maximal OD in each image to improve visibility. (c) Evolution of the mean separation $d$ between the droplets as a function of time. (d) Blue circles: evolution of the width $σ$ obtained from a Gaussian fit to their density profiles (average of transverse and axial radii). Red diamonds: evolution of the size of a BEC for comparison. The data in panels (c) and (d) are obtained by averaging at least four experimental realizations; the error bars indicate the statistical standard deviation The convention for the axes used through the Letter is indicated in panel (a).
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Figure 2
Derivative of the chemical potential with respect to density as a function of density, at the center of a droplet using a Gaussian ansatz (1) ( $g = 4 π ℏ^{2} a / m$ ). The blue shaded region expresses our uncertainty on the scattering length. Negative values imply mechanical instability. The experimental value obtained from expansion measurements (Fig. 4) is shown as a red circle assuming a Gaussian distribution and as an orange square assuming an inverted parabola. The dashed line shows the same quantity obtained using a three-body repulsion using parameters from Ref. [22], which stabilizes at a higher density.
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Figure 3
Ratio of the lifetime $τ_{f} / τ i$ of the droplets between scattering lengths $a_{f}$ and $a_{i}$ . We use here $a_{i} = 94 (12) a_{0}$ obtained at $B_{i} = 6.573 (5) G$ . The data points are taken down to $B_{f} = 6.159 (5) G$ . The filled blue and green hatched areas represent the expected scaling using quantum fluctuations and three-body repulsion, respectively, taking into account the uncertainty range on the droplets’ aspect ratio: $0 \leq κ \leq 0.2$ .
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Figure 4
Time-of-flight expansion measurements. The field is held at $B_{1} = 6.656 (10) G$ until release when it is quenched to a different value. (a),(b) Images where the field is kept at $B_{1}$ during expansion and (c),(d) quenched to 6.86 G. In (a) and (b) one sees expanding droplets, whereas in (c) and (d) they overlap and clear interference fringes appear along the $x$ axis while we can still measure the expansion size in the $y$ direction.
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