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arXiv:1307.6004 · Physical Review A

Time-of-flight roton spectroscopy in dipolar Bose-Einstein condensates

M. Jona-Lasinio, Kazimierz Łakomy, Luis Santos

Published Aug 30, 2013• 13 citations
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Abstract

Dipolar Bose-Einstein condensates may present a rotonlike dispersion minimum, which has yet to be observed in experiments. We discuss a simple method to reveal roton excitations based on the response of quasi-two-dimensional dipolar condensates against a weak lattice potential. By employing numerical simulations for realistic scenarios, we analyze the response of the system as a function of both the lattice spacing and the $s$-wave scattering length, showing that the roton minimum may be readily revealed in current experiments by the resonant population of Bragg peaks in time-of-flight measurements.

DOI
10.1103/physreva.88.025603

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Dipolar Bose-Einstein condensates may present a rotonlike dispersion minimum, which has yet to be observed in experiments. We discuss a simple method to reveal roton excitations based on the response of quasi-two-dimensional dipolar condensates against a weak lattice potential. By employing numerical simulations for realistic scenarios, we analyze the response of the system as a function of both the lattice spacing and the sss-wave scattering length, showing that the roton minimum may be readily revealed in current experiments by the resonant population of Bragg peaks in time-of-flight measurements.
We study the stability of a quasi-one-dimensional dipolar Bose-Einstein condensate that is perturbed by a weak lattice potential along its axis. Our numerical simulations demonstrate that systems exhibiting a roton-maxon structure destabilize readily when the lattice wavelength equals either half the roton wavelength or a low roton subharmonic. We apply perturbation theory to the Gross-Pitaevskii and Bogoliubov--de Gennes equations to illustrate the mechanisms behind the instability threshold. The features of our stability diagram may be used as a direct measurement of the roton wavelength for quasi-one-dimensional geometries.
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 measure the excitation spectrum of a stable dipolar Bose-Einstein condensate over a wide momentum range via Bragg spectroscopy. We precisely control the relative strength ε_{dd} of the dipolar to the contact interactions and observe that the spectrum increasingly deviates from the linear phononic behavior for increasing ε_{dd}. Reaching the dipolar-dominated regime ε_{dd}>1, we observe the emergence of a roton minimum in the spectrum and its softening towards instability. We characterize how the excitation energy and the strength of the density-density correlations at the roton momentum vary with ε_{dd}. Our findings are in excellent agreement with numerical calculations based on mean-field Bogoliubov theory. When including beyond-mean-field corrections, in the form of a Lee-Huang-Yang potential, we observe a quantitative deviation from the experiment, questioning the validity of such a description in the roton regime.
Dilute quantum gases offer a controllable platform for investigating quantum liquids, such as superfluid helium, in which correlations and fluctuations are encoded in the form of a quasiparticle energy (i.e., roton-maxon) dispersion. An approach to extracting the roton-maxon spectrum of a Bose-Einstein condensate is theoretically developed: the method relies on using an external one-dimensional optical lattice that effectively controls the response of the system, giving access to its elementary excitations.