Stability spectroscopy of rotons in a dipolar Bose gas

Abstract

We study the stability of a quasi-one-dimensional dipolar Bose-Einstein condensate (dBEC) 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 threshhold. The features of our stability diagram may be used as a direct measurement of the roton wavelength for quasi-one-dimensional geometries.It is widely believed that ultracold, gaseous samples of bosonic atoms or molecules possessing sufficiently large dipole moments will exhibit internal structure reminiscent of the roton in superfluid helium [1]. The basic phenomenology of the roton, in analogy with helium, is a local minimum in the quasiparticle dispersion ω(k). The existence of such a minimum is predicted to lead to a host of attendant phenomena in these dilute gases, including structured ground-state density profiles [2-4], reduced and anisotropic critical superfluid velocity [1,5,6], enhanced sensitivity to external perturbations [7], abrupt transitions in Faraday patterns [8,9], short-wavelength immiscibility phases [10], and strongly-oscillatory twobody correlations on the roton length scale [11]. Signatures of the roton in Bragg spectroscopy of trapped dipolar Bose-Einstein condensates (dBECs) have been calculated in Ref. [12]. While these many exciting predictions are in principle observable in current experiments with highly magnetic atoms [13][14][15], or in future experiments with electrically polar molecules [16][17][18], rotons remain to be seen directly in dBECs [19].In a dipolar condensate, the roton represents a mode of finite wavelength that has an anomolously low energy -hence the minimum in ω(k). The location of this minimum is given by a momentum approximately equal to /l t , where l t = /mω t denotes the harmonic oscillator length of the tightest confinement of the dBEC (usually along the polarization axis). Without this confinement, a homogeneous dBEC would be energetically unstable to collapse due to the attraction between dipoles that are aligned head-to-tail. In the presence of this confinement, the collapse is prevented by the zero-point energy introduced by the confinement, at least up until a critical dipole moment or density. When this critical parameter is exceeded, the condensate collapses in localized "clumps" of size λ rot ∼ l t , that is, via a dynamical instability into the roton mode [20]. For dBECs that are just barely stable, the energy minimum ω(k rot ) is achieved at the roton wave vector k rot = 2π/λ rot .A low-energy roton is therefore a mode that is linked intrinsically to condensate instability. This link suggests that the dBEC may respond nontrivially as an object of conventional spectroscopy, that is, that it would absorb and distribute energy differently from different wa...

Nonequilibrium dynamics of an ultracold dipolar gas

“…Note that, if the classical trajectory of a single particle in the trap can be solved analytically (which is obviously straightforward in the case of a harmonic potential), then Eqs. (8) can be replaced with this analytic solution. This provides an advantage in that At need not be small compared to the trap period (but still must remain small compared to the mean collision time).…”

“…D ipolar m olecules are another source of potentially even stronger interactions in dipolar gases [13,[27][28][29][30][31]. Developing theoretical tools to understand dipolar gases is currently a very active area o f research [8,[32][33][34][35][36][37], A particularly challenging task in m any-body physics is to develop theoretical m ethods for treating out-of-equilibrium physics. To this end, w e report on our progress towards a general tool for sim ulating out-of-equilibrium dynam ics o f the normal dipolar gas.…”

“…Aspects of this influence include changing the shape and mechanical stability of the gas [1][2][3][4][5], as well as altering the excitation spectrum to include low-energy roton modes in a Bose-Einstein condensate [6][7][8][9]. A host of related phenomena have been predicted and observed [10][11][12][13], driven by the direct action of the long-ranged, anisotropic dipolar interaction on the particles' motion.…”

Dipolar Gases — Theory

“…24 In addition, in situ measurements may reveal the strong density fluctuations associated with deep roton-like minima. 25 The presence of the roton-like minimum may be revealed as well by the so-called stability spectroscopy, 26 which analyzes the BEC stability in the presence of a weak lattice. Further, a stable but deeply rotonized BEC has an enhanced susceptibility against density modulations in the presence of a weak lattice that may be revealed in time-of-flight experiments.…”

Roton in a few-body dipolar system

“…The dispersion curve of such systems is related to a specific k-dependence of an effective interaction potential rather than to strong correlations. Possibility of changing the particles polarization as well as almost free tuning of the short-range interactions combined with the trap geometry modifications enables unprecedented flexibility in the study of the roton spectrum in dipolar gases [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39] ending with a recent experimental confirmation of the phenomenon [40]. Usually the dipolar system is studied within the Bogoliubov approximation, so that there is no access to the detailed structure of the low-lying excitations.…”