Observation of Roton Mode Population in a Dipolar Quantum Gas L. Chomaz1, R. M. W. van Bijnen2, D. Petter1, G. Faraoni1;3, S. Baier1, J. H. Becher1, M. J. Mark1;2, F. Wachtler¨ 4, L. Santos4, F. Ferlaino1;2;∗ 1Institut fur¨ Experimentalphysik,Universitat¨ Innsbruck, Technikerstraße 25, 6020 Innsbruck, Austria 2Institut fur¨ Quantenoptik und Quanteninformation,Osterreichische¨ Akademie der Wissenschaften, 6020 Innsbruck, Austria 3Dipartimento di Fisica e Astronomia, Universita` di Firenze, Via Sansone 1, 50019 Sesto Fiorentino, Italy 4Institut fur¨ Theoretische Physik, Leibniz Universitat¨ Hannover, Appelstr. 2, 30167 Hannover, Germany The concept of a roton, a special kind of elementary ex- the interparticle interactions - and correlations - are typically citation, forming a minimum of energy at finite momen- weak, meaning that classically their range of action is much tum, has been essential to understand the properties of su- smaller than the mean interparticle distance. Because of this perfluid 4He [1]. In quantum liquids, rotons arise from diluteness, roton excitations are absent in ordinary quantum the strong interparticle interactions, whose microscopic gases, i. e. in Bose-Einstein condensates (BECs) with contact description remains debated [2]. In the realm of highly- (short-range) interactions [12]. However, about 15 years ago, controllable quantum gases, a roton mode has been pre- seminal theoretical works predicted the existence of a roton dicted to emerge due to magnetic dipole-dipole interac- minimum both in BECs with magnetic dipole-dipole inter- tions despite of their weakly-interacting character [3]. actions (DDIs) [3] and in BECs irradiated by off-resonant This prospect has raised considerable interest [4–12]; yet laser light [15]. Following the lines of the latter proposal, roton modes in dipolar quantum gases have remained elu- a roton softening has been recently observed in BECs cou- sive to observations. Here we report experimental and pled to an optical cavity [16]. Here, the excitation arises theoretical studies of the momentum distribution in Bose- from the infinite-range photon-mediated interactions and the Einstein condensates of highly-magnetic erbium atoms, inverse of the laser wavelength sets the value of krot. Addi- revealing the existence of the long-sought roton mode. By tionally, roton-like softening has been created in spin-orbit- quenching the interactions, we observe the roton appear- coupled BECs [17, 18] and quantum gases in shaken optical ance of peaks at well-defined momentum. The roton mo- lattices [19] by engineering the single-particle dispersion re- mentum follows the predicted geometrical scaling with the lation. inverse of the confinement length along the magnetisation Our work focuses on dipolar BECs (dBECs). As in super- axis. From the growth of the roton population, we probe fluid 4He, the roton spectrum in such systems is a genuine the roton softening of the excitation spectrum in time and consequence of the underlying interactions among the parti- extract the corresponding imaginary roton gap. Our re- cles. However, in contrast to helium, the emergence of a mini- sults provide a further step in the quest towards superso- mum at finite momentum does not require strong inter-particle lidity in dipolar quantum gases [13]. interactions. It instead exists in the weakly-interacting regime Quantum properties of matter continuously challenge our and originates from the peculiar anisotropic and long-range intuition, especially when many-body effects emerge at a character of the DDI in real and momentum space [3–12]. De- macroscopic scale. In this regard, the phenomenon of su- spite the maturity achieved in the theoretical understanding, perfluidity is a paradigmatic case, which continues to reveal the observation of dipolar roton modes has remained so far fascinating facets since its discovery in the late 1930s [2, 12]. an elusive goal. For a long time, the only dBEC available in A major breakthrough in understanding superfluidity thrived experiments consisted of chromium atoms [20], for which the on the concept of quasiparticles, introduced by Landau in achievable dipolar character is hardly sufficient to support a 1941 [1]. Quasiparticles are elementary excitations of mo- roton mode. With the advent of the more magnetic lanthanide mentum k, whose energies e define the dispersion (energy- atoms [21, 22], a broader range of dipolar parameters became momentum) relation e(k). available, opening the way to access the regime of dominant To explain the special thermodynamic properties of super- DDI. In this regime, novel exciting many-body phenomena fluid 4He, Landau postulated the existence of two types of have been recently observed, as the formation of droplet states low-energy quasiparticles: phonons, referring to low-k acous- stabilised by quantum fluctuations [23–25], which may be- tic waves, and rotons, gapped excitations at finite k initially in- come self-bound [26]. Lanthanide dBECs hence open new terpreted as elementary vortices. The dispersion relation con- roads toward the long-sought observation of roton modes. arXiv:1705.06914v2 [cond-mat.quant-gas] 27 Mar 2019 tinuously evolves from linear at low k (phonons) to parabolic- Prior to this work, dipolar rotons have been mostly con- like with a minimum (roton) at a finite k = krot. Neutron nected to pancake-like geometries [3–6, 8–12]. Here, we ex- scattering experiments confirmed Landau‘s remarkable intu- tend the study of roton physics to the case of a cigar-like ge- 4 ition [14]. In liquid He, krot scales as the inverse of the inter- ometry with trap elongation along only one direction (y) trans- atomic distance. This manifests a tendency of the system to verse to the magnetisation axis (z) (Fig. 1a). The anisotropic establish a local order, which is driven by the strong correla- character of the DDI (Fig. 1b, inset) together with the tighter tions among the atoms [2]. confinement along z is responsible for the rotonization of the In the realm of low-temperature quantum physics, ultra- excitation spectrum along y (Fig. 1b). To illustrate this phe- cold quantum gases realise the other extreme limit for which nomenon, we consider an infinite cigar-shaped dBEC and 2 ñ (a.u.) z the system undergoes a roton instability and the population at 1.0 a c ky = 0 is transferred in ±krot at an exponential rate [5, 6]. The 0.8 population of the roton mode is then readily visible in the mo- x y 0.6 kx mentum distribution of the gas (Fig. 1c-d). In the extensively- 0.4 studied pancake geometries, the roton population in k-space 0.2 spreads over a ring of radius k = k because of the radial 0 rot attraction k b y symmetry of the confinement (Fig. 1d). Such a spread can be repulsion d avoided using a cigar geometry. Here, the roton population focuses in two prominent peaks at k = ±k , enhancing the (k) y rot ϵ a s visibility of the effect (Fig. 1c). We explore the above-described physics using strongly 166 Energy, magnetic Er atoms. The experiment starts with a stable kx dBEC in a cigar-shaped harmonic trap of frequencies nx;y;z, elongated along the y axis. The trap aspect ratio, l = nz=ny, k Momentum, ky rot can be tuned from about 4 to 30, corresponding to nz rang- k y ing from 150 Hz to 800 Hz, whereas ny and nz=nx are kept b1 b2 constant at about 35Hz and 1:6, respectively (Methods). An external homogeneous magnetic field, B, fixes the dipole ori- z entation (magnetisation) with respect to the trap axes and sets the values of as through a magnetic Feshbach resonance, cen- dominantly repulsive DDI y dominantly attractive DDI tered close to B = 0G. In previous experiments, we precisely calibrated the B-to-a conversion for this resonance [25]. The Figure 1 — Roton mode in a dBEC. a, axially elongated ge- s BEC is prepared at ai = 61a (B = 0:4G) with transverse ometry with dipoles oriented transversely. b, real (solid lines) s 0 (z) magnetisation. The characteristic dipolar length, defined and imaginary (norm of the dotted line) parts of the disper- as a = m m2 m=12ph¯ 2, is 65:5a , with m the mass and m sion relation of a dBEC in the geometry a, showing the emer- dd 0 m 0 m the magnetic moment of the atoms, h¯ = h=2p is the reduced gence of a roton minimum for decreasing a (dashed arrow). s Planck constant, m the vacuum permeability and a the Bohr The DDI changes from repulsive (blue) to attractive (red) de- 0 0 radius. pending on the dipole alignment (inset). b1, b2, the dipole alignment (color code as in inset) associated to small- (b1) To excite the roton mode, we quench as to a desired lower value, af, and shortly hold the atoms in the trap for a time and large-ky (b2) density modulations. c, d, distributions on s th. We measure that as converges to its set value with a the kx ky-plane associated with the roton population in cigar a or pancake d geometries with an identical roton population characteristic time constant of 1ms during th. We then re- and colorscale. lease the atoms from the trap, change as back close to its initial value and let the cloud expand for 30ms. We probe the momentum distributionn ˜(kx;ky) by performing standard resonant absorption imaging on the expanded cloud (Meth- focus on its axial elementary excitations, of momentum ky. ods). The measurement is then repeated at various values of These excitations correspond in real space to a density modu- as < add in a fixed trap geometry. The momentum distribu- lation along y of wavelength 2p=ky. For low ky, the atoms sit tion shows a striking behaviour (Fig. 2). For large enough as, mainly side-by-side and the repulsive nature of the DDI pre- n˜(kx;ky) shows a single narrow peak with an inverted aspect vails, stiffening the phononic part of the dispersion relation ratio compared to the trapped gas, typical of a stable BEC [12] (Fig.