• dipolar Bose Einstein condensate
• rotonic instability

Bose-Einstein Condensates (BECs) are realized with dilute gases in trapped geometries and are composed of interacting particles. Early BECs were realized with alkali atoms, interacting via van der Waals forces. The isotropic potential accounting for such interactions is modelled as a contact potential characterized by an s-wave scattering length as.
In the latest years also neutral atoms with a large magnetic dipole moment have been successfully condensed, leading to 'dipolar quantum gases'. Such systems have a new kind of interaction between atoms, the dipole-dipole interaction (DDI), characterized by the dipolar length add.
DDI is of particular interest because of its long-range and anisotropic nature, which means that the interaction can be either repulsive or attractive depending on the relative angle between dipoles.
External magnetic fields are exploited to align the dipoles as well as to control the scattering length as via Feshbach resonances. The interplay between anisotropic dipole-dipole interaction, isotropic contact interaction and confining potential is the main feature of dipolar systems. The subject of this Master thesis is related to various phenomena arising from such interplay, that are increasingly attracting the attention of the scientific community.
A peculiar feature induced by the combination of potential and interaction strengths in dipolar gases is the appearance of a local minimum in the excitation spectrum characterized by a finite momentum.
The quasi-particle associated with this new minimum is the so called 'roton' in analogy with superfluid He.
Features of a roton mode have been recently observed through the appearance of a stripe-like density modulation in a dipolar BEC.
Dipolar systems are also very peculiar for their instabilities. Two kinds of instabilities can be recognized: a phononic instability driven by phonons, the quasi-particles associated with the lowest momenta of the dispersion curve, and a rotonic instability driven by rotons.
The mean-field theory predicts such instabilities to lead to a collapse, however the appearance of a self-bound structure was discovered in a Dy condensate. This state is called 'quantum droplets' and is due to the short range stabilization against mean-field collapse by the zero-point energy of quantum fluctuations. This beyond mean-field effect is represented by the Lee-Huang-Yang energy term, it can prevent collapse and leads to the formation of a stable phase.
My thesis demonstrates the observation of both a long lived ‘stripe phase’ due to a rotonic instability and a droplet phase in a Dysprosium BEC.
The work is based on an experiment with Dy (isotope 162) atoms in an asymmetric 3D trap polarized by an external magnetic field Bext. The trap geometry is chosen in order to break the cylindrical symmetry and allow the formation of a one-dimensional rotonic excitation. Furthermore the trap is relatively weak to avoid constraining the dynamics of the instability along a single spatial direction, differently from previous experiments.
The observable is the momentum distribution n(k), in the plane perpendicular to the polarization axis, obtained by absorption imaging of the expanding atomic cloud after release from the trap.
Atoms of Dy in their ground state have a dipolar length add = µ0µ2m/12π¯ h2 ∼130a0, to be compared to the background s-wave scattering length value abg ∼160a0. The system is initially created with abg, the magnetic field is then changed to reduce the scattering length until for as '100aB the system reaches the unstable regime. For a limited range of scattering lengths we observe the appearance of small peaks in the momentum distribution in addition to a central spot, representing the expansion of a stable BEC, along the weak axis of the trap. From the analysis of the images, observables such as roton momentum, phase, number of atoms and contrast, i.e. the population involved in the excitation process, can be extracted as a function of the scattering length as. A relatively long lived and coherent stripe phase is found, with a characteristic momentum close to the roton momentum predicted for an unconfined system at the instability. The lifetime is ’long’ relatively to the formation time of the structure. The interpretation is then of a roton mode softening, thus undergoing an instability, but then stabilized to a stripe phase. By further reducing the scattering length the stripe phase disappears and more complex patterns are found and identified as quantum droplets. In this frame the atom number plays an important role for two reasons. First it is connected to the presence of the instability, i.e. below a critical number the instability disappears. Second the N decay rate allows an indirect estimation of the mean density, which is related to the stabilization mechanism. The proof that quantum fluctuations are the stabilization mechanism for the stripe phase is provided by the observation of comparable decay rates for the stripe and droplet regimes. The work is organized as follows. The first two chapters are intended to give an overview of BEC theory and latest studies. In chapter 3 the experimental apparatus leading to BEC is described. Characterization of the condensate is reported in chapter 4. Chapter 5 is devoted to the analysis of the observed features in the unstable regime and it is the core of my thesis. It discusses the models I used to determine the experimental parameters and interpretations of results. In conclusion this work represents the first attempt of connecting droplet and stripe regimes, which are observed for different values of the scattering length. On one hand such regimes are found to share the same stabilization mechanism. On the other while quantum droplets are incoherent stripe phase seems to have a relatively long coherence time. This characteristic makes the stripe phase an appealing candidate for the quest of a supersolid state, i.e. a self-organized, spatially ordered phase with superfluid properties.