by Daniel Petter
Abstract:
The current era of dilute, ultracold quantum gas experiments, allows experimentalists to study a vast number of new physical topics, ranging from Hubbard-models to strongly correlated quantum matter to liquid-like, gaseous droplets. At the heart of all these experiments lies the exquisite control over system parameters and over the interactions between atomic constituents. So far, the majority of experiments worked with contact-interacting atoms, and only recently the magnetic atoms chromium, dysprosium, and erbium could be brought to quantum degeneracy. The magnetic interaction between these atoms gives rise to numerous new physical phenomena and effects. One prime example is the formation of a roton minimum in the excitation spectrum of a dipolar Bose-Einstein condensate (BEC), similar to the one observed in superfluid helium. Other important features arise from the fact that dipolar interactions can be used to carefully cancel contact interactions in a BEC. This yields small interaction energies at the mean-field level in the system, where higher order effects from quantum fluctuations become important. The work in the present thesis is carried out with bosonic erbium, an element with one of the highest magnetic interactions among current atomic quantum gas experiments. The aim of our studies lies in further understanding dipolar quantum gases in a regime, where dipolar and contact interactions cancel and the system is close to a mean-field instability. Our experiments focus on two regimes: (i) in the first one, a global collapse of the BEC is expected from standard mean-field theory, whereas (ii) in the second one, the BEC is expected to collapse under a modulational instability. Starting with the former case, instead of globally collapsing, our experiments showed a smooth crossover from a BEC to a highly dense macrodroplet state. A careful comparison of the excitation frequency of a low-lying collective mode with an extended mean-field theory – including a Lee-Huang-Yang (LHY) energy correction – could show that the macrodroplet state is stabilised by quantum fluctuations. In the second case, the BEC is expected to exhibit a roton minimum in its excitation spectrum. Here, a fully softened roton minimum is expected to trigger a collapse of the BEC under a modulational instability. We could prove the existence of the roton minimum in a dipolar BEC for the first time and confirmed the tunability of the roton momentum with the trapping geometry of the BEC. Furthermore, by performing Bragg spectroscopy measurements of the full excitation spectrum, we could observed the formation of the roton minimum in the excitation spectrum and its energy softening when tuning the interatomic interactions. Due to the stabilising role of quantum fluctuations, also the modulational instability of a BEC is arrested, resulting typically in an incoherent assembly of small quantum droplets, first observed in the group of T. Pfau in Stuttgart with dysprosium atoms. However, for high enough densities, our two groups and the group from G. Modugno in Pisa, found a parameter regime, where the dipolar BEC features a globally linked and phase coherent state, that is density modulated and stabilised by quantum fluctuations. This state shows the spontaneous breaking of the U(1) gauge symmetry and the translational invariance simultaneously and, hence, has properties of a supersolid. The present thesis investigates the lifetime of these supersolid states with erbium and examines their coherence properties, as well as dynamics that appear due to the dynamical formation process.
Reference:
Study of Quantum Droplets, Rotonic Quasiparticles and Supersolid States in Ultracold Quantum Gases of Dipolar Erbium Atoms,
Daniel Petter,
PhD Thesis, 2020.
Daniel Petter,
PhD Thesis, 2020.
Bibtex Entry:
@article{PetterPhD,
title = {Study of Quantum Droplets, Rotonic Quasiparticles and Supersolid States in Ultracold Quantum Gases of Dipolar Erbium Atoms},
author = {Petter, Daniel},
journal = {PhD Thesis},
year = {2020},
month = {Nov},
abstract = {The current era of dilute, ultracold quantum gas experiments, allows experimentalists to
study a vast number of new physical topics, ranging from Hubbard-models to strongly correlated
quantum matter to liquid-like, gaseous droplets. At the heart of all these experiments
lies the exquisite control over system parameters and over the interactions between atomic
constituents. So far, the majority of experiments worked with contact-interacting atoms,
and only recently the magnetic atoms chromium, dysprosium, and erbium could be brought
to quantum degeneracy. The magnetic interaction between these atoms gives rise to numerous
new physical phenomena and effects. One prime example is the formation of a roton
minimum in the excitation spectrum of a dipolar Bose-Einstein condensate (BEC), similar
to the one observed in superfluid helium. Other important features arise from the fact that
dipolar interactions can be used to carefully cancel contact interactions in a BEC. This yields
small interaction energies at the mean-field level in the system, where higher order effects
from quantum fluctuations become important.
The work in the present thesis is carried out with bosonic erbium, an element with one
of the highest magnetic interactions among current atomic quantum gas experiments. The
aim of our studies lies in further understanding dipolar quantum gases in a regime, where
dipolar and contact interactions cancel and the system is close to a mean-field instability.
Our experiments focus on two regimes: (i) in the first one, a global collapse of the BEC
is expected from standard mean-field theory, whereas (ii) in the second one, the BEC is
expected to collapse under a modulational instability. Starting with the former case, instead
of globally collapsing, our experiments showed a smooth crossover from a BEC to a highly
dense macrodroplet state. A careful comparison of the excitation frequency of a low-lying
collective mode with an extended mean-field theory - including a Lee-Huang-Yang (LHY)
energy correction - could show that the macrodroplet state is stabilised by quantum fluctuations.
In the second case, the BEC is expected to exhibit a roton minimum in its excitation
spectrum. Here, a fully softened roton minimum is expected to trigger a collapse of the
BEC under a modulational instability. We could prove the existence of the roton minimum
in a dipolar BEC for the first time and confirmed the tunability of the roton momentum
with the trapping geometry of the BEC. Furthermore, by performing Bragg spectroscopy
measurements of the full excitation spectrum, we could observed the formation of the roton
minimum in the excitation spectrum and its energy softening when tuning the interatomic
interactions.
Due to the stabilising role of quantum fluctuations, also the modulational instability of a
BEC is arrested, resulting typically in an incoherent assembly of small quantum droplets,
first observed in the group of T. Pfau in Stuttgart with dysprosium atoms. However, for high
enough densities, our two groups and the group from G. Modugno in Pisa, found a parameter
regime, where the dipolar BEC features a globally linked and phase coherent state, that is
density modulated and stabilised by quantum fluctuations. This state shows the spontaneous
breaking of the U(1) gauge symmetry and the translational invariance simultaneously and,
hence, has properties of a supersolid. The present thesis investigates the lifetime of these
supersolid states with erbium and examines their coherence properties, as well as dynamics
that appear due to the dynamical formation process.},
url = {http://www.erbium.at/FF/wp-content/uploads/2020/11/Dissertation_DanielPetter.pdf},
}