In this thesis we develop a model of ultracold dipolar bosons in a highly anisotropic quasi-one-dimensional optical lattice. We will see that the model is identical to one describing quasi-one-dimensional superconductivity in condensed matter systems giving rise to the possibility \nof using this ultracold atoms system as an analogue simulator of interesting electronic systems. \n \nIn investigating the properties of this model we find a rich phase diagram containing density wave, superfluid, and possibly supersolid phases, accessible by tuning the optical lattice parameters and the alignment of the dipole moments. \n \nAn important property of this model turns out to be the existence of an enhanced symmetry at the self dual point where the density wave and superfluid orders are maximally competing. At this point the Berezinskii-Kosterlitz-Thouless transition temperature of either phase must necessarily vanish to zero due to the Hohenberg-Mermin-Wagner theorem. \n \nInspired by this model we go on to study a more general system in two dimensions with O(M) x O(2) symmetry which has an enhanced symmetry point of O(M + 2) symmetry. The BKT transition in the O(2) sector is mediated by vortex excitations, but these must somehow disappear as the high symmetry point is approached. Using both a variational argument adapting the standard BKT argument, and a more rigorous RG analysis we show that the size of the vortex cores in such a system must diverge as 1/\\(\\sqrt{\\Delta}\\) where \\(\\Delta\\) measures the distance from the high symmetry point, and further that the BKT transition temperature must vanish as 1/ln(1/\\(\\Delta\\)).
In this thesis we develop a model of ultracold dipolar bosons in a highly anisotropic quasi-one-dimensional optical lattice. We will see that the model is identical to one describing quasi-one-dimensional superconductivity in condensed matter systems giving rise to the possibility \nof using this ultracold atoms system as an analogue simulator of interesting electronic systems. \n \nIn investigating the properties of this model we find a rich phase diagram containing density wave, superfluid, and possibly supersolid phases, accessible by tuning the optical lattice parameters and the alignment of the dipole moments. \n \nAn important property of this model turns out to be the existence of an enhanced symmetry at the self dual point where the density wave and superfluid orders are maximally competing. At this point the Berezinskii-Kosterlitz-Thouless transition temperature of either phase must necessarily vanish to zero due to the Hohenberg-Mermin-Wagner theorem. \n \nInspired by this model we go on to study a more general system in two dimensions with O(M) x O(2) symmetry which has an enhanced symmetry point of O(M + 2) symmetry. The BKT transition in the O(2) sector is mediated by vortex excitations, but these must somehow disappear as the high symmetry point is approached. Using both a variational argument adapting the standard BKT argument, and a more rigorous RG analysis we show that the size of the vortex cores in such a system must diverge as 1/\(\sqrt{\Delta}\) where \(\Delta\) measures the distance from the high symmetry point, and further that the BKT transition temperature must vanish as 1/ln(1/\(\Delta\)).
This thesis concerns ultracold two-dimensional atomic gases and the associated novel superfluid phases in an optical lattice subjected to staggered rotations. In the first part, we study the Berezinskii-Kosterlitz-Thouless (BKT) transition in a two-dimensional Bose gas. Motivated by recent experiments on the cold gas in the BKT regime, we employ a modified Popov theory and a renormalization group theory to describe the system. The two-dimensional renormalization group flow equations display unique features, which we interpret as precursors of the BKT physics. We further calculate higher correlation functions close to the BKT transition, which can serve as observables for detecting effects beyond mean-field. Finally, we obtain the density profile under the conditions of the experiment performed in the group of Dalibard in Paris, France. In the second part of the thesis, we study a recent experimental proposal of a time-dependent optical lattice with staggered rotations. We show that in the tight-binding regime, the system can be effectively described by a (Bose-)Hubbard model subjected to an artificial staggered magnetic field. The staggered magnetic field (flux) in the lattice leads to conical points in the band structure which possesses distinct minima for different strength, and can give rise to Dirac-like dispersions. For bosons, we show that besides the homogenous superfluid phase, a staggered-vortex superfluid phase is stabilized for large flux values. We show that the staggered flux renormalizes the phase boundary and find a multi-critical point separating the two superfluid phases and the Mott insulating phase. Finally, the full phase diagram of the generalized Bose-Hubbard model at zero temperature is determined. We then generalize the model for a mixture of ultracold bosons and spin-1/2 fermions. By using the Bogoliubov theory for the bosonic sector, we show that the bosonic superfluid mediates attractive interactions between fermions up to the nearest-neighbor site. The resulting model is an extended Hubbard model in the presence of a staggered magnetic field, where the on-site and the nearest-neighbor attractive interactions can be tuned independently. We then employ the Bardeen-Cooper-Schrieffer theory for superconductivity, by considering an on-site pairing order parameter competing with a nearest-neighbor resonating-valence-bond order parameter. Due to conical points in the energy band, the system possesses quantum critical property and the resulting phase diagram displays features which are strikingly similar to that of high-critical-temperature superconductors or heavy-fermion superconductors.
This thesis discusses the experiments on 2D dipolar Bose gas of ultracold erbium atoms. Long-range and anisotropic dipole-dipole interaction induces complex orders in quantum many-body systems. Highly magnetic lanthanide atoms such as dysprosium and erbium have the largest magnetic moment in the periodic table, which has attracted significant attention in the past decades. Starting from quantum degenerate dysprosium and erbium atoms, exotic phases like quantum droplets, supersolid, dipolar quantum solid in the Hubbard regime have been studied. However, the 2D dipolar superfluid still remains understudied, despite being theoretically discussed for over two decades. Although tremendous theoretical proposals predict different phenomena in 2D dipolar superfluids, our first interest is to know how the superfluidity emerges in the 2D dipolar gases at finite temperatures. Our observations suggest that the superfluid transition can be well described by the Berezinskii-Kosterlitz-Thouless transition with an effective contact interaction as a function of dipolar orientation. With the 2D dipolar superfluid with strong DDI, we characterized the elementary excitation of the matter: the collective breathing mode. Our measurements establish how the competition between local and nonlocal interaction in strongly dipolar 2D superfluid retains quasi-scale invariance or strongly breaks scale invariance. By further searching the interaction parameters, we created stripes with global coherence, which are the first supersolid stripes in 2D. Experiments including measuring density fluctuation, coherence, and collective mode have been performed to understand the 2D supersolid. At last, we also observe unconventional light scattering from round-disk dipolar BECs, which provides new possibilities for atom optics.
We discuss a model of dipolar bosons trapped in a weakly coupled planar array of one-dimensional tubes. We consider the situation where the dipolar moments are aligned by an external field, and we find a rich phase diagram as a function of the angle of this field exhibiting quantum phase transitions between solid, superfluid, and supersolid phases. In the low energy limit, the model turns out to be identical to one describing quasi-one-dimensional superconductivity in condensed matter systems. This opens the possibility of using bosons as a quantum analog simulator of electronic systems, a scenario arising from the intricate relation between statistics and interactions in quasi-one-dimensional systems.
A two-dimensional quantum system of dipoles, with a polarization angle not perpendicular to the plane, shows a transition from a gas to a stripe phase. We have studied the thermal properties of these two phases using the path-integral Monte Carlo (PIMC) method. By simulating the thermal density matrix, PIMC provides exact results for magnitudes of interest such as the superfluid fraction and the one-body density matrix. As it is well known, in two dimensions the superfluid-to-normal phase transition follows the Berezinskii-Kosterlitz-Thouless (BKT) scenario. Our results show that both the anisotropic gas and the stripe phases follow the BKT scaling laws. At fixed density and increasing the tilting angle, the transition temperature decreases in going from the gas to the stripe phase. Superfluidity in the perpendicular direction to the stripes is rather small close to the critical temperature but it becomes larger at lower temperatures, mainly close to the transition to the gas. Our results are in qualitative agreement with the supersolidity observed recently in a quasi-one-dimensional array of dipolar droplets.
Motivated by a recent experiment that realizes nearest-neighbor dipolar couplings in an optical lattice [C. Lagoin et al., Nature (London) 609, 485 (2022)], we study a one-dimensional version of the two-component extended Bose-Hubbard model via the density-matrix renormalization group method. By using the nearest-neighbor and on-site interaction parameters from the experiment, we start by mapping the quantum phase diagram in the hopping parameter ${t}_{A}\text{\ensuremath{-}}{t}_{B}$ plane with boson densities ${\ensuremath{\rho}}_{A}={\ensuremath{\rho}}_{B}=1/2$. In addition to the density-wave phase reported in the experiment, we find several regimes of superfluidity when one or both hopping parameters are large enough, and interestingly there is a supercounterfluid phase at moderate and comparable hopping parameters. The universality classes of these phase transitions are analyzed from the correlation functions, excitation gaps, and entanglement entropy. In particular, a Berezinskii-Kosterlitz-Thouless type is recognized for several gapped-to-gapless transitions. In addition, we also study the quantum phase transitions by varying ${\ensuremath{\rho}}_{B}$ from 0 to 1 while keeping ${\ensuremath{\rho}}_{A}=1/2$. We identify a supersolid phase in a wide range of $1/2<{\ensuremath{\rho}}_{B}<1$. Our work paves the way for realizing exotic many-body phases in cold-atom experiments upon proper tuning of experimental parameters.
In a recent article [R. Bombin, F. Mazzanti, and J. Boronat, Phys. Rev. A 100, 063614 (2019)], it is contended that a two-dimensional system of dipolar bosons, with dipole moments aligned at particular angles with respect to the direction perpendicular to the plane of motion, featuring a ``striped'' crystalline ground state, in turn undergoes a Berezinskii-Kosterlitz-Thouless superfluid transition at low temperature, making it a two-dimensional supersolid. We show here that the results provided therein, obtained by means of quantum Monte Carlo simulations, do not actually support such a conclusion. Rather, they are consistent with that expounded in our work [J. Low Temp. Phys. 196, 413 (2019)], namely that the striped ground state is insulating (i.e., nonsuperfluid in the conventional sense), essentially behaving like a system of quasi-one-dimensional, parallel independent chains. We attribute the incorrectness of the conclusion reached by Bombin, Mazzanti, and Boronat to the very small sizes of their simulated system, which do not allow for a reliable extrapolation to the thermodynamic limit.