Condensed Matter

We develop a multimode model that describes the dynamics on a rotating Bose-Einstein condensate confined by a ring-shaped optical lattice with large filling numbers. The parameters of the model are obtained as a function of the rotation frequency using full 3D Gross-Pitaevskii simulations. From such numerical calculations, we extract the velocity field induced at each site and analyze the relation and the differences between the phase of the hopping parameter of our model and the Peierls phase. To this end, a detailed discussion of such phases is presented in geometrical terms which takes into account the position of the junctions for different configurations. For circularly symmetric onsite densities a simple analytical relation between the hopping phase and the angular momentum is found for arbitrary number of sites. Finally, we confront the results of the rotating multimode model dynamics with Gross-Pitaevskii simulations finding a perfect agreement.

I consider general interacting systems of quantum particles in one spatial dimension. These consist of bosons or fermions, which can have any number of components, arbitrary spin or a combination thereof, featuring low-energy two- and multiparticle interactions. The single-particle dispersion can be Galilean (non-relativistic), relativistic, or have any other form that may be relevant for the continuum limit of lattice theories. Using an algebra of generalized functions, statistical transmutation operators that are genuinely unitary are obtained, putting bosons and fermions in a one-to-one correspondence without the need for a short-distance hard core. In the non-relativistic case, low-energy interactions for bosons yield, order by order, fermionic dual interactions that correspond to the standard low-energy expansion for fermions. In this way, interacting fermions and bosons are fully equivalent to each other at low energies. While the Bose-Fermi mappings do not depend on microscopic details, the resulting statistical interactions heavily depend on the kinetic energy structure of the respective Hamiltonians. These statistical interactions are obtained explicitly for a variety of models, and regularized and renormalized in the momentum representation, which allows for theoretically and computationally feasible implementations of the dual theories. The mapping is rewritten as a gauge interaction, and one-dimensional anyons are also considered.

Anyons with arbitrary exchange phases exist on 1D lattices in ultracold gases. Yet, known continuum theories in 1D do not match. We derive the continuum limit of 1D lattice anyons via interacting bosons. The theory maintains the exchange phase periodicity fully analogous to 2D anyons. This provides a mapping between experiments, lattice anyons, and continuum theories, including Kundu anyons with a natural regularization as a special case. We numerically estimate the Luttinger parameter as a function of the exchange angle to characterize long-range signatures of the theory and predict different velocities for left- and right-moving collective excitations.

In this manuscript we analyse properties of bound states of an atom interacting with a set of static impurities. We begin with the simplest system of a single atom interacting with two static impurities. We consider two types of atom-impurity interaction: (i) zero-range potential represented by regularized delta, (ii) more realistic polarization potential, representing long-range part of the atom-ion interaction. For the former we obtain analytical results for energies of bound states. For the latter we perform numerical calculations based on the application of finite element method. Then, we move to the case of a single atom interacting with one-dimensional (1D) infinite chain of static ions. Such a setup resembles Kronig-Penney model of a 1D crystalline solid, where energy spectrum exhibits band structure behaviour. For this system, we derive analytical results for the band structure of bound states assuming regularized delta interaction, and perform numerical calculations, considering polarization potential to model atom-impurity interaction. Both approaches agree quite well when separation between impurities is much larger than characteristic range of the interaction potential.

Dirac delta-function potential is widely studied in quantum mechanics because it usually can be exactly solved and at the same time is useful in modeling various physical systems. Here we study a system of delta-potential trapped spinorbit coupled cold atoms. The spin-orbit coupled atomic matter wave has two kinds of evanescent modes, one of which has pure imaginary wavevector and is an ordinary evanescent wave; while the other with a complex number wave vector is recognized as oscillating evanescent wave. We identified the eigenenergy spectra and the existence of bound states in this system. The bound states can be constructed analytically using the two kinds of evanescent modes and we found that they exhibit typical features of stripe phase, separated phase or zero-momentum phase. In addition to that, the properties of semi-bound states are also discussed, which is a localized wave packet on a plane wave background.

We present an experimental feasible proposal for synthesizing second-order topological superfluids that support Majorana corner modes in spin-orbit coupled Fermi gases. For this purpose, we consider the staggered spin-orbit coupling introduced in one direction. This results in a system consisted of two sublattices, providing extra degree of freedom for the emergent higher-order topological state. We find the topological trivial superfluids, first-order topological superfluids and boundary-obstructed second-order topological superfluids, as well as different topological phase transitions among them with respect to the the experimental tunable parameters. At the weak interaction regime, the phase transition is characterized by the Chern number accompanied by the bulk gap closing and reopening. However, at the strong interaction regime, we find the system can support the boundary-obstructed topological superfluids with Majorana corner modes, but topological phase transition dose not undergo the gap-closing of bulk bands. Instead the transition is refined by the quadrupole moment and signaled out by the gap-closing of edge-state. The proposal is simply based on the s -wave interaction and readily feasible via existing experimental techniques, which suggests new possibilities in interacting spin-orbit coupled systems by unifying both first- and higher-order topological superfluids in a simple but realistic microscopic model.

In dissipative quantum systems, strong symmetries can lead to the existence of conservation laws and multiple steady states. The investigation of such strong symmetries and their consequences on the dynamics of the dissipative systems is still in its infancy. In this work we investigate a strong symmetry for bosonic atoms coupled to an optical cavity, an experimentally relevant system, using adiabatic elimination techniques and numerically exact matrix product state methods. We show the existence of multiple steady states for ideal bosons coupled to the cavity. We find that the introduction of a weak breaking of the strong symmetry by a small interaction term leads to a direct transition from multiple steady states to a unique steady state. We point out the phenomenon of dissipative freezing, the breaking of the conservation law at the level of individual realizations in the presence of the strong symmetry. For a weak breaking of the strong symmetry we see that the behavior of the individual trajectories still shows some signs of this dissipative freezing before it fades out for a larger symmetry breaking terms.

We consider impurity atoms embedded in a two-component Bose-Einstein condensate in a quasi-one dimensional regime. We study the effects of repulsive coupling between the impurities and Bose species on the equilibrium of the system for both miscible and immiscible mixtures by numerically solving the underlying coupled Gross-Pitaevskii equations. Our results reveal that the presence of impurities may lead to a miscible-immiscible phase transition due to the interaction of the impurities and the two condensates. Within the realm of the Bogoliubov-de Gennes equations we calculate the quantum fluctuations due to the different types of interactions. The breathing modes and the time evolution of harmonically trapped impurities in both homogeneous and inhomogeneous binary condensates are deeply discussed in the miscible case using variational and numerical means. We show in particular that the self-trapping, the miscibility and the inhomogeneity of the trapped Bose mixture may strongly modify the low-lying excitations and the dynamical properties of impurities. The presence of phonons in the homogeneous Bose mixture gives rise to the damping of breathing oscillations of impurities width.

By including the effect of a trap with characteristic energy given by the Fermi temperature T F in a two-body two-channel model for Feshbach resonances, we reproduce the experimental closed-channel fraction Z across the BEC-BCS crossover and into the BCS regime of a 6 Li atomic Fermi gas. We obtain the expected behavior Z∝ T F − − − √ at unitarity, together with the recently measured proportionality constant. Our results are also in agreement with recent measurements of the Z dependency on T F on the BCS side, where a significant discrepancy between experiments and theory has been repeatedly reported.

We investigate the behavior of a one-dimensional Bose-Hubbard model whose kinetic energy is made to oscillate with zero time-average. The effective dynamics is governed by an atypical many-body Hamiltonian where only even-order hopping processes are allowed. At a critical value of the driving, the system passes from a Mott insulator to a superfluid formed by a cat-like superposition of two quasi-condensates with opposite non-zero momenta. We analyze the robustness of this unconventional ground state against variations of a number of system parameters. In particular we study the effect of the waveform and the switching protocol of the driving signal. Knowledge of the sensitivity of the system to these parameter variations allows us to gauge the robustness of the exotic physical behavior.