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A problem of collisions of atoms with two-channel zero-range interaction in an atomic waveguide is solved by using of a renormalization procedure. A matching of the solution to a solution of the related one-dimensional problem leads to…
Exchange-antisymmetric pair wavefunctions in fermionic systems can give rise to unconventional superconductors and superfluids with non-trivial transport properties. The realisation of these states in controllable quantum systems, such as…
Ultracold fermionic Feshbach molecules are promising candidates for exploring quantum matter with strong $p$-wave interactions, however, their lifetimes were measured to be short. Here, we characterize the $p$-wave collisions of ultracold…
We investigate the scattering properties and bound states of a quasi-two-dimensional (q2D) spin-polarized Fermi gas near a $p$-wave Feshbach resonance. Strong confinement promotes the out-of-plane spatial wave functions to a discrete,…
We detail the rich electronic and vibrational structure of triatomic "butterfly" molecules, ultra-long-range Rydberg molecules bound by resonant $p$-wave scattering. We divide these molecules into two sub-classes depending on their parity…
Strongly confining an ultracold atomic gas in one direction to create a quasi-2D system alters the scattering properties of this gas. We investigate the effects of confinement on Feshbach scattering resonances and show that strong…
We develop and analyze a theoretical model to study p-wave Feshbach resonances of identical fermions in atomic waveguides by extending the two-channel model of A.D. Lange et. al. [Phys. Rev. A 79, 013622 (2009)] and S. Saeidian et. al.…
We derive analytical solutions for the system of two ultracold spin-polarized fermions interacting in p wave and confined in an axially symmetric harmonic trap. To this end we utilize p-wave pseudopotential with an energy-dependent…
We study a spin-polarized degenerate Fermi gas interacting via a p-wave Feshbach resonance in an optical lattice. The strong confinement available in this system allows us to realize one- and two-dimensional gases and therefore to restrict…
We use the diagrammatic $T$-matrix approach to analyze the three-body scattering problem between two identical fermions and a third particle (which could be a different species of fermion or a boson). We calculate the s-wave dimer-atom…
The Efimov effect represents a cornerstone in few-body physics. Building on the recent experimental observation with ultracold atoms, we report the first experimental signature of Efimov physics in a heteronuclear system. A mixture of…
It is well-known that the magnetic Feshbach resonances of cold atoms are sensitive to the magnitude of the external magnetic field. Much less attention has been paid to the direction of such a field. In this work we calculate the scattering…
The signature of an unatomic system is revealed by a continuous scale invariance that appears during a progressive dimensional squeezing of a resonantly interacting trimer. The unatomic regime is reached at the dimension $\overline D$,…
We use exact four-boson scattering equations in the momentum-space framework to study the universal properties of shallow Efimov tetramers and their dependence on the two-boson scattering length. We demonstrate that, in contrast to previous…
The possibility of using ultracold atoms to observe strong localization of matter waves is now the subject of a great interest, as undesirable decoherence and interactions can be made negligible in these systems. It was proposed that a…
We consider two-dimensional weakly-bound heterospecies molecules formed in a Fermi-Bose mixture with attractive Fermi-Bose and repulsive Bose-Bose interactions. Bosonic exchanges lead to an intermolecular attraction, which can be controlled…
We report on observations and modeling of interspecies magnetic Feshbach resonances in dilute ultracold mixtures of open-shell alkali-metal $^6$Li and closed-shell $^{173}$Yb atoms with temperatures just above quantum degeneracy for both…
We experimentally investigate the mix-dimensional scattering occurring when the collisional partners live in different dimensions. We employ a binary mixture of ultracold atoms and exploit a species-selective 1D optical lattice to confine…
Tunable scattering resonances are crucial for controlling atomic and molecular systems. However, their use has so far been limited to ultracold temperatures. These conditions remain hard to achieve for most hybrid trapped ion-atom systems…
The topic of the present lecture notes are two-species quantum mixtures composed of a deeply degenerate Fermi gas and a second component, the latter being fermionic or bosonic. A key ingredient is the possibility to tune the $s$-wave…