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New Journal of Physics

Spin-dynamics of pairs of submerged-4f-shell atoms in cylindrically symmetric harmonic traps: connecting multi-channel models to effective analytical approaches

Hui Li, Eite Tiesinga, Ming Li, Svetlana Kotochigova

Published Mar 31, 2025• 0 citations
Publisher

Abstract

Abstract We study spin dynamics and quantum magnetism with ultracold highly-magnetic atoms. In particular, we focus on the interactions among rare-earth atoms localized in a site of an optical-lattice potential, modeled as a cylindrically symmetric harmonic oscillator in the presence of a weak external magnetic field. The interactions between the atoms are modeled using a multi-channel Hamiltonian containing multiple spin–spin and anisotropic spin–orbit interactions with strengths that depend on the separation between the atoms. We studied the eigenenergies of the atom pair in a site for different lattice geometries and magnetic field strengths. In parallel, we compared these energies to those found from a simplified approach, where the complex-collisional physics is replaced by a two-length-scale pseudopotential containing the contact and magnetic dipole–dipole interactions. The eigenenergies of this model can be computed analytically within the Born approximation as well as non-perturbatively for strong contact interactions. We have shown that the pseudopotential model can accurately represent the multi-channel Hamiltonian in certain parameter regimes of the shape of the site of an optical lattice. The pseudopotential forms the starting point for many-body, condensed matter simulations involving many atom pairs in different sites of an optical lattice.

DOI
10.1088/1367-2630/adc764

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Abstract We study spin dynamics and quantum magnetism with ultracold highly-magnetic atoms. In particular, we focus on the interactions among rare-earth atoms localized in a site of an optical-lattice potential, modeled as a cylindrically symmetric harmonic oscillator in the presence of a weak external magnetic field. The interactions between the atoms are modeled using a multi-channel Hamiltonian containing multiple spin–spin and anisotropic spin–orbit interactions with strengths that depend on the separation between the atoms. We studied the eigenenergies of the atom pair in a site for different lattice geometries and magnetic field strengths. In parallel, we compared these energies to those found from a simplified approach, where the complex-collisional physics is replaced by a two-length-scale pseudopotential containing the contact and magnetic dipole–dipole interactions. The eigenenergies of this model can be computed analytically within the Born approximation as well as non-perturbatively for strong contact interactions. We have shown that the pseudopotential model can accurately represent the multi-channel Hamiltonian in certain parameter regimes of the shape of the site of an optical lattice. The pseudopotential forms the starting point for many-body, condensed matter simulations involving many atom pairs in different sites of an optical lattice.
Ultracold atomic gases have been of great theoretical and experimental interest in the last two decades. In these systems, the de Broglie wavelength of the particles is much greater than the two body van der Waals length. As a result, the details of the two body interaction potential are irrelevant for a large number of applications and the realistic two body interaction potential can be replaced by a simple finite range or zero range model potential that reproduces the scattering quantities of the full interaction potential. This thesis develops zero range pseudopotentials and applies them to trapped two-particle systems. Ultracold gases loaded into optical lattices can be used to realize two particle systems under approximately harmonic confinement. We use pseudopotentials to obtain the eigenspectrum of two particles under external harmonic confinement semi-analytically. Advancements in trapping technology have resulted in the realization of low dimensional systems. We develop pseudopotentials to treat two body interactions in one and two dimensions. We also elaborate on the physics that is unique to one and two dimensional systems. Feshbach resonances allow for the tunability of the effective two body interaction strength in the presence of a magnetic field. To model Feshbach resonances in two and three dimensions we develop coupled two channel zero range potentials. Dipole-dipole interactions in Chromium and polar molecules have been the subject of a lot of recent research. Unlike the interactions between two alkali atoms, these interactions are long range and anisotropic. We explore the scattering properties of two aligned dipoles using a simple shape dependent model potential. To understand a system two aligned dipoles under confinement, we develop a pseudopotential treatment for cylindrically symmetric interaction potentials under cylindrically symmetric harmonic confinement. This pseudopotential can be used to model any cylindrically symmetric interaction potential. Our zero range treatment describes many features of two aligned dipoles under spherically symmetric harmonic confinement accurately but breaks down when applied to two aligned dipoles under cylindrically symmetric harmonic confinement. The breakdown is unique to the long range nature of the dipole-dipole interaction and expected to be absent for short range interactions.
We study the spin dynamics of two magnetic chromium atoms trapped in a single site of a deep optical lattice in a resonant magnetic field. Dipole-dipole interactions couple spin degrees of freedom of two particles to their quantized orbital motion. A trap geometry combined with two-body contact sss-wave interactions influence a spin dynamics through the energy spectrum of the two-atom system. Anharmonicity and anisotropy of the site results in a ``fine'' structure of two-body eigenenergies. The structure can be easily resolved by weak magnetic dipole-dipole interactions. As an example we examine the effect of anharmonicity and anisotropy of the binding potential on demagnetization processes. We show that weak dipolar interactions provide a perfect tool for precision spectroscopy of the energy spectrum of the interacting few particle system.
We theoretically investigate the properties of two interacting ultracold highly magnetic atoms trapped in a one-dimensional harmonic potential. The atoms interact via an anisotropic long-range dipole-dipole interaction, which in one dimension effectively can be modeled by the contact interaction. We investigate the interplay of the external magnetic field, the spin-spin interaction, and the trapping potential and how they affect the magnetization of the system. We show the role of indistinguishability and symmetries in the dynamics by studying the time evolution of the observables that could be measured experimentally. The presented model may depict the on-site interaction of the extended Hubbard models, therefore giving a better understanding of the fundamental building block of the respective many-body quantum simulators.
We study the dynamics of spin-1 atoms in a periodic optical-lattice potential and an external magnetic field in a quantum quench scenario where we start from a superfluid ground state in a shallow lattice potential and suddenly raise the lattice depth. The time evolution of the nonequilibrium state shows collective collapse-and-revival oscillations of matter-wave coherence as well as oscillations in the spin populations. We show that the complex pattern of these two types of oscillations reveals details about the superfluid and magnetic properties of the initial many-body ground state. Furthermore, we show that the strengths of the spin-dependent and spin-independent atom-atom interactions can be deduced from the observations. The Hamiltonian that describes the physics of the final deep lattice not only contains two-body interactions but also effective multibody interactions, which arise due to virtual excitations to higher bands. We derive these effective spin-dependent three-body interaction parameters for spin-1 atoms and describe how spin mixing is affected. Spinor atoms are unique in the sense that multibody interactions are directly evident in the in situ number densities in addition to the momentum distributions. We treat both antiferromagnetic (e.g., 23{}^{23}23Na) and ferromagnetic (e.g., 87{}^{87}87Rb and 41{}^{41}41K) condensates.
In this work we study the effect of interactions in an optical lattice clock based on fermionic Sr atoms. In current one-dimensional lattice clocks nuclear spin-polarized atoms are known to have contact interactions of p-wave character and collective in nature. Here we focus on interactions that will influence the design of future optical lattice clocks. We study the case where atoms are no longer confined to a single nuclear spin state. By using samples of atoms with different distributions among the ten nuclear spin states of Sr we show that these interactions are SU(N) symmetric up to a 3% uncertainty in our measurements. Through these measurements we are also able to determine all the s-wave and p-wave scattering lengths.\nWe also study the case of nuclear spin-polarized interacting atoms that are allowed to tunnel between different lattice sites where the electronic spin and the motion of these atoms become coupled. We observe spectroscopically the precession of the collective magnetization and evolution of spin locking effects arising from the interplay between p-wave interactions and interactions induced by the spin-orbit coupling. The many-body dynamics are captured by a spin model that describes a broad class of condensed matter systems ranging from superconductors to quantum magnets.\nBy loading a dense sample of atoms into a magneto-optical trap we are able to observe long-range dipole-dipole interactions between our Sr atoms. These interactions will be important for atomic clocks based on a three dimensional lattice, such as the one recently demonstrated in our lab. In these clocks it is possible to remove the contact interactions between the atoms by loading only one atom per lattice site. In this case the dominant interactions will be from the long-range dipole-dipole interactions that will take place between the atoms.
Rydberg-dressed ground state atoms are atoms with an electron off-resonantly excited to a very high energy state, i.e., a state of high principal quantum number n ≫ 1. This thesis investigates the quantum dynamics of interacting Rydberg-dressed ground state atoms trapped in several multi-well potential traps. Rydberg atoms are atoms with exaggerated properties. One of their most interesting properties is that they exhibit a strong and long-ranged interaction that can be tuned leading to a variety of different quantum behaviours. My work focuses on studying the effects of these interacting atoms when loaded in multi-well potential traps. Generally, multi-well systems are considered as the simplest example of a finite optical lattice structure. For this reason, this thesis covers three research topics that examine the effects of long-range interaction on Rydberg-dressed atoms trapped in several potential confinements. I begin, in the introduction, by discussing the theoretical background of relevance to this work. It starts with presenting the physics of Bose-Einstein condensate. Then, the fundamentals of the interaction between two-level atom and light are analytically studied. This study has the purpose of understanding both; the dressed interacting atoms and optical lattices. The definition, characteristics, and the nature of the interaction between Rydberg atoms are analysed afterwards. The second chapter examines the dynamics of an ensemble of interacting Rydberg- dressed atoms trapped in static, i.e., time-independent, multi-well potentials using a mean-field theoretical approach. I choose one-dimensional double- and triple-well in addition to a two-dimensional quadruple-well potentials. The time-dependent non-linear Gross-Pitaevskii equation is used to numerically explore the ensemble’s quantum dynamics. Solving the dynamical differential equations along with tuning the strength of the applied long-range interaction shows that the behaviour of non-interacting Rydberg-dressed atoms does not differ conceptually according to the geometry of the trapping potential. However, this changes when the interactions are switched on where the shape of the confinement leads to interesting outcomes especially in the non-linear interacting limit, such as macroscopic quantum self-trapping. After investigating an ensemble of interacting Rydberg-dressed atoms in static multi-well potential traps, the second research topic examines the dynamical evolution of these atoms when loaded in a finite optical lattice using the extended Bose-Hubbard model. In this chapter, the atoms ensemble is assumed to be in a superfluid state where I investigate both, the order parameter when the Rydberg excitation laser is applied and the interference pattern of the condensates in different dimensions. The study shows the emerging long-range interactions lead to a rapid collapse of the superfluid order parameter and in general allow only for partial revivals. In addition, the interference experiments can directly reveal the interaction between Rydberg-dressed atoms. In the fourth chapter, the dynamics of Rydberg-dressed atoms trapped in a dynamical, i.e., time-dependent, potential confinement is presented. The dynamical trap is constructed such that it begins as a harmonic oscillator and ends as a double- well potential. The analysis investigates an ensemble of contact-interacting atoms via the time-dependent non-linear GP equation.