1. Discuss the Coulomb interaction, the spin-orbit coupling, and the hyperfine coupling as the three effects that determine atomic structure. 2. Highlight the importance of the separation of energy scales of these three effects. 3. Introduce different atomic structures of alkali-metal, alkaline-earth-metal, and magnetic atoms. 4. Introduce the long-lived excited states in alkaline-earth atom and their applications, such as in atomic optical clocks. 5. Discuss the Zeeman structure of atoms in a magnetic field. 6. Discuss the idea of magnetic trapping that can naturally lead to the emergence of a synthetic gauge field. 7. Introduce the scalar light shift and its applications, such as laser trapping, optical lattices, and laser cooling. 8. Introduce the vector light shift and its applications, such as the light-induced Zeeman field and synthetic spin-orbit coupling. 9. Discuss the synthetic spin-orbit coupling and various kinds of gauge fields generated by the vector light shift. 10. Introduce the basic idea of the stimulated Raman adiabatic passage.
Discuss the Coulomb interaction, the spin-orbit coupling, and the hyperfine coupling as the three effects that determine atomic structure. 2. Highlight the importance of the separation of energy scales of these three effects. 3. Introduce different atomic structures of alkali-metal, alkaline-earth-metal, and magnetic atoms. 4. Introduce the long-lived excited states in alkaline-earth atom and their applications, such as in atomic optical clocks. 5. Discuss the Zeeman structure of atoms in a magnetic field. 6. Discuss the idea of magnetic trapping that can naturally lead to the emergence of a synthetic gauge field. 7. Introduce the scalar light shift and its applications, such as laser trapping, optical lattices, and laser cooling. 8. Introduce the vector light shift and its applications, such as the light-induced Zeeman field and synthetic spin-orbit coupling. 9. Discuss the synthetic spin-orbit coupling and various kinds of gauge fields generated by the vector light shift. 10. Introduce the basic idea of the stimulated Raman adiabatic passage.
We begin our study of atomic physics by relying on the phenomenological notions summarized in chapter 1 and by fully exploiting the quantum mechanical formalism outlined in chapter 2. A hierarchy of approximations will be introduced in the first instance to describe the hydrogen atom, which allows one to focus on the main features of its energy spectrum and quantum properties, including the key ‘atomic orbital’ concept. Next, these results will be extended to the more general case of hydrogenic atoms. The physical picture will be made more rigorous by introducing the magnetic interactions, included those linked to the intrinsic spin degree of freedom, leading to the full description of the fine and hyperfine structure of one-electron atoms. The effects of a static external magnetic or electric field will be eventually discussed by calculating the corresponding energy shifts and splittings of the energy levels.
The recent experimental realization of clock-laser-induced synthetic gauge fields and one-dimensional spin-orbit coupling in ultracold alkaline-earth(-like) atoms provides a new way to explore topological quantum states with suppressed heating effects. Here, we propose a scheme for realizing a synthetic quantum Hall tube and ribbon in an optical lattice clock system with multiple optical clock transition couplings. The legs of the synthetic Hall system are composed of the atomic ground and metastable orbital states, and the couplings between the legs are generated by clock lasers, resulting in a synthetic gauge flux. We investigate the band structure and topological phase diagram under various conditions and demonstrate the phase transition. The momentum-resolved quench dynamics of the synthetic Hall system is analyzed to demonstrate the presence of gauge flux on plaquettes and reveal the critical point of the phase transition. The hyperfine spin can serve as an additional synthetic dimension, allowing a two-component Hall system to be realized in synthetic dimensions. A size-enlarged Hall system could be realized by coupling the magnetic sublevels and orbital states simultaneously. Our scheme is within reach of existing optical lattice clocks and thus provides a realistic method to achieve topological quantum Hall systems with ultracold alkaline-earth(-like) atoms. This study paves the way for realizing quantum spin Hall states with hyperfine spins and has the potential to explore more interesting topological phases.
This concise and accessible book provides a detailed introduction to the fundamental principles of atomic physics at an undergraduate level. Concepts are explained in an intuitive way and the book assumes only a basic knowledge of quantum mechanics and electromagnetism. With a compact format specifically designed for students, the first part of the book covers the key principles of the subject, including the quantum theory of the hydrogen atom, radiative transitions, the shell model of multi-electron atoms, spin-orbit coupling, and the effects of external fields. The second part provides an introduction to the four key applications of atomic physics: lasers, cold atoms, solid-state spectroscopy and astrophysics. This highly pedagogical text includes worked examples and end of chapter problems to allow students to test their knowledge, as well as numerous diagrams of key concepts, making it perfect for undergraduate students looking for a succinct primer on the concepts and applications of atomic physics.
Ultracold gases are remarkably versatile and controllable systems with untapped potential to emulate a variety of quantum phenomena [1]. Atoms are, however, electrically neutral and therefore it is highly desirable to make them behave as charged particles. This capability has recently been demonstrated in a series of recent experiments [2–4]. Although many challenges remain ahead, atoms exposed to synthetic gauge field offer great opportunities for the realization of new classes of quantum materials with custom-designed properties, and with unforeseen applications. The first implementation of an effective magnetic field was accomplished by rotating an atomic cloud [5]. In the rotating frame of reference, an atom experiences the Coriolis force that emulates the Lorentz force experienced by a charged particle in a uniform magnetic field. Large vortex lattices have been created in this way, however, so far the strength of the effective magnetic field achieved by rotation is too weak to lead to new physics. An alternative approach invokes the vector potential, A, that induces a geometric phase as a charged particle moves around a closed loop. This notion of geometric phase can be adapted to a neutral atom that slowly moves in the presence of laser fields. If the lasers are chosen to ‘dress’ the internal atomic levels, so that the dressed eigenstates become position dependent, the center of mass adiabatically evolves according the operator p-A, instead of just p = −iℏ∇. The atom thus effectively moves as a charged particle in a magnetic field B = ∇ × A (see Fig. 1a). Exploiting this idea series of experiments have implemented artificial magnetic and electric fields [2–4]. The idea has also been implemented in the presence of a superimposed periodic optical lattice potential (see Fig. 1b). In this case, the length scale imposed by the lattice competes with the one associated with the magnetic field and can lead to frustration, manifested as an energy spectrum with fractal characteristics [2,3]. Light induced synthetic gauge fields: (a) A gas of neural atoms (green oval) can behave as a gas of charged particles when it is illuminated by a pair of laser beams (red arrows) that imparts momentum to the atoms and couples their internal (.|↑.〉, .|↓.〉) and motional degrees of freedom. The Raman beams that induce transitions between internal states also transfer two units of their linear momentum 2kL. This leads to the formation of dressed states (superpositions of states with different internal levels and center of mass momenta) which experience a modified kinetic energy, with an effective vector potential. If the effective vector potential has nonzero curl, the atoms move as charged particles in a magnetic field. (b) In the presence of an optical lattice potential, Raman beams can also induce an effective vector potential. In this case, the lattice is engineered so that along one direction atoms can tunnel between adjacent lattice sites (Jlight) only by absorbing and emitting photons from the beams. The imparted momentum from the lasers produces path-dependent phases that resemble the magnetic flux accumulated by a charged particle as it moves in a closed loop. The flux accumulated by the atoms when they move around a single unit cell, ϕ, can be significant (equivalent to the one generated by a real magnetic field of thousands tesla in an electronic system) and induce a fractal energy spectrum. Generalizations to emulate non-Abelian gauge potentials, associated in many cases to spin-orbit coupling can emerge when the geometric phase is replaced by a matrix acting on the internal Hilbert space [2–5]. This happens if there is a manifold of degenerate dressed states, such that even for arbitrarily slow motion, after traveling around a contour the particle ends up in a different internal state. Although various proposals for generating non-Abelian potentials exist, they remain to be implemented. On the other hand, Abelian spin-orbit coupling, arising from the momentum kicks imparted on the atom by the laser photons that drive internal transitions, has been realized in several laboratories using different laser configurations in alkali-metal (one outer electron) and alkaline-earth (two outer electrons) atoms [2–5]. There is a great vista ahead. For example, the inclusion of collisions or dipolar interactions will open a window to engineer fractional Hall liquids, unconventional superfluids and interacting topological phases. The creation of dynamical gauge fields important in many areas of physics such as quantum chromodynamics is also an open direction. The time is just ripe for investigating rich and unexplored physics with synthetic gauge fields for ultracold matter.
Abstract Optical Raman lattices in ultra-cold alkali-metal and alkaline-earth atoms provide a powerful method to synthesize spin–orbit (SO) coupling. While the ground-state energy splittings (divided by Planck’s constant) can reach the range of tens of megahertz in alkali-metal atoms, the typical ground-state energy splittings are on the order of tens of kilohertz or smaller in alkaline-earth atoms (AEAs) such as 87 Sr. For AEAs, because such limited ground-state energy splittings are rather close to the kilohertz-scale recoil energy that is relevant for optical lattice physics, a standard implementation of a two-dimensional (2D) optical Raman lattice can lead to parasitic periodic moving potentials that heat up the atoms and severely limit the atomic lifetime. Recently, an improved optical Raman lattice scheme was proposed and experimentally realized in ultra-cold strontium fermions, which significantly enhanced the lifetime of 2D-SO-coupled fermions. However, a concrete electro-optical setup has yet to be demonstrated, and its control precision needs to be quantified. Here we demonstrate the electro-optical setup of an improved optical Raman lattice scheme that suppresses the effect of moving lattice potentials for alkaline-earth fermions by introducing a sufficiently large frequency separation between two sets of laser polarization components, where each set yields an independent Raman coupling. To quantify the precision of this setup, we feedback-control the relative phase between the two sets of Raman couplings, which is an important parameter characterizing the 1D–2D crossover of SO couplings, and measure the stability of this phase over hour-long periods. We also investigate the optimum range for the applied frequency separation. Our approach provides a useful tool that helps achieve long-lived SO-coupled systems using AEAs.