Any introductory books/articles on ultra-cold atoms? I am currently only a high school student wanting to pursue physics at the tertiary level of education.
Are there any books people can recommend on ultra-cold atoms? I would like to discover more about them, but the ones I have viewed so far require lots of mathematics, and I only want some introductory knowledge.
 A: Ultracold atom is an exciting study field and I'm impressed that you as a high school student even know this concept.
As Alexander said in the comment, to understand the basic phenomena of ultracold atoms -- quantum degeneracy, you must have solid quantum mechanical and stat-mech basics. These are not within the scope of this question, but I would recommend textbooks by Sakurai (Modern quantum mechanics) and Kardar (Statistical physics of particles; the second volume about fields might be a bit advanced and not extremely helpful).
Getting back to ultracold atoms; this concept is actually originated from a very important and well-developed sub-field: quantum precision measurement. Early atomic research cared nothing about many-atom features since these would only make the spectrum noisy. For this part of development, Wolfgang Ketterle's great lecture 8.421 (note that 8.422 is also related but a bit more related to quantum optics) comprehensively covered the necessary information. You can read it together with Foot's atomic physics book.
Since the late 90s, quantum degeneracy has been achieved in atomic systems, marking that the many-atom features are finally considered as properties to study rather than noise. Recently there are few books about ultracold atoms, but to the best of my knowledge, non is well organized to study. Some are good as references though, and I recommend you to read Claude Cohen-Tannoudji's Advances in Atomic Physics: An Overview. This book overlaps w/ WOlfgange's course, which offers you another point of view about these interesting topics. In parts 7&8 the developments (up to ~ 2010) about these many-body features are discussed.
One important thing is that the ultracold atoms are known to have very good controls of parameters, and among all parameters, the atomic interaction is considered the most difficult one to control. Physicists developed a way that was originally proposed for nuclear physics to control the interaction: Feshbach resonance, where the interactions are strongly mediated by an additional energy level whose detuning can be changed precisely. For a review, see this RMP paper.
From these good properties of ultracold atoms, the concept of quantum simulation, firstly proposed by Richard Feynman, is revisited and has get popular in recent years. The idea is to use well-controlled ultracold atoms to mimic some complicated and unresolved quantum many-body questions like high T_c superconductors, and use extremely precise optical tools (aka quantum gas microscope) to probe the system at individual atom level. This overlaps strongly with condensed matter physics, and I recommend you to read this review paper by Immanuel Bloch and other great physicists.
These materials can guide you to the developments up to maybe 2017 before the concept of the tweezer array was proposed and achieved in Harvard-MIT Center of Ultracold Atoms. The tweezer array with Rydberg atoms seems like a much more promising platform for certain types of applications including quantum computing. This, however, is too new to be written into even a review paper. You can, however, look into some thesis by Misha Lukin's tweezer subgroup or Antoine Browaeys's group.
Along the above timeline, the optical modes are mostly classical. One slightly deviated development in the ultracold atoms is to study the behavior with quantum light, at least quantum light mode. This is pioneered in the field called cavity QED, and led by groups in ETH Zurich, MIT, Caltech, and many other places. A good, modern but not complete review can be found here.
