Quantum Gas Experiments

The following sections are included:

• Contents

Quantum gases provide an exciting arena for studying many-body quantum physics. Model systems that approximate more complex materials in solid state and condensed matter can be realized and probed with high precision. Due to the various degrees of freedom present in ultracold gases, fully novel systems with no previously studied counterparts can also be realized…

We provide an introduction to the experimental physics of quantum gases. At the low densities of ultracold quantum gases, confinement can be understood from single-particle physics, and interactions can be understood from two-body physics. The structure of atoms provides resonances both in the optical domain and in the radio-frequency domain. Atomic structure data is given for the 27 atomic isotopes that had been brought to quantum degeneracy at the time this chapter was written. We discuss the motivations behind choosing among these species and we review how static and oscillatory fields are treated mathematically. An electric dipole moment can be induced in a neutral atom, and is the basis for optical manipulation as well as short-range interactions. Many atoms have permanent magnetic dipole moments, which can be used for trapping or long-range interactions. The Toronto ⁴⁰K/⁸⁷Rb lattice experiment provides an illustration of how these tools are combined to create an ultracold, quantum-degenerate gas.

The experimental realization of correlated quantum phases with ultracold gases in optical lattices and their theoretical understanding has witnessed remarkable progress during the last decade. In this review we introduce basic concepts and tools to describe the many-body physics of quantum gases in optical lattices. This includes the derivation of effective lattice Hamiltonians from first principles and an overview of the emerging quantum phases. Additionally, state-of-the-art numerical tools to quantitatively treat bosons or fermions on different lattices are introduced.

In this chapter, we describe scattering resonance phenomena in general, and focus on the mechanism of Feshbach resonances, for which a multi-channel treatment is required. We derive the dependence of the scattering phase shift on magnetic field and collision energy. From this, the scattering length and effective range coefficient can be extracted — expressions which are particularly useful for ultracold gases.

The generation of periodic potential structures builds the basis for studying solid state type physics with ultracold quantum gases. This chapter introduces the underlying principles of optical lattices and discusses some of themore recent developments towards lattice structures beyond simple cubic ones.

One exciting progress in recent cold atom experiments is the development of high resolution, in situ imaging techniques for atomic quantum gases.^1–3 These new powerful tools provide detailed information on the distribution of atoms in a trap with resolution approaching the level of single atom and even single lattice site, and complement the welldeveloped time-of-flight method that probes the system in momentum space. In a condensed matter analogy, this technique is equivalent to locating electrons of a material in a snap shot. In situ imaging has offered a new powerful tool to study atomic gases and inspired many new research directions and ideas. In this chapter, we will describe the experimental setup of in situ absorption imaging, observables that can be extracted from the images, and new physics that can be explored with this technique.

Quantum gases in optical lattices have proven a prolific platform to study condensed matter models such as the Bose–Hubbard model. The recently achieved in situ fluorescence imaging of low-dimensional systems has pushed the detection capabilities to a fully microscopic level. The method yields single-site and single-atom resolved images of the lattice gas in a single experimental run, thus giving direct access to fluctuations and correlation functions in the many-body system. These quantum gas microscopes have been used to study the superfluid–Mott insulator quantum phase transition at the single-atom level. Moreover, singlesite resolved addressing allows flipping the spin of individual atoms in a Mott insulator, thus deterministically creating local spin excitations whose dynamics can be observed. In this chapter, we will describe the implementation of the technique and discuss some of the obtained results.

Noise correlation analysis is a detection tool for spatial structures and spatial correlations in the in-trap density distribution of ultracold atoms. In this chapter, we discuss the implementation, properties and limitations of the method applied to ensembles of ultracold atoms in optical lattices, and describe some instances where it has been applied.

This chapter presents the crossover from the Bardeen–Cooper–Schrieffer (BCS) state of weakly correlated pairs of fermions to the Bose–Einstein condensation (BEC) of diatomic molecules in the atomic Fermi gas. Our aim is to provide a pedagogical review of the BCS–BEC crossover, with an emphasis on the basic concepts, particularly those that are not generally known or are difficult to find in the literature. We shall not attempt to give an exhaustive survey of current research in the limited space here; where possible, we will direct the reader to more extensive reviews.

This chapter explains how various spectroscopies can be used for probing the many-body quantum state of ultracold gas systems. It starts with a brief reminder of the basic theory of field-matter interactions. The general theory of linear response in the context of many-body quantum physics is then presented. A detailed theoretical description of RF spectroscopy, both the usual one and the momentum-resolved version, is given. This description applies to Raman spectroscopy as well. The basic theory behind Bragg spectroscopy and lattice modulation spectroscopy is also discussed. I explain how RF spectroscopy relates to the spectral function and how Bragg spectroscopy relates to the dynamical/static structure factor. The derivations are detailed and Green's functions are not used, so it is possible to follow this chapter based on simply knowing the basics of second quantization. Finally, self-consistent linear response theory and the use of sum rules is discussed in an overall manner.

The determination of the energy spectrum is an essential step in the characterization of a many-body phase. This chapter gives an experimental overview of the spectroscopic tools which are currently available for probing ultracold lattice gases, with a focus on fermionic systems.

In this chapter we review the progress in experiments with hybrid systems of trapped ions and ultracold neutral atoms. We give a theoretical overview over the atom–ion interactions in the cold regime and give a summary of the most important experimental results. We conclude with an overview of remaining open challenges and possible applications in hybrid quantum systems of ions and neutral atoms.

In this chapter, we briefly review some important aspects of the theory of dipolar gases, focusing on those aspects in which the physics of dipolar gases differs qualitatively from that of non-dipolar ones.

In this chapter, we review experimental aspects of dipolar quantum gases. We focus especially on magnetic dipolar atomic quantum gases held in a single trap and in multiple spatially separated traps.

The following section is included:

• Index