Frequency combs and precision spectroscopy of atomic hydrogen

A laser frequency comb allows the phase coherent conversion of the very rapid oscillations of visible light of some 100s of THz down to frequencies that can be handled with conventional electronics. This capability has enabled the most precise laser spectroscopy experiments yet, which have allowed the testing of quantum electrodynamics, to determine fundamental constants and to construct an optical atomic clock. The chapter reviews the development of the frequency comb, derives its properties, and discusses its application for high resolution spectroscopy of atomic hydrogen.

Molecular-physics aspects of cold chemistry

Molecular-physics aspects of cold chemistry are introduced with the example of few-electron molecules. After a brief overview of general aspects of molecular physics, the solution of the molecular Schrödinger equation is presented based on the Born-Oppenheimer approximation and the subsequent evaluation of adiabatic, nonadiabatic, relativistic and radiative (QED) corrections. Low-temperature chemical phenomena are introduced with the example of ion-molecule reactions, using the classical Langevin model for barrier-free exothermic reactions as reference. Then, methods to generate cold few-electron molecules by supersonic-beam-deceleration methods such as Stark, Zeeman, and Rydberg-Stark decelerations are presented. Two astrophysically important reactions, the reaction between H2 and H2+ forming H3+ and H, a very fast reaction following Langevin-capture going over to quantum-Langevin capture at low temperature, and the radiative association reaction H+ + H forming H2+, a very slow reaction in which quantum effects (shape resonances) become important at low temperatures, are used to illustrate the concepts introduced.

Generation of high-order harmonics and attosecond pulses

The interaction of atoms with intense laser radiation leads to the generation of high-order harmonics of the laser field. In the time domain, this corresponds to a train of pulses in the extreme ultraviolet range and with attosecond duration. The first section introduces the physics of high-order harmonic generation and attosecond pulses on the single atom level while the second section discusses phase matching and propagation effects. The attosecond time scale is that of the electron motion in atoms and molecules. Attosecond light pulses are used to study, for example, the dynamics of atomic or molecular photoionization. The third section will present an interferometric method developed for measuring attosecond pulses and discuss some of the applications, in particular concerning photoionization dynamics.

Ultrafast electron dynamics as a route to explore chemical processes

These lecture notes give a concise overview of the problem of describing quantum-mechanically the correlated motion of electrons and nuclei in a molecule. The focus is put on the methodology allowing to study the ultrafast, pure electron dynamics triggered by ionization of a molecule. It is shown that due to the electron correlation the removal of an electron from a molecular orbital can create electronic coherences manifesting in the migration of the positive charge throughout the system on a few-femtosecond time scale; a phenomenon known as correlation-driven charge migration. Some interesting perspectives for designing schemes to influence the chemical reactivity of the molecule by manipulating the charge migration dynamics are also briefly discussed.

Quantum jumps, Born’s rule, and objective classical reality via quantum Darwinism

Emergence of the classical from the quantum substrate is a long-standing conundrum. The chapter describes its resolution based on three insights that stem from the recognition of the role of the environment. The chapter begins with the derivation of preferred states that define “events”, the essence of everyday classical reality. They arise from the tension between the unitary quantum dynamics and the nonlinear amplification inherent in replicating information. The resulting pointer states are consistent with these obtained via environment-induced superselection (einselection). They determine what can happen by defining events such as quantum jumps without appealing to Born’s rule for probabilities. Probabilities can be now deduced from envariance (a symmetry of entangled quantum states). With probabilities at hand one can quantify information flows accompanying decoherence. Effective amplification they represent explains perception of objective classical reality arising from within the quantum universe through redundancy of the pointer state records in their environment—through quantum Darwinism.

Searches for new, massive particles with AMO experiments

These lectures aim to explain how certain types of atomic, molecular, and optical physics experiments can have a substantial impact in modern particle physics. A central pedagogical goal is to describe, using only concepts familiar to atomic experimentalists, how new particles can lead to new terms in the atomic or molecular Hamiltonian. Well-motivated examples are discussed, including potential dark matter candidates known as “dark photons”, known and as-yet unknown Higgs bosons, and supersymmetric particles leading to CP violation. The observable effects of new Hamiltonian terms associated with these phenomena are worked out, and state-of-the-art strategies for detecting them, using atomic and molecular experiments, are described for some cases. Remarkably, the sensitivity of atomic/molecular experiments can make it possible to detect new particles even more massive than those that can be created directly at the largest high-energy colliders.

Matter-wave physics with nanoparticles and biomolecules

The chapter discusses advances in matter-wave optics with complex molecules, generalizing Young’s double slit to high masses. The quantum wave-particle duality is visualized by monitoring the arrival patterns of molecules diffracted at nanomechanical masks. Each molecule displays particle behavior when it is localized on the detector; however, the overall interference pattern requires their delocalization in free flight. Internal particle properties influence the de Broglie waves in the presence of surfaces or fields—even in interaction with atomically thin gratings. To probe the quantum nature of high-mass molecules, universal beam splitters are combined in a multi-grating interferometer to observe high-contrast matter-wave fringes even for 500 K hot molecules, containing 810 atoms with a mass of 10 000 amu. The high sensitivity of the nanoscale interference fringes to deflection in external fields enables non-invasive measurements of molecular properties. The chapter concludes by discussing research on beam techniques that extend molecular quantum optics to large biomolecules.

Schrödinger cat states in circuit QED

Circuit quantum electrodynamics (‘circuit QED’) describes the quantum mechanics and quantum optics of superconducting electrical circuits operating in the microwave regime near absolute zero temperature. It is the analog of cavity QED in quantum optics with the role of the atoms being played by superconducting qubits. The present lecture notes present a brief overview of circuit QED and then focus on some of the novel quantum states that can be produced and measured (via photon number parity and the Wigner function) using the strong coupling between an artificial atom and one or more cavities. Of particular importance are Schrödinger cat states of photons. Despite long being considered exemplars of frail quantum superpositions that quickly decohere, such states have recently been used as the basis for quantum error correction codes which have reached the long-sought goal of enhancing the lifetime of quantum information through active quantum error correction.

Macroscopic scale atom interferometers: introduction, techniques, and applications

This chapter introduces the fundamental principles and some of the applications of light-pulse atom interferometry. It includes tutorials on various atom optics techniques and on interferometer phase shift calculations. Recent advances in large momentum transfer atom optics and in the generation and manipulation of ultra-low-velocity-spread atom clouds have enabled atom interferometers that cover macroscopic scales in space (tens of centimeters) and in time (multiple seconds), dramatically improving interferometer sensitivity in a wide range of applications. This chapter reviews these advances and recent experiments performed with macroscopic scale atom interferometers in the 10-meter-tall atomic fountain at Stanford.

Collective effects in quantum systems

The goal of the course was to introduce the methods allowing to treat quantum systems of interacting particles and discuss the resulting physics. Unfortunately time constraints prevent the author from writing a fully redacted version of the course. These notes just provide some links or references where the reader can find the material presented in the course.