Quantum optics has evolved from being of most interest to folks identifying themselves as atomic, molecular and optical (AMO) scientists to a much broader research community focusing on areas ranging from astrophysics to condensed matter physics and to quantum information science, from high-energy physics to cosmology and to life sciences, and much more. I thought that it might therefore be useful to write a quantum optics text that is less AMO-centric than has typically been the case in the past, and to present the basic tools and ideas of the trade in a form that this broader community might find attractive and to the point.

 The first step when undertaking such a project was to identify what makes quantum optics so valuable. In my view, the roots of its success can be traced back to a number of breakthrough advances enabled by the invention of the laser. At the time, these may have seemed largely disconnected from each other (at least they did so to me), but taken together, they have resulted in extraordinarily powerful tools to tame the quantum.

 Five developments that I personally find to have been particularly significant are, in no particular order

• The trapping of single electrons, ions and atoms and their manipulation and control at the quantum level;
• The demonstration of the violation of Bell’s inequalities in entangled AMO systems;
• The deeper understanding of the fundamental limits of quantum measurements, driven to a significant extent by the development of gravitational wave antennas;
• The development of a rich variety of superbly controlled artificial electromagnetic environments;
• The optical cooling of atoms and ions to extraordinarily low temperatures.

 While these advances originated largely in AMO physics environments, their impact is now significantly broader. For example, trapped ions, combined with laser cooling and the control of quantum entanglement, have led to spectacular progress in quantum metrology and quantum information science. Controlled electromagnetic environments are central to cavity QED and more recently to circuit QED, and offer much promise in quantum information applications, the study of many-body systems, the search for physics past the standard model, and more. Laser cooling has been instrumental in the ground-breaking realization of Bose-Einstein condensates, rapidly followed by a wide range of other quantum degenerate systems. Combined with optical lattices, these systems provide in turn powerful bridges with solid state physics and metrology, and allow the realization of atomic clocks of unfathomable precision. Finally, the mastery of the mechanical effects of light has ushered remarkable advances in matter-wave interferometry and gave birth to the emerging field of quantum optomechanics. These are just a few examples; the list could go on and on. 

It is therefore not surprising that there is increased interest in exploiting the main ideas and tools of quantum optics in areas ranging from the full spectrum of physics to engineering, to medicine, and even to the philosophy of science. Importantly, these developments contribute significantly to breaking the silos in which much of modern research tends to be confined and help draw together people from different backgrounds to collaborate on the solution of some of its most challenging questions.

It is these observations that guided the way in which I decided to organize the book. Because it is after all about quantum optics the starting point had to be the quantization of the electromagnetic field and the description of some of its possible states (coherent field, thermal state, squeezed states), followed by a first discussion of how it interacts with quantum matter at the simplest level: two-state systems, or qubits in the jargon of quantum information science.

Since this is one of the simplest examples of a quantum system consisting of two subsystems, at this point the reader is already prepared to be exposed to quantum entanglement, a property of quantum systems that is central for many of the modern applications of quantum optics. I believe that this early introduction of the Einstein-Rosen-Podolsky paradox, Bell inequalities, no-cloning theorem, and basic properties of entanglement (points 1 and 2 on my list) presents the considerable advantage of immediately identifying the unique power of quantum systems as compared to their classical counterparts. 

Of course, simple systems consisting of just one light field and one or a few qubits are challenging at best to prepare – it is impossible in practice to completely isolate them from their environment. The next step must therefore be to start confronting this important issue. We show how the environment plays a double role: not just as a source of noise and dissipation that needs to be understood if we want to control and/or tailor it for some specific goal, but also because it is a key ingredient of the quantum measurement problem. Understanding its role is central to the third and fourth points of my list. It leads naturally to cavity QED and circuit QED and provides an important bridge to a number of cross-disciplinary interests of the broader, non-AMO community.

The last breakthrough that I needed to address, laser cooling, requires one to turn to a study of the mechanical effects of light. The associated light forces are central to atom interferometry – with remarkable metrological applications ranging from tests of the foundation of physics to geoscience – and even more importantly perhaps to the laser trapping and cooling of atomic systems down to the picokelvin range and to the study of quantum degenerate atomic systems.

The mechanical effects of light are also at the core of the emerging field of quantum optomechanics, which is the last topic discussed in some detail in the book. It extends the idea that light forces can achieve the quantum control of atoms, molecules and ions to the realm of mesoscopic and macroscopic systems. Hybrid systems composed of such mechanical oscillators and light offer the promise of sensors of extraordinary sensitivity applicable in a broad range of situations, for instance in experiments exploring the boundary between quantum mechanics and relativity and even in searches for dark matter and dark energy.   

A difficult and recurring question when writing the book has been `where to stop?’ How many examples of cavity QED should I describe?  How deeply should I go into quantum entanglement or measurement theory? How much detail to give of the various types of qubits that can be realized in circuit QED? Should I limit the discussion of quantum degenerate systems to bosons, or cover fermions as well? Should I talk in any detail of the extraordinary atomic clocks now being realized with Strontium atoms trapped on optical lattices? What about the optical levitation of mesoscopic systems? And how about these all-important optical tweezers? So many astounding developments, so many difficult choices…

The reality, though, is that the rate and breadth of progress of the field are such that today’s most amazing results may well be tomorrow’s routine. With this reality in mind, I decided to limit myself to just a few examples that I found particularly elegant or instructive rather than focus on the hottest and latest new results. My hope and my wish is that these will prove pedagogical and inspiring enough to provide the reader with the needed background and intuition to start producing hottest and latest results of their own!