ar X iv : q ua nt - p h / 01 12 12 8 v 1 2 1 D ec 2 00 1 1 Squeezing and feedback

Electro-optical feedback has many features in common with optical nonlinearities and hence is relevant to the generation of squeezing. First, I discuss theoretical and experimental results for traveling-wave feedback, emphasizing how the " in-loop " squeezing (also known as " squashing ") differs from free squeezing. Although such feedback, based on ordinary (demolition) photodetection cannot create free squeezing, it can be used to manipulate it. Then I treat feedback based on nonlinear quantum optical measurements (of which non-demolition measurements are one example). These are able to produce free squeezing, as shown in a number of experiments. Following that I discuss theories showing that intracavity squeezing can be increased using ordinary feedback, and produced using QND-based feedback. Finally, I return to " squashed " fields and present recent results showing that the reduced in-loop fluctuations can suppress atomic decay in a manner analogous to the effect for squeezed fields. In its broadest conception, feedback could be defined to be any mechanism by which a system acts upon itself, via an intermediate system. This definition would classify, for example, a nonlinear refractive index as feedback on a beam of light. The light polarizes the medium in which it is propagating, which then affects the propagation of the light in that medium. If one is interested in the light as a quantum system, then such feedback can be modeled by modifying the Hamiltonian for the field. This is a well-known mechanism for generating squeezed states of light [1]. In this chapter I am concerned with a different concept of feedback, in which the intermediate system is external to the system of interest. That is to say, the system is an open system, in constant interaction with its environment. Feedback will occur if the change in the environment due to the system is significant in affecting the system's dynamics. Since an environment is by definition large compared to the system, it is usual for this feedback to be ignored. This is the essence of the Born, or perturbative, approach to open systems [2]. However, the system's environment can be deliberately engineered so that the feedback is important.