The coupling of coherent (laser based) optical systems to micromechanical devices, combined with breakthroughs in nanofabrication and in ultracold science, has opened up an exciting new field of research, cavity optomechanics. Several groups have now demonstrated very significant cooling of the vibrational motion of a broad range of moving mirrors, from nanoscale cantilevers to LIGO-class mirrors, and there is every reason to believe that their quantum mechanical ground state of motion of these systems will soon be achieved. In a parallel development, ultracold gases as well as Bose-Einstein condensates placed inside optical resonators have been shown to behave under appropriate conditions much like moving mirrors. Cavity optomechanics is rapidly becoming a very active sub-field or fundamental and applied research at the boundary between AMO physics, condensed matter physics, and nanoscience. With these breakthrough developments in mind, the main goal of this research is to develop a detailed theoretical understanding of key aspects of cavity optomechanics, including in particular the dynamics of mirror cooling, and to study a number of applications that include novel quantum sensors as well as the quantum and coherent control of ultracold atomic and molecular systems.
Cavity optomechanics presents considerable promise both in opening the way to address fundamental questions related to pushing quantum mechanics toward increasingly macroscopic systems, but also in applications that span a variety of areas from quantum detection to the coherent control of microscopic systems and/or of nanoscale devices. On the applied side it will enable the development of ultrasensitive force sensors and may find applications in quantum information processing technology. In addition, the study of these problems is an excellent training ground for students in view of their interdisciplinary nature at the interface of several subfields of considerable fundamental and practical interest.
The research carried out under this NSF grant comprised a series of theoretical investigations in the emerging field of quantum optomechanics. Broadly speaking, quantum optomechanics provides a universal tool to achieve the quantum control of mechanical motion, beyond what is normally possible in the presence of thermal and technical noise. At a fundamental level, it offers a route to determine and control the quantum state of truly macroscopic objects and paves the way to experiments that may lead to a more profound understanding of quantum mechanics; and from the point of view of applications, quantum optomechanical techniques in both the optical and microwave regimes will provide motion and force detection near the fundamental limit imposed by quantum mechanics. The pace of development of quantum optomechanics during the last years has been breathtaking. The numerous designs that achieve optomechanical control via radiation pressure effects in high-quality resonators have, within only a short period, opened the door to completely new parameter regimes with respect to size, mass, frequency, and scalability: they range from nanometer-sized devices of as little as 107 atoms and a mass of 10-20 kg to micromechanical structures of 1014 atoms and 10-11 kg, and to macroscopic centimeter-sized mirrors used in gravitational wave detectors comprising more than 1020 atoms and weighing up to several kilos. Ultracold atoms-based optomechanical systems have also been used for impressive demonstrations of quantum optomechanics, with key milestones including the demonstration the back-action of the quantum fluctuations of light on a mechanical system, a consequence of the fact that in quantum mechanics measurements always influence the object being measured. This rapid progress makes it increasingly realistic to consider the use of mechanical systems operating in the quantum regime to make precise and accurate measurements of feeble forces and fields. In many cases, these measurements amount to the detection of exceedingly small displacements, and in that context the remarkable potential for functionalization of mechanical devices is particularly attractive. Their motional degree(s) of freedom can be coupled to a broad range of other physical systems, including photons, spin(s), electric charges, atoms, molecules, and even "artificial atoms." In that way, the mechanical element can serve as a universal transducer or intermediary that enables the coupling between otherwise incompatible systems. In the last three years we have carried out a number of theoretical studies of hybrid optomechanical systems consisting of an atomic Bose-Einstein condensate trapped inside an optical resonator with an optically driven, oscillating end-mirror. In one specific example we showed how such a hybrid mechanical oscillator plus cold-atom system can be exploited to study many-body effects, including so-called quantum phase transitions. These are phenomena of great interest in condensed-matter physics, as they lie at the core of a number of still poorly understood effects. Generally speaking, atoms come in two types. Bosons, which are in a sense "social" atoms that satisfy Bose-Einstein statistics and have a tendency to want to behave all in exactly the same way, and "antisocial" fermions, subjected to the Pauli exclusion principle that forbids two of them to be in precisely the same state. In addition to bosonic atoms, we have also worked on fermions, exploring theoretically the optomechanical interaction between a light field and a mechanical mode of oscillation of ultracold fermionic atoms inside an optical cavity. One key step in achieving the promise of cavity optomechanics has to be the ability to fully characterize the quantum state of the mechanical element. To solve this problem we have proposed a novel detection scheme that provides hence a direct measurement of the quantum state of the oscillator. As we already indicated, the improved understanding of hybrid quantum optomechanical systems resulting from this word paves the way to the development of a new class of functionalized quantum sensors and detectors on the applied side. At a more fundamental level, it also paves the way to a more profound understanding of fundamental aspects of quantum physics, in particular of the transition from the quantum to the classical worlds. Educational component: My graduate students Wenzhou Chen and Steve Steinke have obtained their PhD in 2010 and 2011, respectively. Wenzhou has now returned to China. Steve is remaining in my group as a postdoc. I am currently supervising two PhD students: Swati Singh and HioJun Seok. I have also worked with an undergraduate student, Greg Phelps, who has now started graduate studies at Harvard. Dr. Mishkat Bhattacharya, who was my postdoc until 2010, has taken up a faculty position at the Rochester Institute of Technology. Dr. Daniel Goldbaum has decided to pursue a career in medical physics. My current postdocs are Dr. Aravind Chiruvelli and Dr. Lukas Buchmann, who both joined my group in 2011. I also had two long-term visitors from China, Dr. Hui Jing and Dr. Lin Zhang, and a visiting scholar from Turkey, Dr. Mehmet Tasgin.
