### Macroscopic Quantum Coherence

**Faculty Coordinators:** W. Kang, K. Levin

We are at the beginning of a new era in electronic materials in which macroscopic quantum coherence will play an essential role in the design and function of novel devices. Macroscopic quantum coherence in a broad new class of materials now on the horizon allows these systems to be readily manipulated. The associated robustness against decoherence enables applications based on their quantum mechanical properties. This coherence is already fundamental to devices such as superconducting SQUID magnetometers. More generally, the high degree of control possible in coherent quantum systems presents a tremendous potential for future applications.

In this IRG, our goal is to advance the state-of-art in the establishment, detection, and manipulation of macroscopically coherent quantum states in diverse classes of materials from semiconductors to superconductors to ultra-cold trapped atoms. We build on a growing trend in which materials science and condensed-matter physics are studied through tunable, artificial systems where many of the complexities of naturally-occurring materials can be stripped away. Because of their high degree of control, these quantum systems can be used to address fundamental problems in condensed matter physics. These artificial materials have the potential to redefine the way in which coherent quantum phenomena are studied both theoretically and experimentally.

The materials of interest here are engineered to enhance specific quantum properties by controlling their geometry, lattice constants, confining potentials, disorder, dimensionality, and interactions. Our choice is guided by focusing on materials that can be finely tuned, enabling transitions from one macroscopic phase to another, permitting both the induction of exotic phases and the ultimate precision control of the associated complex quantum dynamics. With such materials in hand, our goal is to develop new tools and techniques for manipulating macroscopically coherent quantum states. In particular, we intend to study superconducting, superfluid and magnetic phases and elucidate the nature of the barriers to coherence, such as those associated, for example, with disorder. Because of the high degree of control possible, the study of macroscopically coherent states in our chosen quantum systems can be used to understand and thereby facilitate the creation of macroscopic quantum coherence in other materials. We envision that the understanding gained from these studies can lead to new classes of materials-by-design in which we can dictate the type and extent of quantum coherence. The materials studied may ultimately become useful for quantum information processing or as elements of quantum logic circuits. Equally important is their role in helping to answer fundamental questions in many-body physics.

One important system on which we propose to concentrate is the two-dimensional electron gas based on GaAs heterostructures. The quantum-Hall phases in such structures are especially exciting because of their potential to exhibit exotic non-Abelian states of matter. These states have been predicted to be particularly resistant to decoherence so that far-from-equilibrium manipulation may ultimately be useful for quantum information processing. Another system with similar promise for precise control are the ultracold-trapped atomic gases which exhibit superfluid as well as insulating phases. Such systems have now become embedded in a branch of materials science based on a new hybrid technology consisting of “atom chips.” These combine the merits of microfabrication with the power of atomic physics and quantum optics for robust manipulation of atomic quantum systems as well as for quantum-information processing. We will also study magnetic phases. In the Li(Ho,Y)F family of magnetic materials, there are readily-manipulated coherent clusters of spins that allow the opportunity to study de-coherence mechanisms in a quantum system where self assembly is key. Beyond these three systems, which are all known to exhibit quantum coherence, we will also investigate the ability of nanoparticle assemblies, such as those created in IRG 3 (*The* *Design of Nanoparticle and Molecule-Based Materials*) to exhibit macroscopically-extended coherent wavefunctions and to display for example, metallic or superconducting behavior. If this coherence can be established, these materials would have a wide range of electronic and optical applications.

To carry out this bold agenda we have assembled a team of researchers that cover a broad range of expertise: low-temperature and electron transport physics (Awschalom, Jaeger, Kang, Simon, and Schuster), novel lithographic fabrication techniques (Ocola), atomic physics (Chin), chemical physics (Guyot-Sionnest), along with theoretical physics (Wiegmann, Levin, Son). This group has the required skills to develop new tools and techniques for the manipulation of macroscopic quantum coherent states in a wide variety of manifestations.

**Summary:** The establishment of coherent macroscopic quantum states in artificial materials requires the specialized experimental expertise we possess in this IRG. Moreover, strong interaction between the experimentalists and theorists will provide guidance, feedback and inter-connects between the wide variety of materials to be studied. We have chosen our materials with care, so that they exemplify the effects that will lead not only to a deeper understanding but also to novel capabilities for eventual applications. For example, if we find the long-sought non-Abelian characteristics in the 5/2 fractional quantum Hall state, it will open up new vistas for applications. Likewise, for the study of superfluid- insulating transitions, we have chosen the ultracold atomic optical lattices that allow precision control and global tuning of the interactions between the particles. This cold-atom program will also clarify the superconductor-insulator transitions to be studied in our nano-particle arrays where we need to establish the role of dimensionality and whether or not there exists an intermediate “metallic phase” or a quantum critical point. Of central interest to our IRG are the intermediate phases which may be accessed

*en route*to coherence. For example, can pairing or local superconductivity exist without macroscopic phase coherence and, if so, how do these incoherent states compete with the fully coherent phase.

In parallel with obtaining the desired coherent quantum state, we intend to study the non-equilibrium properties related to control, manipulation and entanglement. Common to all these systems are external magnetic fields used to arrive at tuneability; also common is the challenge of characterizing projected states without destroying coherence. Among the shared approaches which we will develop in a concerted fashion are spin echo techniques. Each of the systems we investigate has notable strengths and shows promise as a useful element of quantum logic circuits: (i) The magnetic cluster schemes have already demonstrated addressability. Disorder can be exploited as a positive attribute, permitting self-organized clusters of coherent spins to decouple from the background spin bath for seconds at a time. (ii) Addressability and scalability are expected to be strengths of our cold atom approach. In addition, there is little thermal noise or disorder in these ultracold gases and long storage times may be easily achieved. (iii) Finally, if non-Abelian Quantum Hall phases are available, their built-in separation from the environment makes them a very promising candidate across the entire range of properties