Research Activities of Dan Gauthier's Group

Our laboratory is involved in a diverse set of research projects in the areas of quantum optics, control and synchronization of chaos in optical and electronic systems, and characterizing and controlling the dynamics of biological systems.  A brief overview of each general area is given below.

Control and Synchronization of Chaos in Optical and Electronic Systems

[high-speed optical chaos apparatus]
Set up for studying high speed optical chaos

Chaos and instabilities often limit the performance of devices and hence it is important to understand their control or suppression.  Also, recent research suggests that controlled chaotic systems may find useful applications in the areas of communication and computation.  The basic idea underlying the control methods is to take advantage of the large number of unstable periodic orbits and unstable steady-states that are embedded in a chaotic attractor.  We are investigating methods for controlling chaos that occurs in optical and electronic systems on a fast (nanosecond) time scale and in spatially extended optical systems. 

Due to technological constraints, a practical limit exists on the response time of an electronic or optical controller. Any system whose dynamics evolve faster than this limit presents a serious challenge to our ability to achieve control. Potential control methods must be as computationally simple as possible to cope with the rapid evolution of the system. We have developed time-delay feedback methods that can be implemented on very fast time scales and are successful in stabilizing the desired behavior using only small perturbations to the dynamical system. Our current experimental effort involves applying these methods to an dynamical system consisting of a diode laser, a Mach-Zehnder interferometer, and a time-delayed electrical feedback from the interferometer output to the injection current of the laser. The time delay in the feedback loop increases the complexity of the dynamics while the use of RF electronics in the loop allows for fast oscillations on the time scale of 1 ns. No system this fast has been successfully controlled... yet.

This research is in collaboration with Prof. Joshua Socolar of the Duke Physics Department.

[hexagonal intensity pattern]
[roll pattern]
Transverse intensity profile of a laser beam in a light valve based dynamical system. Roll or hexagon patterns form when diffraction length is sufficient.

We are also investigating control in spatially extended optical systems. One such system uses a 'Liquid Crystal Light Valve' as a nonlinear element in a diffractive optical system with feedback. A pattern of light applied to the 'Write' side of the light valve is imprinted onto light reflected from the 'Read' side by phase modulation. This pattern diffracts through a fixed difference and is fed back to the Write side. The resulting dynamics include spatial pattern formation and spatio-temporal chaos. We are currently interested in exploring the limits of control of spatio-temporal chaos in this complex dynamical system. For example, must the control signal be spatially extended to control spatial dynamics? Or perhaps a few control signals applied to certain spatial points will suffice. If so, do these point controllers require global knowledge of the dynamics?

Jonathan Blakely and Lucas Illing are currently working on these projects.  This material is based upon work supported by the US Army Research Office under Grant No. DAAD19-02-1-0223.

In addition, we are also investigating how coupling can cause two chaotic systems to synchronize their behavior.  Synchronized chaos is interesting from the perspective of fundamental nonlinear dynamics, and may be the cornerstone of communication systems based on masking information in a chaotic signal.  In our work, we have been investigating a recently discovered dynamical behavior known as attractor bubbling.  During attractor bubbling, small random perturbations occurring in the chaotic systems (due to the ever present `noise,' for example) cause brief desynchronization events for coupling strengths where previous theories would predict the occurrence of high-quality synchronization.  We are investigating the transition from attractor bubbling to high quality synchronization in one-way coupled chaotic (and hyperchaotic) electronic circuits and comparing our experimental results to emerging theories on this behavior.

This research is in collaboration with Prof. Edward Ott of the University of Maryland and Dr. Lou Pecora of the Naval Research Laboratory.

Jon Blakely and Seth Boyd are currently working on these projects.  This material is based upon work supported by the US Army Research Office under Grant No. DAAD19-02-1-0223.

Characterizing and Controlling Cardiac Dynamics

[frog heart apparatus]
Microelectrode study of a small piece of periodically-paced frog heart

One intriguing application of the chaos control methods we have developed is in the biological area.  We have initiated a program to characterize in vitro the dynamics of small pieces of rapidly paced cardiac muscle and to use feedback methods to suppress or control the observed bifurcations by applying small perturbations to the tissue.  We find that there are only a small number of classes of bifurcations in the tissue, but that there is significant variation in the prevalence of these behaviors from animal to animal.

This research is collaboration with John Cain (Math), Hana Dobrovolny, Colleen Mitchell (Math), Marie Guerraty (Math), Ann Pitruzzello (BME), Soma Sau (BME), Dr. Monica Romeo (Math), Dr. Elena Tolkacheva, and Profs. Wanda Krassowska (Biomedical Engineering), David Schaeffer (Mathematics), Joshua Socolar (Physics), and Patrick Wolf (Biomedical Engineering).  This material is based upon work supported by the National Science Foundation under Grant No. PHY-9982860.

[in vivo sheep heart with electrodes]
An in vivo sheep heart with the plaque of electrodes

In addition, we are using similar methods to control in vivo a fibrillating sheep atrium.  The eventual long term goal of this project is to develop an implantable defibrillator that will maintain a healthy rhythm in humans prone to the onset of atrial fibrillation using only small electrical shocks.  In our current experiments with sheep, we use a high-density mapping system to record the spatial-temporal complexity occurring on the surface of the heart during atrial fibrillation.  Small control shocks are applied to a single electrode attached to the surface of the heart based on real-time measurements of the cardiac dynamics at a nearby spatial location.

This research is collaboration with Mr. Robert Oliver (graduate student in Biomedical Engineering), and Profs. Wanda Krassowska (Biomedical Engineering), David Schaeffer (Mathematics), Joshua Socolar (Physics), and Patrick Wolf (Biomedical Engineering).  This project is currently supported by the National Institute of Health.

Past Research

Information Velocity Research

We are generally interested in the velocity of information on optical pulses. The best-known question in this area is, of course, can information go faster than the speed of light in vacuum, c? We address this question and the more general question of how fast does information go? by creating pulses of light that travel very fast (much much faster than c) or very slow (much much slower than c) and measuring information encoded on them.

For more about our information velocity research, please visit the Information Velocity Research section of our web site.

Quantum Optics Research

[two-photon interaction]
An illustration of the two-photon stimulated emission process

In the area of quantum optics, we worked to develop a new type of quantum oscillator known as a two-photon laser. It differs from all other known laser sources in that it is based on the two-photon stimulated emission process whereby two photons induce an atom to make a transition to a lower energy state and four photons are scattered. We create a two-photon gain medium by strongly driving potassium atoms with a (normal) laser beam. The interaction between the potassium atoms and the laser beam is so strong that it creates a `composite' atom+field system that has very interesting quantum optical properties. These composite atoms are placed in an very high finesse optical resonator that selectively enhances the two-photon stimulated emission process while simultaneously suppressing other competing nonlinear optical processes. We have recently achieved two-photon lasing in our laboratory using this technique. To the best of our knowledge, this is the only two-photon optical laser operating in the world.

[picture of the cavity]
A close up image of the two-photon laser cavity

It is expected that the photons emitted from the two-photon laser cavity will posses unique quantum correlations that might be useful for precision measurement, quantum computing, and quantum communication, for example.

Andy Dawes, Michael Stenner, Jean-Phillipe Smits, and Heejeong Jeong worked on this project. This material is based upon work supported by the National Science Foundation under Grant No. PHY-0139991.

Any opinions, findings and conclusions or recomendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF), the US Army Research Office (US ARO), or the National Institute of Health (NIH).