| Quantum Technologies |
Active manipulation and control of quantum states is now becoming possible in a number of experimental contexts. Several exciting applications have been identified and substantial effort is now being expended to develop these technologies. The Theoretical Division at Los Alamos, as part of its Quantum Enabled Science and Technology (QUEST) initiative, has picked three areas of research to focus on. These areas are quantum devices and materials, quantum control, and cold atom physics. The QUEST initiative involves collaborations between Los Alamos and Caltech, UC Berkeley, UNM, UC Santa Barbara, and UT Austin. Our ongoing work on quantum control is described below.
| Investigators |
Tanmoy Bhattacharya (T-8), Andrew Doherty (Caltech), John Doyle (Caltech), Salman Habib (T-8, PI), Asa Hopkins (Caltech), Kurt Jacobs (Artabel), Hideo Mabuchi (Caltech), Keith Schwab (LPS), Kosuke Shizume (Tsukuba), Daniel Steck (T-8), and Sze Tan (Auckland).
| Abstract |
Our aim is to develop a theoretical and computational framework for the design and analysis of quantum feedback control systems and an extension of this paradigm to the study of feedback control of fragile dynamical systems in general. This requires substantial progress in our understanding of, and our ability to simulate, conditioned stochastic partial differential equations, such as Schrodinger equations with quantum feedback, stochastic Master equations with feedback (that take into account imperfect quantum measurements), and generalizations of the equations for optimal control to incorporate measurement backaction (quantum-mechanical or of some other form). The new theory will provide critical strategic guidance for experimental investigations. The development of quantum feedback control as an engineering discipline will play an essential role in promoting technological applications of mesoscale quantum systems which operate at the interface of classical and quantum mechanics. In addition, we foresee broad and significant implications of our results for the ubiquitous fields of measurement science and predictive control.
| Background |
The fateful inception of quantum mechanics during the early part of this century provoked a radical shift in our fundamental beliefs about physics. Above all else, we learned to embrace the idea that events in the microworld transpire according to laws and physical principles that directly contradict those governing the macroworld of human experience. However strange such notions may seem, their validity has been confirmed time and again by numerous experiments performed over the last fifty years.
It is exciting to look forward to a new scientific era where we can truly participate in bizarre microworld processes. Yet we have been forced in almost all of our experiments to date to accept the role of mere spectators of naturally occurring quantum phenomena. Despite impressive engineering achievements (e.g. jet aircraft, the Internet), we have yet to demonstrate any significant degree of control over the microphysical realm where quantum mechanics holds sway. Indeed, one may justly say that the development of manifestly quantum technologies for the active manipulation of microscopic processes has fallen far behind our ability to observe and to understand them.
We point to two principal reasons for the relatively primitive state of quantum technology: (1) lack of a comprehensive theory for understanding the effects of feedback upon the evolution of a quantum dynamical system, and (2) technical complications brought by noise and decoherence, which can never truly be eliminated from real laboratory experiments. Although these are formidable issues to address, recent advances in fields such as atomic physics, quantum optics, and nano-electromechanics have begun to provide the tools required to surmount them. Thus, the time is now ripe to develop a practical theory of quantum feedback control (QFC) and to exploit it in the design of new experimental systems to be implemented within the next few years.
| Research Program (General) |
In an unusual twist for a physics research program, our aim is to arrive at a theory that constitutes a direct extension of methods from macroscopic feedback-controller design, in order best to assimilate the vast body of knowledge accumulated since the invention of the Watt governor in 1769 (the first differential equation-based analysis of which is due to James Clerk Maxwell). At the classical (macroscopic) level, feedback is necessary to compensate for the effects of unpredictable disturbances on a system under control, or to make control possible when the initial state of the system is unknown. Faced with such uncertainties, we must continually improve our estimate of the evolving system state through real-time measurements made on the system as we are trying to control it.
Measurement backaction greatly complicates the notion of feedback control in quantum-mechanical contexts. Due to dynamical analogues of the uncertainty principle, it is impossible to gain information about the state of a quantum system without perturbing it in a manner that cannot be determined beforehand. Hence, any strategy for continually reducing one's uncertainty about the state of an evolving quantum system necessarily induces an excess unpredictable component in its dynamics. For Markovian open quantum systems, however, stochastic equations can be derived that self-consistently incorporate the effects of continuous, indirect observation on the evolution of the system state. Significantly, the form of these equations is such that they may be used to analyze the effects of quantum feedback, which is the process of continually adjusting the system evolution operator in a manner determined by measurement results. Having this essential tool for analysis in hand, the next step towards experimental investigations is to elucidate useful principles for QFC synthesis.
The ambition to incorporate quantum-dynamical effects into the formalism of stochastic feedback control engages a formidable new level of computational complexity. Fortunately, methods for dealing with just such problems have been under development during the last several years at Los Alamos and, more recently, there has been substantial progress involving a collaboration with the experimental program at Caltech. The highest resolution analyses anywhere of complex, nonlinear quantum dynamical systems relevant to quantum control are now being performed by our collaboration.
The implementation of practical methods for the control of quantum processes could have an enormous impact on the development of wide-ranging fields such as precision measurement and microelectronics. The most ambitious precision-measurement program today is the Laser Interferometer Gravitational-Wave Observatory (LIGO). The projected sensitivity of LIGO lies very close to the Standard Quantum Limit (SQL) for monitoring the position of the gravitational test masses. One goal of our research program is the potential utility of QFC in novel approaches to surpassing the SQL in experimental configurations similar to that of LIGO. Turning to the unrelated case of microelectronics, it has well been appreciated that the ongoing trend in miniaturization of integrated circuits could bring us down to a truly microscopic regime for individual transistors sometime within the next decade. One can easily envision a need for quantum control techniques to assist in the development of ultrascale microelectronic integration, and the inherent robustness of feedback control methods could well be crucial for reliable operation of such integrated circuits.
| Research Program (Details) |
In anticipation of experiments to be performed within the next several years, a key area of research is the paradigm of atomic motion inside a high-finesse optical microcavity. Strong coupling between single atoms and single photons within the mode volume of a high-Q optical resonator provides a novel basis for both monitoring the spatial trajectories of individual atoms in real time, and for influencing the atomic motion via single-photon Stark-shift forces. The combination of laser cooling techniques with cavity QED effects a crucial separation of timescales in which the characteristic rate of atomic motion within the cavity is much smaller than the dissipative rates, which are themselves much smaller than the system's fundamental dynamical rates. Such a hierarchy of timescales constitutes an absolute prerequisite for QFC to be possible, and has been achieved in the current experiments being conducted at Caltech.
Our specific short-term goal is to investigate controller designs for using measurements and real-time feedback to cool one atom to the ``ground'' state of the quantized mechanical potential produced by several photons in a Fabry-Perot cavity. The average number of photons circulating inside such a cavity can be maintained at a very low value N~1-10 by using a very weak driving laser that barely balances the slow rate at which individual photons leak out. If the cavity mode volume is sufficiently small, just a few photons can give rise to dipole (AC Stark-shift) forces that are strong enough to bind an atom near a local maximum of the optical field distribution. At the same time, the atomic motion can be monitored in real time via phase-sensitive measurements of the light leaking out of the cavity. To a degree determined by the fidelity of these measurements, the information gained can be used continually to adjust the strength of the driving laser (and hence the depth of the optical potential) in a manner that tends to remove kinetic energy from the atomic center-of-mass motion.
The essential computational tool we require is an efficient set of codes for numerical solution of stochastic Schrodinger and Master equations conditioned on measurement. Such numerical facilities will allow us to simulate and to evaluate specific control algorithms, and therefore to implement convex optimizations over appropriately-parametrized sets of algorithms. We have implemented a suite of parallel solvers using split-operator techniques and dynamic grids to simulate feedback on observed quantum systems. These solvers can solve directly for the density matrix or obtain a good approximation via the use of quantum Monte Carlo techniques which are much more easily implemented on parallel computing platforms. At present we are running our programs at the Advanced Computing Laboratory (ACL), LANL and at the National Energy Research Scientific Computing Center (NERSC), LBNL.
Nanomechanical resonators are now being built with resonant frequencies of a few MHz to several hundred MHz and quality factors of Q~10^4 (upper limits with present technology appear to be 10 GHz and Q~10^9). The observation of quantum behavior in these devices is becoming a real possibility. To detect such behavior the resonator must be sufficiently cold and, since a quantum harmonic oscillator driven by thermal noise behaves as a classical oscillator driven by thermal noise, one must ensure that the signatures of quantum effects are not swamped by the thermal behavior. The approach which has been taken so far to achieve low temperatures is to place the resonator in a refrigerator, however, cooling very small devices in this way is inherently inefficient. We are exploring the possibility of using feedback control to effect `active' cooling of the resonator, rather than the `passive' refrigeration technique.
To perform such feedback cooling the resonator must be monitored, and the result fed back in real time to affect the dynamics. A practical method of performing a continuous measurement of the position of the resonator is to use a SET. To do this one locates the oscillator next to the central island of the SET. When the oscillator is charged, and the SET is biased so that current flows through it, changes in the oscillator's position change the energy of the central island, which causes changes in the current. The current therefore provides a continuous measurement of the position of the oscillator, and this is just what is required for implementing a linear feedback cooling algorithm. A feedback force can be applied by an actuating gate, or by passing a current through the oscillator, and varying an applied magnetic field. We have carried out a detailed analysis of this situation and the results are quite encouraging. As shown in the Figure, it is possible to cool a high-Q nanomechanical oscillator operating in the range of 10 - 100 Mhz very close to its ground state using active cooling. Such nanoresonators already exist in the laboratory and it is our hope that active cooling technologies will be demonstrated in the very near future.
| Outlook |
Due to the complexity of the overall situation, which includes N^(1/2) fluctuations of the intracavity photon number, atomic spontaneous emission, and backaction from the atomic position measurements, we expect that it may be rather difficult to determine and to characterize optimal schemes for varying the laser intensity in response to measurement results. Mathematically speaking, we will need to develop efficient strategies for functional optimization of large, strongly-coupled systems of nonlinear stochastic partial differential equations. In return for our efforts, we stand to gain valuable insights into the interplay between measurement backaction and dynamical complexity in open quantum systems that should provide a crucial foundation for implementing control strategies in a diverse range of experimental systems beyond cavity QED. Indeed, in the long run we believe that QFC will provide a unique paradigm for probing the ultimate quantum-mechanical limits to prediction and control of the evolution of dynamical systems.
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| Salman Habib / LANL / habib@lanl.gov / revised December 2002 | |