A New Atom Trap: The Annular Shell Atom Trap (ASAT)

In the course of exploring some aspects of atom guiding in a hollow, optical fiber, a small negative potential energy well was found just in front of the repulsive or guiding barrier. This results from the optical dipole and the van der Waals potentials. The ground state for atoms bound in this negative potential well was determined by numerically solving the Schrodinger eq. and it was found that this negative well could serve as an atom trap. This trap is referred to as the Annular Shell Atom Trap or ASAT because of the geometry of the trapped atoms which are located in the locus of points defining a very thin annular shell just in front of the guiding barrier. A unique feature of the ASAT is the compression of the atoms from the entire volume to the volume of the annular shell resulting in a very high density of atoms in this trap. This trap may have applications to very low temperatures using evaporative cooling and possibly the formation of BEC. Finally, a scheme is discussed for taking advantage of the de Broglie wavelength to store atoms in a bottle trap based on the inability of long de Broglie wavelengths to escape through a selective de Broglie wavelength filter in the atom bottle trap.Comment: 13 pages total, 5 figure

Shunto, Rational Expectations, and Output Growth in Japan

This paper describes a theoretical and empirical study of the Japanese macroeconomy that focuses on the role of predetermined nominal wages in the relation between monetary policy and aggregate output. The main features of the model are that nominal wage rates set at Shunto are equal to rational expectations of the nominal wage rates that would be consistent with target levels of real output and that firms determine employment and output by equating marginal productivities to real wage rates. The essential implication of the model is that the current deviation of aggregate output from its target level depends only on innovations in inflation and productivity since the last Shunto. The equation derived to implement the model empirically relates current aggregate output growth in a precise way to past values of output growth and inflation since the last Shunto and includes an explicit specification of a white noise error term. The results of econometric analysis of this restricted model equation are consistent with the hypothesis that nominal wages predetermined according to Shunto with rational expectations are important tor the determination of real aggregates. The empirical analysis, however, also suggests that the assumptions about monetary policy used to close the model are not adequate, a result that leads to directions for further research.

Self-degradation of heat shock proteins

The 70-kDa heat shock protein of Drosophila decays in vivo at a much faster rate than other abundantly labeled proteins. Degradation also occurs in vitro, even during electrophoresis. It appears that this degradation is not mediated by a general protease and that the 70-kDa heat shock protein has a slow proteolytic action upon itself. Heat-induced proteins in CHO cells and a mouse cell line also degrade spontaneously in vitro, as do certain non-heat shock proteins from Drosophila tissues as well as the cell lines

Exploring constrained quantum control landscapes

The broad success of optimally controlling quantum systems with external fields has been attributed to the favorable topology of the underlying control landscape, where the landscape is the physical observable as a function of the controls. The control landscape can be shown to contain no suboptimal trapping extrema upon satisfaction of reasonable physical assumptions, but this topological analysis does not hold when significant constraints are placed on the control resources. This work employs simulations to explore the topology and features of the control landscape for pure-state population transfer with a constrained class of control fields. The fields are parameterized in terms of a set of uniformly spaced spectral frequencies, with the associated phases acting as the controls. Optimization results reveal that the minimum number of phase controls necessary to assure a high yield in the target state has a special dependence on the number of accessible energy levels in the quantum system, revealed from an analysis of the first- and second-order variation of the yield with respect to the controls. When an insufficient number of controls and/or a weak control fluence are employed, trapping extrema and saddle points are observed on the landscape. When the control resources are sufficiently flexible, solutions producing the globally maximal yield are found to form connected `level sets' of continuously variable control fields that preserve the yield. These optimal yield level sets are found to shrink to isolated points on the top of the landscape as the control field fluence is decreased, and further reduction of the fluence turns these points into suboptimal trapping extrema on the landscape. Although constrained control fields can come in many forms beyond the cases explored here, the behavior found in this paper is illustrative of the impacts that constraints can introduce.Comment: 10 figure

Letters to the Editor

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65147/1/j.1752-7325.1989.tb02065.x.pd

Foundations for Cooperating with Control Noise in the Manipulation of Quantum Dynamics

This paper develops the theoretical foundations for the ability of a control field to cooperate with noise in the manipulation of quantum dynamics. The noise enters as run-to-run variations in the control amplitudes, phases and frequencies with the observation being an ensemble average over many runs as is commonly done in the laboratory. Weak field perturbation theory is developed to show that noise in the amplitude and frequency components of the control field can enhance the process of population transfer in a multilevel ladder system. The analytical results in this paper support the point that under suitable conditions an optimal field can cooperate with noise to improve the control outcome.Comment: submitted to Phys. Rev.

The landscape of quantum transitions driven by single-qubit unitary transformations with implications for entanglement

This paper considers the control landscape of quantum transitions in multi-qubit systems driven by unitary transformations with single-qubit interaction terms. The two-qubit case is fully analyzed to reveal the features of the landscape including the nature of the absolute maximum and minimum, the saddle points and the absence of traps. The results permit calculating the Schmidt state starting from an arbitrary two-qubit state following the local gradient flow. The analysis of multi-qubit systems is more challenging, but the generalized Schmidt states may also be located by following the local gradient flow. Finally, we show the relation between the generalized Schmidt states and the entanglement measure based on the Bures distance

A Simplified Approach to Optimally Controlled Quantum Dynamics

A new formalism for the optimal control of quantum mechanical physical observables is presented. This approach is based on an analogous classical control technique reported previously[J. Botina, H. Rabitz and N. Rahman, J. chem. Phys. Vol. 102, pag. 226 (1995)]. Quantum Lagrange multiplier functions are used to preserve a chosen subset of the observable dynamics of interest. As a result, a corresponding small set of Lagrange multipliers needs to be calculated and they are only a function of time. This is a considerable simplification over traditional quantum optimal control theory[S. shi and H. Rabitz, comp. Phys. Comm. Vol. 63, pag. 71 (1991)]. The success of the new approach is based on taking advantage of the multiplicity of solutions to virtually any problem of quantum control to meet a physical objective. A family of such simplified formulations is introduced and numerically tested. Results are presented for these algorithms and compared with previous reported work on a model problem for selective unimolecular reaction induced by an external optical electric field.Comment: Revtex, 29 pages (incl. figures

Cooperating or Fighting with Decoherence in the Optimal Control of Quantum Dynamics

This paper explores the use of laboratory closed-loop learning control to either fight or cooperate with decoherence in the optimal manipulation of quantum dynamics. Simulations of the processes are performed in a Lindblad formulation on multilevel quantum systems strongly interacting with the environment without spontaneous emission. When seeking a high control yield it is possible to find fields that successfully fight with decoherence while attaining a good quality yield. When seeking modest control yields, fields can be found which are optimally shaped to cooperate with decoherence and thereby drive the dynamics more efficiently. In the latter regime when the control field and the decoherence strength are both weak, a theoretical foundation is established to describe how they cooperate with each other. In general, the results indicate that the population transfer objectives can be effectively met by appropriately either fighting or cooperating with decoherence