Improving techniques for diagnostics of laser pulses by compact representations.

We propose and demonstrate, numerically and experimentally, use of sparsity as prior information for extending the capabilities and performance of techniques and devices for laser pulse diagnostics. We apply the concept of sparsity in three different applications. First, we improve a photodiode-oscilloscope system's resolution for measuring the intensity structure of laser pulses. Second, we demonstrate the intensity profile reconstruction of ultrashort laser pulses from intensity autocorrelation measurements. Finally, we use a sparse representation of pulses (amplitudes and phases) to retrieve measured pulses from incomplete spectrograms of cross-correlation frequency-resolved optical gating traces.

Dynamical pruning of the multiconfiguration time-dependent Hartree (DP-MCTDH) method: An efficient approach for multidimensional quantum dynamics.

We present two strategies for combining dynamical pruning with the multiconfiguration time-dependent Hartree (DP-MCTDH) method, where dynamical pruning means on-the-fly selection of relevant basis functions. The first strategy prunes the primitive basis that represents the single-particle functions (SPFs). This is useful for smaller systems that require many primitive basis functions per degree of freedom, as we will illustrate for NO2. Furthermore, this allows for higher-dimensional mode combination and partially lifts the sum-of-product-form requirement onto the structure of the Hamiltonian, as we illustrate for nonadiabatic 24-dimensional pyrazine. The second strategy prunes the set of configurations of SPF at each time step. We show that this strategy yields significant speed-ups with factors between 5 and 50 in computing time, making it competitive with the multilayer MCTDH method.

Efficient molecular quantum dynamics in coordinate and phase space using pruned bases.

We present an efficient implementation of dynamically pruned quantum dynamics, both in coordinate space and in phase space. We combine the ideas behind the biorthogonal von Neumann basis (PvB) with the orthogonalized momentum-symmetrized Gaussians (Weylets) to create a new basis, projected Weylets, that takes the best from both methods. We benchmark pruned time-dependent dynamics using phase-space-localized PvB, projected Weylets, and coordinate-space-localized DVR bases, with real-world examples in up to six dimensions. For the examples studied, coordinate-space localization is the most important factor for efficient pruning and the pruned dynamics is much faster than the unpruned, exact dynamics. Phase-space localization is useful for more demanding dynamics where many basis functions are required. There, projected Weylets offer a more compact representation than pruned DVR bases.

Three-level systems as amplifiers and attenuators: a thermodynamic analysis.

Thermodynamics of a three-level maser was studied in the pioneering work of Scovil-Schulz-DuBois [Phys. Rev. Lett. 2, 262 (1959)10.1103/PhysRevLett.2.262]. In this Letter we consider the same three-level model, but we give a full thermodynamic analysis based on Hamiltonian and dissipative Lindblad superoperators. The first law of thermodynamics is obtained using a recently developed alternative [Phys. Rev. A 74, 063823 (2006)10.1103/PhysRevA.74.063823] to Alicki's definitions for heat flux and power [J. Phys. A 12, L103 (1979)10.1088/0305-4470/12/5/007]. Using a novel variation on Spohn's entropy production function [J. Math. Phys. (N.Y.) 19, 1227 (1978)10.1063/1.523789], we obtain Carnot's efficiency inequality and the Scovil-Schulz-DuBois maser efficiency formula when the three-level system is operated as a heat engine (amplifier). Finally, we show that the three-level system has two other modes of operation--a refrigerator mode and a squanderer mode--both of which attenuate the electric field.

Negative mass instability for interacting particles in a 1D box: theory and application.

We demonstrate that the synchronization effect observed [Pedersen et al., Phys. Rev. Lett. 87, 055001 (2001)]], when a bunch of ions oscillates between two mirrors in an electrostatic ion beam trap, can be explained as a negative mass instability. We derive simple necessary conditions for the existence of a regime in which this dispersionless behavior occurs and demonstrate that in this regime, the ion trap can be used as a high resolution mass spectrometer.

Semiclassical calculation of chemical reaction dynamics via wavepacket correlation functions.

Calculation of chemical reaction dynamics is central to theoretical chemistry. The majority of calculations use either classical mechanics, which is computationally inexpensive but misses quantum effects, such as tunneling and interference, or quantum mechanics, which is computationally expensive and often conceptually opaque. An appealing middle ground is the use of semiclassical mechanics. Indeed, since the early 1970s there has been great interest in using semiclassical methods to calculate reaction probabilities. However, despite the elegance of classical S-matrix theory, numerical results on even the simplest reactive systems remained out of reach. Recently, with advances both in correlation function formulations of reactive scattering as well as in semiclassical methods, it has become possible for the first time to calculate reaction probabilities semiclassically. The correlation function methods are contrasted with recent flux-based methods, which, although providing somewhat more compact expressions for the cumulative reactive probability, are less compatible with semiclassical implementation.

Extension of the mapped Fourier method to time-dependent problems.

A numerical method is described for integration of the time-dependent Schrödinger equation within the presence of a Coulomb field. Because of the singularity at r=0, the wave packet has to be represented on a grid with a high density of points near the origin; at the same time, because of the long-range character of the Coulomb potential, the grid must extend to large values of r. The sampling points are chosen, following E. Fattal, R. Baer, and R. Kosloff [Phys. Rev. E 53, 1217 (1996)], using a classical phase space criterion. Following those workers, the unequally spaced grid points are mapped to an equally spaced grid, allowing use of fast Fourier transform propagation methods that scale as N ln N, where N is the number of grid points. As a first test, eigenenergies for the hydrogen atom are extracted from short-time segments of the electronic wave-packet autocorrelation function; high accuracy is obtained by using the filter-diagonalization method. As a second test, the ionization rate of the hydrogen atom resulting from a half-cycle pulse is calculated. These results are in excellent agreement with earlier calculations.