Bruce W. Shore

The Jaynes-Cummings Model

Abstract The Jaynes-Cummings model (JCM), a soluble fully quantum mechanical model of an atom in a field, was first used (in 1963) to examine the classical aspects of spontaneous emission and to reveal the existence of Rabi oscillations in atomic excitation probabilities for fields with sharply defined energy (or photon number). For fields having a statistical distributions of photon numbers the oscillations collapse to an expected steady value. In 1980 it was discovered that with appropriate initial conditions (e.g. a near-classical field), the Rabi oscillations would eventually revive, only to collapse and revive repeatedly in a complicated pattern. The existence of these revivals, present in the analytic solutions of the JCM, provided direct evidence for discreteness of field excitation (photons) and hence for the truly quantum nature of radiation. Subsequent study revealed further non-classical properties of the JCM field, such as a tendency of the photons to antibunch. Within the last two years it ha...

High-efficiency multilayer dielectric diffraction gratings.

The design and performance of a new type of high-efficiency diffraction grating for use in either transmission or reflection are described. The gratings are produced in a multilayer dielectric coating deposited upon optically flat substrates. By proper design of the multilayer stack and grating structure, a diffraction efficiency in excess of 96% for polarized light in the m = -1 order in reflection has been achieved.

Robust creation and phase-sensitive probing of superposition states via stimulated Raman adiabatic passage (STIRAP) with degenerate dark states

We describe a method for creating an arbitrary coherent superposition of two atomic states in a controlled and robust way by using a sequence of three pulses in a four-state system. The proposed technique is based on the existence of two degenerate dark states (i.e. states having no component of the excited state) and their interaction. The mixing of the dark states can be controlled by changing the relative delay of the pulses, and thus an arbitrary superposition state can be generated. It is shown that the method is robust against small variations of parameters (e.g. the area of the pulses) and is insensitive to radiative decay from the intermediate excited state. A time reversed version of the technique makes possible the determination of phase occurring in a superposition of two atomic states.

Comparison of matrix methods applied to the radial Schrödinger eigenvalue equation: The Morse potential

This paper demonstrates the application of matrix methods based on finite differences and on variational (Rayleigh‐Ritz‐Galerkin) procedures to solution of the radial Schrodinger equation for bound states of the Morse potential. It demonstrates sources of numerical inaccuracy: truncation, termination, tolerance, and quadrature. Cubic splines, harmonic oscillators, floating Gaussians, and sines are used as basis functions.

Solving the radial Schrödinger equation by using cubic‐spline basis functions

This paper demonstrates the use of piecewise continuous (class C2) polynomial basis functions (B splines or hill functions) in solving the l=0 radial Schrodinger equation, with examples of scattering from Eckart, exponential, and static hydrogen potentials, and eigenvalues for Coulomb, harmonic oscillator, and Morse potentials. Simple nonlinear placement of spline centroids can improve accuracy by orders of magnitude. Comparisons demonstrate the greater accuracy of the Galerkin method, compared with collocation, simple finite difference, and Numerov methods.

Efficient adiabatic population transfer by two-photon excitation assisted by a laser-induced Stark shift

We demonstrate and analyze a novel scheme for complete transfer of atomic or molecular population between two bound states, by means of Stark-chirped rapid adiabatic passage (SCRAP). In this two-laser technique a delayed-pulse laser-induced Stark shift sweeps the transition frequency between two coupled states twice through resonance with the frequency of the population-transferring coupling laser. The delay of the Stark-shifting pulse with respect to the pulse of the coupling-laser Rabi frequency guarantees adiabatic passage of population at one of the two resonances while the evolution is diabatic at the other. The SCRAP method can give a population-transfer efficiency approaching unity. We discuss the general requirements on the intensity and timing of the pulses that produce the Rabi frequency and, independently, the Stark shift. We particularly stress extension to a double-SCRAP technique, a coherent variant of stimulated emission pumping in the limit of strong saturation. We demonstrate the success ...

HIGH-EFFICIENCY FUSED-SILICA TRANSMISSION GRATINGS

We describe the design, fabrication, and performance of high-efficiency transmission gratings fabricated in bulk fused silica for use in high-power ultraviolet laser systems. The gratings exhibit a diffraction efficiency of 94% in order m=-1 and a damage threshold greater than 13>J/cm( 2) for 3-ns pulses at 351 nm. Model calculations and experimental measurements are in good agreement.

Perspective: Stimulated Raman adiabatic passage: The status after 25 years

The first presentation of the STIRAP (stimulated Raman adiabatic passage) technique with proper theoretical foundation and convincing experimental data appeared 25 years ago, in the May 1st, 1990 issue of The Journal of Chemical Physics. By now, the STIRAP concept has been successfully applied in many different fields of physics, chemistry, and beyond. In this article, we comment briefly on the initial motivation of the work, namely, the study of reaction dynamics of vibrationally excited small molecules, and how this initial idea led to the documented success. We proceed by providing a brief discussion of the physics of STIRAP and how the method was developed over the years, before discussing a few examples from the amazingly wide range of applications which STIRAP now enjoys, with the aim to stimulate further use of the concept. Finally, we mention some promising future directions.

Coherent population transfer among three states: full algebraic solutions and the relevance of non adiabatic processes to transfer by delayed pulses

Ongoing work aimed at developing highly efficient methods of populating a chosen sublevel of an energy level highlights the need to understand off-resonant effects in coherent excitation. This motivated us to re-examine some aspects of the theory of coherent excitation in a three-state system with a view to obtaining algebraic expressions for off-resonant eigenvalues and eigenvectors. Earlier work gives simple closed-form expressions for the eigenvalues this system, expressions applying even when the system is not on two-photon resonance. We present here expressions of similar simplicity for the components of the normalised eigenvectors. The analytic properties of these components explain the observed sensitivity of the stimulated-Raman-adiabatic-passage process (STIRAP) to the condition of two-photon resonance. None of the eigenstates is ‘trapped’ or ‘dark’ unless the system is on two-photon resonance; off resonance, all states have nonzero projections on the unperturbed intermediate state. A simple argument shows that no dressed state can be adiabatically connected to both the unperturbed initial and final states when the system is off two-photon resonance. That is, adiabatic transfer from initial to final state requires that these be degenerate before and after the STIRAP pulse sequence, and this implies zero two-photon detuning. However, substantial transfer probabilities are observed experimentally for very small two-photon detunings. We show that such systems are characterised by very sharp avoided crossings of two eigenvalues, and that the observed population transfer can be understood as an effect of non adiabatic transitions occurring at the avoided crossings.

Modelling laser ionisation

The authors examine the detailed dynamics of an idealised photoionisation process by examining numerical solutions to a model of monochromatic photoionisation: a one-dimensional single bound-state square well. They find, as would occur when modelling photoionisation by a complex energy operator, exponential decay of the bound-state probability. They also observe oscillations in the bound-state probability at the driving frequency; these originate in oscillatory localised motion of the probability packet as would be expected for a classical particle driven by an oscillatory field. They further find, when excitation frequencies are slightly above threshold and the interaction is sufficiently intense, slowly modulated departures from exponential decay. These originate in the action of the dipole force over large distances.