Murray Sargent

Mechanical Effects of Light

In this chapter we study the effects of light forces on the center-of-mass motion of two-level atoms. This discussion naturally leads to the distinction between two operating regimes: The first one, which we call “ray atom optics”, is characterized by the fact that the center-of-mass motion of the atoms can be treated classically. This regime is important from many atomic cooling schemes, such as Doppler cooling which is discussed in Sect. 6.2. “Wave atom optics” is reached when the atomic center-of-mass motion must be treated quantum-mechanically. In that case, it is useful to think of atoms as matter waves subject to the laws of diffraction. This regime is important for ultracold atomic samples, as can now be obtained by several cooling methods such as, e.g., evaporative cooling, as well as in the study of diffraction of atoms by optical and material gratings, and in atom interferometry.

Introduction to Laser Theory

This chapter gives a simple theory of the laser using the classical electromagnetic theory of Chap. 1 in combination with Chap. 5’s discussion of the interaction of radiation with two-level atoms. We consider arrangements of two or three highly reflecting mirrors that form cavities as shown in Fig. 6-1. Light in these cavities leaks out (decays to its 1/e value) in a time Q/v where v is the frequency of the light and Q is the cavity quality factor (the higher the Q the lower the losses). An active gain medium is inserted between the mirrors to compensate for the losses. In the simple cases we consider in this chapter, the electromagnetic field builds up until it saturates the gain down to the cavity losses. Chapter 10 considers some more complicated cases. Chapter 7 discusses a related cavity problem in which the medium in the cavity is not a gain medium, i.e., it has dispersion and/or absorption. This nonlinear cavity problem can lead to two or more stable output intensities for a given input intensity, and hence belongs to a class of problems called optical bistability. In the present chapter we also see a bistable configuration that involves active media, namely the homogeneously broadened ring laser.

First 25 years of quantum optics at Optics Sciences Center

Quantum Optics at the Optical Sciences Center is traced from a gleam in Steve Jacobs’ eyes to a world class set of endeavors. The people involved include Jacobs, Scully, Sargent, Lamb, Hopf, Shoemaker, Meystre, Chow, Rogovin, Franken, Gibbs, Khitrova, Peyghambarian, Wright, Moloney, Lindberg, Koch and their students. The research areas include a wide variety of nonlinear interactions of electromagnetic radiation with atomic, molecular, and solid state matter. The theories in these investigations range from classical to semiclassical to fully quantal.

CW Field Interactions

This chapter uses the density matrix methods of Chap. 4 to find the polarization induced by one or two continuous (cw) plane waves in two-level media. The density matrix is extended in a form known as the population matrix, which treats collections of atomic responses simply. Section 5-1 deals with homogeneously-broadened media, while Sec. 5-2 includes inhomogeneous broadening. The induced polarization is used as a source in the slowly-varying Maxwell equations to yield a nonlinear Beer’s law for propagation. The population matrix equations of motion are solved in the important rate equation approximation, which assumes that the dipole lifetime T 2 is short compared to times for which the field envelope or population difference vary appreciably. The concepts of power-broadening and spectral hole burning are developed.

System-Reservoir Interactions

The Weisskopf-Wigner theory of spontaneous emission of Chap. 13 is an example of a general class of problems involving the coupling of a small system to a large system. In that case the small system is the atom and the large system is the continuum of modes of the electromagnetic field. When computing the atomic decay rate, we were not interested in the field itself, but only on its effect on the atomic dynamics. Thus we never explicitly computed the field dynamics. Our theory lead to an irreversible decay of the upper state population. At first this should come as a surprise, since our starting equation (the Schrodinger equation) is reversible. Irreversibility results from two main approximations: 1) the assumption that the probability amplitude C α 0(t) varies little during the time interval defined by the inverse bandwidth of the continuum of modes of the electromagnetic field, and 2) the replacement of the remaining non-local time integration in Eq. (13.58) by a δ-function. These choices comprise the Weisskopf-Wigner approximation.

Squeezed States of Light

The Heisenberg uncertainty principle \( \Delta A\Delta B \geqslant \frac{1} {2}\left| {\left\langle {\left[ {A,B} \right]} \right\rangle } \right| \) between the standard deviations of two arbitrary observables, ΔA = 〈(A - (A))2〉1/2 and similarly for ΔB, has a built-in degree of freedom: one can squeeze the standard deviation of one observable provided one “stretches” that for the conjugate observable. For example, the position and momentum standard deviations obey the uncertainty relation

Interaction Between Atoms and Quantized Fields

\Delta x\Delta p \geqslant \hbar /2

Elements of Quantum Optics

(17.1) and we can squeeze Δx to an arbitrarily small value at the expense of accordingly increasing the standard deviation Δp. All quantum mechanics requires is than the product be bounded from below. As discussed in Sect. 13.1, the electric and magnetic fields form a pair of observables analogous to the position and momentum of a simple harmonic oscillator. Accordingly, they obey a similar uncertainty relation