David L. Aronstein

General series solution for finite square-well energy levels for use in wave-packet studies

We develop a series solution for the bound-state energy levels of the quantum-mechanical one-dimensional finite square-well potential. We show that this general solution is useful for local approximations of the energy spectrum (which target a particular energy range of the potential well for high accuracy), for global approximations of the energy spectrum (which provide analytic expressions of reasonable accuracy for the entire range of bound states), and for numerical methods. This solution also provides an analytic description of dynamical phenomena; with it, we compute the time scales of classical motion, revivals, and super-revivals for wave-packet states excited in the well.

Absorptionless self phase modulation in a "dark state" electromagnetically induced transparency system

Summary form only given. The field of quantum optics was greatly enriched with the discovery of dark states and electromagnetically induced transparency (EIT). Although these two processes give similar effects, they are distinctly different. Dark states (Gray et al, 1978) are quantum states created in a three-level lambda system that is decoupled from the excited state. Some of the main features are zero linear absorption, no population in the excited state and no spontaneous emission. One limiting factor of a dark state system is that self-phase modulation disappears together with absorption. EIT is a nonlinear effect that can provide transparency to a probe field in a variety of systems. Much work has been done on two-level, cascaded-three-level and even four-level systems. It has also been shown that a large third-order nonlinear susceptibility is present in the absence of absorption. However, spontaneous emission cannot be eliminated in such system, thereby limiting their applications, particularly, to squeezed light generation. Here, we combine the effects of both dark state and EIT to create a system that is suitable for squeezed light generation via self phase modulation.

Enhanced self-action effects and slow-light optical solitons by electromagnetically induced transparency in the two-level atom

Electromagnetically induced transparency (EIT) has been studied primarily within the context of a multilevel atomic system. We show that EIT can occur in a two-level atomic system and can lead to strong self-action effects that are not hampered by material absorption, with important implications for processes such as squeezed-light generation and the propagation of optical solitons.

Comment on “On the energy levels of a finite square-well potential” [J. Math. Phys. 41, 4551 (2000)]

levels of the finite square-well potential, derived using the solution of the Riemann‐Hilbert boundary problem from the theory of analytic functions. The authors developed an asymptotic expansion for the energy levels E( p, k) in the limit of large p @where p5A2mV0L/(2\), m is the particle mass, V0 is the potential depth, L is the length of the finite well, and k is the quantum number#, and showed that the finite-well energy levels are approximately equal to those of an infinitely deep square well of length L8.L. In this comment, we correct an error in this asymptotic expansion @specifically in Ref. 1, Eq. ~28!# and point out that the connection between a finite well and a longer infinite well has been noted previously by other researchers. Paul and Nkemzi calculated @in Ref. 1, Eqs. ~25! and ~27!# that in the limit of large p, the quantized values of z5iA(V0 /E)21 take on the asymptotic form z p,k5pik~21! k S 1 4p 2 1 3p 2 2 2~ p11! p 2 k 2 D 1OS 1 p 3D . ~1! The energy levels of the finite square well are given in terms of z p, k by E~ p, k!5 V0