Manifestation of classical wave delays in a fully quantized model of the scattering of a single photon

We consider a fully quantized model of spontaneous emission, scattering, and absorption, and study propagation of a single photon from an emitting atom to a detector atom both with and without an intervening scatterer. We find an exact quantum analog to the classical complex analytic signal of an electromagnetic wave scattered by a medium of charged oscillators. This quantum signal exhibits classical phase delays. We define a time of detection which, in the appropriate limits, exactly matches the predictions of a classically defined delay for light propagating through a medium of charged oscillators. The fully quantized model provides a simple, unambiguous, and causal interpretation of delays that seemingly imply speeds greater than c in the region of anomalous dispersion.Comment: 18 pages, 4 figures, revised for clarity, typos corrrecte

Manifestations of classical physics in the quantum evolution of correlated spin states in pulsed NMR experiments

Multiple-pulse NMR experiments are a powerful tool for the investigation of mole- cules with coupled nuclear spins. The product operator formalism provides a way to understand the quantum evolution of an ensemble of weakly coupled spins in such experiments using some of the more intuitive concepts of classical physics and semi- classical vector representations. In this paper I present a new way in which to inter- pret the quantum evolution of an ensemble of spins. I recast the quantum problem in terms of mixtures of pure states of two spins whose expectation values evolve identi- cally to those of classical moments. Pictorial representations of these classically evolving states provide a way to calculate the time evolution of ensembles of weakly coupled spins without the full machinery of quantum mechanics, offering insight to anyone who understands precession of magnetic moments in magnetic fields

Numerical analysis of Bose-Einstein condensation in a three-dimensional harmonic oscillator potential

Bose–Einstein condensation is the anomalous accumulation of particles in the ground state of a system of bosons, when compared with the population in a system of particles obeying classical statistics. I use undergraduate-level statistical mechanics and a symbolic algebra computer program to study the occupation numbers of the energy levels of a finite number of noninteracting particles confined in a three-dimensional harmonic oscillator potential. I also calculate the heat capacity of the gas. The harmonic oscillator potential simplifies the calculations and approximates the conditions of the recent experiments achieving Bose–Einstein condensation in laser-cooled alkali vapors

Spectroscopy of Isolated Prebiotic Nucleobases

We use multiphoton ionization and double resonance spectroscopy to study the excited state dynamics of biologically relevant molecules as well as prebiotic nucleobases, isolated in the gas phase. Molecules that are biologically relevant to life today tend to exhibit short excited state lifetimes compared to similar but non-biologically relevant analogs. The mechanism is internal conversion, which may help protect the biologically active molecules from UV damage. This process is governed by conical intersections that depend very strongly on molecular structure. Therefore we have studied purines and pyrimidines with systematic variations of structure, including substitutions, tautomeric forms, and cluster structures that represent different base pair binding motifs. These structural variations also include possible alternate base pairs that may shed light on prebiotic chemistry. With this in mind we have begun to probe the ultrafast dynamics of molecules that exhibit very short excited states and search for evidence of internal conversions

Dynamic origin of non-Abelian Berry\u27s phase effects in a simple atomic system

The full effect of adiabatically varying Hamiltonians on systems prepared in eigenstates of the stationary Hamiltonian often includes geometric Berry\u27s phases. For degenerate systems these effects may result in transitions between distinct degenerate eigenstates that can be described in terms of a non-Abelian gauge potential. I demonstrate the explicit dynamic origin of such transitions between degenerate angular-momentum sublevels in an atom that is subject to collinear electric and magnetic fields that rotate adiabatically. The origin of the effects becomes clear when eigenstates of the total Hamiltonian, which includes the rotating fields, are calculated. The total Hamiltonian removes the degeneracy, and the eigenstates are in some cases linear combinations of the angular-momentum sublevels. Thus a system prepared in a specific sublevel may not remain in that sublevel, and the transition probability is exactly that given by an analysis of the geometric phase

Electromagnetically induced transparency and reduced light speeds for single photons in a fully quantized model

We introduce a simple model for electromagnetically induced transparency in which all fields are treated quantum mechanically. We study a system of three separated atoms at fixed positions in a one-dimensional multimode optical cavity. The first atom serves as the source for a single spontaneously emitted photon; the photon scatters from a three-level lambda-configuration atom which interacts with an additional single-mode field coupling two of the atomic levels; the third atom serves as a detector of the total transmitted field. We find an analytical solution for the quantum dynamics. From the quantum amplitude describing the excitation of the detector atom we extract information that provides exact single-photon analogues to wave delays predicted by semi-classical theories. We also find complementary information in the expectation value of the electric field intensity operator