A three-dimensional electromagnetic field quantization scheme is developed using the Green’s-function method in a homogeneous medium that shows loss and dispersion. Special attention is paid to the decomposition of the quantized fields into their longitudinal and transverse parts. The characteristic nature of these two parts is discussed. To demonstrate the generality of this formulation, the field quantization in lossless dispersive media and in free space is obtained by imposing appropriate limits. We also calculate the vacuum fluctuations of the field for the transverse and longitudinal parts separately.

A theoretical treatment of light scattering from a degenerate Fermi gas of trapped ultracold ${}^6\mathrm{Li}$ atoms is presented. We find that the scattered light contains information that directly reflects the quantum pair correlation due to the formation of atomic Cooper pairs resulting from a Bardeen-Cooper-Schrieffer phase transition to a superfluid state. Evidence for pairing should be observable in both the space and time domains.

We present results of our experimental investigations of phase-conjugate four-wave mixing in a nearly Doppler-free, collisionless, two-level quantum system with a partially coherent non-Markovian laser field. The two components of the laser field—an intense pump and a weak, time-delayed probe—are derived from a single narrow-band cw laser source on which phase and frequency fluctuations conforming to the phase diffusion model are superimposed. We carry out these measurements using the $D_2$ transition in an optically pumped diffuse beam of atomic sodium. We vary the pump intensity, laser bandwidth, and temporal delay between the pump and probe, and measure the peak signal strength, the bandwidth, and the asymmetry of the four-wave-mixing spectrum. For comparison with our experimental results of the peak signal strength, we also analyze the same interaction numerically, through direct integration of the optical Bloch equations. The numerical results are in good agreement with the measurements.

An adaptive optimization technique to improve the precision of quantum homodyne tomography is presented. The method is based on the existence of so-called null functions, which have a zero average for an arbitrary state of radiation. The addition of null functions to the tomographic kernels does not affect their mean values, but changes statistical errors, which can then be reduced by an optimization method that “adapts” kernels to homodyne data. Applications to tomography of the density matrix and other relevant field observables are studied in detail.

Theoretical results are presented that show that noiseless phase quadrature amplification is possible, and limited experimentally only by the efficiency of the phase-detection system. Experimental results obtained using a neodymium-doped yttrium aluminum garnet laser show a signal gain of 10 dB and a signal transfer ratio of $T_s=0.9\mathrm{}$. This result easily exceeds the standard quantum limit for signal transfer. The results also explicitly demonstrate the phase-sensitive nature of the amplification process.

We find a simple and general law for stable multimode laser operation, which shows a nonlinear cooperative relation of frequencies and intensities of laser modes.

We perform a quantum theoretical calculation of the noise power spectrum for a phase measurement of the light output from a coherently driven optical cavity with a freely moving rear mirror. We examine how the noise resulting from the quantum back action appears among the various contributions from other noise sources. We do not assume an ideal (homodyne) phase measurement, but rather consider phase-modulation detection, which we show has a different shot noise level. We also take into account the effects of thermal damping of the mirror, losses within the cavity, and classical laser noise. We relate our theoretical results to experimental parameters, so as to make direct comparisons with current experiments simple. We also show that in this situation, the standard Brownian motion master equation is inadequate for describing the thermal damping of the mirror, as it produces a spurious term in the steady-state phase-fluctuation spectrum. The corrected Brownian motion master equation [L. Diosi, Europhys. Lett. 22, 1 (1993)] rectifies this inadequacy.

Using a circularly polarized basis, we derive the differential equations governing the copropagation of two waves of different frequencies and arbitrary initial amplitudes and polarizations in an isotropic Kerr medium, and we give exact analytical solutions for waves that are initially linearly polarized. In this latter case, the ellipticities and orientations of both polarization ellipses generally vary periodically as the waves propagate through the medium; when each wave is linearly polarized, the deviation of the orientation of its polarization ellipse from its initial value is either zero or close to its maximum value. Situations are identified in which this deviation is close to π/2, thus allowing one wave to switch the other on and off with the aid of a linear polarizer placed at the exist from the medium. All the results obtained are generalizable to copropagation in nonbirefringent optical fibers.

Quantum noise suppression in a Raman laser is investigated theoretically using a model system of homogeneously broadened three-state atoms, driven by an external pump field. Arbitrary pump, Raman, and cavity detunings are allowed, and the full dynamical response of the system is included in the treatment of quantum noise. The behavior of the intensity squeezing of both the pump and Raman fields is reported for a wide parameter regime in which optically bistable switching occurs.

We examine the evolution of a two-level atom when its population is monitored. The detection proposed is an interaction-free measurement, so that the observation occurs without photon exchange between the atom and the apparatus. It is shown that the observed dynamics exhibits features that an isolated two-level atom cannot accommodate. Such phenomena are explained in terms of an atom-apparatus effective interaction.

The dual Dyson series [M. Frasca, Phys. Rev. A $58$ 3439 (1998)] is used to develop a general perturbative method for the study of atom-field interaction in quantum optics. In fact, both the Dyson series and its dual, by renormalization-group methods to remove secular terms from the perturbation series, give the opportunity for a full study of the solution of the Schrödinger equation in different ranges of the parameters of the given Hamiltonian. In view of recent experiments with strong laser fields, this approach seems well-suited to give a clarification and an improvement of the applications of the dressed states as currently done through the eigenstates of the atom-field interaction, showing that these are just the leading order of the dual Dyson series when the Hamiltonian is expressed in the interaction picture. In order to best exploit the method, a study is accomplished of the well-known Jaynes-Cummings model in the rotating-wave approximation, whose exact solution is known, comparing the perturbative solutions obtained by the Dyson series and its dual with the same approximations obtained by Taylor expanding the exact solution. Finally, a full perturbative study of high-order harmonic generation is given, obtaining, through analytical expressions, a clear account of the power spectrum using a two-level model, even if the method can be successfully applied to a more general model that can account for ionization too. The analysis shows that to account for the power spectrum it is necessary to go to first order in the perturbative analysis. The spectrum obtained gives a way to measure experimentally the shift of the energy levels of the atom interacting with the laser field by looking at the shifting of hyper-Raman lines.

Starting from first principles we simulate numerically the dynamics of a system of two-level atoms interacting with a multimode electromagnetic field in a one-dimensional cavity. In particular, we investigate the spontaneous emission of an excited two-level atom in the cavity. We show how the decay depends on the mode spectrum and on the position of the atom in the cavity. We study how the spontaneous emission is modified when the initially excited atom is surrounded by a material medium modeled as a system of two-level atoms. We also study the propagation of photon wave packets emitted by the atom within the material media. Our microscopic model provides us with a deeper understanding of the atom-field interaction and offers us a framework for a systematic investigation of the transition from a microscopic to a macroscopic (phenomenological) description of the spontaneous decay in material media (e.g., dielectrics).

A number of multiphoton interference schemes involving independent fields from parametric down-conversion are analyzed. They include fourth-order (two-photon) interference between two fields from two independent parametric down-conversion processes, interference with two independent single photon Fock states (produced by gated parametric down-conversion), and quantum state teleportation and entanglement swapping. It is shown that the visibility in these interference experiments is related to a quantity that is responsible for the photon bunching effect in one of the fields (signal or idler) from the parametric down-conversion process. Besides the two-photon interference schemes, a four-photon interference scheme is discussed where we consider four-photon partition at a beamsplitter. It is found that probability distribution of the partition is dramatically changed by four-photon interference of six paths and the four-photon effect also depends on the same quantity responsible for photon bunching. We will discuss the difference between two-photon interference and four-photon interference.

Analytic solutions of the optical Bloch equations for a two-level atom interacting with a strong polychromatic field whose frequencies are symmetrically positioned with respect to the atomic frequency are used to obtain the polarization spectrum of the atom. The spectrum is found to consist of a series of discrete peaks or dips superimposed on the continuous part of the spectrum. Physical interpretation of resonances exhibited in the continuous part of the spectrum is given using a semiclassical dressed-atom approach.

We study lasing without inversion in a Doppler-broadened V-type three-level system in the frequency up-conversion regime. We show that the ratio $R\equiv {\omega }_l/{\omega }_d$ of generated laser frequency to driving laser frequency that can be achieved using a vapor cell is modest $(R<~2)$. Our analysis demonstrates that using an atomic beam the frequency of the generated field can be substantially larger than that of the driving field $R\sim 10$. Two different configurations are considered: (a) copropagating driving and laser beams orthogonal to the atomic beam, and (b) counterpropagating driving and atomic beams and laser beam at a determined angle with the driving beam.

An oscillator with stochastic frequency is discussed as a model for evaluating the quantum coherence properties of a physical system. It is found that the choice of jump statistics has to be considered with care if unphysical consequences are to be avoided. We investigate one such model, evaluate the damping it causes, the decoherence rate and the correlations it results in, and the properties of the state for asymptotically long times. Also the choice of initial state and its effect on the time evolution of the correlations are discussed.

Long ago, Bohr, Pauli, and Mott argued that it is not, in principle, possible to measure the spin components of a free electron. One can try to use a Stern-Gerlach type of device, but the finite size of the beam results in an uncertainty of the splitting force that is comparable with the gradient force. The result is that no definite spin measurement can be made. Recently there has been a revival of interest in this problem, and we will present our own analysis and quantum-mechanical wave-packet calculations which suggest that a spin measurement is possible for a careful choice of initial conditions.

The analytical expression for the lasing threshold for whispering-gallery-mode microsphere lasers under the strong-coupling condition is obtained by solving a quasi-three-level quantized model. It explicitly displays the dependence of the lasing threshold on the cavity radius, the homogeneous linewidth, the quality factors and linewidths of the relevant cavity modes.

We present extensive experimental investigations of the dynamics of semiconductor lasers subject to optical feedback in dependence on the linewidth enhancement factor α which accounts for the amplitude phase coupling of the optical field. A reduction of α leads to conspicuous changes of the dynamics of the system which are characterized and classified in the phase space of feedback strength versus injection current, thus demonstrating the importance of α as the system’s main nonlinearity. In particular, we demonstrate a drastic extension of the regime of coexistence between coherence collapsed dynamics and stable emission, and an increased stability of this stable emission state. We show that a theoretical analysis of the Lang-Kobayashi rate equation model provides a qualitative understanding of the physical mechanisms underlying the observed dynamical behavior and its dependence on α. Finally, being able to control the nonlinearity of the system, we open up new perspectives for the stabilization of semiconductor lasers subject to moderate to strong optical feedback.

We demonstrate that an autoionizing medium can, under specific conditions, become transparent to a short laser pulse propagating in the medium. The interference that leads to transparency is intrinsic to the system and relies on the establishment of a “dark,” or “trapped,” state that exists as a consequence of Fano interference between direct and resonant photoionization processes.