We study the thermodynamical properties of a mesoscopic Fermi gas in view of recent possibilities to trap ultracold atoms in a harmonic potential. We focus on the effects of shell closure for finite small atom numbers. The dependence of the chemical potential, the specific heat, and the density distribution on particle number and temperature is obtained. Isotropic and anisotropic traps are compared. Possibilities of experimental observations are discussed.

We show that the gravitational modification of the phase of a neutron beam [the Colella-Overhauser-Werner (COW) experiment] has a classical origin, being due to the time delay that classical particles experience in traversing a background gravitational field. Similarly, we show that classical light waves also undergo a phase shift in traversing a gravitational field. We show that the COW experiment respects the equivalence principle even in the presence of quantum mechanics.

We present the excitation spectrum of a double Bose-Einstein condensate for the JILA time orbiting potential trap including the effects of gravity. We consider two cases: (i) fixed scattering lengths and equal numbers of each atomic species as a function of the number of atoms and (ii) fixed intraspecies scattering lengths and a fixed, equal number of atoms in each state as a function of interspecies scattering length. The spectra reveal the rich dynamics of the system and in particular show simultaneous collective excitations of both condensates.

We present a numerical study of a trapped binary Bose-condensed gas by solving the corresponding Hartree-Fock equations. The density profile of the binary Bose gas is solved with a harmonic trapping potential as a function of temperature in two and three dimensions. We find a symmetry breaking in the two-dimensional case where the two condensates separate. We also present a phase diagram in the three-dimensional case of the different regions where the binary condensate becomes a single condensate and eventually an ordinary gas as a function of temperature and the interaction strength between the atoms.

We investigate the zero-temperature collective excitations of a Bose-condensed atomic gas in anisotropic parabolic traps. The condensate density is determined by solving the Gross-Pitaevskii (GP) equation using a spherical harmonic expansion. The GP eigenfunctions are then used to solve the Bogoliubov equations to obtain the collective excitation frequencies and mode densities. The frequencies of the various modes, classified by their parity and the axial angular momentum quantum number, m, are mapped out as a function of the axial anisotropy. Specific emphasis is placed upon the evolution of these modes from the modes in the limit of an isotropic trap.

A fully quantum-mechanical model of feedback to the pump source of a four-level laser is developed with a view to predicting the achievable intensity noise reduction. For solid-state lasers, the model shows that quantum noise sources due to laser dynamics have a significant impact on the optimization of the feedback loop. Experimental results obtained with a diode pumped neodymium:yttrium aluminum garnet (Nd:YAG) laser are found to be in good agreement with the theoretical model. The ultimate limit to the noise suppression comes from the quantum noise due to the measurement processes in the feedback loop. A scheme to overcome this limit using a squeezed vacuum is theoretically demonstrated to be a highly efficient method of generating bright intensity squeezed light, particularly in the kHz regime where bright squeezing is otherwise difficult to obtain.

The quantum trajectories method is illustrated for the resonance fluorescence of a two-level atom driven by a multichromatic field. We discuss the method for the time evolution of the fluorescence intensity in the presence of bichromatic and trichromatic driving fields. We consider the special case wherein one multichromatic field component is strong and resonant with the atomic transition whereas the other components are much weaker and arbitrarily detuned from the atomic resonance. We find that the phase-dependent modulations of the Rabi oscillations, recently observed experimentally [Q. Wu, D. J. Gauthier, and T. W. Mossberg, Phys. Rev. A 49, R1519 (1994)] for the special case when the weaker component of a bichromatic driving field is detuned from the atomic resonance by the strong-field Rabi frequency, appear also for detunings close to the subharmonics of the Rabi frequency. Furthermore, we show that for the atom initially prepared in one of the dressed states of the strong field component the modulations are not sensitive to the phase. We extend the calculations to the case of a trichromatic driving field and find that apart from the modulations of the amplitude there is a modulation of the frequency of the Rabi oscillations. Moreover, the time evolution of the fluorescence intensity depends on the phase regardless of the initial conditions and a phase-dependent suppression of the Rabi oscillations can be observed when the sideband fields are tuned to the subharmonics of the strong-field Rabi frequency.

An analytical expression for the low-temperature optical susceptibility of quantum-well semiconductor lasers is presented based on a simple parabolic band model. The optical susceptibility obtained keeps the nonlinear dependence on the carrier density, providing both a broad gain spectrum and a dispersion curve, so it can be used to analyze the dynamics of multimode devices or devices with large carrier density variations. The resulting peak gain, differential peak gain, and linewidth enhancement factor are discussed. cw operation of a single-mode laser is studied as a function of the frequency of the cavity resonance. An analytical approximation to the finite-temperature gain spectrum is also presented, although the refractive index spectrum must be determined numerically.

Coexisting attractors, which arise from different external-cavity modes of the same longitudinal mode of the solitary laser, retain distinct stability properties, particularly when the laser is biased far above threshold and subjected to moderately strong optical feedback from a distant reflector. When the laser is modeled by the Lang and Kobayashi equations with additional gain nonlinearity, the dynamics is limited to external-cavity attractors that develop from the external-cavity modes which have a positive but not too large frequency shift with respect to the solitary laser emission frequency ${\omega }_0.$ Although relaxation oscillations about these external-cavity modes are the first to become undamped as the feedback intensity increases, the attractors that arise from these modes remain stable over the largest range of feedback strengths. Stronger feedback destabilizes the individual attractors, creating new solutions which form from their ruins. At the beginning of the merging, the attractor ruins are not equally visited; the most visited ruins are those of the attractors last destabilized. We explore and explain these results by examining the dynamics of the laser when operating on a single external-cavity attractor.

An experimental observation of transparency on a transition in the blue spectral region, induced by a continuous-wave (cw) infrared coupling field in a Doppler-broadened medium, is presented. This experimental result is supported by extensive theoretical modeling of the system, a V-type scheme in atomic rubidium vapor. Transparency is observed by a 422-nm probe field on the transition between the hyperfine split ground state ${5S}_{1/2}$ and the excited state ${6P}_{1/2}.$ The coupling laser is employed on the linked transition ${5S}_{1/2}{-5P}_{3/2},$ inducing significant levels of transparency $\mathrm{}(>70\%)\mathrm{}$ nondissipatively and in the absence of optical pumping effects.

Time-resolved quantum measurements using active detectors are analyzed. It is shown that the time-resolved observation of a quantum field leads to a mode mismatch between observed field and detection device that unavoidably introduces vacuum modes into the measurement. When active detectors are used, this gives rise to considerable background noise. The same conclusion may be drawn when considering other highly resolved quantum measurements of, e.g., energy, position, etc. Special emphasis is put on the analysis of time-resolved optical homodyne detection as an important example of an active detector.

We present a theoretical method to study a trapped gas of bosonic two-level atoms interacting with a single mode of a microwave cavity. This interaction is described by a trilinear Hamiltonian that is formally completely equivalent to the one describing parametric down-conversion in quantum optics. A system of differential equations describing the evolution, including the long-time behavior, of not only the mean value but also the variance of the number of excited atoms is derived and solved analytically. For different initial states the mean number of excited atoms exhibits periodically reappearing dips, with an accompanying peak in the variance, or fractional collapses and revivals. Closed expressions for the period and the revival time are obtained.

A strong coupling standing wave, interacting with three-level Λ-type (or ladder-type) atoms, can diffract a weak probe field (propagating along a direction normal to the standing wave) into high-order diffractions, a phenomenon which we name electromagnetically induced grating (EIG). We develop in this work a theory for studying EIG in a homogeneously broadened medium consisting of three-level Λ-type atoms. We show that by taking advantage of the absorption and dispersion properties of electromagnetically induced transparency one can create an atomic grating that can effectively diffract light into the first-order direction.

The harmonic-generation spectrum of an anharmonic oscillator perturbed by a high-frequency, high-intensity external field is discussed from both classical and quantum mechanical points of view. The classical theory of harmonic generation in this regime is shown to provide a simple analytical expression for the probability to emit the $k$th harmonic of the external field frequency. The theory is applied to the harmonic generation by a charged particle moving in Morse and “soft-core” Coulomb model potentials and interacting with a time-periodic electric field. For both models the probability to emit the $k$th harmonic attains a maximal value at some $k_{\max }$ so that a single harmonic peak dominates the spectrum. $k_{\max }$ can be controlled by properly choosing the field and oscillator parameters. The quantum mechanical numerical results are shown to be in excellent agreement with the classical predictions due to the localization of the wave function around either stable (in the case of Morse potential) or unstable (in the case of “soft-core” Coulomb potential) equilibrium position of the corresponding effective Kramers-Henneberger potential.

The probe-field absorption spectra are investigated for three-level atoms interacting with mono- or bichromatic fields in the presence of bath reservoirs of different kinds. Two configurations of atoms with lower-level and upper-level couplings are considered on the basis of Floquet-state dynamics. The multipeak Autler-Townes splitting induced by the resonant interaction of atoms with bichromatic fields is investigated and driving-field effects as well as squeezed-bath effects on the absorption spectra are analyzed. Ultrasharp absorption lines can be obtained in the upper-level coupling scheme due to a mixing of two atomic decay channels by the bichromatic field.

We show that the Bloch oscillation in semiconductor superlattices under the external dc bias is able to generate nonclassical photon states. The time development operator of the photon field in such systems is obtained and is shown to be equivalent approximately to the displacement operator, the phase-quadrature amplitude squeezing operator, or the optical Kerr operator, depending on the external dc bias. Such equivalence is discussed also in terms of Stark-ladder formation.

We propose a reconstruction scheme for the quantum-mechanical state of a field inside a microwave cavity in the Fock representation. It will be shown that two experimental steps are required for this purpose: (i) the quantum state under consideration has to be shifted in phase space, and (ii) it has to be examined by state-selective detection of two-level atoms after a resonant interaction with the field. The method is examined in a computer simulation including measurement errors.

We consider the electromagnetic vacuum field inside a perfect plane cavity with moving mirrors, in the nonrelativistic approximation. We show that low-frequency photons are generated in pairs that satisfy simple properties associated to the plane geometry. We calculate the photon generation rates for each polarization as functions of the mechanical frequency by two independent methods: on one hand from the analysis of the boundary conditions for moving mirrors and with the aid of Green functions; and on the other hand by an effective Hamiltonian approach. The angular and frequency spectra are discrete, and emission rates for each allowed angular direction are obtained. We discuss the dependence of the generation rates on the cavity length and show that the effect is enhanced for short cavity lengths. We also compute the dissipative force on the moving mirrors and show that it is related to the total radiated energy as predicted by energy conservation.

A scheme to obtain ultrashort-pulse coherent x rays, via population inversion following inner-shell photoionization, is analyzed for C at 45 Å. We calculate that a driving laser with a pulse duration of 40 fs, a $10\hspace{0.5em}\mu \mathrm{m}\times 1\hspace{0.5em}\mathrm{cm}$ line focus, and an energy of 1 J gives an effective gain length product $\mathrm{}\left(\mathrm{gl}\right)\mathrm{}$ of 10. At saturation $\left(gl\sim 18\right)$ we expect an output of $\sim 0.1\hspace{0.5em}\mu \mathrm{J}$ per pulse. The short duration of x-ray lasing $(<\mathrm{}100\mathrm{}\hspace{0.5em}\mathrm{fs})$ combined with a 10-Hz repetition rate ${(P}_{\mathrm{avg}}=1\mathrm{}\hspace{0.5em}\mu \mathrm{W})$ makes this source of coherent x rays ideal for pump-probe experiments to study fast dynamical processes in chemistry and material science.

We propose a scheme for a compact nickel-like-tungsten soft-x-ray laser operating on the $4d$-$4p$, $J=0-1\mathrm{}$ transition at 43.2 Å. High gains are achieved by operating at high electron densities ${(n}_e>{10}^{22}$ cm${}^{-3})$. In this regime, the gain during nonequilibrium ionization can greatly exceed that of the steady state. The duration of this transient gain is on the order of the ionization time, which makes picosecond-pulsed optical pumps ideal. Two target designs, solid tungsten slabs, and tungsten aerogels foams, are considered. We predict gains of 220 cm${}^{-1}$ for a 1-$\mu$m pump of intensity $I=2.5\mathrm{}\times {10}^{16}$ W/cm${}^2$.