We develop a systematic theory of quantum fluctuations in the driven optical parametric oscillator, including the region near threshold. This allows us to treat the limits imposed by nonlinearities to quantum squeezing and noise reduction in this nonequilibrium quantum phase transition. In particular, we compute the squeezing spectrum near threshold and calculate the optimum value. We find that the optimal noise reduction occurs at different driving fields, depending on the ratio of damping rates. The largest spectral noise reductions are predicted to occur with a very high-$Q$ second-harmonic cavity. Our analytic results agree well with stochastic numerical simulations. We also compare the results obtained in the positive-$P$ representation, as a fully quantum-mechanical calculation, with the truncated Wigner phase-space equation, also known as the semiclassical theory.

We develop a systematic theory of critical quantum fluctuations in the driven parametric oscillator. Our analytic results agree well with stochastic numerical simulations. We also compare the results obtained in the positive-P representation, as a fully quantum-mechanical calculation, with the truncated Wigner phase-space equation, also known as the semiclassical theory. We show when these results agree and differ in calculations taken beyond the linearized approximation. We find that the optimal broadband noise reduction occurs just above threshold. In this region where there are large quantum fluctuations in the conjugate variance and macroscopic quantum superposition states might be expected, we find that the quantum predictions correspond very closely to the semiclassical theory.

When resonant laser light passes through a vapor, the laser’s intrinsic phase fluctuations induce random variations in the atomic coherence, which in turn give rise to fluctuations in the medium’s absorption cross section. Hence, laser phase modulation noise (PM) is converted to transmitted laser intensity (i.e., amplitude) modulation noise (AM). Here, we consider the influence of collisional dephasing on the PM-to-AM conversion process. Specifically, we measure the relative intensity noise of a diode laser beam, resonant with the Rb $D_1$ transition at 794.7 nm, after it has passed through a ${\mathrm{Rb}}^{87}/{\mathrm{N}}_2$ vapor as a function of nitrogen number density. Our results demonstrate that when collisional dephasing is very rapid, the spectral density of cross-section fluctuations is reduced, so that there is a significant decrease in the efficiency of PM-to-AM conversion at low Fourier frequencies. These results imply that, in general, when laser PM-to-AM conversion is the dominant noise process, pressure broadening can actually increase spectroscopic sensitivity.

I give a first characterization of the class of generalized measurements that can be exactly realized on a pair of qudits encoded in indistinguishable particles, by using only linear elements and particle detectors. Two immediate results follow from this characterization. (i) The Schmidt number of each element in the positive operator valued measure cannot exceed the number of initial particles. This rules out any possibility of performing perfect Bell measurements for qudits. (ii) The maximum probability of performing a generalized incomplete Bell measurement is one-half.

In this paper, we demonstrate the use of a cold trapped sample of neutral atoms to perform high-precision measurement of the lifetime for a sequence of Rydberg states of ${}^{85}\mathrm{Rb}.$ States of principal quantum number lying between $n=31\mathrm{}$ and $n=45\mathrm{}$ are produced and their lifetimes measured using field ionization. Experimental results are compared with existing theories. This is an important demonstration concerning the possibilities of high-precision spectroscopy in the time domain using cold atomic samples.

By solving the Maxwell-Bloch equations, we study the area evolution of a few-cycle pulse laser propagating in a resonant two-level-atom medium. We find that in short propagation distance, the pulse envelope, obtained within the slowly varying envelope approximation and the rotating-wave approximation, agrees nicely with the carrier field. In this case, the area theorem can still predict the profile of the area evolution of a few-cycle optical pulse. However, contrary to the long-pulse case, the variation of the few-cycle pulse area is caused by the pulse splitting but not by the pulse broadening or the pulse compression. Furthermore, the negative area occurs when the pulse area decreases. As a result, a pulse with area less than $\pi$ is not absorbed rapidly according to the usual Beer’s law of absorption but evolves to nonvanishing zero $\pi$ pulse.

We present a theoretical study on the response of a hydrogen atom to the simultaneous irradiation of ultrashort extreme ultraviolet (xuv) and laser pulses. The calculation is based on the time-dependent Schrödinger equation. The xuv photon energy is chosen to induce the $1s-2p$ transition. Our results indicate that we can transiently reduce the xuv absorption and change the atomic state within a few femtoseconds by injecting a femtosecond laser pulse. The laser-induced photoemission is affected by the addition of an xuv pulse and its yield depends much on the temporal overlap of the two pulses.

We study the radiative emission due to the self-dressing of a two-level atom, initially in its bare ground state, interacting with the zero-point electromagnetic field. Evolution in time leads to the formation of a dressed ground state of lower energy. This energy difference between bare and dressed ground state is taken into account by the emission of real photons. In order to describe this aspect of the self-dressing process we study the transition probability amplitude from the initial bare state to an asymptotic state consisting of the atom in its dressed ground state plus some real photons. Adopting nonperturbative techniques based on the resolvent method we find that the bare-dressed transition occurs at the lowest order with the emission of two photons. The spectral distribution obtained shows that there is a probability for emission of photons at frequency of the order of the atom’s transition frequency.

We show using a numerical approach, which gives necessary and sufficient conditions for the existence of local realism, that the bound entangled state presented in Bennett et al. [Phys. Rev. Lett. 82, 5385 (1999)] admits a local and realistic description. We also find the lowest possible amount of some appropriate entangled state that must be ad-mixed to the bound entangled state so that the resulting density operator has no local and realistic description and as such can be useful in quantum communication and quantum computation.

A proof of Bell’s theorem without inequalities valid for both inequivalent classes of three-qubit entangled states under local operations assisted by classical communication, namely Greenberger-Horne-Zeilinger (GHZ) and $W,$ is described. This proof leads to a Bell inequality that allows more conclusive tests of Bell’s theorem for three-qubit systems. Another Bell inequality involving both tri- and bipartite correlations is introduced which illustrates the different violations of local realism exhibited by the GHZ and $W$ states.

The Heisenberg uncertainty principle for material objects is an essential corner stone of quantum mechanics and clearly visualizes the wave nature of matter. Here, we report a demonstration of the Heisenberg uncertainty principle for the fullerene molecule ${\mathrm{C}}_{70}$ at a temperature of 900 K. We do this by showing the increase in molecular momentum spread after passage through a narrow slit with a variable width down to 70 nm. We find good quantitative agreement with the theoretical expectation.

A discrete protocol for teleportation of superpositions of coherent states of optical-cavity fields is presented. Displacement and parity operators are unconventionally used in Bell-like measurement for field states.

In a magnetic field anions are known to possess, within the approximation of infinite nuclear mass, an infinite manifold of bound states. This approximation, however, neglects effects due to the coupling of the anionic center-of-mass (c.m.) motion to the electronic motion. Recently these effects have been reported to be crucial for the mere existence and properties of the field-induced anions [Phys. Rev. Lett. 86, 5450 (2001)]. We develop a theoretical approach to study anions in the presence of a magnetic field including the motional c.m. effects. We aim at weak to moderate magnetic-field strengths typical for present-day laboratories. Our approach involves canonical transformations of the original Hamiltonian, implementing the integrals of motion and reasonable adiabatic approximations. As a result we derive a three-dimensional Hamiltonian that can be universally applied to atomic or molecular negative ions in a magnetic field by specifying the properties of the underlying neutral systems. We consider this Hamiltonian to be suitable for rigorous investigations of moving anions in fields. For the classical dynamics a reduction to an effective two-dimensional problem is possible. This can serve as a basis for future studies, for instance, of the autodetachment dynamics of anions due to c.m. effects.

We present vibrationally resolved photoelectron spectra of the gadolinium oxide anion ${\mathrm{GdO}}^{-}$ using 3.495-eV photons. The molecules have been produced in a laser vaporization source and have been mass selected prior to the detachment process. An electron affinity of $1.19\pm 0.1\hspace{0.5em}\mathrm{eV}$ is measured. The vibrational frequencies of the ground state and the first excited state are determined to be $790\pm 40$ and $887\pm 40\hspace{0.5em}{\mathrm{cm}}^{-1},$ respectively. A group of states at 2.6-eV binding energy is interpreted to correlate with the ${4f}^7{(}^{8}S\left)\hspace{0.5em}{6p(}^2{P}_{1/2}\right)\hspace{0.5em}|{\Omega }_{6p}|=1/2\mathrm{}$ configuration.

The stochastic variational method (SVM) is used in conjunction with stabilization ideas in order to compute low-energy phase shifts. The method is tested by applying it to a simple model problem, and to s-wave positron-hydrogen scattering. The SVM is then applied to the calculation of the s- and p-wave phase shifts for Ps-H scattering. The scattering lengths obtained were ${4.34a}_0$ for the electronic-spin-singlet state and ${2.22a}_0$ for the triplet state. The present scattering lengths are probably accurate to $\pm 3\%$ and are the most accurate that have so far been computed for the Ps-H systems.

Radiation trapping causes the optical emission cross sections for transitions from an atomic resonance level to lower levels to be dependent on the atom number density. We have measured the optical emission cross sections for a number of heavy rare-gas resonance transitions over the pressure range of 0.04 to 30 mTorr. We compare the results with the theory of Heddle, using it to extrapolate our cross-section data to the high-pressure regime where the resonance radiation is completely reabsorbed. This allows us to obtain the apparent excitation cross section for seven resonance levels of Ne, Ar, and Kr without measuring the resonance radiation that would otherwise entail vacuum ultraviolet radiometry. In some cases, our analysis of the measured pressure dependence of the optical emission cross sections points out the need for improved transition probabilities values.

The population dynamics of the internal state of 60 MeV/u ${\mathrm{Kr}}^{35+}$ ions traversing amorphous carbon foils is studied theoretically and experimentally. This system is of particular interest as the times scales for collisional distribution, mixing due to the wake field, and radiative processes are comparable to each other. A transport theory based on a quantum-trajectory Monte Carlo method is developed, which treats the collisional and radiative redistribution of states on the same footing. The simulations exhibit clear signatures for the interplay between radiative decay and collisional mixing. Good agreement with experimental data is found.

A Gaussian ansatz for the wave function of two-dimensional harmonically trapped anisotropic Bose-Einstein condensates is shown to lead, via a variational procedure, to a coupled system of two second-order, nonlinear ordinary differential equations. This dynamical system is shown to be in the general class of Ermakov systems. Complete integrability of the resulting Ermakov system is proven. Using the exact solution, collapse of the condensate is analyzed in detail. Time dependence of the trapping potential is allowed.

We present a mesoscopic theory for the spatiotemporal carrier and light-field dynamics in quantum-dot lasers. Quantum-dot Maxwell-Bloch equations have been set up that mesoscopically describe the spatiotemporal light-field and interlevel/intralevel carrier dynamics in each quantum dot (QD) of a typical QD ensemble in quantum-dot lasers. In particular, this includes spontaneous luminescence, counterpropagation of amplified spontaneous emission, and induced recombination as well as carrier diffusion in the wetting layer (quantum-well media) of the quantum-dot laser. Intradot scattering via emission and absorption of phonons, as well as scattering with the carriers and phonons of the surrounding wetting layer are dynamically included on a mesoscopic level. The spatiotemporal light-field dynamics reveals a characteristic interplay of spontaneous and stimulated emission in quantum-dot lasers that depends on typical spatial fluctuations in size and energy levels of the quantum dots and irregularities in the spatial distribution of the quantum dots in the active layer. Those effects are simulated via statistical methods. They are shown to directly affect the propagation of an ultrashort pulse in a quantum-dot waveguide. The strong influence of the localized carrier dynamics is seen in the selective depletion and refilling of quantum-dot energy levels.