O. Zobay

Quantum optics of a Bose-Einstein condensate coupled to a quantized light field

We consider the interaction between a Bose-Einstein condensate and a single-mode quantized light field in the presence of a strong far-off-resonant pump laser. The dynamics is characterized by an exponential instability, hence the system acts as an atom-photon parametric amplifier. Triggered by a small injected probe field, or simply by quantum noise, entangled atom-photon pairs are created which exhibit nonclassical correlations similar to those seen between photons in the optical parametric amplifier. In addition, the quantum statistics of the matter and light field depend strongly on the initial state which triggers the amplifier. Thus, by preparing different initial states of the light field, one can generate matter waves in a variety of quantum states, demonstrating optical control over the quantum statistics of matter waves.

Creation of gap solitons in Bose-Einstein condensates

We discuss a method to launch gap solitonlike structures in atomic Bose-Einstein condensates confined in optical traps. Bright vector solitons consisting of a superposition of two hyperfine Zeeman sublevels can be created for both attractive and repulsive interactions between the atoms. Their formation relies on the dynamics of the atomic internal ground states in two far-off-resonance counterpropagating

Two-atom dark states in electromagnetic cavities

({ensuremath{sigma}}^{+}ensuremath{-}{ensuremath{sigma}}^{ensuremath{-}})

Semiclassical interferences and catastrophes in the ionization of Rydberg atoms by half-cycle pulses

-polarized laser beams that form the optical trap. Numerical simulations show that these solitons can be prepared from a one-component state provided with an initial velocity.

Phase dynamics in a binary-collision atom-laser scheme

The center-of-mass motion of two two-level atoms coupled to a single damped mode of an electromagnetic resonator is investigated. For the case of one atom being initially excited and the cavity mode in the vacuum state, it is shown that the atomic time evolution is dominated by the appearance of dark states. These states, in which the initial excitation is stored in the internal atomic degrees of freedom and the atoms become quantum mechanically entangled, are almost immune against photon loss from the cavity. Various properties of the dark states within and beyond the Raman-Nath approximation of atom optics are worked out. @S1050-2947~99!06105-3#

Probing Quantum States of Rydberg Electrons by Half-Cycle Pulses

High-power, nearly unipolar electromagnetic-field pulses are a useful spectroscopic tool, in particular for studying the dynamics of weakly bound Rydberg electrons. Various experimental @1‐3# and theoretical @4,5# investigations on the interaction between Rydberg atoms and half-cycle pulses ~HCPs! have already been performed. In particular, the theoretical approaches that have been used so far involve either fully quantum-mechanical calculations, purely classical simulations, or simplified one-dimensional model problems. Fully quantum-mechanical treatments are capable of yielding quantitatively exact results, but due to the large spatial extension of highly excited Rydberg states they demand a huge computational effort. Furthermore, they allow only for a restricted qualitative understanding of the system, in general. Purely classical approaches are of interest, as they yield insight into the underlying classical aspects of the motion of the Rydberg electron. But they cannot deal properly with quantum-mechanical interference effects and are therefore also of limited applicability. One-dimensional model problems, finally, are not capable of describing all spatial aspects of the excitation process. Thus the natural question arises whether a proper three-dimensional theoretical description of the excitation process can be developed that is numerically highly accurate even for very large principal quantum numbers, which gives direct insight into the underlying classical aspects of the dynamics of the Rydberg electron and which is capable of dealing with all quantum-mechanical interference phenomena properly. In this Rapid Communication it is shown that such a theoretical description can be developed on the basis of a multidimensional semiclassical description of the excitation process. This approach is easily applicable to any spatial or temporal pulse form of the exciting HCP, and it is particularly accurate in the region of high principal quantum numbers, which is difficult to access by fully quantummechanical calculations. Based on this treatment different oscillatory structures are discussed, which appear in energyand angle-resolved ionization spectra and which should be accessible to experimental observation in view of the recently developed imaging method @6#. It is shown that these structures are caused by quantum-mechanical interferences between probability amplitudes that can be associated with classical trajectories of the ionized Rydberg electron. In order to demonstrate the numerical accuracy of the multidimensional semiclassical approach a comparison with numerical results is presented in the impulse approximation. Modifications of these oscillatory structures due to finite pulse durations are also discussed. Let us consider a typical HCP-excitation process. Initially an atom is prepared in a Rydberg state un0l 0m0& with a large principal quantum number n0@1 and a small angularmomentum quantum number l 0!n0. Around t50 a linearly polarized HCP with vector potential A(x,t)ez and duration t interacts with the Rydberg electron. The time evolution of the state c(x,t) of the Rydberg electron is determined by the ‘

Characterization and manipulation of matter-wave coherence

Various aspects of the phase dynamics of an atom laser scheme based on binary collisions are investigated. Analytical estimates of the influence of elastic atom-atom collisions on the laser linewidth are given, and linewidths achievable in a recently proposed atom laser scheme [Phys. Rev. A 56, 2989 (1997)] are evaluated explicitly. The extent to which a relative phase can be established between two interfering atom lasers, as well as the properties of that phase, are also investigated.

COHERENCE OF ATOMIC MATTER-WAVE FIELDS

Recently performed experiments 1 have demonstrated that half-cycle pulses (HCPs), i.e. unimodular electromagnetic pulses, arc a useful new spectroscopic tool which is particularly well suited for investigating the dynamics of weakly bound Rydberg electrons. Typically their pulse durations range from the subpicosecond to the nanosecond regime and these pulses have already been produced with electric field strengths up to So far work in this context has concentrated mainly on studies of total ionization or survival probabilities and on energy-resolved ionization spectra of Rydberg electrons 1, 2 , 3 . Thus it has been shown with the help of a classical picture of the ionization process that energy-resolved ionization spectra yield direct information about the initial momentum distribution of a Rydberg electron. However, this way any phase information about the initial quantum state is lost. In the following we address the question whether this phase information can be obtained from energy- and angle-resolved ionization probabilities. For this purpose a (multidimensional) semiclassical description of the ionization process of Rydberg electrons by half-cycle pulses is presented. In this theoretical approach it is particularly apparent how phase information about the initial quantum state of the Rydberg electron manifests itself in the angle- and energy-resolved ionization spectra. Furthermore, this way a detailed understanding of the ionization dynamics is obtained which is based on the underlying classical dynamics. In order to emphasize the essential physical aspects our subsequent discussion focuses on the sudden-ionization approximation 2 in which the ionizing HCP can be approximated by a delta-function in time. However, it should be mentioned that besides numerical advantages as far as the treatment of the Coulomb problem is concerned the presented semiclassical approach is also well suited for describing all effects which might arise from finite pulse durations or from spatial variations of realistic HCPs.

Nonlinear optics of matter waves

We review an extension of the optical coherence theory to the case of atomic Schrodinger waves, and show that this requires the introduction of several classes of coherence. Optical methods to manipulate the coherence of matter-wave fields are discussed.