Axel Schenzle

Output from an atom laser: theory vs. experiment

Abstract.Atom lasers based on rf-outcoupling can be described by a set of coupled generalized Gross–Pitaevskii equations (GPE). We compare the theoretical predictions obtained by numerically integrating the time-dependent GPE of an effective one-dimensional model with recently measured experimental data for the F=2 and F=1 states of Rb-87. We conclude that the output of a rf atom-laser can be described by this model in a satisfactory way.

Atomic waiting-times and correlation functions

Abstract The quantum statistical properties of photon fields can be characterized by the counting probability known as the Kelley-Kleiner- or Glauber-formula. For the population statistics of an atomic beam, interacting with a quantized cavity field, an equivalent analytical approach does not exist yet. Here we present a concept for evaluating the atomic counting probability, the waiting-time distribution and the “two-atom correlation” function for a Poissonian atomic beam exiting the micro-maser cavity. We show by an analytical treatment how the waiting-time distribution converges into the atom correlation function for vanishing detection efficiency.

Investigations of a two-mode atom-laser model

Atom lasers based on rf-outcoupling from a trapped Bose-Einstein condensate can be described by a set of generalized, coupled Gross-Pitaevskii equations (GPE). If not only one but two radio frequencies are used for outcoupling, the atoms emerging from the trap have two different energies and the total wavefunction of the untrapped spin-state is a coherent superposition which leads to a pulsed atomic beam. We present results for such a situation obtained from a 1D-GPE model for magnetically trapped Rb-87 in the F=1 state. The wavefunction of the atomic beam can be approximated by a sum of two Airy functions. In the limit of weak coupling we calculate the intensity analytically.

Illusion or reality: The measurement process in quantum optics

Whereas a measurement in the domain of classical physics merely collects information on the examined object, measurements on the microscopic scale unavoidably leave their traces on the measured system. Experiments with single atoms and few photons contribute to our understanding of this fundamental property of quantum mechanics.

Radiation in waveguides and cavities: fundamental aspects of three-level system damping

Abstract A three-level ladder configuration is the most fundamental physical system required for cw laser action. In this paper we present an exact quantum calculation of three-level system radiation in simple waveguides and cavities which covers weak and strong coupling. A small effect exists even for a residual kind of cavity, a single reflecting wall. We show that lower level relaxation has the same effect on upper level spontaneous decay as cavity transmission losses. In contrast, the excitation probability of a strong two-level dipole subject to pure polarization noise differs from the three-level system. This suggests that the threshold behavior of microscopic lasers with small numbers of active atoms would depend not only on the amount but also on the origin of homogeneous broadening. Finally analytic expressions for the onset of strong coupling and the microlaser threshold are given and compared to the traditional laser threshold.

Dynamics and symmetry of a laser with a squeezed reservoir

We present a detailed analysis of the stationary and the dynamic behaviors of a single-mode laser coupled to a squeezed reservoir. The eigenfunctions and eigenvalues of the corresponding Fokker–Planck equation are obtained numerically, since the condition of detailed balance is destroyed because of the phase dependence of squeezed noise.

Cavity QED with many atoms

A new method is presented for describing an arbitrary number of atoms interacting with a resonant cavity mode. The state space of the atoms is symmetrized over permutations of the atoms. The symmetrized states are characterized by collective variables like angular momentum and its projection numbers. It is shown that the collective description is still applicable when spontaneous emission is included. The theory is in good agreement with experimental results.

Interference of Bose condensates: testing the paradigm of broken gauge symmetry

Abstract We studied theoretically the macroscopic interference of two independent Bose condensates released from a double potential trap. The observation of fringes could serve as a test for the paradigm of broken gauge symmetry. By numerical solution of the non-linear Schrodinger equation in three dimensions, the consecutive stages of expansion, overlap and interference were investigated in order to facilitate the design of future experiments. It turns out that the period of the interference fringes grows linearly in time with a velocity inversely proportional to the initial distance of the two condensates.

Coherence of bose condensates

Abstract We study the coherence of interacting Bose condensates in recent magnetic trap experiments. The coherent evolution manifests itself in the macroscopic interference of two independent Bose condensates. The theoretical predictions from the time-dependent Gross–Pitaevskii equation are in excellent agreement with the measured interference patterns. A coherent coupling of two condensates represents the atomic analogon of a Josephson junction. The dependence of the magnetic confinement on the nuclear spin orientation allows one to build a controllable beam splitter by magnetic resonance. The application of this beam splitter to realize an atom laser is studied theoretically. The coherence of the output beam is limited only by phase diffusion of the condensate.

Classical and quantum noise in nonlinear optical systems

In quantum optics noise plays an important role, since many of the nonlinear optical systems are quite sensitive to the subtle influences of weak random perturbations, being either classical of quantum mechanical in nature. We discuss the origin of quantum noise emerging from the reversible or the irreversible part of the dynamics and compare it with the properties of purely classical fluctuations. These general features are illustrated by a number of physical examples, such as the laser with loss or gain noise, nonlinear optical devices, and the phenomenon of quantum jumps. These processes have been chosen mainly to illustrate the different aspects of noise, but also because, to a large extent, they can be described in analytical terms.