Self-organization of atoms in a cavity field: threshold, bistability and scaling laws

We present a detailed study of the spatial self-organization of laser-driven atoms in an optical cavity, an effect predicted on the basis of numerical simulations [P. Domokos and H. Ritsch, Phys. Rev. Lett. 89, 253003 (2002)] and observed experimentally [A. T. Black et al., Phys. Rev. Lett. 91, 203001 (2003)]. Above a threshold in the driving laser intensity, from a uniform distribution the atoms evolve into one of two stable patterns that produce superradiant scattering into the cavity. We derive analytic formulas for the threshold and critical exponent of this phase transition from a mean-field approach. Numerical simulations of the microscopic dynamics reveal that, on laboratory timescale, a hysteresis masks the mean-field behaviour. Simple physical arguments explain this phenomenon and provide analytical expressions for the observable threshold. Above a certain density of the atoms a limited number of ``defects'' appear in the organized phase, and influence the statistical properties of the system. The scaling of the cavity cooling mechanism and the phase space density with the atom number is also studied.Comment: submitted to PR

Loading atoms from a large magnetic trap to a small intra-cavity dipole trap

We show that an optimized loading of a cold ensemble of rubidium-87 atoms from a magnetic trap into an optical dipole trap sustained by a single, far-red-detuned mode of a high-Q optical cavity can be efficient despite the large volume mismatch of the traps. The magnetically trapped atoms are magnetically transported to the vicinity of the cavity mode and released from the magnetic trap in a controlled way meanwhile undergoing an evaporation period. Large number of atoms get trapped in the dipole potential for several hundreds of milliseconds. We monitor the number of atoms in the mode volume by a second tone of the cavity close to the atomic resonance. While this probe tone can pump atoms to another ground state uncoupled to the probe, we demonstrate state-independent trapping by applying a repumper laser

Quantum stability of self-organized atomic insulator-like states in optical resonators

We investigate a paradigm example of cavity quantum electrodynamics with many body systems: an ultracold atomic gas inside a pumped optical resonator. In particular, we study the stability of atomic insulator-like states, confined by the mechanical potential emerging from the cavity field spatial mode structure. As in open space, when the optical potential is sufficiently deep, the atomic gas is in the Mott-like state. Inside the cavity, however, the potential depends on the atomic distribution, which determines the refractive index of the medium, thus altering the intracavity field amplitude. We derive the effective Bose-Hubbard model describing the physics of the system in one dimension and study the crossover between the superfluid -- Mott insulator quantum states. We determine the regions of parameters where the atomic insulator states are stable, and predict the existence of overlapping stability regions corresponding to competing insulator-like states. Bistable behavior, controlled by the pump intensity, is encountered in the vicinity of the shifted cavity resonance.Comment: 13 pages, 6 figures. Replaced with revised version. Accepted for publication in New J. Phys., special issue "Quantum correlations in tailord matter

Multimode mean-field model for the quantum phase transition of a Bose-Einstein condensate in an optical resonator

We develop a mean-field model describing the Hamiltonian interaction of ultracold atoms and the optical field in a cavity. The Bose-Einstein condensate is properly defined by means of a grand-canonical approach. The model is efficient because only the relevant excitation modes are taken into account. However, the model goes beyond the two-mode subspace necessary to describe the self-organization quantum phase transition observed recently. We calculate all the second-order correlations of the coupled atom field and radiation field hybrid bosonic system, including the entanglement between the two types of fields.Comment: 10 page

Advances in structure elucidation of small molecules using mass spectrometry

The structural elucidation of small molecules using mass spectrometry plays an important role in modern life sciences and bioanalytical approaches. This review covers different soft and hard ionization techniques and figures of merit for modern mass spectrometers, such as mass resolving power, mass accuracy, isotopic abundance accuracy, accurate mass multiple-stage MS(n) capability, as well as hybrid mass spectrometric and orthogonal chromatographic approaches. The latter part discusses mass spectral data handling strategies, which includes background and noise subtraction, adduct formation and detection, charge state determination, accurate mass measurements, elemental composition determinations, and complex data-dependent setups with ion maps and ion trees. The importance of mass spectral library search algorithms for tandem mass spectra and multiple-stage MS(n) mass spectra as well as mass spectral tree libraries that combine multiple-stage mass spectra are outlined. The successive chapter discusses mass spectral fragmentation pathways, biotransformation reactions and drug metabolism studies, the mass spectral simulation and generation of in silico mass spectra, expert systems for mass spectral interpretation, and the use of computational chemistry to explain gas-phase phenomena. A single chapter discusses data handling for hyphenated approaches including mass spectral deconvolution for clean mass spectra, cheminformatics approaches and structure retention relationships, and retention index predictions for gas and liquid chromatography. The last section reviews the current state of electronic data sharing of mass spectra and discusses the importance of software development for the advancement of structure elucidation of small molecules

Ground state bistability of cold atoms in a cavity

We experimentally demonstrate an optical bistability between two hyperfine atomic ground states, using a single mode of an optical resonator in the collective strong coupling regime. Whereas in the familiar case, the bistable region is created through atomic saturation, we report an effect between states of high quantum purity, which is essential for future information storage. The nonlinearity of the transitions arise from cavity-assisted pumping between ground states of cold, trapped atoms and the stability depends on the intensity of two driving lasers. We interpret the phenomenon in terms of the recent paradigm of first-order, driven-dissipative phase transitions, where the transmitted and driving fields are understood as the order and control parameters, respectively. The saturation-induced bistability is recovered for infinite drive in one of the controls. The order of the transition is confirmed experimentally by hysteresis in the order parameter when either of the two control parameters is swept repeatedly across the bistability region and the underlying phase diagram is predicted in line with semiclassical mean-field theory