Both far off-resonance and resonant scattering of light from single atoms trapped by 3D harmonic potentials has thoroughly been studied. Novel effects are predicted for different physical regimes. We have shown that dynamics of the atomic center-of-mass strongly influences the scattering cross section. Possibility of using spectrum of the scattered light in far-off-resonance regime to nondestructively measure the temperature of ultracold atoms is advocated: off-resonance scattering can be used as an ‘optical thermometer’. The realistic Compton-like regime in resonant scattering has been investigated in detail. Another interesting quantum effect in resonant regime, which has not been discussed here due to the lack of space, is the time resolved scattering, showing up when the atom can remain in the excited state long enough to make many trips back and forth in the trap before emitting a photon. The possibility of the experimental observation of the predicted effects is now being scrutinized.
Both far off-resonance and resonant scattering of light from single atoms trapped by 3D harmonic potentials has thoroughly been studied. Novel effects are predicted for different physical regimes. We have shown that dynamics of the atomic center-of-mass strongly influences the scattering cross section. Possibility of using spectrum of the scattered light in far-off-resonance regime to nondestructively measure the temperature of ultracold atoms is advocated: off-resonance scattering can be used as an ‘optical thermometer’. The realistic Compton-like regime in resonant scattering has been investigated in detail. Another interesting quantum effect in resonant regime, which has not been discussed here due to the lack of space, is the time resolved scattering, showing up when the atom can remain in the excited state long enough to make many trips back and forth in the trap before emitting a photon. The possibility of the experimental observation of the predicted effects is now being scrutinized.
The light scattered by a cold trapped ion, which is in the stationary state of laser cooling, presents features due to the mechanical effects of atom-photon interactions. These features appear as additional peaks (sidebands) in the spectrum of resonance fluorescence. Among these sidebands the literature has discussed the Stokes and anti-Stokes components: namely, the sidebands of the elastic peak. We show that the motion also gives rise to sidebands of the inelastic peaks. These are not always visible, but, as we show, can be measured in parameter regimes which are experimentally accessible.
Abstract There are an increasing number of experimental scenarios where near-resonant light is applied to atoms tightly trapped in far off-resonant optical fields, such as for quantum optics applications or for atom imaging. Oftentimes, the electronic ground and excited states involved in the optical transition experience unequal trapping potentials. Here, we systematically analyze the effects of unequal trapping on near-resonant atom–light interactions. In particular, we identify regimes where such trapping can lead to significant excess heating compared to atoms in state-independent potentials, and a reduction of total and elastic scattering cross sections associated with a decreased atom–photon interaction efficiency. Understanding these effects can be valuable for achieving maximum efficiency in quantum optics experiments or atom imaging setups, where efficient atom–light interactions on resonance are desired, but achieving equal trapping is not feasible.
We study the scattering of light by a single ultracold trapped atom initially in the ground state of the trapping harmonic potential. We have found interesting features of scattering in the regime where the atomic recoil energy is much larger than the separation between oscillatory trap levels. Although we present the quantum-mechanical expression for the scattering cross section, special attention is paid to the semiclassical analysis of the process. We show that the major characteristics of the scattering might be deduced from two conservation laws: conservation of energy and momentum in absorption and emission of photon process separately. These conservation laws impose a strong correlation between scattered light characteristics and the position of the trapped atom at the moment of photon emission. \textcopyright{} 1996 The American Physical Society.
This is a review of state-of-the-art theory and experiment of the motion of cold and ultracold atoms coupled to the radiation field within a high-finesse optical resonator in the dispersive regime of the atom-field interaction with small internal excitation. The optical dipole force on the atoms together with the backaction of atomic motion onto the light field gives rise to a complex nonlinear coupled dynamics. As the resonator constitutes an open driven and damped system, the dynamics is nonconservative and in general enables cooling and confining the motion of polarizable particles. In addition the emitted cavity field allows for real-time monitoring of the particle's position with minimal perturbation up to subwavelength accuracy. For many-body systems, the resonator field mediates controllable long-range atom-atom interactions, which set the stage for collective phenomena. Besides the correlated motion of distant particles, one finds critical behavior and nonequilibrium phase transitions between states of different atomic order in conjunction with superradiant light scattering. Quantum-degenerate gases inside optical resonators can be used to emulate optomechanics as well as novel quantum phases such as supersolids and spin glasses. Nonequilibrium quantum phase transitions as predicted by, e.g., the Dicke Hamiltonian can be controlled and explored in real time via monitoring the cavity field. In combination with optical lattices, the cavity field can be utilized for nondestructive probing Hubbard physics and tailoring long-range interactions for ultracold quantum systems.
This thesis summarizes the research work we did in the past years, which focuses on the theoretical study of quantum effects of ordered atomic structures interacting with the quantum electric field of an optical resonator. Within this work we investigated the quantum properties of the light at the cavity output, emitted by this kind of system, and the quantum state of the atoms confined by the light fields of the cavity mode. Following one possible partition, we have organized the thesis in two parts. The first part of the thesis is devoted to the quantum properties of the light at the output of optical cavities, in which atoms are confined. After a brief introduction on the basics of atom-photon interactions, we show theoretically, that two atomic dipoles in a resonator can behave as a quantum non-linear medium, whose response can be controlled through the interactomic distance of the atoms inside the resonator. We identify the parameter regime, for which the system operates as a parametric amplifier, based on the atoms' collective dipole cascade emission. Moreover we also determine the corresponding field squeezing spectrum at the cavity output. These dynamics could be observed as a result of self-organization processes of laser-cooled atoms in resonators. The second part of the thesis studies the quantum ground state of an ultracold atomic gas trapped inside an optical resonator by the mechanical effects of atom-photon interactions. Due to the strong coupling regime, the ultracold atomic gas feels a quantum potential, where the fluctuations at the single photon level may be relevant in determining the trapping conditions. This potential depends on the atomic distribution, which at the same time determines the intracavity field amplitude. Here, after a brief introduction on ultracold atoms in optical lattices, we study the low temperature physics of an ultracold atomic gas in the quantum potential formed inside a pumped cavity, by mapping the dynamics to an effective Bose-Hubbard model. We predict the existence of non-compressible states of the atomic gas, and determine a phase diagram as a function of the cavity parameters. Novel effects are encountered, such as the existence of overlapping stability regions corresponding to competing insulator-like states when the laser pumps the cavity, to provide one example out of many. At the end of the thesis a concluding chapter presents some general outlooks to this thesis work.
In the present thesis we study several schemes where the detection of the emitted light from an atomic ensemble gives information about the state of the atoms. In chapter 1 we review the basic theory for the light matter interaction in second quantized form. In chapter 2 we show how conservative potentials for the atoms, such as dispersive optical lattices, can be realized experimentally due to the dispersive interaction with a far detuned laser We then review some basic properties of the physics of a particle in a periodic potential. We show that the ground state and the lowest lying excitations of a Bose-Einstein condensate in a dispersive optical lattice can be described by the Bose-Hubbard Hamiltonian. In chapter 3 we study the photonic bandstructure of a chain of fixed pointlike atoms in a biperiodic configuration. We calculate the photonic spectra and the probe transmission if the atoms are in free space and inside a standing wave optical resonator. In chapter 4 we consider light scattering from ultracold atoms in an optical lattice where we calculate the photonic scattering cross section as a function of energy and direction of emission along the Mott-insulator-superfluid phase transition. We take into account the finite tunneling rate for the atoms, when evaluating the scattering cross section of the photons and the effect of photon recoil onto the atoms. In chapter 5 we consider a gas of ultracold atoms trapped at two spatially separated regions in space. Using a two Raman lasers to couple atoms out of the systems we show that it is possible to measure the mean value of the atomic field operator of the two systems by measuring the scattered light intensity of one of the Raman lasers. We show how this setup might be used to measure the temperature of a Bose-Einstein condensate and to monitor the superfluid to Mott-insulator phase transition for a gas of ultracold atoms in an optical lattice.