Optical trapping of atoms employs high-intensity fields that necessarily alter atomic level structure. The calculation of light shifts by perturbation theory fails for scenarios that arise, for example, when the trapping light is near an excited-state transition or for polychromatic fields. We show here that non-perturbative methods based on Floquet’s theorem elegantly handle such scenarios. We compare our calculation to precision absorption spectroscopy on cold 87Rb atoms in a bichromatic optical dipole trap at 1560 + 1529 nm. Proximity to excited-state resonances induces highly nonlinear level shifts, providing a strong test of theory. The good theory-experiment agreement suggests a new method for accurate measurements of excited-state electric-dipole matrix elements and a precision tool for engineering custom atomic level structures.
Optical trapping of atoms employs high-intensity fields that necessarily alter atomic level structure. The calculation of light shifts by perturbation theory fails for scenarios that arise, for example, when the trapping light is near an excited-state transition or for polychromatic fields. We show here that non-perturbative methods based on Floquet’s theorem elegantly handle such scenarios. We compare our calculation to precision absorption spectroscopy on cold 87Rb atoms in a bichromatic optical dipole trap at 1560 + 1529 nm. Proximity to excited-state resonances induces highly nonlinear level shifts, providing a strong test of theory. The good theory-experiment agreement suggests a new method for accurate measurements of excited-state electric-dipole matrix elements and a precision tool for engineering custom atomic level structures.
We present a non-perturbative numerical technique for calculating strong light shifts in atoms under the influence of multiple optical fields with arbitrary polarization. We confirm our technique experimentally by performing spectroscopy of a cloud of cold 87Rb atoms subjected to ∼ kW/cm2 intensities of light at 1560.492 nm simultaneous with 1529.269 nm or 1529.282 nm. In these conditions the excited state resonances at 1529.26 nm and 1529.36 nm induce strong level mixing and the shifts are highly nonlinear. By absorption spectroscopy, we observe that the induced shifts of the 5P3/2 hyperfine Zeeman sublevels agree well with our theoretical predictions.. We propose the application of our theory and experiment to accurate measurements of excited-state electric-dipole matrix elements.
This thesis reports on theory and results from two experiments related to nonlinear behaviour in ensembles of optically-trapped ultracold atoms. The first experiment, performed at ICFO in Barcelona, regards the prediction and measurement of strong ac Stark shifts (light shifts). We present a numerical method based on Floquet's theorem for calculating light shifts to all orders with fewer approximations than the usual calculation based on second-order perturbation theory. The method is experimentally validated by performing absorption spectroscopy of a optically-trapped cloud of cold 87Rb atoms in three scenarios. 1) The atoms are trapped in a singly-polarised monochromatic dipole trap with a wavelength detuned aprox 30nm from the nearest atomic transition. 2) A bichromatic two-polarisation trap, where one wavelength is much closer to atomic transitions (aprox 0:01nm detuning), and finally 3) Another monochromatic trap but with the wavelength variable and scanned close to atomic transitions, again with aprox 0:01nm detuning but three times the intensity of the near-resonant light in the previous experiment, producing nonlinear light shifts of the D2 transition upto aprox 1 GHz. We discuss the potential application of the method to the accuratemeasurement of electric dipole transition matrix elements. The method is extendedto calculate atomic energy level shifts in the presence of light and staticmagnetic fields. The second experiment was performed at LENS in Florence, and involves 39K atoms with tunable interactions cooled into the ground- and first-excited state of a two-mode optical potential. We derive a diferential equation to describe behaviour of a two-mode quantum system with tunable interactions, and then solve it to model behaviour of the system in the three distinct regimes of attractive, zero, and repulsive interatomic interactions. With attractive interactions the system is shown to exhibit a quantum phase transition, and with repulsive interactions is shown to exhibit nonlinear dynamics, including behaviour analogous to a superconducting Josephson junction. As background material the thesis presents a summary of standard laser cooling and trapping echniques, namely Doppler cooling, o+ o- polarisation gradient cooling, magneto-optical trapping, and optical trapping. Optical traps are discussed in detail. We discuss relevant basic physics, derive and analyse a technique for using light shifts to characterise an optical trap, discuss optical Bose-Einstein condensation and control of light intensity to reduce noise-induced heating. Also described is a theoretical proposal for optical evaporation with a constant-depth trap. Esta tesis describe la investigación teórica y los resultados de dos experimentos relacionados con el comportamiento no lineal en un conjuntos de áatomos ultrafríos atrapados ópticamente. En el primer experimento, realizado en ICFO en Barcelona, se presenta la predicción y unos resultados de fuertes cambios de ac Stark (light shifts). Se explica un método numérico basado en el teorema de Floquet para calcular light shifts a todos órdenes con menos aproximaciones que el método habitualmente usado basado en teoría de perturbaciones de segundo orden. El método se valida experimentalmente mediante la realización de espectroscopía de absorción en una nube de átomos de 87Rb ópticamente atrapados en tres escenarios distintos. En el primero, los átomos están atrapados en una trampa de dipolo monocromática de polarización única con una longitud de onda desintonizada 30nm a la transición atómica más cercana. En el segundo se emplea una trampa bicromática de dos polarizaciones, donde una longitud de onda está mucho más cerca de las transiciones atámicas (0.01nm fuera de resonancia). En el tercer y ultimo escenario, se usa una trampa monocromática con la longitud de onda variable y escaneado cerca de transiciones atómicas, nuevamente con 0.01nm desintonizada pero tres veces más intensa que la luz casi resonante del experimento anterior, produciendo light shifts no lineales de la transición D2 hasta 1 GHz. Se discute la aplicabilidad del método para la medición precisa de los elementos de la matriz de transición dipolar eléctrica. Por último, el método se extiende permitiendo calcular los cambios de niveles de energía atómica en presencia de luz y campos magnéticos estáticos. El segundo experimento que se describe en esta tesis se realizó en LENS, en Florencia, e involucra átomos de 39K con interacciones sintonizables en átomos fríos ocupando al estado fundamental y el primer estado excitado de un potencial óptico de dos modos. Se deriva una ecuación diferencial para describir el comportamiento de un sistema cuántico de dos modos con nteracciones sintonizables. Esta se resuelve para modelar el comportamiento del sistema en tres regímenes distintos de interacciones inter-atómicas: atractivas, nulas y repulsivas. En el caso de interacciones atractivas se muestra que el sistema exhibe una transición de fase cuántica. En presencia de interacciones repulsivas el sistema muestra dinámica no lineal, incluyendo un comportamiento análogo a una unión superconductora de Josephson. Como material de referencia, la tesis presenta un resumen de las técnicas estándar de enfriamiento y atrapamiento láser, concretamente enfriamiento Doppler, enfriamiento por gradiente de polarización, atrapamiento magneto-óptico y atrapamiento óptico. Las trampas ópticas se revisan en detalle. Discutimos la física básica relevante, derivamos y analizamos una técnica para usar los light shift para caracterizar una trampa óptica. Analizamos la condensación óptica de Bose-Einstein y el control de la intensidad de la luz para reducir el calentamiento inducido por el ruido. También se presenta una propuesta teórica para la evaporación óptica con una trampa de profundidad constante.
The light frequency shifts induced by an external laser field are calculated for the spin-forbidden 3 P J — 1 S 0 transitions in Mg, Sr, and Yb atoms. The calculations are performed within the framework of the perturbation theory using experimentally measured transition energies. The calculations of the higher-order dynamic Stark effect were initiated by precision measurements of trapped and cooled atoms as well as by the development of a highly stable optical atomic clock. The dispersion properties of the polarisability and hyperpolarisability components are analysed in the vicinity of resonances and so-called cross points for the ground and excited atomic levels. The radial matrix elements were calculated by the Green function method for the model potential.
Manipulation of cold atoms by lasers has so far been studied solely within the framework of the conventional dipole approximation, and the atom-light interaction has been treated using low order perturbation theory. Laser control of atomic motions has been ascribed exclusively to the corresponding light-induced dipole forces. In this work, we present a general theory to derive the potential experienced by an atom in a monochromatic laser field in a context analogous to the Born-Oppenheimer approximation for molecules in the field-free case. The formulation goes beyond the dipole approximation and gives rise to the field-atom coupling potential terms which so far have not been taken into consideration in theoretical or experimental studies. Contrary to conventional approaches, our method is based upon the many electron Floquet theory and remains valid also for high intensity laser fields (i.e., for a strongly nonperturbative atom-light interaction). As an illustration of the developed theory, we investigate the trapping of cold atoms in optical lattices. We find that for some atoms for specific laser parameters, despite the absence of the dipole force, the laser trapping is still possible due to the electric quadrupole forces. Namely, we show that by using realistic laser parameters one can form a quadrupole optical lattice which is sufficiently strong to trap Ca and Na atoms.
The light shift caused by an optical dipole force trap on a single 87Rb atom was recently studied by Shih and Chapman [Phys. Rev. A 87, 063408 (2013)] using a dipole-matrix-element-based approach. A separate study by Neuzner et al. [Phys. Rev. A 92, 053842 (2015)] considered the same system using a polarizability-based approach. We find that the results of these two studies do not agree, which we ascribe to an error in the theoretical part of Shih and Chapman's paper. We correct this error, offer an alternative formulation for the energy-level shift using the matrix-element-based approach, and find good agreement between our predictions and those obtained with the polarizability-based method. Furthermore, our predictions are in better agreement with Shih and Chapman's experimental results in comparison to their predictions. In contrast to the polarizability-based method, our formulation can be easily extended to different trapping wavelengths and atomic species.
We have developed and tested an efficient mathematical model for calculating a coherent population trapping (CPT) resonance in a periodically modulated laser field when the modulation frequency f is close to the fractional part of the hyperfine splitting frequency (HFS) in the ground state ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{HFS}}/N$ (where N=1,2,3,…). In such a polychromatic light, only two frequency components that are most resonant with the working optical transitions in the atom are taken into account exactly, while all other off-resonant frequency components are taken into account by using the second-order perturbation theory in the field magnitude. Within the framework of our concept, an equation for the atomic density matrix is obtained, in which all off-resonant frequency components are described by two operators (which are nondiagonal in the general case): a shift operator and a relaxation operator. This model has been verified by numerical calculations for various dependencies, in which we have not found visual differences from the results of exact calculations. Thus, in our bichromatic model, the infinite variety of periodically modulated fields in CPT spectroscopy can be uniformly described by only five parameters. In addition to a significant mathematical simplification, our model provides a clear physical picture of the various features of CPT spectroscopy in a periodically modulated laser field, including some effects that have not yet been discussed in the scientific literature. In particular, we show a widespread viewpoint that the CPT resonance shift is determined by standard ac Stark shifts of the lower levels is, in general, fundamentally incorrect, since the contribution to the light shift due to beats at the frequency ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{HFS}}$ between different off-resonant frequency components can be comparable to the value of standard ac Stark shift (or even dominate it). Therefore, even if we have detailed information on the spectral composition of the modulated field (e.g., using a spectrum analyzer), this is, in general, absolutely insufficient for determining the light shift of the CPT resonance.