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Investigation of the van der waals interactions in a Bose-Einstein condensate via electromagnetically-induced transparency

Anushyam Mohan

Published Jan 1, 2013• 1 citation
Publisher

Abstract

This thesis focusses on the development of the experimental system used to study the eff ect of Rydberg blockade interactions in clouds of ultracold atoms and quantum degenerate gases. Initial measurements have been performed quantifying these interactions, like the Rydberg blockade radius and its variation\n\n\n\nwith the density of sample, which can be very useful in devising eff cient systems for quantum information processing in quantum gates and/or as probes for detecting impurities in a sample as has been recently proposed [1]. The e ffects of the Rydberg atom interactions are probed via electromagnetically-induced\n\n\n\ntransparency (EIT). The experimental system and apparatus required for the production and detection of ultracold atoms and quantum degenerate gases is developed. Furthermore, the laser systems used for the production of Rydberg atoms via the two-photon transitions are also described. To highlight the density dependent eff ects of the Rydberg atom interactions and the\n\n\n\nunique advantages o ered to us by the Rydberg blockade eff ect, we compare the EIT experiments performed on a Λ-system using Raman lasers and the experiments performed with a ladder system involving the ground state, the fi rst excited state and a Rydberg state of Rb-87. The manifestation of the blockade eff ect with atom number density, with temperature of the atoms and with the principal quantum number of the Rydberg state to which the\n\n\n\natoms are excited, is discussed. The usefulness of the Rydberg blockade interaction as a phenomenon to be exploited in quantum information processing and an outline of the future directions of our experiments concludes the thesis.

DOI
10.32657/10356/51126

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In this thesis, the development of an experimental system for microscopic dipole trapping of ultracold neutral rubidium atoms is presented. The purpose of this system is to advance towards the experimental realisation of a quantum computational protocol utilising neutral atoms as qubits. It is intended that the quantum gate operations between qubits will be implemented by a scheme using Rydberg blockade, imposing a restriction on the maximum size of the dipole-trapped atom cloud; the spatial extent of the atomic ensemble contained in this trap must be smaller than the blockade radius to ensure that one single collective Rydberg state per qubit can be achieved. Therefore the experiment was designed with the intent of fulfilling these challenging requirements. This project involved the design and construction of an improved ultra-high vacuum chamber containing the optical setup for the experiment, successfully achieving pressures below 5 x 10-10 mbar. A magneto-optical trap was produced to act as a background reservoir of atoms from which to load the dipole trap. Numerous experimental measurements were done to characterise the physical properties of the trapped atoms, including the number, density and temperature of atoms, as well as the lifetime of the trap. The results of these measurements led to the conclusion that a suitable reservoir for loading the dipole trap had been produced. Significant work was carried out to set up and obtain the dipole trap in the laboratory. Measurements of the characteristic properties of the trap and the atoms confined in the trap were carried out to investigate the behaviour of the atoms and to validate our design. Ultimately a trap containing tens of atoms was achieved, with an atom cloud diameter of ~1.2 µm in two dimensions, being well within the estimated Rydberg blockade radius of ~4.4 µm for n ~ 60 as intended. The two-photon excitation laser system for the probing of Rydberg states, for future applications in Rydberg blockade-based quantum gate operations, was also developed during the course of this work. Different Rydberg states were detected experimentally by the observation of Autler-Townes splitting in a three-level atom scheme. Overall, the work presented in this thesis provides a strong groundwork for the advancement towards neutral atom-based quantum gates, including the development of the experimental system and the production of standard procedures to carry out characterisation measurements of the traps efficiently in the future. The main achievements of this work are the establishment of the experimental apparatus, the achievement of a microscopic dipole trap which conforms to the requirements of an atomic qubit, and the significant growth in the knowledge of atom trapping specific to our system.
This thesis investigates the effects of strong Rydberg-Rydberg interactions in the presence of three-level coherent phenomena such as electromagnetically induced transparency (EIT), Autler-Townes splitting (ATS) and coherent population trapping (CPT). As a result of their remarkable properties, highly excited Rydberg atoms have great potential for applications in diverse areas. The interaction-induced dipole blockade between the Rydberg atoms has been proposed as a fundamental tool in quantum information processing with neutral atoms. Yet, they require an increasing level of understanding and control. A many-body theory is developed for the Rydberg excitation dynamics in various atomic systems with different densities and velocity distributions such as for atoms in a vapour cell, ultracold atoms in magneto-optical and optical dipole traps, or a system of optical lattices or dipole trap arrays. The systems were investigated by solving the optical Bloch equations numerically for a two-photon ladder excitation scheme, taking into consideration various experimentally relevant conditions for the emergence of the effects of Rydberg-Rydberg interactions. The lineshape properties of the EIT/ATS/CPT spectra are observed and reviewed while the physical arguments for how the lineshape properties change as a function of various parameters are provided. To account for the differing atomic distributions in the atomic systems, a many-body model based on Monte-Carlo simulation is developed to describe the optical response of the multiatoms systems to two-photon excitation laser lights in the regimes of EIT, ATS and CPT and strong atomic interactions. The study of the lineshape properties allows one to understand possible ways to detect the emergence of interaction-induced excitation suppression, asymmetry, line shift and excitation "antiblockade" enhancement effects. Besides these, the main result of this study is the demonstration that the linewidth properties of the Rydberg EIT/ATS/CPT spectra can reveal collective many-body behaviour associated with the creation of many-body entangled states. The linewidth properties provide compelling evidence of the creation of collective states by confirming the predicted dependence of the generalised Rabi frequency on the square root of the number of atoms in the mesoscopic ensemble. This study could help to quantify and control the conditions necessary for creating many-body entanglement within atomic ensembles. The thesis also describes the step towards experimentally investigating the response of an atomic system to excitation lasers and studying the excitation dynamics of interacting atoms in such systems. Significant work was done to set up the two-photon excitation system for preparing atoms in high-lying Rydberg states and performing Rydberg-based vapour cell experiments. Qualitative analysis of the Rydberg states transparency features allows to obtain laser parameters such as the laser linewidths and Rabi frequencies that are used in the theoretical model to create the similarity between the experimental and theoretical parameters. Further works were carried out towards realising the building blocks for experimentally investigating the interactions between Rydberg atoms in ultracold atom systems. This is by setting-up a trapping system capable of producing a highly dense ultracold atom ensemble within a magneto-optical trap, cold enough to serve as a reservoir from which the optical dipole trap can be loaded efficiently. The optical dipole trap is designed and set up to achieve a micron-size trapping potential capable of producing a sub-micron sized atomic cloud, with a controllable number of atoms, where a full blockade effect can be achieved and exploited to implement a qubit system for quantum gate operations.
This thesis presents a new experimental facility that has been developed in the course of the PhD of the author together with the experimental measurements of the dipole moments for transitions between 5P3/2 and nD5/2 states in Rb atoms, where 20 ≤ n ≤ 48. A laser cooling setup for rubidium atoms was designed and built that allows to produce 3 x 10 atoms at temperature of few microkelvins. A laser system for coherent excitation to Rydberg states was realised that exploits a two-photon ladder excitation scheme. Such setup allowed to directly measure transition dipole moments from the first excited state to high n Rydberg states. The electromagnetically induced transparency and Autler-Townes splitting phenomena were exploited in order to obtain the values of the dipole moments, which were found to be in an excellent agreement with the theoretical values calculated using the quasiclassical approach by our collaborators in Novosibirsk. To the author's knowledge, these are the first direct measurements of such dipole moments. The data shown in the thesis proves the reliability of the measurement method. The obtained results are extremely useful to validate theoretical models and gain insight in the physics of the interactions that will be an object of subsequent studies. The methods presented in the dissertation will be used in the future to detect in a non-destructive way Rydberg-Rydberg interactions within mesoscopic samples.
This thesis investigates how a single highly excited atom, called Rydberg atom, can be optically imaged. Direct detection methods based on the scattering of light are hardly applicable due to the small scattering rate of the ground to Rydberg state transition. Instead, a cloud of ground state atoms, normally absorptive, is rendered transparent using electromagnetically induced transparency (EIT), involving an auxiliary probe Rydberg state. The cloud acts as a contrast medium, whose optical response is locally perturbed by the strong Rydberg-Rydberg interaction between the probe and the Rydberg impurity which we want to detect. This perturbation restores absorption within a small volume around the impurity, readily detected and \nspatially resolved on a camera. We call this technique Interaction Enhanced Imaging (IEI). To implement IEI we characterize the optical response of the EIT contrast \nmedium in absence of interactions. By combining measurements of the spatially resolved optical spectrum and of the total Rydberg atom number, we can reconstruct \nthe full one-body density matrix of the three-level system. Next, we excite |nS> or |nP> states and, using IEI, we demonstrate spatially resolved imaging, enabling us \nto study dipolar energy transport. To reach single impurity sensitivity we investigate our current detection fidelity and characterize the signal and noise contributions in \nIEI. We model our interacting system, finding good agreement with experimental data. Based on this model, we predict combinations of Rydberg states for which single-shot single impurity sensitivity should be possible in future experiments.
We propose a method of measuring the van der Waals interaction in an ensemble of cold Rydberg atoms via electromagnetically induced transparency (EIT). By using the method of mean-field approximation, we examine the influence of the van der Waals interaction on the EIT spectrum. It is interesting to find that the van der Waals interaction strength is proportional to frequency shift of the transmission spectrum. This can be used to probe the van der Waals interaction strength. In addition, we discuss the evolution of the van der Waals interaction by adopting the model of the cubic lattice. It is found that the total atoms blockade appears in dense gases under the condition of the strong coupling. Also, we discuss the boundary condition of the total blockade and explain the evolution of the van der Waals interaction.
We report the measurement of the electromagnetically induced transparency (EIT) with Rydberg states in ultracold 40 K Fermi gases, which is obtained through a two-photon process with the ladder scheme.Rydberg-EIT lines are obtained by measuring the atomic losses instead of the transmitted probe beam.Based on the laser frequency stabilization locking to the superstable cavity, we study the Rydberg-EIT line shapes for the 37s and 35d states.We experimentally demonstrate the significant change in the Rydberg-EIT spectrum by changing the principal quantum number of the Rydberg state (n = 37=52 and l = 0).Moreover, the transparency peak position shift is observed, which may be induced by the interaction of the Rydberg atoms.This work provides a platform to explore many interesting behaviors involving Rydberg states in ultracold Fermi gases.