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Many-Body Effects in Rydberg Gases : Coherent Dynamics of Strongly Interacting Two-Level Atoms and Nonlinear Optical Response of a Rydberg Gas in EIT Configuration

Martin Gärttner

Published Jan 1, 2014• 1 citation
Publisher

Abstract

Subject of this thesis is the theoretical investigation of ensembles of atoms that are coherently laser-excited to a Rydberg state. Rydberg excited atoms interact with each other over large distances, which leads to strongly correlated many-body dynamics, demanding powerful numerical tools for their modeling. The first part of the thesis deals with effective two-level atoms consisting of a ground and a Rydberg state only. For resonant laser excitation a modified scaling behavior of the excitation number is observed, which is caused by effects of finite system size and coarse graining of the medium due to the finite atomic density. For off-resonant excitation, ordered structures arise out of an initially homogeneous gas, which are reflected in strongly peaked spatial correlations and modified excitation statistics. In the second part a fast decaying intermediate level is additionally taken into account. In this situation the phenomenon of electromagnetically induced transparency (EIT) is encountered. This effect is suppressed in the presence of strong interactions between the Rydberg atoms leading to an optical nonlinearity. A model predicting the properties of a cloud of Rydberg atoms in EIT configuration is developed. In both parts the models are validated by comparing their predictions to recent experimental observations.

DOI
10.11588/heidok.00015992

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Subject of this thesis is the theoretical investigation of ensembles of atoms that are coherently laser-excited to a Rydberg state. Rydberg excited atoms interact with each other over large distances, which leads to strongly correlated many-body dynamics, demanding powerful numerical tools for their modeling. The first part of the thesis deals with effective two-level atoms consisting of a ground and a Rydberg state only. For resonant laser excitation a modified scaling behavior of the excitation number is observed, which is caused by effects of finite system size and coarse graining of the medium due to the finite atomic density. For off-resonant excitation, ordered structures arise out of an initially homogeneous gas, which are reflected in strongly peaked spatial correlations and modified excitation statistics. In the second part a fast decaying intermediate level is additionally taken into account. In this situation the phenomenon of electromagnetically induced transparency (EIT) is encountered. This effect is suppressed in the presence of strong interactions between the Rydberg atoms leading to an optical nonlinearity. A model predicting the properties of a cloud of Rydberg atoms in EIT configuration is developed. In both parts the models are validated by comparing their predictions to recent experimental observations.
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.
Light propagation through an ensemble of ultracold Rydberg atoms in an electromagnetically-induced-transparency (EIT) configuration is studied. In strongly interacting Rydberg EIT media, nonlinear optical effects lead to a nontrivial dependence of the degree of probe-beam attenuation on the medium density and on its initial intensity. We develop a Monte Carlo rate equation model that self-consistently includes the effect of the probe-beam attenuation to investigate the steady state of the Rydberg medium driven by two laser fields. We compare our results to recent experimental data and to results of other state-of-the-art models for light propagation in Rydberg EIT media. We find that for low probe field intensities, our results match the experimental data best if a density-dependent dephasing rate is included in the model. At higher probe intensities, our model deviates from other theoretical approaches, because it predicts a spectral asymmetry together with line broadening. These are likely due to off-resonant excitation channels, which, however, have not been observed in recent experiments. Atomic motion and coupling to additional Rydberg levels are discussed as possible origins for these deviations.
This thesis investigates new phenomena that arise when light is strongly coupled to an interacting atomic gas. For this, a new apparatus has been built which allows to create ultracold and dense atomic samples and to detect individual atoms in high-lying atomic states, so-called Rydberg atoms. Strong light-matter coupling is achieved using the collective coupling of the atomic cloud to the light field under conditions of electromagnetically induced transparency (EIT). In experiments on EIT involving non-interacting Rydberg states, we characterize the light-matter coupling and demonstrate the first combined optical and matter based probing of EIT. By coupling to strongly-interacting Rydberg states, we investigate the effect of interactions which we observe as a strong nonlinear optical \nresponse of the atomic gas as well as in the emergence of strong correlations between the hybrid quasiparticles associated with the strong light-matter coupling. We employ the nonlinear response of the atomic cloud to image Rydberg atoms immersed in the atomic cloud. In a theoretical proposal, we show that this novel imaging technique allows to investigate many-body Rydberg states with single particle sensitivity. Using the proposed imaging method, we demonstrate imaging of small numbers of Rydberg atoms with high time-resolution in single shot experiments. In experiments exploiting the dipolar exchange interaction between Rydberg atoms, we employ the new imaging technique to follow dipole-mediated transport of Rydberg excitations through the cloud. The transport dynamics is determined by the continuous spatial projection of the electronic quantum state under observation and features an emergent spatial scale of micrometer size induced by Rydberg-Rydberg interactions.
High optical nonlinearities can be achieved at the single photon level by coupling the photon states to strongly interacting Rydberg excitations under the conditions of electromagnetically induced transparency. The nonlinear response in Rydberg quantum optics comes as a direct result of the long range dipole-dipole interactions via Rydberg blockade and interaction induced dephasing. In this thesis, Rydberg quantum optics experiments are performed with two spatially separated mediums with a nonlinear response at the single photon level. Two ultracold rubidium atomic clouds are tightly confined by a pair of in-vacuo aspheric lenses such that only a few Rydberg excitations can exist in each one of the clouds simultaneously. The long range character of the dipole-dipole interactions leads to the generation of quantum states of light. The effective photon-photon interactions are directly observed as an anti-correlation in the simultaneous photon retrieval as a result of the non resonant van der Waals interactions. The collective Rydberg excitations, stored in the non-overlapping mediums, experience an additional spatial non-uniform phase. In addition, we experimentally characterize the cooperative optical response of a cold atomic medium at a single photon level. This aims to exploit the enhancement of the spontaneous emissions decay rate (superradiance) as a dependence of the number of atoms involved in the ensemble. The observed atomic response in two different regimes gives a further understanding of the system dynamics and unlocks a promising potential route towards the implementation in scalable, multichannel quantum optical devices.
During this thesis, the Physics of interacting systems has been investigated experimentally using Cold Rydberg gases. Rydberg atoms are very excited atoms and have the particularity to interact strongly together through long-range electrostatic interaction. A first highlight of the thesis is a direct experimental observation of a 4-body process. This process consists in internal exchanges of excitations between 4 Rydberg atoms due to their mutual interactions. In addition to its experimental observation, the process has been succefully described theoretically at a quantum level. A second highlight of this thesis has concerns the study of the laser excitation of strongly interacting Rydberg gases. In this regime, many-body quantum correlations play a central role leading to fascinating many-body behavior. In addition to fundamental interests, such systems could be used to implement quantum simulator or non-classical light sources. The system has been investigated during this thesis through the counting statistics of the Rydberg excitation. A highly sub-poisonian, i.e correlated, statistics has been observed in the regim of strong interactions proving the many-body nature of the system. A third highlight of this thesis is the development of an original theoretical model to describe the laser excitation of strongly interacting Rydberg gases. Using the so-called Dicke collective states, it has been possible to catch several interesting features of this many-body problem.
Mapping the strong interaction between Rydberg excitations in ultra-cold atomic ensembles onto single photons enables the realization of optical nonlinearities which can modify light on the level of individual photons.This novel approach forms the basis of a growing Rydberg quantum optics toolbox, which already contains photonic logic building-blocks such as single-photon sources, switches, transistors, and conditional π-phase shifts.This thesis reports on two experiments investigating strong photon-photon interactions mediated by Rydberg interactions.First, applying a ladder-type EIT scheme to Rydberg atoms in D-states with high principal quantum number results in the Rydberg interaction mediated nonlinearity accompanied by a time-dependent decay of transmission of probe light through the medium.In a joint experimental and theoretical analysis, this effect is attributed to the dephasing of propagating polaritons into stationary Rydberg excitations caused by the state mixing interaction occurring with Rydberg D-state atoms.Second, via a two-photon Raman excitation scheme Rydberg atoms are efficiently excited in a small atomic cloud.As the size of the Rydberg blockade exceeds the dimension of the medium, only a single Rydberg excitation can be present at a time.By fast engineered dephasing this Rydberg excitation is decoupled from the light field.Measurement of the transmitted light and the amount of excited Rydberg atoms gives evidence for the realization of a deterministic single-photon absorber.