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Modelling and Exploiting the Hyperfine Structure of Alkali Atoms for Generation of Nonclassical Light and Rydberg-Atom-Based Field Sensing

A. E. J. Elliott

Published Feb 28, 2025• 0 citations
OpenAlex

Abstract

Alkali atoms are a workhorse in quantum optics, owing to the relative simplicity of their elec- tronic structure, which affords remarkable and reliable control over their behaviour. In particular, the ability to probe and manipulate alkali atoms with electromagnetic fields provides an important resource for studying and harnessing their fundamental properties. This thesis explores interac- tions between alkali atoms and light, to uncover ways of exploiting their properties for a variety of purposes. The main results of the thesis are divided into three main parts, as we detail below. Firstly, we develop theoretical models of effective interactions between alkali atoms in cavity quantum electrodynamics (cavity QED) systems, building on previous work in this area. The models are based on Raman transitions between the Zeeman sublevels of hyperfine ground states in an alkali atom. We show that by coupling light to both D-lines of the atom simultaneously, a versatile effective Hamiltonian can be realised with terms that can be manipulated independently. Additionally, we show that, with careful arrangement of the fields, the effective interactions can persistinsteadystate, continuouslyoutputtinglightthatcarriessignaturesoftheinteraction. These models reveal novel mechanisms for generating nonclassical states of light, with the potential for producing Wigner-negative and quadrature-squeezed light from single-atom sources. We simulate full hyperfine structure models of the interactions, using parameters inspired by modern cavity QED architectures, to demonstrate the robustness of their implementation in a real atom. Secondly, we explore nonclassical photon statistics through specific configurations of single- atom nanofibre cavity QED systems. By coupling an alkali atom to nanofibre cavity modes, we demonstrate antibunching and strong two-mode correlations, showcasing the versatility of these systems for generating nonclassical photon statistics. We consider two schemes for their photon correlations, each based on coupling two cavity modes to a single atom. First, the generation of nonclassical light at telecom-band wavelengths is studied, using cascaded transitions within a caesium atom. The atomic states are chosen such that one of the cavity modes is resonant at a telecom-band frequency. Second, we explore the coupling an adjacent pair of resonances of a long cavity to a strongly-driven atom. The characteristic emission spectrum is matched to the free spectral range of the cavity. In both cases, we consider simplified models to understand the critical behaviour of the systems, and then use full hyperfine structure models to examine the viability of implementing them in modern nanofibre cavity QED systems. Finally, we present a model for the interaction of light with a thermal cloud of Rydberg atoms. The random thermal motion of a room-temperature gas necessitates ensemble averaging in order to predict the absorption spectrum for a probe beam. The effective model that we develop accurately predicts the absorption profile of electromagnetically-induced transparency in the atomic cloud, offering insights for experiments in atom-based sensing of microwave-frequency electromagnetic fields. Overall, this thesis enhances the fundamental understanding of alkali atom-light interactions and adds to the ever-growing quantum-optical toolbox.

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Alkali atoms are a workhorse in quantum optics, owing to the relative simplicity of their elec- tronic structure, which affords remarkable and reliable control over their behaviour. In particular, the ability to probe and manipulate alkali atoms with electromagnetic fields provides an important resource for studying and harnessing their fundamental properties. This thesis explores interac- tions between alkali atoms and light, to uncover ways of exploiting their properties for a variety of purposes. The main results of the thesis are divided into three main parts, as we detail below. Firstly, we develop theoretical models of effective interactions between alkali atoms in cavity quantum electrodynamics (cavity QED) systems, building on previous work in this area. The models are based on Raman transitions between the Zeeman sublevels of hyperfine ground states in an alkali atom. We show that by coupling light to both D-lines of the atom simultaneously, a versatile effective Hamiltonian can be realised with terms that can be manipulated independently. Additionally, we show that, with careful arrangement of the fields, the effective interactions can persistinsteadystate, continuouslyoutputtinglightthatcarriessignaturesoftheinteraction. These models reveal novel mechanisms for generating nonclassical states of light, with the potential for producing Wigner-negative and quadrature-squeezed light from single-atom sources. We simulate full hyperfine structure models of the interactions, using parameters inspired by modern cavity QED architectures, to demonstrate the robustness of their implementation in a real atom. Secondly, we explore nonclassical photon statistics through specific configurations of single- atom nanofibre cavity QED systems. By coupling an alkali atom to nanofibre cavity modes, we demonstrate antibunching and strong two-mode correlations, showcasing the versatility of these systems for generating nonclassical photon statistics. We consider two schemes for their photon correlations, each based on coupling two cavity modes to a single atom. First, the generation of nonclassical light at telecom-band wavelengths is studied, using cascaded transitions within a caesium atom. The atomic states are chosen such that one of the cavity modes is resonant at a telecom-band frequency. Second, we explore the coupling an adjacent pair of resonances of a long cavity to a strongly-driven atom. The characteristic emission spectrum is matched to the free spectral range of the cavity. In both cases, we consider simplified models to understand the critical behaviour of the systems, and then use full hyperfine structure models to examine the viability of implementing them in modern nanofibre cavity QED systems. Finally, we present a model for the interaction of light with a thermal cloud of Rydberg atoms. The random thermal motion of a room-temperature gas necessitates ensemble averaging in order to predict the absorption spectrum for a probe beam. The effective model that we develop accurately predicts the absorption profile of electromagnetically-induced transparency in the atomic cloud, offering insights for experiments in atom-based sensing of microwave-frequency electromagnetic fields. Overall, this thesis enhances the fundamental understanding of alkali atom-light interactions and adds to the ever-growing quantum-optical toolbox.
We propose and investigate a scheme for the steady-state emission of quantum-correlated, telecom-band light from a single multilevel atom. By appropriately tuning the frequency of a pair of lasers, a two-photon transition is continually driven to an atomic excited state that emits photons at the desired wavelength. We show that resonantly coupling a cavity mode to the telecom transition can enhance the rate of emission while retaining the antibunched counting statistics that are characteristic of atomic light sources. We also explore coupling a second, independent cavity mode to the atom, which increases the telecom emission rate and introduces quantum correlations between the cavity modes. A model for the hyperfine structure of a single cesium atom is then described and numerically integrated to demonstrate the viability of implementing the scheme with a modern cavity QED system.
We present a proposal to control and improve the nonclassicality of photons in a single-atom cavity-QED system with a strong coupling strength, where the atom is directly driven by external fields. Exploring the eigenvalues and the corresponding eigenstates of the system, we show that the dressed states can be optically manipulated by changing the control field intensity. In particular, tuning the control field frequency to be resonant with the one-photon excitation state, we show that the nonclassicality of cavity photons arising from the two-photon blockade can be actively controlled. We also show that there exists a magic control field Rabi frequency at which the two-photon blockade phenomenon can be significantly improved. The work presented here provides an optical method to control the statistical features of the cavity field that could find utility in nonclassical light generation, photon gateway operation, and exotic quantum-state generation.
Understanding and manipulating quantum materials is a long-sought goal in both the condensed matter and cold atom communities. Photons have recently emerged as a good candidate for studying quantum many-body states due to their fast dynamics and convenient manipulation. Tremendous efforts have been made to engineer single particle Hamiltonian with non-trivial topology. Having individual photons to strongly collide with each other and form an entangled many-body state remained as a challenge in optical domain. ,In this thesis, I will first demonstrate how to engineer artificial magnetic field and non-trivial topology for microwave photons. In a classical lumped element circuit, we demonstrate the edge modes for microwave photons within the bulk band, and also show that these modes propagates with topological protection against the local lattice disorder. This work paves the way to synthesize correlated quantum materials in a lattice using microwave photons, combined with circuit QED technique. ,Recently, Rydberg-Rydberg interaction has been broadly used in cold atom experiment to generate long-range inter-particle coupling for quantum information processing and quantum material simulation. We combine this technique with cavity electromagnetically induced transparency and create a robust quasi-particle, cavity Rydberg polaritons, which harness the power from both cavity photons with exotic topology and Rydberg atoms with strong interactions. We first demonstrate the interaction in the single quanta level in a quantum dot with single cavity mode and further expand it into multi-mode regime with modulated atomic states.
Designing materials with specific properties has been a long-time goal of the physics community. Optical photons have recently emerged as a promising candidate for such metamaterials due to their fast dynamics and available manipulation toolkit. In conjunction with carefully engineered optical resonators, it is possible to precisely control the properties of individual photons through the resonator Hamiltonian. The only missing ingredient to photonic materials is strong photon-photon interactions. This thesis describes the characterization of cavity Rydberg polaritons and the emergence of strong interactions in such a system. Electromagnetically induced transparency (EIT) is used to create quasiparticles that inherit the properties of both photons and Rydberg atoms: fast dynamics and trapping from the photons and long-range dipole-dipole interactions from the Rydberg atoms. The emergent polaritonic properties are characterized and controlled through the dark-state rotation angle and agree very well with theoretical predictions. We then expand upon this understanding of polaritons by putting them inside a zerodimensional quantum dot. Confining the polaritons in such an object allows for strong interparticle interactions to manifest. We observe these interactions through the temporal auto-correlation intensity function g2(t) and verify the dimensionality of the quantum dot itself by measure the polariton Rabi oscillations. With the experimental demonstration of strong photonic interactions, a complete understanding of Rydberg atoms and polaritons is needed to allow for better control of the system. To this effect, the properties of Rydberg atoms are analytically and numerically understood and the full formalism needed to describe resonator Rydberg polaritons is developed, along with their interactions and various sources of decoherence. Furthermore, a renormalized effective field theory for single mode cavities is developed and tested against full numerical models, paving the way for the simulation of the physical phenomena of manybody states in multi-mode cavities. Strongly interacting cavity polaritons can be utilized in quantum gate and repeater protocols for quantum information processing. Furthermore, combining the experimental and theoretical work here with non-planar resonators presents a clear path to non-trivial topological synthetic materials and strongly correlated quantum states.
In this thesis, we examined a series of techniques for controlling the interaction of light with matter that could be employed to optimize or to control physical phenomena in various potential applications. Some of these schemes are described with classical electrodynamic theory while others require a semi-classical or full quantum framework. \nIn Ch.(2), we study numerically two implementations of stretchable photonic crystals (SPCs) embedded in elastic polymers. Our analysis, which classifies the bandgaps in terms of two simply determined parameters, indicates that such structures exhibit bandgaps that can be readily adjusted by straining the polymer. \nIn Ch.(3), we considered a five-level atomic system in a dense gas interacting with two low-intensity fields. By examining the influence of different parameters on the refraction index we found that by adjusting the ratio of the two magnetic amplitudes associated with the fields the effects of atomic coherence can be simply controlled. As well, a negative index of refraction can be achieved and controlled over a wide wavelength range with minimal absorption. \nIn Ch.(4), we theoretically investigated the double Lambda scheme inside a Fabry-Perot cavity. By introducing a weak probe beam and two strong driving fields and employing an incoherent pumping mechanism we found that when the intensity of the two driving fields are equal, a single giant white band was generated. However, when they are not equal, three white bands can be present in one cavity. This procedure can also be employed to displace the center frequency of the white band. \nIn Ch.(5), we studied the interaction of a N-type four-level atom with a single field in the presence of an intensity-dependent coupling in a nonlinear Kerr medium. The exact analytic solution is obtained in the case that the atom and electromagnetic field are initially in a higher excited state and a coherent state, respectively. It is then demonstrated that nonclassical properties such as the degree of entanglement stabilization, Kerr medium nonclassical control, and squeezed light can be more efficiently realized and controlled within this four-level framework than in many competing procedures. \nFinally, in Ch.(6), we theoretically studied the superposition of two nearly identical coherent states. This ``near coherent'' state exhibits numerous nonclassical properties such as sub-Poissonian statistics, squeezing for certain relative phases of the superposition and a partially negative Wigner function.
Cavity quantum electrodynamics (QED), the system of a single atom interacting with a single mode of a high finesse optical resonator, has tremendous potential for use in quantum logic, quantum information processing, and in enabling observation of quantum mechanical effects in the laboratory. The work of this thesis demonstrates a number of steps toward realizing these goals, by employing an experimental system with the strongest atom-field coupling achieved to date in optical cavity QED. The effects of strong coupling in cavity QED are studied for single cold atoms measured one at a time, in real time. The passage of single atoms through the cavity is employed to map out the frequency response of the system, and to demonstrate that quantum rather than semiclassical theory provides the correct theoretical model. The mechanical effects of strong coupling on single atoms are explored, these experiments demonstrating the first trapping of single atoms with single photons. Additionally, strong coupling enables high signal-to-noise ratio for monitoring atomic position at single photon field strengths; this capability is employed to investigate the motion of atoms trapped within the cavity. The transmitted cavity field is used to reconstruct the trajectories of single atoms, thereby realizing a new form of microscopy - the Atom-Cavity Microscope. Technical developments necessary to create the cavities used in this experiment are detailed. Ideas for future extensions to the experiment are proposed; a zero light-shift dipole force trap, and measurement of photon statistics of a single strongly coupled atom (which realizes a photon blockade device) are discussed.