Probe spectrum of alkali atoms in a weakly driven two mode cavity

James Clemens

James Clemens

We calculate the probe spectrum for multilevel atoms in a damped, weakly driven cavity supporting two degenerate orthogonally polarized modes. One mode is weakly driven by a linearly polarized external field. The atoms, initially prepared in a ${m}_{F}=0$ hyperfine ground state, couple to the driven mode by making a $\ensuremath{\Delta}{m}_{F}=0$ transition and to the orthogonally polarized mode by making $\ensuremath{\Delta}{m}_{F}=\ifmmode\pm\else\textpm\fi{}1$ transitions to other hyperfine sublevels. We compare probe spectra, the intensity of the driven mode, the undriven mode, and the atomic excitation probability as a function of the detuning of the driving laser from the cavity resonance for three- and four-level atomic models. In both cases the spectrum of the driven mode is a vacuum Rabi doublet familiar from the driven, damped Jaynes-Cummings model. The undriven mode spectrum is a triplet with the maximum on resonance for the three-level model while the four-level model has a four-peaked spectrum. We discuss the role of strong coupling to the undriven mode in accounting for the qualitative difference between the models.

A. E. J. Elliott

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.

Luis A. Orozco, G. T. Foster, J. Gripp +1 more

Rheinischen Friedrich-Wilhelms-UniversitBonn

H. J. Carmichael, Robert J. Brecha, Mark G. Raizen +2 more

We calculate the spontaneous-emission spectrum and the spectrum of weakly driven fluorescence for a two-level atom coupled to a resonant-cavity mode. For strong atom-cavity coupling the spectra split into two peaks that can have subnatural linewidths. If the cavity linewidth is negligible, the spontaneous-emission spectrum has half the radiative linewidth of the atom; the spectrum of weakly driven fluorescence shows an additional 36% squeezing-induced narrowing. These effects can be observed using coupled-field and collective-polarization oscillators excited in a cavity containing N two-level atoms.