Collective effects in the interaction of light with ensembles of identical scatterers play an important role in many fields of physics. However, often the term ``identical'' is not accurate due to the presence of hyperfine fields which induce inhomogeneous transition shifts and splittings. Here we develop a formalism based on the Green's-function method to model the linear response of such inhomogeneous ensembles in one-dimensional waveguides. We obtain a compact formula for the collective spectrum, which exhibits deviations from the uniform frequency shift and broadening expected of two-level systems. In particular, if the coherent contribution to the collective coupling is large, the effect of inhomogeneous broadening can be suppressed, with the linewidth approaching that of the superradiant value. We apply this formalism to describe collective effects in x-ray scattering off thin-film waveguides for inhomogeneous hyperfine parameters.
Collective effects in the interaction of light with ensembles of identical scatterers play an important role in many fields of physics. However, often the term ``identical'' is not accurate due to the presence of hyperfine fields which induce inhomogeneous transition shifts and splittings. Here we develop a formalism based on the Green's-function method to model the linear response of such inhomogeneous ensembles in one-dimensional waveguides. We obtain a compact formula for the collective spectrum, which exhibits deviations from the uniform frequency shift and broadening expected of two-level systems. In particular, if the coherent contribution to the collective coupling is large, the effect of inhomogeneous broadening can be suppressed, with the linewidth approaching that of the superradiant value. We apply this formalism to describe collective effects in x-ray scattering off thin-film waveguides for inhomogeneous hyperfine parameters.
This thesis is dedicated to the study of collective effects of nuclei in single xray photon superradiance. To this end we investigate aspects of superradiance in both nuclear forward scattering and in thin-film cavities with an embedded 57Fe nuclear layer. A general theoretical framework is developed to investigate a single-photon cooperative emission from a cloud of resonant systems, atoms or nuclei, in the presence of magnetic hyperfine splitting. In the limit of a thick sample, we present our results for two means to coherently control the collective single x-ray photon emission in nuclear forward scattering. In the limit of a thin sample in a thin-film cavity with embedded resonant nuclei, we find out that unlike the magnetic hyperfine splitting of a single atom or nucleus, interesting collective effects may occur which modify the hyperfine level structure. In addition, for a certain parameter regime a spectrum reminiscent of electromagnetically induced transparency (EIT) can be achieved. Based on this EIT-like effect, a theoretical control mechanism for stopping x-ray pulses in the thin-film x-ray cavity is put forward. Finally, we show theoretically that for the case of two nuclear ensembles in the thin-film cavity, pseudo-Rabi splitting due to the strong coupling between the two layers should occur. The latter findings are confirmed by preliminary experimental data.
In an ensemble of identical atoms, cooperative effects like sub- and superradiance may alter the decay rates and the energies of specific transitions may be shifted from the single-atom value by the so-called collective Lamb shift. While such effects in ensembles of two-level systems are by now well understood, realistic multilevel systems are more difficult to handle. In this work we show that in a system of atoms under the action of an external magnetic field, the collective contribution to the level shifts can amount to sizable quantitative and qualitative deviations from the single-atom Zeeman splitting picture. We develop a formalism to describe single-photon superradiance in multilevel systems and identify three-parameter regimes, two of which present measurable deviations in the radiation spectrum compared to the case of single-atom magnetic-field-induced splitting.
This thesis contributes to the field of collective effects in atomic ensembles. We explore synchronization of superradiant lasers in different coupling configurations and study superradiance in off-resonantly probed atomic ensembles, where we take into account the complete level structure of alkali metal atoms. In the first part we introduce the superradiant laser and extend the discussion of synchronization of symmetrically coupled superradiant lasers to unidirectional coupled superradiant lasers. We show that synchronization is also present when we replace the superradi- ant laser couplings with classical channels, meaning the synchronization can be considered a classical effect. In the second part we generalize a widely used approximation method taking into account lower order atom-atom correlations — the cumulant expansion method — to a basis independent formalism. We implement this formalism in a Python program allowing us to numerically calculate the n-atom reduced density matrix and two-time correlation functions for ensembles of multi-level atoms. This method allows us to study the stationary state of an ensemble of off-resonantly probed alkali metal atoms with a ground-state manifold consisting of many hyperfine levels. We show that collective effects in light-matter interaction depends on the tensor-polarizability of atoms and therefore cannot be explained on the basis of two-level-approximations.
The electromagnetic transitions of Mössbauer nuclei provide ideal two-level systems to study the cooperative effects of X-rays with matter. Recently, we have observed the collective Lamb shift (CLS) in nuclear γ-ray superradiance [Röhlsberger, R.; Schlage, K.; Sahoo, B.; Couet, S.; Rüffer, R. Science 2010, 328, 1248–1251]. An ensemble of resonant 57Fe nuclei was embedded in the center of a planar cavity and was collectively excited by synchrotron radiation into a purely superradiant state. The decay of the superradiant state can be almost two orders of magnitude faster than the single-atom nuclear decay and can be accompanied by a CLS of more than 10 times the natural linewidth. Here we review the basic features of cooperative effects that occur in nuclear γ-ray superradiance in comparison with similar effects observed in the optical regime of the electromagnetic spectrum. We show that nuclear resonant scattering of synchrotron radiation opens new ways for systematic studies of cooperative effects in the interaction of X-rays with matter.
The objective of this thesis is to expand our understanding of collective light-scattering phenomena, which manifest themselves in the strong suppression of radiation from the scattering medium. In particular, we are interested in subradiance, a collective effect in spontaneous emission which, as a result of the dissipative coupling of atoms through common electromagnetic modes, creates long-lived excitation modes in an ensemble of cold atoms, with lifetimes much longer than those of individual, isolated atoms. Previously, subradiance had been well-characterized for dilute cold-atom scattering media and the low-intensity limit of the driving laser (linear-optics regime). In this thesis, we study this collective phenomenon beyond the linear-optics and dilute regimes.To study experimentally subradiance beyond the linear-optics regime, we varied the saturation parameter of the excitation laser up to relatively large values and we have observed the increase of the subradiant population with increasing saturation parameter. More importantly, we have identified the super-linear scaling of the subradiant population beyond the linear-optics regime, due to a process similar to optical pumping via multi-excitation superradiant states. This study showed that the increase in the intensity of the driving laser beyond the linear-optics regime can overcome the weak coupling of subradiant modes with the external world.Moreover, we have numerically studied subradiance using the vectorial coupled-dipole model, with a focus on understanding the effect of the near-field dipole-dipole interaction. For that, we extensively compared the vectorial and scalar (which does not contain near-field interaction terms) models and studied the subradiant lifetime as a function of the density and optical thickness of the cold-atom cloud. We observed that the near-field terms are detrimental for subradiance, which was seen in the reduction of the subradiant lifetimes with increasing density. This detrimental character of near-field terms can be interpreted as being due to an effective inhomogeneous broadening induced by the near-field interaction, which reduces the subradiant lifetimes as the density increases.The detrimental character of near-field interaction has also been previously numerically identified for Anderson localization of light waves (Anderson localization is a coherent multiple-scattering wave phenomenon in a strongly scattering medium that results in a cessation of a diffusive wave transport; it also yields long-lived modes): the scalar coupled-dipole model predicts Anderson localization of light waves, but not the vectorial one. However, adding a strong magnetic field allows one to recover localized modes for vectorial light. In this context, we numerically studied a possible signature of Anderson localization of light in cold atoms, based on the measurement of intensity fluctuations of the scattered light. We have shown that at the transition to the localized regime, the fluctuations are enhanced. In particular, for vectorial light, we have demonstrated the absence and recovery of enhanced intensity fluctuations without and with the applied magnetic field, which further corroborates that the intensity fluctuations could serve as an experimental way to probe the localized states.
When an ensemble of quantum emitters interacts with a common radiation field, their emission becomes collective, giving rise to superradiant and subradiant states, characterized by broadened and narrowed linewidths. In this work, we propose to harness subradiant states for quantum metrology; such states naturally arise in subwavelength-spaced atomic arrays in free space and in small ensembles of emitters coupled to one-dimensional waveguides. We demonstrate that their collective optical response yields sharp, narrow features in the transmittance spectrum, which can be used to enhance sensitivity to external perturbations. This improved sensitivity can be applied to atomic clock operation, spatially resolved imaging of emitter positions, and enables precise detection of both global and spatially varying detunings (such as those induced by electromagnetic fields or gravitational gradients).