This thesis focuses on theoretical quantum optics, with special emphasis on developing protocols in which engineered vacuum forces enable one to construct hybrid systems. In these systems, atoms are combined with solid-state devices in order to take advantage of their unique properties such as long coherence times of atoms and flexibility, tunability, scalability, and fast response offered by solid-state systems. Special attention is given to the study of atom-surface interactions with Rydberg atoms, where exact Fano-type diagonalization of the interaction Hamiltonian is obtained showing that, not only do Rydberg atoms suffer energy shifts, the presence of a surface leads to an alteration and admixture of the unperturbed eigenstates. Of particular interest are dispersion forces on graphene systems. We investigate whether and under which circumstances the Casimir-Polder potential between an atom and a graphene-substrate system is dominated by the interaction with graphene such that the effect of the substrate does not play an important role. We also explore the possibility to create a setup where dispersion forces could be use to bend a graphene sheet. Placing an atom close, at distances of a few hundred nanometers, to a free-standing graphene membrane we show that temporal changes in the atomic state change the Casimir-Polder interaction, thereby leading to the creation of a backaction force in the graphene sheet. Finally, we look at nonlinear atom--surface coupling processes with the aim of proposing a hybrid quantum circuit device in which individual field-excitations can be transferred between atoms and surface polaritons on demand. Deeper investigations of nonlinear processes reveal the existence of a sum rule for two-photon spontaneous decay rates that can be simply understood as a redistribution of photonic modes across the frequency spectrum where the total integrated number of modes is still conserved.
This thesis focuses on theoretical quantum optics, with special emphasis on developing protocols in which engineered vacuum forces enable one to construct hybrid systems. In these systems, atoms are combined with solid-state devices in order to take advantage of their unique properties such as long coherence times of atoms and flexibility, tunability, scalability, and fast response offered by solid-state systems. Special attention is given to the study of atom-surface interactions with Rydberg atoms, where exact Fano-type diagonalization of the interaction Hamiltonian is obtained showing that, not only do Rydberg atoms suffer energy shifts, the presence of a surface leads to an alteration and admixture of the unperturbed eigenstates. Of particular interest are dispersion forces on graphene systems. We investigate whether and under which circumstances the Casimir-Polder potential between an atom and a graphene-substrate system is dominated by the interaction with graphene such that the effect of the substrate does not play an important role. We also explore the possibility to create a setup where dispersion forces could be use to bend a graphene sheet. Placing an atom close, at distances of a few hundred nanometers, to a free-standing graphene membrane we show that temporal changes in the atomic state change the Casimir-Polder interaction, thereby leading to the creation of a backaction force in the graphene sheet. Finally, we look at nonlinear atom--surface coupling processes with the aim of proposing a hybrid quantum circuit device in which individual field-excitations can be transferred between atoms and surface polaritons on demand. Deeper investigations of nonlinear processes reveal the existence of a sum rule for two-photon spontaneous decay rates that can be simply understood as a redistribution of photonic modes across the frequency spectrum where the total integrated number of modes is still conserved.
Highly excited (Rydberg) atoms have exaggerated properties making them extremely sensitive to external electromagnetic fields and interacting strongly with their environment. Atomic vapor cells represent an attractive platform for studying Rydberg atoms and fabricating quantum devices. For example, Rydberg atoms in vapor cells have been used as sensitive detectors of electric fields of frequencies ranging from DC up to the THz range but also as single photon sources for quantum technology applications exploiting collective phenomena due to the Rydberg blockade effect [1]. Rydberg atoms also find applications in fundamental physics, in particular for the measurement of dispersive interactions of the Casimir-Polder type (atom-surface interactions) [2]. One major advantage of Rydberg atoms is that they expose limitations in the traditional perturbative approach of Casimir-Polder (CP) theory [3, 4]. Indeed, in the extreme near-field, the dipole approximation breaks down and higher-order terms need to be considered. We report on extensive experimental measurements of the Rydberg-surface interaction using spectroscopy in cesium vapor nanocells of a thickness ranging roughly from 200-700nm, as well as selective reflection spectroscopy on a macroscopic cesium all-sapphire cell. Atoms are first excited to the Cs(6P) level with a 894nm pump laser and subsequently a green laser ≈ 510nm probes Rydberg nD or nS states, where the principal quantum number n ranges between 15-17. Our experiments evidence the dipole-dipole term of the Casimir-Polder interaction providing a measurement of the C3 coefficient for cesium Rydberg states. Furthermore, our experiment clearly evidences an additional interaction that induces shifts and broadens the linewidth of the probed transitions in the vicinity of the dielectric windows of our cells. We believe that this interaction is due to electric fields that are either generated by patch charges (trapped on the surface or induced by the excitation lasers), or by cesium adsorbants. We show that the different polarizability (of opposing sign) between S and D Rydberg states can be exploited to extract quantitative measurements of the strength and distance scaling (z-dependence) of such parasitic electrostatic interactions.Our experiments suggest that the sensitivity of Rydberg atoms to external electric fields could provide a unique tool for probing electrostatic interactions in the vicinity of surfaces. This could allow systematic error corrections in Casimir-Polder experiments with excited or even ground state atoms that aim at putting bounds on the existence of non-Newtonian gravity [5]. We are currently exploring the possibility of coating the internal window interfaces with conducting 2D material such as graphene to reduce the influence of parasitic charges. This could allow us to probe atoms closer to the surface, where quadrupole interactions could be experimentally attainable for the first time [4].References[1] H. Kubler, J. P. Shaffer, T. Baluktsian, R. Loew, T. Pfau, Nat. Photon., 4, 112–116 (2013).[2] V. Sandoghdar et al., Phys. Rev. Lett 68, 3432–3435 (1993).[3] J. A. Crosse et al., Phys. Rev. A 82, 3010901 (2010).[4] B. Dutta et al., Phys. Rev. Res. 6, L022035 (2024).[5] A. Laliotis, B-S. Lu, M. Ducloy, D. Wilkowski, AVS Quantum Sci. 3, 043501 (2021).
Dispersion forces have a sizeable effect on the energy levels of highly excited Rydberg atoms when brought close to material surfaces. Rydberg atoms experience energy shifts in the GHz range at micrometer distances, suggestive of considerable state admixture. We show that despite the non-applicability of perturbation theory for Rydberg atoms near a surface, the energy shift due to the dispersion interaction can be obtained from an exact diagonalization of the interaction Hamiltonian by finding the zeros of the Pick function. Moreover, we show that contrary to intuition from single-mode approaches, surface-induced state mixing is generally suppressed even for large interaction energies. We give a tailored example where mixing is observable despite this effect.
Dispersion forces have a sizeable effect on the energy levels of highly excited Rydberg atoms when brought close to material surfaces. Rydberg atoms experience energy shifts in the GHz range at micrometer distances, suggestive of considerable state admixture. We show that despite the non-applicability of perturbation theory for Rydberg atoms near a surface, the energy shift due to the dispersion interaction can be obtained from an exact diagonalization of the interaction Hamiltonian by finding the zeros of the Pick function. Moreover, we show that contrary to intuition from single-mode approaches, surface-induced state mixing is generally suppressed even for large interaction energies. We give a tailored example where mixing is observable despite this effect.
We explore the possibility to create hybrid quantum systems that combine ultracold atoms with graphene membranes. We investigate a setup in which a cold atom cloud is placed close to a free-standing sheet of graphene at distances of a few hundred nanometers. The atoms then couple strongly to the graphene membrane via Casimir-Polder forces. Temporal changes in the atomic state of the atomic cloud changes the Casimir-Polder interaction, thereby leading to the creation of a back-action force in the graphene sheet. This setup provides a controllable way to engineer ripples in a graphene sheet with cold atoms.
This thesis is a theoretical study of the behavior of electrons in atoms and molecules subjected to external electromagnetic fields. Three electronic systems have been central in this work, the atomic and quasimolecular Rydberg states and the carbon allotrope graphene. The exaggerated properties of the highly excited Rydberg atoms, such as long lifetime, large spatial extension and low binding energy make them excellent candidates for both theoretical and experimental considerations. The analytical solutions of the hydrogen atom in quantum mechanics provide a good description for most Rydberg atoms. This is exploited in the work presented in this thesis and the accompanying papers, where we show results of numerical computations on interacting Rydberg atoms, with and without the presence of radiating fields, as well as dynamic Rydberg wave packets influenced by a train of femtosecond laser pulses. In the final part of the thesis the optical process of high-order harmonic generation in an extended molecular structure, represented by graphene, is considered. Rydberg atoms have a large dipole moment due to the large average electronic radius in the atom, which leads to a very strong dipole-dipole coupling between interacting particles in a gas of cold Rydberg atoms. This interaction, which is dependent on the internuclear separation between the atoms, induces a shift in the energy levels, which again prohibits the excitation of more than one atom in the gas, an effect commonly known as the Rydberg blockade. A correlated behavior is observed for the intrashell transitions in mutually excited Rydberg atoms. The microwave field driven dynamics is significantly supressed for internuclear distances below a given conditional radius which scales linearly with the principal quantum number n. Such an entangled electronic behavior may open for the realization of quantum gates applied in quantum informatics. The long-range interaction of Rydberg atoms is dominated by the dipole-dipole terms. Nevertheless, the investigation of two interacting Rydberg atoms, without the influence of electromagnetic radiation, has shown that the lower order multipolar terms play a vital role in the energy shifts as well as for the electronic probability distributions. We found that the energy curves, when including all multipole orders, correspond to both repulsive and attractive states with a stronger repulsion than attraction. We also propose a laser assisted approach for stabilization of Rydberg gases by controlled transitions between such attractive and repulsive energy states. Single-electron ionization of a dynamic Rydberg wave packet confined within a single energy level has been investigated. The ionization probability of an intrashell Rydberg wave packet depends strongly on the degree of polarization. For a wave packet driven repeatedly between the circular (least polarized) state and the linear (most polarized) state by a rotating microwave field and subjected to a train of femtosecond laser pulses, the ionization probability will depend crucially on the laser repetition rate and number of pulses. The angular-resolved ionization probability and energy distribution in the continuum are also influenced by these parameters. The last part of the thesis is devoted to the study of high-order harmonic generation (HHG) in graphene. In the simple man’s model HHG can be described by an electron that is ionized and driven in an external field, after which it returns to the parent atom and recombines, emitting a high-energy photon with frequency that is a multiple of the incident laser frequency. We show that the harmonic spectra obtained from the interaction with linearly as well as circularly polarized femtosecond lasers yield harmonics up the classical limit for extended molecules. In contrast to diatomic molecules, the stable grid structure of graphene ensures that the harmonic generation cutoff remains constant with increasing signal power as the graphene diameter extends beyond the classical limit. Additionally, for circularly polarized lasers harmonics exceeding the classical predictions have been observed.
Optically controlled dipole-dipole interaction at submicrometers and subwavelength scales leads to many interesting phenomenon and remarkable potential applications in quantum optics, condensed matter physics, and today’s micro-devices. In this dissertation, we study the applications of quantum optical coherence to nano-optics in the following systems and aspects. On the one hand, chiral metamaterials has been previously reported as excellent candidates to realize both attractive and repulsive Casimir forces, where the existence of a repulsive Casimir force depends upon the strength of the chirality. On the other hand, nanoscale integration of metal nanoparticles and semiconductors is particularly interesting because the strengths of both materials are combined in such a hybrid system. In the first part of this work, we proposed a technical scheme to coherently control of the Casimir interaction energy with two identical chirality mediums. We took explicit caution regarding the requirements of passivity and causal response of the materials, since these requirements are essential for the application of the Lifshitz formula. The rare-earth metals’ atomic species, for instance, dysprosium, is proposed as an applicable medium for the forthcoming studies of possible experimental implementation of our technique. Secondly, we fully investigated the coherent control of the quantum optical properties of spontaneous emission spectra of a semiconductor quantum dot coupled to a metallic nanoparticle. The properties of the spontaneous emission spectra of such a system are studied in detail with and without involving the coherent field. The Rabi splitting effect in the spectrum emitted by the quantum dot under particular conditions is predicted for different sizes of the metal nanoparticles. We show that the spontaneous emission spectra of the transition coupled to surface plasmons may be further modified by adjusting the external coherent control on the adjacent transitions. In the third part, we propose a robust protocol to study the entanglement generation in a hybrid structure consisting of two quantum dots in the proximity of a metallic nanoshell. The entanglement arises impulsively due to common coupling to the plasmonic nanostructure, without demanding postselective measurement or mediating the dissipative environment. The long-lived entangled states can be created deterministically by optimizing the shell thickness as well as the ratio of the distances between the quantum dots and the surface of the shell. The loss of the system is greatly reduced even when the quantum dots are ultraclose to the shell, which signifies a slow decay rate of the coherence information and longtime entanglement preservation.