This thesis investigates the response of coherently coupled spin-mixture Bose-Einstein condensates across a broad range of nonlinear regimes, extending from the deep-Rabi regime to the strongly nonlinear regime. On the theoretical side, collision processes induced and enhanced by strong coherent coupling are analyzed within a perturbative framework. Interaction channels arising from both mean-field and beyond-mean-field processes are identified, providing a microscopic description of the mechanisms through which few-body interactions contribute to the energy of the many-body system. On the experimental side, precise control over the interaction landscape is achieved in a 39-K spin mixture through improved stabilization of the magnetic field near 57 G, the operating point of the system. A feedforward compensation circuit is implemented to suppress magnetic-field noise, and Ramsey spectroscopy measurements demonstrate a twelvefold reduction in field fluctuations, corresponding to a residual root-mean-square noise level of a few tens of μG. This enhanced stability enables controlled measurements of the density-dependent equation of state of the coherently driven two-component condensate. As the density is increased, the system exhibits distinct interaction regimes. At low densities, the equation of state is dominated by repulsive two-body interactions. At intermediate densities, three-body contributions emerge and become increasingly relevant. At higher densities, the interaction energy shows an unusual saturation-like behavior. This behaviour reflects the nontrivial interplay between coherent coupling and interactions.
This thesis investigates the response of coherently coupled spin-mixture Bose-Einstein condensates across a broad range of nonlinear regimes, extending from the deep-Rabi regime to the strongly nonlinear regime. On the theoretical side, collision processes induced and enhanced by strong coherent coupling are analyzed within a perturbative framework. Interaction channels arising from both mean-field and beyond-mean-field processes are identified, providing a microscopic description of the mechanisms through which few-body interactions contribute to the energy of the many-body system. On the experimental side, precise control over the interaction landscape is achieved in a 39-K spin mixture through improved stabilization of the magnetic field near 57 G, the operating point of the system. A feedforward compensation circuit is implemented to suppress magnetic-field noise, and Ramsey spectroscopy measurements demonstrate a twelvefold reduction in field fluctuations, corresponding to a residual root-mean-square noise level of a few tens of μG. This enhanced stability enables controlled measurements of the density-dependent equation of state of the coherently driven two-component condensate. As the density is increased, the system exhibits distinct interaction regimes. At low densities, the equation of state is dominated by repulsive two-body interactions. At intermediate densities, three-body contributions emerge and become increasingly relevant. At higher densities, the interaction energy shows an unusual saturation-like behavior. This behaviour reflects the nontrivial interplay between coherent coupling and interactions.
Rabi-coupled spinor Bose-Einstein condensates, with competing intra-and interspecies interactions, enable independent control of two-and three-body interactions. We show that coupling can also drive the system into a strongly nonlinear regime of saturating interaction. More precisely, the equation of state interpolates between low-and high-density regimes described by two different two-body scattering lengths. Interestingly, the transition can be determined by the strength of the coupling. We experimentally demonstrate this saturation phenomenon by measurements of the interaction energy of a Bose-Einstein condensate as a function of the detuning and of the strength of the Rabi coupling in spin mixtures of potassium 39.
We theoretically calculate and experimentally measure the beyond-mean-field (BMF) equation of state in a coherently coupled two-component Bose-Einstein condensate (BEC) in the regime where averaging of the interspecies and intraspecies coupling constants over the hyperfine composition of the single-particle dressed state predicts the exact cancellation of the two-body interaction. We show that with increasing the Rabi-coupling frequency ?, the BMF energy density crosses over from the nonanalytic Lee-Huang-Yang scaling ?n5/2 to an expansion in integer powers of density, where, in addition to a two-body BMF term ?n2?, there emerges a repulsive three-body contribution ?n3/?. We experimentally evidence these two contributions, thanks to their different scaling with ?, in the expansion of a Rabi-coupled two-component K39 condensate in a waveguide. By studying the expansion with and without Rabi coupling, we reveal an important feature relevant for observing BMF effects and associated phenomena in mixtures with spin-asymmetric losses: Rabi coupling helps preserve the spin composition and thus prevents the system from drifting away from the point of the vanishing mean field.
Contrôle des interactions dans des condensats de Bose-Einstein à couplage cohérent Cette thèse étudie la réponse de condensats de Bose-Einstein de mélanges de spins couplés de manière cohérente à travers une large gamme de régimes non linéaires, s'étendant du régime de Rabi profond au régime fortement non linéaire. Du côté théorique, les processus de collision induits et renforcés par un fort couplage cohérent sont analysés dans le cadre d'une approche perturbative. Les canaux d'interaction issus à la fois de processus de champ moyen et au-delà du champ moyen sont identifiés, fournissant une description microscopique des mécanismes par lesquels les interactions à quelques corps contribuent à l'énergie du système à plusieurs corps.Du côté expérimental, un contrôle précis des interactions est obtenu dans un mélange de spins de 39K grâce à une amélioration de la stabilisation du champ magnétique autour de 57 G, le point de fonctionnement du système. Un circuit de compensation feedforward est mis en œuvre afin de supprimer le bruit du champ magnétique, et des mesures de spectroscopie de Ramsey démontrent une réduction d'un facteur douze des fluctuations du champ, correspondant à un niveau résiduel de bruit quadratique moyen de quelques dizaines de SImicroG. Cette stabilité accrue permet des mesures contrôlées de l'équation d'état dépendante de la densité du condensat à deux composantes entraîné de manière cohérente. Lorsque la densité est augmentée, le système présente des régimes d'interaction distincts. Aux faibles densités, l'équation d'état est dominée par des interactions répulsives à deux corps. Aux densités intermédiaires, des contributions à trois corps émergent et deviennent de plus en plus pertinentes. Aux densités plus élevées, l'énergie d'interaction présente un comportement inhabituel de type saturation. Ce comportement reflète l'interaction complexe entre le couplage cohérent et les interactions.
We theoretically calculate and experimentally measure the beyond-mean-field (BMF) equation of state in a coherently coupled two-component Bose-Einstein condensate (BEC) in the regime where averaging of the interspecies and intraspecies coupling constants over the hyperfine composition of the single-particle dressed state predicts the exact cancellation of the two-body interaction. We show that with increasing the Rabi-coupling frequency Ω, the BMF energy density crosses over from the nonanalytic Lee-Huang-Yang scaling ∝n^{5/2} to an expansion in integer powers of density, where, in addition to a two-body BMF term ∝n^{2}sqrt[Ω], there emerges a repulsive three-body contribution ∝n^{3}/sqrt[Ω]. We experimentally evidence these two contributions, thanks to their different scaling with Ω, in the expansion of a Rabi-coupled two-component ^{39}K condensate in a waveguide. By studying the expansion with and without Rabi coupling, we reveal an important feature relevant for observing BMF effects and associated phenomena in mixtures with spin-asymmetric losses: Rabi coupling helps preserve the spin composition and thus prevents the system from drifting away from the point of the vanishing mean field.
In this Thesis is presented a study on dynamical properties of mixtures of ultraold Bose gases. The behaviour of this system in different regimes is analysed: with and without coherent coupling between the two components, in homogeneous and harmonic shaped trapping potentials and in different dimensions and geometries. Most of the results presented here have been obtained by means of numerical solutions of coupled Gross-Pitaevskii equations and have been compared with theoretical predictions (and sometimes experiments), describing the same phenomena. In particualr the stability of persistent currents in a two-component Bose-Einstein condensate in a toroidal trap is studied in both the miscible and the immiscible regime. In the miscible regime we show that superflow decay is related to linear instabilities of the spin-density Bogoliubov mode. We find a region of partial stability, where the flow is stable in the majority component while it decays in the minority component. We also characterize the dynamical instability appearing for a large relative velocity between the two components. In the immiscible regime the stability criterion is modified and depends on the specific density distribution of the two components. The effect of a coherent coupling between the two components is also discussed. A study on the collective modes of the minority component of a highly unbalanced Bose-Bose mixture is also presented. In the immiscible case we find that the ground state can be a two-domain walls soliton. Although the mode frequencies are continuous at the transition, their behaviour is very different with respect to the miscible case. The dynamical behaviour of the solitonic structure and the frequency dependence on the inter- and intra-species interaction is numerically studied using coupled Gross-Pitaevskii equations. The results of the study on the static and the dynamic response of coherently coupled two component Bose-Einstein condensates due to a spin-dipole perturbation is also sown. The static dipole susceptibility is determined and is shown to be a key quantity to identify the second order ferromagnetic transition occurring at large inter-species interactions. The dynamics, which is obtained by quenching the spin-dipole perturbation, is very much affected by the system being paramagnetic or ferromagnetic and by the correlation between the motional and the internal degrees of freedom. In the paramagnetic phase the gas exhibits well defined out-of-phase dipole oscillations, whose frequency can be related to the susceptibility of the system using a sum rule approach. In particular in the interaction SU (2) symmetric case, when all the two-body interactions are the same, the external dipole oscillation coincides with the internal Rabi flipping frequency. In the ferromagnetic case, where linear response theory is not applicable, the system shows highly non-linear dynamics. In particular we observe phenomena related to ground state selection: the gas, initially trapped in a domain wall configuration, reaches a final state corresponding to the magnetic ground state plus small density ripples. Interestingly, the time during which the gas is unable to escape from its initial configuration is found to be proportional to the square root of the wall surface \ntension.
The remarkable progress in control over cold atomic gases has led to a point where people are no longer satisfied with merely studying these systems, but rather put them to use to understand complex quantum many-body systems. The basis of this development is a deep understanding of the interaction between atoms, and how to exploit those in order to engineer interesting and novel quantum-systems. The aim of this particular thesis is to contribute to this third quantum revolution [1] and hence help to understand the inner workings of complex many-body systems. We present a method to control the shape and character of the interaction between cold atoms based on dressing the atomic ground-state with a Rydberg-state. The latter induces a van der Waals interaction between all the atoms in the ensemble, and allows for control via the coupling light-field. We find that with increasing atom densities the ensemble shows a direct transition into a collective regime that preempts the onset of three-body interactions associated with a break-down of the first Born-approximation. The reason for this intriguing behavior is the strong interaction between Rydberg atoms that gives rise to the blockade-mechanism, and prevents the simultaneous excitation to the Rydberg-state for spatially close atoms. The non-trivial behavior of the interaction-potential within the collective regime yields a novel tool for shaping the interaction between ground-state atoms beyond s-wave scattering. We study this collective regime and the resulting interaction-potential between the atoms within a variational/mean-field approach, and discuss its effects on a trapped Bose-Einstein condensate. Artificial atoms show remarkable properties, that are often superior to real atoms. In particular, since they are built out of many constituents, such systems often exhibit an enhanced coupling to the light-field as well as strong optical non-linearities even for small light-fields. On the other hand, noise in quantum-mechanical systems can not only destroy coherence, but rather can be used in order to robustly drive a system into an interesting state. We study the effect of a controlled dephasing onto an artificial atom in the context of an ensemble of atoms coherently coupled to a Rydberg state and demonstrate that such an enhanced artificial atom allows for the deterministic absorption of a single photon from an arbitrary incoming probe field. Such behavior yields a unique tool in light-matter interaction, and opens the path to realise quantum-networks or to fabricate novel quantum-devices. Here, we discuss the applicability of this single-photon absorber as a single-photon transistor, a high fidelity n-photon counter, and a device that allows for the deterministic creation of non-classical states of light via photon-subtraction. A non-trivial topological order of quantum-states leads to conservation of certain properties and, hence, increases their robustness against external perturbations. This can even stabilize quantum-states against local fluctuations. The latter usually corrupts the coherence within a macroscopic object and thereby prevents quantum-phenomena to occur in our macroscopic world. As an example of such a topological state, we study the behavior of vortex-excitations in a two-dimensional superfluid confined to a periodic potential, as can be realised within a cold atomic gas in an optical lattice. For large superfluid filling factors and strong interactions, the healing-length and, accordingly, the vortex core is much smaller than the lattice spacing. As a result, vortices are confined to the plaquettes of the lattice, and can be described in the framework of an effective tight-binding Hamiltonian. Via a first-principle calculation based on coherent-state path-integrals we derive the microscopic parameters of this model and provide an analytic expression for the vortex mass. Moreover, we show that such a quantum vortex is not obliged to follow the superfluid flow, but rather exhibits Bloch-oscillations perpendicular to it, which is a telltale sign for quantum interference of this macroscopic many-body excitation. Recently, Jonathan Simon et al. [2] performed a major step towards simulating quantum many-body systems in cold atomic gases by simulating the paramagnet-antiferro-magnet transition of a one-dimensional Ising-model. Fundamental excitations in the phase with broken translational symmetry are domain-walls carrying fractional statistics. The question is, whether experimentally accessible single-particle excitations, which correspond to two closely-bound domain-walls, decay into fractional excitations or remain closely-bound. By use of perturbation theory, we derive an analytic model for the time-evolution of these fractional excitations in the framework of a tilted Bose-Hubbard model, and demonstrate the existence of a repulsively bound state above a critical center-of-mass momentum. The validity of the perturbative approach is confirmed by the use of t-DMRG simulations. Together with the recent demonstration of single-site addressing and readout in optical lattices, these findings open the path for experimental observation of fractional excitations within cold atomic gases.