We present experimental results on the preparation of a desired quantum state in a two-level system with the maximum possible fidelity using driving protocols ranging from generalizations of the linear Landau-Zener protocol to transitionless driving
protocols that ensure perfect following of the instantaneous adiabatic ground state. We also study the minimum time needed to achieve a target fidelity and explore and compare the robustness of some of the protocols against parameter variations simulating a possible experimental uncertainty. In our experiments, we realize a two-level model system using Bose-Einstein condensates inside optical lattices, but the results of our investigation should hold for any quantum system that can be approximated by a two-level system.
We experimentally realize Rydberg excitations in Bose-Einstein condensates of rubidium atoms loaded into quasi one-dimensional traps and in optical lattices. Our results for condensates expanded to different sizes in the one-dimensional trap agree we
ll with the intuitive picture of a chain of Rydberg excitations. We also find that the Rydberg excitations in the optical lattice do not destroy the phase coherence of the condensate, and our results in that system agree with the picture of localized collective Rydberg excitations including nearest-neighbour blockade.
We demonstrate laser frequency stabilization to excited state transitions using cascade electromagnetically induced transparency (EIT). Using a room temperature Rb vapor cell as a reference, we stabilize a first diode laser to the D2 transition and a
second laser to a transition from the intermediate state to a Rydberg state with principal quantum number n=19 - 70. A combined laser linewidth of 280 kHz over a 0.1 ms time period is achieved. This method may be applied generally to any cascade system and allows laser stabilization to an atomic reference in the absence of strong optical transitions.
We study the effect of a control beam on a Lambda electromagnetically induced transparency (EIT) system in 87Rb. The control beam couples one ground state to another excited state forming a four level N-system. Phase coherent beams to drive the N-sys
tem are produced using a double injection scheme. We show that the control beam can be used to Stark shift or split the EIT resonance. Finally, we show that the when the control beam is on-resonance one observes a Doppler-free and sub-natural absorptive resonance with a width of order 100 kHz. Crucially, this narrow absorptive resonance only occurs when atoms with a range of velocities are present, as is the case in a room temperature vapour.
The electro-optic effect, where the refractive index of a medium is modified by an electric field, is of central importance in non-linear optics, laser technology, quantum optics and optical communications. In general, electro-optic coefficients are
very weak and a medium with a giant electro-optic coefficient would have profound implications for non-linear optics, especially at the single photon level, enabling single photon entanglement and switching. Here we propose and demonstrate a giant electro-optic effect based on polarizable dark states. We demonstrate phase modulation of the light field in the dark state medium and measure an electro-optic coefficient that is more than 12 orders of magnitude larger than in other gases. This enormous Kerr non-linearity also creates the potential for precision electrometry and photon entanglement.
We demonstrate a multiphoton Rydberg dark resonance where a Lambda-system is coupled to a Rydberg state. This N-type level scheme combines the ability to slow and store light pulses associated with long lived ground state superpositions, with the str
ongly interacting character of Rydberg states. For the nd_{5/2} Rydberg state in 87Rb (with n=26 or 44) and a beam size of 1 mm we observe a resonance linewidth of less than 100 kHz in a room temperature atomic ensemble limited by transit-time broadening. The resonance is switchable with an electric field of order 1 V/cm. We show that, even when photons with different wavevectors are involved, the resonance can be Doppler-free. Applications in electro-optic switching and photonic phase gates are discussed.
