Accurately controlling a quantum system is a fundamental requirement in quantum information processing and the coherent manipulation of molecular systems. The ultimate goal in quantum control is to prepare a desired state with the highest fidelity allowed by the available resources and the experimental constraints. Here we experimentally implement two optimal high-fidelity control protocols using a two-level quantum system comprising Bose-Einstein condensates in optical lattices. The first is a short-cut protocol that reaches the maximum quantum-transformation speed compatible with the Heisenberg uncertainty principle. In the opposite limit, we realize the recently proposed transitionless superadiabatic protocols in which the system follows the instantaneous adiabatic ground state nearly perfectly. We demonstrate that superadiabatic protocols are extremely robust against control parameter variations, making them useful for practical applications

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.PACS numbers: 32.80.Rm, 42.50.Gy In 1875 Kerr showed that the refractive index (n r ) of a medium can be changed by applying an electric field [1] according to ∆n r = λ 0 B 0 E 2 0 , where λ 0 is the wavelength of the light field, E 0 is the applied electric field and B 0 is the electro-optic Kerr coefficient. Subsequently, the Kerr effect, or quadratic electro-optic effect, and the related linear electro-optic effect have become widely used in photonic devices such as electro-optic modulators (EOMs) [2,3]. The ac Kerr effect where the electric field is produced by another light beam is the basis of Kerr lens mode-locking [4], and has led to the development of femto and attosecond pulses [5]. Outside these successes, the wider applicability of the Kerr effect is limited by the fact that, in general, the Kerr non-linearity is very small. A larger non-linearity occurs close to a resonance, but at the expense of higher absorption of the signal light. A way around this problem is to use electromagnetically induced transparency (EIT) [6,7,8] where an additional light field, the coupling beam, renders a medium transparent on resonance. Enhanced ac Kerr non-linearities were predicted [9], and have been studied in experiments on Bose Einstein condensates [10] and cold atoms [11]. However, such an EIT medium produces insufficient non-linearity to implement single photon non-linear optics [8]. In addition, the potential to implement all-optical quantum computation using the ac Kerr effect [12] is limited by pulse distortion effects [13], so a new Kerr mechanism based on interactions [14] is desirable.In this paper, we demonstrate a giant dc electro-optic effect in an EIT medium by coupling to a highly excited Rydberg state which has a large polarizability. This renders the transmission through the medium highly sensitive to electric fields produced either externally or internally due to interparticle interactions. The Rydberg states have a polarizability that scales as the principal quantum number, n 7 , and the interactions between Rydberg atoms scale with an even higher power (n 11 for van der Waals interactions) [15]. These strong interac-tions lead to strongly correlated quantum st...

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 well 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-neighbor blockade.

The dipole blockade of Rydberg excitations is a hallmark of the strong interactions between atoms in these high-lying quantum states [1,2]. One of the consequences of the dipole blockade is the suppression of fluctuations in the counting statistics of Rydberg excitations, of which some evidence has been found in previous experiments. Here we present experimental results on the dynamics and the counting statistics of Rydberg excitations of ultra-cold Rubidium atoms both on and off resonance, which exhibit sub-and super-Poissonian counting statistics, respectively. We compare our results with numerical simulations using a novel theoretical model based on Dicke states of Rydberg atoms including dipole-dipole interactions, finding good agreement between experiment and theory.PACS numbers: 32.80. Ee,42.50.Ct,03.67.Lx Atoms excited to high-lying quantum states, so-called Rydberg atoms, are highly polarizable and, therefore, can interact strongly with each other at large distances [1,2]. The study of ultracold gases has opened up new avenues of the investigation of strong atomic interactions. A wealth of potential applications is associated with the manipulation of ultracold atoms excited to Rydberg states interacting through strong van der Waals (vdW) or long-range dipolar interactions, ranging from studies of strongly correlated quantum systems to quantum information [3]. A key signature of interactions between Rydberg atoms is the suppression of fluctuations in the number of excitations due to the dipole blockade. While evidence of the dipole blockade has been observed in several experiments [4][5][6][7], prior studies were unable to demonstrate sub-Poissonian behaviour with a statistically significant confidence level. Also, those studies were carried out for resonant excitation only, leaving open the question of how Rydberg excitations in the strongly interacting regime evolve for finite detuning from resonance.The dipole blockade is a hallmark of the strong interactions between Rydberg atoms in an ultra-cold atomic gas. When an ensemble of atoms is irradiated by laser light resonant with a Rydberg excitation (either using a single laser or a multi-step excitation scheme), due to the interaction between Rydberg atoms, the excitation of a particular atom can be suppressed by a neighbouring one that is already in a Rydberg state. The radius of influence of an atom in this sense is called the blockade radius, which depends on the interaction strength and the linedwidth of the Rydberg excitation. As a result of the dipole blockade the excitation dynamics of the atoms are strongly correlated, leading to a cut-off in the excitation when all the available blockade volumes in the sample have been exhausted [30]. Another way of describing the phenomenon is to view the atoms within a blockade volume as a 'superatom', meaning that rather than individual atoms, collective states of several atoms are excited [15]. In the regime where the size of the sample is larger than the blockade radius, quantum correlations are expecte...

We study electromagnetically induced transparency (EIT) of a weakly interacting cold Rydberg gas. We show that the onset of interactions is manifest as a depopulation of the Rydberg state and numerically model this effect by adding a density-dependent non-linear term to the optical Bloch equations. In the limit of a weak probe where the depopulation effect is negligible, we observe no evidence of interaction induced decoherence and obtain a narrow Rydberg dark resonance with a linewidth of <600 kHz, limited by the Rabi frequency of the coupling beam.PACS numbers: 03.67. Lx, 32.80.Rm, 42.50.Gy Ensembles of Rydberg atoms display fascinating manybody behavior due to their strong interactions [1]. These interactions lead to interesting cooperative effects such as superradiance [2,3,4] and dipole blockade [5,6,7,8], which may provide the basis for applications such as single-photon sources [9] and quantum gates [10,11,12]. For quantum information applications one is interested in the coherent evolution of the ensemble. Coherent excitation of Rydberg states has been achieved using adiabatic passage [13,14]. Rabi oscillations between ground and Rydberg states with dipole-dipole interactions have been observed [15,16]. Also, the coherence of a Rydberg ensemble has been measured directly using a spin echo technique [17]. In most experiments on ultracold Rydberg gases, the Rydberg atoms are detected indirectly following field ionization and subsequent detection of electrons (or ions) using a micro channel plate (MCP). However, recently we demonstrated non-destructive optical detection of Rydberg states in room temperature Rb vapor [18,19] using EIT [20,21]. The same technique was subsequently used to detect Rydberg states in a Sr atomic beam [22]. Rydberg EIT has number of potential applications, for example, a Rydberg EIT medium displays a dc electro-optic effect many orders of magnitude larger than other systems [23], and Rydberg EIT enables direct measurement of the coherence of the Rydberg ensemble.In this work we demonstrate EIT involving Rydberg states in an ultra-cold atomic sample. We show that interactions between Rydberg atoms lead to a rapid depopulation of the Rydberg state, and that the EIT spectra are extremely sensitive to small changes in the interaction strength. For example, changing the principal quantum number of the Rydberg state from n to n + 1 produces a significant change in the EIT spectrum. By using a weak probe, where the probability of populating the Rydberg state is low, we can eliminate this depopulation effect and obtain narrow Rydberg dark resonances with a linewidth of < 600 kHz, limited by the Rabi frequency of the coupling beam.The experimental setup and simplified level scheme are shown in figure 1 (a) and (b) respectively. A probe and coupling beam are combined using dichroic mirrors and counter-propagate through a cloud of laser-cooled 85 Rb atoms. The polarization of the beams are chosen to max- imize transition strengths (σ + -σ + ). The probe beam is derived from a diode laser a...