We demonstrate Rabi flopping at MHz rates between ground hyperfine states of neutral 87 Rb atoms that are trapped in two micron sized optical traps. Using tightly focused laser beams we demonstrate high fidelity, site specific Rabi rotations with crosstalk on neighboring sites separated by 8 µm at the level of 10 −3 . Ramsey spectroscopy is used to measure a dephasing time of 870 µs which is ≈ 5000 times longer than the time for a π/2 pulse.PACS numbers: 03.67. Lx, 32.80.Pj, 39.25.+k Over the last decade quantum computing has attracted much attention due to the possibility of solving certain problems much faster than a classical computer [1]. A number of different approaches are currently being pursued to build a scalable quantum computer and significant progress has been made with trapped ions [2], nuclear magnetic resonance [3], single photons [4], and solid state josephson junctions [5]. Neutral atoms trapped by optical fields are also being studied intensively as a viable approach to demonstrating quantum logic. Neutral atom approaches are attractive for a number of reasons starting with the availability of well developed techniques for laser cooling and trapping [6,7] and the potential for scalability [8]. The qubit basis states can be represented by ground state hyperfine levels which have long decoherence times and are therefore suitable for storing quantum information. The qubits can be rapidly initialized and manipulated with near resonant optical fields through optical pumping and stimulated Raman processes. A number of protocols for two-qubit gates have been proposed [9] including ground state collisions, optically induced short range dipole-dipole interactions, and dipoledipole interactions between highly excited Rydberg levels [10,11,12]. The Rydberg atom approach appears particularly attractive since it has the potential for achieving fast, MHz rate gates whose fidelity is only weakly dependent on the motional state of the atoms [13].We report here on progress towards demonstrating quantum logic operations using neutral atom qubits in optical traps. Recent achievements in neutral atom quantum computing include the implementation of a five qubit quantum register by Meschede and colleagues [14,15] and subpoissonian loading of single atoms to nearby dipole traps by the Grangier group [16,17]. Advancing on these pioneering works, we demonstrate loading and ground state manipulation of neutral 87 Rb atoms in two closely spaced microscopic optical traps. By optically addressing each of these traps, we demonstrate twophoton Rabi flopping between ground hyperfine states |0 ≡ |F = 1, m F = 0 and |1 ≡ |F = 2, m F = 0 at a rate of 1.36 MHz. This rate corresponds to a time period of 183 ns to perform a π/2 Rabi rotation. The Rabi rotations are performed with negligible cross talk between the two traps: a π rotation on one site causes less than 1.4 × 10 −3 π rotation on the other site. Using Ramsey spectroscopy, we measure a dephasing time of 870 µs. To our knowledge, our results demonstrate the best figure ...

We suggest a type of scanning fluorescence microscope that is capable of resolving nanometer-size objects in the far field. The key idea is to use the spatial sensitivity of the dark state of electromagnetically induced transparency and localize an atomic excitation to a spot much smaller than the wavelength of light.It is well known that, by using the nonlinear interaction between atoms and laser beams, one can localize atoms to a spot much smaller than the wavelength of light. In their pioneering work, Thomas and colleagues have suggested and experimentally demonstrated subwavelength position localization of atoms using spatially varying energy shifts ͓1-3͔. If a very small object is embedded into an atomic medium, subwavelength atom localization can be used to obtain a shadow image of the object ͓2͔. Recently, there has been a growing interest in various techniques of manipulation of atoms at the subwavelength scale. Zubairy and colleagues have discussed atom localization using resonance fluorescence and phase and amplitude control of the absorption spectrum ͓4-6͔. Knight and colleagues discussed localization via quantum interference at the probability amplitude of the excited state ͓7͔. There is also substantial literature on subwavelength localization of atoms utilizing excitation in a standing wave ͓8,9͔. Although these are very exciting developments, a practical optical microscope utilizing nanoscale localization of atoms has not yet been demonstrated. If constructed, such a microscope may provide a unique way to image small objects, including large biological molecules at the nanometer scale. Although significant advances have been made in recent years, such as the invention of stimulated emission depletion microscopy ͓10͔, it is still a big challenge to map and understand the structure of single molecules.In this Rapid Communication, we suggest a type of microscope that is based on tight localization of atoms. The key idea of our scheme is to localize atomic excitation to a spot much smaller than the diffraction limit, using the dark state of electromagnetically induced transparency. Our scheme is the extension of the suggestion of Agarwal and colleagues to tightly focused beams and utilizes adiabatic evolution instead of optical pumping ͓9͔. As will be detailed below, a key advantage of our scheme is its insensitivity to fluctuations in experimental parameters. This is due to the robust nature of the adiabatic preparation of the dark state. Noting Fig. 1, we consider a nanometer-scale object embedded in an ultracold atomic medium with four atomic states. As an example, the atomic medium can be submillikelvin temperature alkalimetal atoms trapped in a magneto-optical trap ͑MOT͒ or in a far-off-resonant dipole trap. The idea of placing nanoscale objects inside an ultracold atomic cloud was motivated by recent experiments of Hakuta and colleagues where optical properties of a nanofiber inside a MOT were studied ͓11͔. Two laser beams couple the two hyperfine states of the atom ͑states ͉1͘ and ͉2͒͘ to an exc...

We present a proof-of-principle experiment in which the population of an atomic level is spatially localized using the technique of electromagnetically-induced transparency (EIT). The key idea is to utilize the sensitive dependence of the dark state of EIT on the intensity of the coupling laser beam. By using a sinusoidal intensity variation (standing-wave), we demonstrate that the population of a specific hyperfine level can be localized much tighter than the spatial period.It is well-known that traditional optical techniques cannot resolve or write features smaller than half the wavelength of light. This barrier, known as the diffraction limit, has important implications for a variety of scientific research areas including biological microscopy and quantum computation. As an example, in a neutralatom quantum computing architecture, the diffraction limit prohibits high-fidelity manipulation of individual atoms if they are separated by less than the wavelength of light. Recently, Agarwal and others [1][2][3] have proposed to use the dark state of electromagnetically induced transparency (EIT) [4,5] to address atoms at potentially nanometer spatial scales. This technique relies on the sensitive dependence of the dark state to the intensities of the driving probe and coupling laser beams. If a standing-wave coupling laser is used, the population of the excited Raman level can be very tightly localized near the intensity nodes, allowing for sub-wavelength control. In this letter, we present a proof-of-principle experiment that demonstrates the key ideas of this approach. By using ultracold Rubidium (Rb) atoms in a magneto-optical trap (MOT) and pulsed coherent transfer, we demonstrate atomic localization to spots much smaller than the spatial period of the coupling-laser intensity profile. Although due to imaging limitations we have used a large spatial period in this work (≈ 600 µm), our results will likely scale to the sub-wavelength regime in the future.Before proceeding, we cite important prior work leading up to this experiment. In their pioneering work, Thomas and colleagues have suggested and experimentally demonstrated sub-wavelength position localization of atoms using spatially varying energy shifts [6][7][8]. Zubairy and coworkers have discussed atom localization using resonance fluorescence and phase and amplitude control of the absorption spectrum [9][10][11]. Knight and colleagues discussed localization via quantum interference at the probability amplitude of the excited electronic state [12]. Li et. al. have experimentally demonstrated probe narrowing beyond the diffraction limit using a spatially-varying coupling laser profile in a vapor cell [13]. There has also been remarkable progress in utilizing the position dependent stimulated emission to achieve nanoscale resolution [14,15]. This last approach, also known as stimulated-emission depletion microscopy, is now a widely used technique in biological imaging. We note that our approach of using the dark state for atomic localization has the followin...

We report a proof-of-principle experiment where the refractive index of an atomic vapor is enhanced while maintaining vanishing absorption of the beam. The key idea is to drive alkali atoms in a vapor with appropriate control lasers and induce a gain resonance and an absorption resonance for a probe beam in a two-photon Raman configuration. The strength and the position of these two resonances can be manipulated by changing the parameters of the control lasers. By using the interference between these two resonances, we obtain an enhanced refractive index without an increase in the absorption.

We suggest a scheme where a laser beam forms an optical trap with a spatial size that is much smaller than the wavelength of light. The key idea is to combine a far-off-resonant dipole trap with a scheme that localizes an atomic excitation.