Blockade interactions whereby a single particle prevents the flow or excitation of other particles provide a mechanism for control of quantum states, including entanglement of two or more particles. Blockade has been observed for electrons 1-3 , photons 4 and cold atoms 5 . Furthermore, dipolar interactions between highly excited atoms have been proposed as a mechanism for 'Rydberg blockade' 6,7 , which might provide a novel approach to a number of quantum protocols [8][9][10][11] . Dipolar interactions between Rydberg atoms were observed several decades ago 12 and have been studied recently in a many-body regime using cold atoms [13][14][15][16][17][18] . However, to harness Rydberg blockade for controlled quantum dynamics, it is necessary to achieve strong interactions between single pairs of atoms. Here, we demonstrate that a single Rydberg-excited rubidium atom blocks excitation of a second atom located more than 10 µm away. The observed probability of double excitation is less than 20%, consistent with a theoretical model of the Rydberg interaction augmented by Monte Carlo simulations that account for experimental imperfections.The mechanism of Rydberg blockade is shown in Fig. 1a. Two atoms, one labelled 'control' and the other 'target', are placed in proximity with each other. The ground state |1 and Rydberg state |r of each atom form a two-level system that is coupled by laser beams with Rabi frequency Ω . Application of a 2π pulse (Ωt = 2π with t being the pulse duration) on the target atom results in excitation and de-excitation of the target atom giving a phase shift of π on the quantum state, |1 t → −|1 t . If the control atom is excited to the Rydberg state before application of the 2π pulse, the dipole-dipole interaction |r c ↔ |r t shifts the Rydberg level by an amount B that detunes the excitation of the target atom so that it is blocked and |1 t → |1 t . Thus, the excitation dynamics and phase of the target atom depend on the state of the control atom. Combining this Rydberg-blockade-mediated controlled-phase operation 6 with π/2 single-atom rotations between states |0 t and |1 t of the target will implement the CNOT gate between two atoms. We have previously demonstrated the ability to carry out ground-state rotations at individual trapping sites 19 , as well as coherent excitation from ground to Rydberg states at a single site 20 . Here, we describe experiments that demonstrate the Rydberg blockade effect between two neutral atoms separated by more than 10 µm, which is an enabling step towards creation of entangled atomic states. Previous demonstrations of neutral-atom entanglement have relied on shortrange collisions at length scales characterized by a low-energy scattering length of about 10 nm (refs 21,22). Our results, using laser-cooled and optically trapped 87 Rb, extend the distance for strong two-atom interactions by three orders of magnitude, and place us in a regime where the interaction distance is large compared with 1 µm, which is the characteristic wavelength of light needed for...

We present the first demonstration of a CNOT gate between two individually addressed neutral atoms. Our implementation of the CNOT uses Rydberg blockade interactions between neutral atoms held in optical traps separated by >8 microm. Using two different gate protocols we measure CNOT fidelities of F=0.73 and 0.72 based on truth table probabilities. The gate was used to generate Bell states with fidelity F=0.48+/-0.06. After correcting for atom loss we obtain an a posteriori entanglement fidelity of F=0.58.

We demonstrate Rabi flopping of small numbers of 87 Rb atoms between ground and Rydberg states with n ≤ 43. Coherent population oscillations are observed for single atom flopping, while the presence of two or more atoms decoheres the oscillations. We show that these observations are consistent with van der Waals interactions of Rydberg atoms. 32.80.Rm, Atoms in highly excited Rydberg states with principal quantum number n >> 1 have very large dipole moments which scale as d ∼ qa 0 n 2 , with q the electron charge and a 0 the Bohr radius. Two such Rydberg atoms can be strongly coupled via a dipole-dipole interaction. It was recognized in recent years that the large interaction strength can potentially be used for fast quantum gates between qubits stored in stable ground states of neutral atoms [1]. When several atoms are sufficiently close together the presence of a single excited atom can cause a shift in the energy of all other atoms which is large enough to prevent resonant excitation of more than one atom in a sample. This "dipole blockade" mechanism has the potential for creating strongly coupled ensembles containing moderate numbers of atoms. Such ensembles can be used for gates [2], as well as several other quantum information tasks including state preparation[3], fast measurement protocols [4], and collective encoding of multiqubit registers [5].A number of recent experiments have revealed signatures of "dipole blockade" by showing that the probability of multiple excitation of Rydberg atoms is suppressed at high n [6]. However, none of the experiments to date have demonstrated blockade at the level of a single atomic excitation which is crucial for applications to quantum information processing. In order to be useful for quantum gates it is also necessary to be able to coherently excite and de-excite a Rydberg state so that the atom is available for further processing. In this letter we demonstrate important steps towards the goal of a fast neutral atom Rydberg gate. We start by preparing single atom states in micron sized optical traps and observe coherent Rabi oscillations between ground and Rydberg states with n ≤ 43 at rates as high as Ω R /2π = 0.5 MHz. We then show that the presence of two or more atoms in the trap causes dephasing of the Rabi oscillations. Comparison with theoretical calculations of the strength of the Rydberg van der Waals interactions [7], confirms that our observations are consistent with the presence of Rydberg interactions.The experiment starts by loading a far-off-resonance optical trap (FORT) from a 87 Rb vapor cell magneto- optical trap (MOT) as described in our recent letter [8].For the experiments reported here, between 1 and 10 atoms are loaded into a 10 mK deep FORT (570 mW of 1030 nm light focused to a 1/e 2 intensity radius waist of w = 2.7 µm). The radial and axial oscillation frequencies are 130 and 12 kHz. The average number of atoms is controlled by varying the amount of time for which the MOT and FORT lasers are simultaneously on from 25 -400 ms. Atom temperatu...

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 ...

A simplified method for calculations of the current in a tunnelling junction with its orientation and spatial distribution is described. The current at test points on either electrode is calculated for the shortest distance with expressions for point-to-point tunnelling by Simmons (1963) and then summed. The calculated distribution of the current in a spherical-tip/planar-sample model of a scanning tunnelling microscope (STM) agrees with that from finite-element simulations. This method may be applied to models having arbitrary shapes, and results are presented for a paraboloidal-tip/corrugated-sample STM model as the first approximation to the atomic structure.