We study the effect of resonances associated with complex molecular interaction of Rydberg atoms on Rydberg blockade. We show that densely-spaced molecular potentials between doubly-excited atomic pairs become unavoidably resonant with the optical excitation at short interatomic separations. Such molecular resonances limit the coherent control of individual excitations in Rydberg blockade. As an illustration, we compute the molecular interaction potentials of Rb atoms near the $100s$ states asymptote to characterize such detrimental molecular resonances, determine the resonant loss rate to molecules and inhomogeneous light shifts. Techniques to avoid the undesired effect of molecular resonances are discussed.
Accurate quantum gates are basic elements for building quantum computers. There has been great interest in designing quantum logic gates by using blockade effect of Rydberg atoms recently. The fidelity and operation speed of these gates, however, are fundamentally limited by an intrinsic blockade error. Here we propose a type of quantum gates, which are based on Rydberg blockade effect, yet free from any blockade error. In contrast to the "blocking" method in previous schemes, we use Rydberg energy shift to realize a rational generalized Rabi frequency so that a $π$ phase for one input state o…
We present the experimental demonstration of Rydberg blockade in thermal atomic vapor where the atoms are not necessarily be frozen. We show that not all the interacting atoms but only the atoms with same velocity collectively participate in the blockade process. Using this observation, we formulated a suitable model based on super atom picture to study blockade interaction in thermal vapor. We performed an experiment to measure Rydberg population in rubidium thermal vapor using optical heterodyne detection technique and density dependent suppression of Rydberg population is observed in suitab…
We explore a single-photon approach to Rydberg state excitation and Rydberg blockade. Using detailed theoretical models, we show the feasibility of direct excitation, predict the effect of background electric fields, and calculate the required interatomic distance to observe Rydberg blockade. We then measure and control the electric field environment to enable coherent control of Rydberg states. With this coherent control, we demonstrate Rydberg blockade of two atoms separated by 6.6(3) μm. When compared with the more common two-photon excitation method, this single-photon approach is advantag…
We demonstrate the phenomenon of blockade in two-photon excitations to the Rydberg state in thermal vapor. A technique based on optical heterodyne is used to measure the dispersion of a probe beam far off resonant to the D2 line of rubidium in the presence of a strong laser beam that couples to the Rydberg state via two-photon resonance. Density dependent suppression of the dispersion peak is observed while coupling to the Rydberg state with principal quantum number, n = 60. The experimental observation is explained using the phenomenon of Rydberg blockade. The blockade radius is measured to b…
We study the spatial performance of the entangling gate proposed by H. Levine et al. (Phys. Rev. Lett. 123, 170503 (2019)). This gate is based on a Rydberg blockade technique and consists of just two global laser pulses which drive nearby atoms. We analyze the multilevel Zeeman structure of interacting $^{87}$Rb Rydberg atoms and model two experimentally available excitation schemes using specific driving beams geometry and polarization. In particular, we estimate the blockade shift dependence on inter-atomic distance and angle with respect to the quantization axis. In addition, we show that u…
We show that the use of shaped pulses improves the fidelity of a Rydberg blockade two-qubit entangling gate by several orders of magnitude compared to previous protocols based on square pulses or optimal control pulses. Using analytical Derivative Removal by Adiabatic Gate (DRAG) pulses that reduce excitation of primary leakage states and an analytical method of finding the optimal Rydberg blockade we generate Bell states with a fidelity of $F>0.9999$ in a 300 K environment for a gate time of only $50\;{\rm ns}$, which is an order of magnitude faster than previous protocols. These results esta…
By coupling a probe transition to a Rydberg state using electro-magnetically induced transparency (EIT) we map the strong dipole-dipole interactions onto an optical field. We characterize the resulting cooperative optical non-linearity as a function of probe strength and density. We show that the effect of dipole blockade cannot be described using a mean-field but requires an $N$-atom cooperative model. Good quantitative agreement is obtained for three atoms per blockade with the $n=60$ Rydberg state. We place an upper-limit on the dephasing rate of the blockade spheres of $<110$ kHz.
We review here the studies performed about interactions in an assembly of cold Rydberg atoms. We focus more specially the review on the dipole-dipole interactions and on the effect of the dipole blockade in the laser Rydberg excitation, which offers attractive possibilities for quantum engineering. We present first the various interactions between Rydberg atoms. The laser Rydberg excitation of such an assembly is then described with the introduction of the dipole blockade phenomenon. We report recent experiments performed in this subject by starting with the case of a pair of atoms allowing th…
We show that Jaynes-Cummings dynamics can be observed in mesoscopic atomic ensembles interacting with a classical electromagnetic field in the regime of Rydberg blockade, where the time dynamics of the average number of Rydberg excitations in mesoscopic ensembles displays collapses and revivals typical of this model. As the frequency of Rabi oscillations between collective states of Rydberg blockaded ensembles depends on the number of interacting atoms, for randomly loaded optical dipole traps we predict collapses and revivals of Rabi oscillations. We have studied the effects of finite interac…
We propose an efficient method to filter out single atoms from trapped ensembles with unknown number of atoms. The method employs stimulated adiabatic passage to reversibly transfer a single atom to the Rydberg state which blocks subsequent Rydberg excitation of all the other atoms within the ensemble. This triggers the excitation of Rydberg blockaded atoms to short lived intermediate states and their subsequent decay to untrapped states. Using an auxiliary microwave field to carefully engineer the dissipation, we obtain a nearly deterministic single-atom source. Our method is applicable to sm…
Long range Rydberg blockade interactions have the potential for efficient implementation of quantum gates between multiple atoms. Here we present and analyze a protocol for implementation of a $k$-atom controlled NOT (C$_k$NOT) neutral atom gate. This gate can be implemented using sequential or simultaneous addressing of the control atoms which requires only $2k+3$ or 5 Rydberg $π$ pulses respectively. A detailed error analysis relevant for implementations based on alkali atom Rydberg states is provided which shows that gate errors less than 10% are possible for $k=35$.
We use coherent excitation of 3-16 atom ensembles to demonstrate collective Rabi flopping mediated by Rydberg blockade. Using calibrated atom number measurements, we quantitatively confirm the expected $\sqrt{N}$ Rabi frequency enhancement to within 4%. The resulting atom number distributions are consistent with essentially perfect blockade. We then use collective Rabi $π$ pulses to produce ${\cal N}=1,2$ atom number Fock states with fidelities of 62% and 48% respectively. The ${\cal N}=2$ Fock state shows the collective Rabi frequency enhancement without corruption from atom number fluctuatio…
We study the Rydberg blockade in a system of three atoms arranged in different 2D geometries (linear and triangular configurations). In the strong blockade regime, we observe high-contrast, coherent collective oscillations of the single excitation probability, and an almost perfect van der Waals blockade. Our data is consistent with a total population in doubly and triply excited states below 2%. In the partial blockade regime, we directly observe the anisotropy of the van der Waals interactions between $|nD\rangle$ Rydberg states in the triangular configuration. A simple model, that only uses…
We demonstrate the first deterministic entanglement of two individually addressed neutral atoms using a Rydberg blockade mediated controlled-NOT gate. Parity oscillation measurements reveal an entanglement fidelity of $F=0.58\pm0.04$, which is above the entanglement threshold of $F=0.5$, without any correction for atom loss, and $F=0.71\pm0.05$ after correcting for background collisional losses. The fidelity results are shown to be in good agreement with a detailed error model.
We demonstrate $|W\rangle$ state encoding of multi-atom ensemble qubits. Using optically trapped Rb atoms the $T_2$ coherence time is 2.6(3) ms for $\bar N=7.6$ atoms and scales approximately inversely with the number of atoms. Strong Rydberg blockade between two ensemble qubits is demonstrated with a fidelity of $0.89(1)$ and a fidelity of $\sim \hspace{-.05cm}1.0$ when postselected on control ensemble excitation. These results are a significant step towards deterministic entanglement of atomic ensembles.
We calculate interspecies Rydberg-Rydberg interaction strengths for the heavy alkalis Rb and Cs. The presence of strong Förster resonances makes interspecies coupling a promising approach for long range entanglement generation. We also provide an overview of the strongest Förster resonances for Rb-Rb and Cs-Cs using different principal quantum numbers for the two atoms. We show how interspecies coupling can be used for high fidelity quantum non demolition state measurements with low crosstalk in qubit arrays.
The Rydberg excitation blockade has been at the heart of an impressive array of recent achievements; however, state-mixing interactions can compromise its efficiency. When ultracold atoms are excited to Rydberg states near Förster resonance, up to $\sim 50\%$ of atoms can be found in dipole coupled product states within tens of ns after excitation. There has been disagreement in the literature regarding the mechanism by which this mixing occurs. We use state-selective field ionization spectroscopy to measure, on a shot-by-shot basis, the distribution of Rydberg states populated during narrowba…
We present experimental results on two-qubit Rydberg blockade quantum gates and entanglement in a two-dimensional qubit array. Without post selection against atom loss we achieve a Bell state fidelity of $0.73\pm 0.05$, the highest value reported to date. The experiments are performed in an array of single Cs atom qubits with a site to site spacing of $3.8 ~ μ\rm m$. Using the standard protocol for a Rydberg blockade C$_Z$ gate together with single qubit operations we create Bell states and measure their fidelity using parity oscillations. We analyze the role of AC Stark shifts that occur when…
Recently, the notion of two-qubit controlled phase gate via off-resonant modulated driving has been introduced into the neutral atom qubit platform, with respect to both single-photon and two-photon ground-Rydberg transitions. In order to reach a better performance practically, further developments are in need to overcome a few known limitations in previous discussions of this promising method. Here, we thoroughly analyze a variety of modulation styles for two-photon transitions, demonstrating the versatility of off-resonant modulated driving protocols. Furthermore, we show that it is possible…
We present a new mechanism contributing to the detection of photoassociated long-range Rydberg molecules via pulsed-field ionization: ionic products, created by the decay of a long-range Rydberg molecule, modify the excitation spectrum of surrounding ground-state atoms and facilitate the excitation of further atoms into Rydberg states by the photoassociation light. Such an ion-mediated excitation mechanism has been previously called "Coulomb anti-blockade". Pulsed-field ionisation typically doesn't discriminate between the ionization of a long-range Rydberg molecule and an isolated Rydberg ato…
The spatial evolution of the Rydberg blockade is studied taking into account Stark-split energy levels across several manifolds. We find that the unexpected restoration of a blockaded Rydberg excitation at small interatomic distances, e.g., experimentally observed by P.Schauss, et al. [Nature 491, 87 (2012)], can be explained by the perturbed energy levels from neighboring manifolds that enter the energy window of excitation defined by the bandwidth of the exciting laser. The same mechanism can also explain why the pair correlation function of Rydberg atoms remains nonzero in the entire region…
We demonstrate experimentally that a single Rb atom excited to the $79d_{5/2}$ level blocks the subsequent excitation of a second atom located more than $10 μ\rm m$ away. The observed probability of double excitation of $\sim 30%$ is consistent with a theoretical model based on calculations of the long range dipole-dipole interaction between atoms.
We show that the Rydberg blockade mechanism, which is well known in the case of s states, can be significantly different for p and d states due to the van der Waals couplings between different Rydberg Zeeman sublevels and the presence of a magnetic-field. We show, in particular, the existence of magic distances corresponding to the laser-excitation of a superposition of doubly excited states.
Strongly Rydberg-blockaded two-level atoms form a Rydberg superatom, which is excited only to a collective symmetrical Dicke state. However, emerging often in the alkali-earth atoms, the spontaneous decay from the Rydberg state to an additional pooling state renders the ensemble no longer a closed superatom. Herein we present a computationally-efficient model to characterize the interaction between a fully Rydberg-blockaded ensemble of $N$ $Λ$-type three-level atoms and a strong probe light field in a coherent state. The model enables us to achieve a decomposition of the coupled dynamics in th…
We present a detailed error analysis of a Rydberg blockade mediated controlled-NOT quantum gate between two neutral atoms as demonstrated recently in Phys. Rev. Lett. 104, 010503 (2010) and Phys. Rev. A 82, 030306 (2010). Numerical solutions of a master equation for the gate dynamics, including all known sources of technical error, are shown to be in good agreement with experiments. The primary sources of gate error are identified and suggestions given for future improvements. We also present numerical simulations of quantum process tomography to find the intrinsic fidelity, neglecting technic…
Due to their strong and tunable interactions, Rydberg atoms can be used to realize fast two-qubit entangling gates. We propose a generalization of a generic two-qubit Rydberg-blockade gate to multi-qubit Rydberg-blockade gates which involve both many control qubits and many target qubits simultaneously. This is achieved by using strong microwave fields to dress nearby Rydberg states, leading to asymmetric blockade in which control-target interactions are much stronger than control-control and target-target interactions. The implementation of these multi-qubit gates can drastically simplify bot…
We present a theoretical analysis of the implementation of an entangling quantum gate between two trapped Ca$^+$ ions which is based on the dipolar interaction among ionic Rydberg states. In trapped ions the Rydberg excitation dynamics is usually strongly affected by mechanical forces due to the strong couplings between electronic and vibrational degrees of freedom in inhomogeneous electric fields. We demonstrate that this harmful effect can be overcome by using dressed states that emerge from the microwave coupling of nearby Rydberg states. At the same time these dressed states exhibit long r…
Previously, we had proposed the technique of light shift imbalance induced blockade which leads to a condition where a collection of non-interacting atoms under laser excitation remains combined to a superposition of the ground and the first excited states, thus realizing a collective state quantum bit which in turn can be used to realize a quantum computer. In this paper, we show first that the light shift imbalance by itself is actually not enough to produce such a blockade, and explain the reason why the limitation of our previous analysis had reached this constraint. We then show that by i…
We analyze the effects of Zeeman degeneracies on the long-range interactions between like Rydberg atoms, with particular emphasis on applications to quantum information processing using van der Waals blockade. We present a general analysis of how degeneracies affect the primary error sources in blockade experiments, emphasizing that blockade errors are sensitive primarily to the weakest possible atom-atom interactions between the degenerate states, not the mean interaction strength. We present explicit calculations of the van der Waals potentials in the limit where the fine-structure interacti…
Results of numerical Monte Carlo simulations for the Stark-tuned Förster resonance and dipole blockade between two to five cold rubidium Rydberg atoms in various spatial configurations are presented. The effects of the atoms' spatial uncertainties on the resonance amplitude and spectra are investigated. The feasibility of observing coherent Rabi-like population oscillations at a Förster resonance between two cold Rydberg atoms is analyzed. Spectra and the fidelity of the Rydberg dipole blockade are calculated for various experimental conditions, including nonzero detuning from the Förster reso…
High resolution laser Stark excitation of np (60 < n < 85) Rydberg states of ultra-cold cesium atoms shows an efficient blockade of the excitation attributed to long-range dipole-dipole interaction. The dipole blockade effect is observed as a quenching of the Rydberg excitation depending on the value of the dipole moment induced by the external electric field. Effects of eventual ions which could match the dipole blockade effect are discussed in detail but are ruled out for our experimental conditions. Analytic and Monte-Carlo simulations of the excitation of an ensemble of interacting Rydberg…
We present schemes for geometric phase compensation in adiabatic passage which can be used for the implementation of quantum logic gates with atomic ensembles consisting of an arbitrary number of strongly interacting atoms. Protocols using double sequences of stimulated Raman adiabatic passage (STIRAP) or adiabatic rapid passage (ARP) pulses are analyzed. Switching the sign of the detuning between two STIRAP sequences, or inverting the phase between two ARP pulses, provides state transfer with well defined amplitude and phase independent of atom number in the Rydberg blockade regime. Using the…
We show that microwave spectroscopy of a dense Rydberg gas trapped on a superconducting atom chip in the dipole blockade regime reveals directly the dipole-dipole many-body interaction energy spectrum. We use this method to investigate the expansion of the Rydberg cloud under the effect of repulsive van der Waals forces and the breakdown of the frozen gas approximation. This study opens a promising route for quantum simulation of many-body systems and quantum information transport in chains of strongly interacting Rydberg atoms.
We propose an experiment to demonstrate a novel blockade mechanism caused by long-range anisotropic interactions in an ultracold dipolar gas composed of the recently observed "butterfly" Rydberg molecules. At the blockade radius, the strong intermolecular interaction between two adjacent molecules shifts their molecular states out of resonance with the photoassociation laser, preventing their simultaneous excitation. When the molecules are prepared in a quasi-one-dimensional (Q1D) trap, the interaction's strength can be tuned via a weak external field. The molecular density thus depends strong…
We present a combined experimental and theoretical study of the effects of Rydberg interactions on Autler-Townes spectra of ultracold gases of atomic strontium. Realizing two-photon Rydberg excitation via a long-lived triplet state allows us to probe the thus far unexplored regime where Rydberg state decay presents the dominant decoherence mechanism. The effects of Rydberg interactions are observed in shifts, asymmetries, and broadening of the measured atom-loss spectra. The experiment is analyzed within a one-body density matrix approach, accounting for interaction-induced level shifts and de…
We study theoretically and experimentally the competing blockade and anti-blockade effects induced by spontaneously generated contaminant Rydberg atoms in driven Rydberg systems. These contaminant atoms provide a source of strong dipole-dipole interactions and play a crucial role in the system's behavior. We study this problem theoretically using two different approaches. The first is a cumulant expansion approximation, in which we ignore third-order and higher connected correlations. Using this approach for the case of resonant drive, a many-body blockade radius picture arises, and we find qu…
We study interactions between polaritons, arising when photons strongly couple to collective excitations in an array of two-level atoms trapped in an optical lattice inside a cavity. We consider two types of interactions between atoms: Dipolar forces and atomic saturability, which ranges from hard-core repulsion to Rydberg blockade. We show that, in spite of the underlying repulsion in the subsystem of atomic excitations, saturability induces a broadband bunching of photons for two-polariton scattering states. We interpret this bunching as a result of interference, and trace it back to the mis…
Neutral atom array serves as an ideal platform to study the quantum logic gates, where intense efforts have been devoted to improve the two-qubit gate fidelity. We report our recent findings in constructing a different type of two-qubit controlled-PHASE quantum gate protocol with neutral atoms enabled by Rydberg blockade, which aims at both robustness and high-fidelity. It relies upon modulated driving pulse with specially tailored smooth waveform to gain appropriate phase accumulations for quantum gates. The major features include finishing gate operation within a single pulse, not necessaril…
We present a detailed analysis of our recent observation of synchronous Rabi oscillations between the electronic ground state and Rydberg states in a mesoscopic ensemble containing roughly 100 ultracold atoms [M. Reetz-Lamour \textit{et al.}, submitted, arXiv:0711.4321]. The mesoscopic cloud is selected out of a sample of laser-cooled Rb atoms by optical pumping. The atoms are coupled to a Rydberg state with principal quantum number around 30 by a two-photon scheme employing flat-top laser beams. The influence of residual spatial intensity fluctuations as well as sources of decoherence such as…
Rydberg blockade sphere persists an intriguing picture by which a number of collective many-body effects caused by the strong Rydberg-Rydberg interactions can be clearly understood and profoundly investigated. In the present work, we develop a new definition for the effective two-atom blockade radius and show that the original spherically shaped blockade surface would be deformed when the real number of atoms increases from two to three. This deformation of blockade sphere reveals spatially anisotropic and shrunken properties which strongly depend on the interatomic distance. In addition, we a…
Due to its potential for implementing a scalable quantum computer, multiqubit Toffoli gate lies in the heart of quantum information processing. In this article, we demonstrate a multiqubit blockade gate with atoms arranged in a three-dimension spheroidal array. The gate performance is greatly improved by the method of optimizing control-qubit distributions on the spherical surface via evolutionary algorithm, which leads to an enhanced asymmetric Rydberg blockade. This spheroidal configuration, not only arises a well preservation for the dipole blockade energy between arbitrary control-target p…
We study a novel regime of the Rydberg excitation blockade using highly Stark-shifted, yet long-living, states of Rb atoms subject to electric fields above the classical ionization limit. Such states allow tuning the dipole-dipole interaction strength while their ionization rate can be changed over two orders of magnitude by small variations of the electric field. We demonstrate laser excitation of the interacting Rydberg states followed by their detection using controlled ionization and magnified imaging with high spatial and temporal resolution. Our work reveals the hitherto unexplored possi…
High resolution laser excitation of np Rydberg states of cesium atoms shows a dipole blockade at Förster resonances corresponding to the resonant dipole-dipole energy transfer of the np + np → ns + (n + 1)s reaction. The dipole-dipole interaction can be tuned on and off by the Stark effect, and such a process observed for relatively low n (25 − 41) is promising for quantum gate devices. Both Penning ionization and saturation in the laser excitation can limit the range of observation of the dipole blockade
We perform a comprehensive investigation of the coupling between a Rydberg-dressed atomic gas and an ultra-cold plasma. Using simultaneous time-resolved measurements of both neutral atoms and ions, we show that plasma formation occurs via a Coulomb anti-blockade mechanism, in which background ions DC Stark shift nearby atoms into resonance at specific distances. The result is a highly correlated growth of the Rydberg population that shares some similarities with that previously observed for van der Waals interactions. We show that a rate equation model that couples the laser-driven Rydberg gas…
In the laser excitation of ultracold atoms to Rydberg states, we observe a dramatic suppression caused by van der Waals interactions. This behavior is interpreted as a local excitation blockade: Rydberg atoms strongly inhibit excitation of their neighbors. We measure suppression, relative to isolated atom excitation, by up to a factor of 6.4. The dependence of this suppression on both laser irradiance and atomic density are in good agreement with a mean-field model. These results are an important step towards using ultracold Rydberg atoms in quantum information processing.
The dipole blockade effect at laser excitation of mesoscopic ensembles of Rydberg atoms lies in the fact that the excitation of one atom to a Rydberg state blocks the excitation of other atoms due to the shift in the collective energy levels of interacting Rydberg atoms. It is used to obtain the entangled qubit states based on single neutral atoms in optical traps. In this paper, we present our experimental results on the observation of the dipole blockade for mesoscopic ensembles of 1-5 atoms when they are detected by the selective field ionization method. We investigated the spectra of the t…
Rydberg blockaded gate is a fundamental ingredient for scalable quantum computation with neutral Rydberg atoms. However the fidelity of such a gate is intrinsically limited by a blockade error coming from a Rydberg level shift that forbids its extensive use. Based on a dark-state adiabatic passage, we develop a novel protocol for realizing a two-atom blockade-error-free quantum gate in a hybrid system with simultaneous van der Waals (vdWsI) and resonant dipole-dipole interactions (DDI). The basic idea relies on converting the roles of two interactions, which is, the DDI serves as one time-depe…
We observe and measure dispersive optical non-linearities in an ensemble of cold Rydberg atoms placed inside an optical cavity. The experimental results are in agreement with a simple model where the optical non-linearities are due to the progressive appearance of a Rydberg blockaded volume within the medium. The measurements allow a direct estimation of the "blockaded fraction" of atoms within the atomic ensemble.
The spin-wave (SW) NOON state is an $N$-particle Fock state with two atomic spin-wave modes maximally entangled. Attributed to the property that the phase is sensitive to collective atomic motion, the SW NOON state can be utilized as a novel atomic interferometer and has promising application in quantum enhanced measurement. In this paper we propose an efficient protocol to deterministically produce the atomic SW NOON state by employing Rydberg blockade. Possible errors in practical manipulations are analyzed. A feasible experimental scheme is suggested. Our scheme is far more efficient than t…
Using time-resolved measurements, we demonstrate coherent collective Rydberg excitation crossing over into Rydberg blockade in a dense and ultracold gas trapped at a distance of 100 $μ$m from a room-temperature atom chip. We perform Ramsey-type measurements to characterize the coherence. The experimental data are in good agreement with numerical results from a master equation using a mean-field approximation, and with results from a super-atom-based Hamiltonian. These results represent significant progress in exploring a strongly interacting driven Rydberg gas on an atom chip.
The Rydberg blockade mechanism has shown noteworthy promise for scalable quantum computation with neutral atoms. Both qubit states and gate-mediating Rydberg state belong to the same optically-trapped atom. The trapping fields, while being essential, induce detrimental decoherence. Here we theoretically demonstrate that this Stark-induced decoherence may be completely removed using powerful concepts of "magic" optical traps. We analyze "magic" trapping of a prototype three-level system: a Rydberg state along with two qubit states: hyperfine states attached to a J=1/2 ground state. Our numerica…
The laser-excitation of Rydberg atoms in ultracold gases is often described assuming that the atomic motion is frozen during the excitation time. We show that this frozen gas approximation can break down for atoms that are held in optical lattices or microtraps. In particular, we show that the excitation dynamics is in general strongly affected by mechanical forces among the Rydberg atoms as well as the spread of the atomic wavepacket in the confining potential. This causes decoherence in the excitation dynamics - resulting in a dissipative blockade effect - that renders the Rydberg excitation…
