We suggest a novel way to use strong Rydberg dipole-dipole interactions in order to induce non-trivial conditional dynamics in individual-atom systems and mesoscopic ensembles. Contrary to previous works, we suggest to excite atoms into different Rydberg states, which results in a potentially richer dynamical behaviour. Specifically, we investigate systems of individual hydrogen-like atoms or mesoscopic ensembles excited into high-lying hydrogen-like s, p or d states and show how to perform three-qubit conditional dynamics on the information they contain through a proper use of dipole-dipole interaction induced energy shifts.
Resonant laser excitation of multiple Rydberg atoms are prohibited, leading to Rydberg blockade, when the long-range van der Waals interactions are stronger than the laser-atom coupling. Rydberg blockade can be violated, i.e. simultaneous excitation of more than one Rydberg atoms, by off-resonant laser excitation, causing an excitation antiblockade. Rydberg antiblockade gives rise to strongly correlated many-body dynamics and spin-orbit coupling, and also finds quantum computation applications. Instead of commonly used van der Waals interactions, we investigate antiblockade dynamics of two Ryd…
We demonstrate Rabi flopping of small numbers of $\rm{^{87}Rb}$ atoms between ground and Rydberg states with $n\le 43$. 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.
We present a detailed analysis and design of a neutral atom quantum logic device based on atoms in optical traps interacting via dipole-dipole coupling of Rydberg states. The dominant physical mechanisms leading to decoherence and loss of fidelity are enumerated. Our results support the feasibility of performing single and two-qubit gates at MHz rates with decoherence probability and fidelity errors at the level of $10^{-3}$ for each operation. Current limitations and possible approaches to further improvement of the device are discussed.
We have observed resonant energy transfer between cold Rydberg atoms in spatially separated cylinders. Resonant dipole-dipole coupling excites the 49s atoms in one cylinder to the 49p state while the 41d atoms in the second cylinder are transferred down to the 42p state. We have measured the production of the 49p state as a function of separation of the cylinders (0 - 80 um) and the interaction time (0 - 25 us). In addition we measured the width of the electric field resonances. A full many-body quantum calculation reproduces the main features of the experiments.
The resonant dipole-dipole interaction between highly excited Rydberg levels dominates the interaction of neutral atoms at short distances scaling as $1/r^3$. Here we take advantage of the combined effects of strong dipole-dipole interaction and multifrequency driving fields to propose one type of selective Rydberg pumping mechanism. In the computational basis of two atoms $\{|00\rangle, |01\rangle,|10\rangle,|11\rangle\}$, this mechanism allows $|11\rangle$ to be resonantly pumped upwards to the single-excited Rydberg states while the transitions of the other three states are suppressed. From…
We propose a scheme for controlling interactions between Rydberg-excited neutral atoms in order to perform a fast high-fidelity quantum gate. Unlike dipole-blockade mechanisms already found in the literature, we drive resonantly the atoms with a state-dependent excitation to Rydberg levels, and we exploit the resulting dipole-dipole interaction to induce a controlled atomic motion in the trap, in a similar way as discussed in recent ion-trap quantum computing proposals. This leads atoms to gain the required gate phase, which turns out to be a combination of a dynamic and a geometrical contribu…
While the Rydberg-blockade regime provides the natural setting for creating $W$-type entanglement with cold neutral atoms, it is demonstrated here that a scalable entanglement resource of this type can even be obtained under completely different physical circumstances. To be more precise, a special instance of twisted $W$ states -- namely, $π$-twisted ones -- can be engineered in one-dimensional arrays of cold neutral atoms with Rydberg-dressed resonant dipole-dipole interaction. In particular, it is shown here that this is possible even when a (dressed) Rydberg excitation is coupled to the mo…
In this paper, we propose a scheme for implementing the nonadiabatic holonomic quantum computation (NHQC+) of two Rydberg atoms by using invariant-based reverse engineering (IBRE). The scheme is based on Förster resonance induced by strong dipole-dipole interaction between two Rydberg atoms, which provides a selective coupling mechanism to simply the dynamics of system. Moreover, for improving the fidelity of the scheme, the optimal control method is introduced to enhance the gate robustness against systematic errors. Numerical simulations show the scheme is robust against the random noise in …
We propose a scheme that employs dissipation to deterministically generate entanglement in an ensemble of strongly interacting Rydberg atoms. With a combination of microwave driving between different Rydberg levels and a resonant laser coupling to a short lived atomic state, the ensemble can be driven towards a dark steady state that entangles all atoms. The long-range resonant dipole-dipole interaction between different Rydberg states extends the entanglement beyond the van der Walls interaction range with perspectives for entangling large and distant ensembles.
We explore the fluorescence signals from a pair of atoms driven towards Rydberg states on a three-level ladder transition. The dipole--dipole interactions between Rydberg excited atoms significantly distort the dark state and electromagnetically induced transparency behavior observed with independent atoms and, thus, their steady state light emission. We calculate and analyze the temporal correlations between intensities and amplitudes of the signals emitted by the atoms and explain their origin in the atomic Rydberg state interactions.
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 the dipole-dipole interaction between two Rydberg atoms can give rise to long range molecules. The binding potential arises from two states that converge to different separated atom asymptotes. These states interact weakly at large distances, but start to repel each other strongly as the van der Waals interaction turns into a resonant dipole-dipole interaction with decreasing separation between the atoms. This mechanism leads to the formation of an attractive well for one of the potentials. If the two separated atom asymptotes come from the small Stark splitting of an atomic Rydbe…
We consider three level atoms driven by two resonant light fields in a ladder scheme where the upper level is a highly excited Rydberg state. We show that the dipole--dipole interactions between Rydberg excited atoms prevents the formation of single particle dark states and leads to strongly correlated photon emission from atoms separated by distances large compared to the emission wavelength. For two atoms, correlated photon pairs are emitted with an angular distribution given by a coherent sum of the independent dipolar fields.
We measure the hyperfine structure of $nP_{1/2}$ Rydberg states using mm-wave spectroscopy on an ensemble of laser-cooled $^{85}$Rb atoms. Systematic uncertainties in our measurement from the Zeeman splittings induced by stray magnetic fields and dipole-dipole interactions between two Rydberg atoms are factored in with the obtained statistical uncertainty. Our final measurement of the $nP_{1/2}$ hyperfine coupling constant is $A_{\text{hfs}}=1.443(31)$~GHz. This measurement is useful for studies of long-range Rydberg molecules, Rydberg electrometry, and quantum simulation with dipole-dipole in…
We analyze the influence of dipole-dipole interactions between Rydberg atoms on the generation of Abelian artificial gauge potentials and fields. When two Rydberg atoms are driven by a uniform laser field, we show that the combined atom-atom and atom-field interactions give rise to new, nonuniform, artificial gauge potentials. We identify the mechanism responsible for the emergence of these gauge potentials. Analytical expressions for the latter indicate that the strongest artificial magnetic fields are reached in the regime intermediate between the dipole blockade regime and the regime in whi…
The dipole blockade between Rydberg atoms has been proposed as a basic tool in quantum information processing with neutral atoms. Here we demonstrate experimentally the Rydberg blockade of two individual atoms separated by 4 $μ$m. Moreover, we show that, in this regime, the single atom excitation is enhanced by a collective two-atom behavior associated with the excitation of an entangled state. This observation is a crucial step towards the deterministic manipulation of entanglement of two or more atoms using the Rydberg dipole interaction.
We propose a two-qubit gate for neutral atoms in which one of the logical state components adiabatically follows a two-atom dark state formed by the laser coupling to a Rydberg state and a strong, resonant dipole-dipole exchange interaction between two Rydberg excited atoms. Our gate exhibits optimal scaling of the intrinsic error probability $E \propto (Bτ)^{-1}$ with the interatomic interaction strength $B$ and the Rydberg state lifetime $τ$. Moreover, the gate is resilient to variations in the interaction strength, and even for finite probability of double Rydberg excitation, the gate does …
We show that the dipole-dipole interaction between three identical Rydberg atoms can give rise to bound trimer states. The microscopic origin of these states is fundamentally different from Efimov physics. Two stable trimer configurations exist where the atoms form the vertices of an equilateral triangle in a plane perpendicular to a static electric field. The triangle edge length typically exceeds $R\approx 2\,μ\text{m}$, and each configuration is two-fold degenerate due to Kramers' degeneracy. The depth of the potential wells and the triangle edge length can be controlled by external paramet…
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 have developed a simple analytical model describing multi-atom signals that are measured in experiments on dipole-dipole interaction at resonant collisions of a few Rydberg atoms. It has been shown that finite efficiency of the selective field-ionization detector leads to the mixing up of the spectra of resonant collisions registered for various numbers of Rydberg atoms. The formulas which help to estimate an appropriate mean Rydberg atom number for a given detection efficiency are presented. We have found that a measurement of the relation between the amplitudes of collisional resonances o…
Cold atoms in highly excited Rydberg states are promising candidates to implement quantum logic gates of a quantum computer via long-range dipole-dipole interaction. Two-qubit gates require a controlled interaction of only two close Rydberg atoms. We report on the first spectroscopic observation of the resonant dipole-dipole interaction between two cold rubidium Rydberg atoms confined in a small laser excitation volume. The interaction strength was controlled by fine-tuning of the Rydberg levels into a Forster resonance using the Stark effect. The observed resonance line shapes are in good agr…
Strong resonant dipole-dipole interactions in flexible Rydberg aggregates enable the formation of exciton pulses, the interplay of atomic motion and electronic excitation transfer which feature high fidelity entanglement transport. Here, we demonstrate the coherent splitting of such pulses into two modes, which induce strongly different atomic motion, leading to clear signatures of nonadiabatic effects in atomic density profiles. The mechanism exploits local nonadiabatic effects at a conical intersection, turning them from a decoherence source into an asset. The conical intersection is a conse…
We show that the dipole-dipole interaction between two Rydberg atoms can lead to substantial Abelian and non-Abelian gauge fields acting on the relative motion of the two atoms. We demonstrate how the gauge fields can be evaluated by numerical techniques. In the case of adiabatic motion in a single internal state, we show that the gauge fields give rise to a magnetic field that results in a Zeeman splitting of the rotational states. In particular, the ground state of a molecular potential well is given by the first excited rotational state. We find that our system realises a synthetic spin-orb…
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…
We present the direct measurements of electric-dipole moments for $5P_{3/2}\to nD_{5/2}$ transitions with $20<n<48$ for Rubidium atoms. The measurements were performed in an ultracold sample via observation of the Autler-Townes splitting in a three-level ladder scheme, commonly used for 2-photon excitation of Rydberg states. To the best of our knowledge, this is the first systematic measurement of the electric dipole moments for transitions from low excited states of rubidium to Rydberg states. Due to its simplicity and versatility, this method can be easily extended to other transitions and o…
We propose to apply stimulated adiabatic passage to transfer atoms from their ground state into Rydberg excited states. Atoms a few micrometers apart experience a dipole-dipole interaction among Rydberg states that is strong enough to shift the atomic resonance and inhibit excitation of more than a single atom. We show that the adiabatic passage in the presence of this interaction between two atoms leads to robust creation of maximally entangled states and to two-bit quantum gates. For many atoms, the excitation blockade leads to an effective implementation of collective-spin and Jaynes-Cummin…
We measure the angular dependence of the resonant dipole-dipole interaction between two individual Rydberg atoms with controlled relative positions. By applying a combination of static electric and magnetic fields on the atoms, we demonstrate the possibility to isolate a single interaction channel at a Förster resonance, that shows a well-defined angular dependence. We first identify spectroscopically the Förster resonance of choice and we then perform a direct measurement of the interaction strength between the two atoms as a function of the angle between the internuclear axis and the quantiz…
Rydberg atoms with dipole-dipole interactions provide intriguing platforms to explore exotic quantum many-body physics. Here we propose a novel scheme with laser-assisted dipole-dipole interactions to realize synthetic magnetic field for Rydberg atoms in a two-dimensional array configuration, which gives rise to the exotic bosonic topological states. In the presence of an external effective Zeeman splitting gradient, the dipole-dipole interaction between neighboring Rydberg atoms along the gradient direction is suppressed, but can be assisted when Raman lights are applied to compensate the ene…
We show that the resonant dipole-dipole interaction can give rise to bound states between two and three Rydberg atoms with non-overlapping electron clouds. The dimer and trimer states arise from avoided level crossings between states converging to different fine structure manifolds in the limit of separated atoms. We analyze the angular dependence of the potential wells, characterize the quantum dynamics in these potentials and discuss methods for their production and detection. Typical distances between the atoms are of the order of several micrometers which can be resolved in state-of-the-ar…
We investigate the effect of degenerate atomic states on the exciton delocalization of dipole-dipole interacting Rydberg assemblies. Using a frozen gas and regular one-, two-, and three-dimensional lattice arrangements as examples, we see that degeneracies can enhance the delocalization compared to the situation when there is no degeneracy. Using the Zeeman splitting provided by a magnetic field, we controllably lift the degeneracy to study in detail the transition between degenerate and non-degenerate regimes.
We predict that ultralong-range Rydberg bi-molecules form in collisions between polar molecules in cold and ultracold settings. The collision of $Λ$-doublet nitric oxide (NO) with long-lived Rydberg NO($nf$, $ng$) molecules forms ultralong-range Rydberg bi-molecules with GHz energies and kilo-Debye permanent electric dipole moments. The Hamiltonian includes both the anisotropic charge-molecular dipole interaction and the electron-NO scattering. The rotational constant for the Rydberg bi-molecules is in the MHz range, allowing for microwave spectroscopy of rotational transitions in Rydberg bi-m…
The dipole blockade of Rydberg excitations is a hallmark of the strong interactions between atoms in these high-lying quantum states. 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 numeric…
In this paper, we propose a scheme to implement the two-qubit controlled-Z gate via the Stark-tuned Förster interaction of Rydberg atoms, where the Förster defect is driven by a time-dependent electric field of a simple sinusoidal function while the matrix elements of the dipole-dipole interaction are time-independent. It is shown that when the system is initially in a specific state, it makes a cyclic evolution after a preset interaction time, returning to the initial state, but picks up a phase, which can be used for realizing a two-atom controlled-Z gate. Due to the interference of sequenti…
Neutral atoms excited to Rydberg states can interact with each other via dipole-dipole interaction, which results in a physical phenomenon named Rydberg blockade mechanism. The effect attracts much attention due to its potential applications in quantum computation and quantum simulation. Quantum teleportation has been the core protocol in quantum information science playing a key role in efficient long-distance quantum communication. Here, we first propose the implementation of teleportation scheme with neutral atoms via Rydberg blockade, in which the entangled states of qubits can readily be …
We propose an efficient free-space scheme to create single photons in a well-defined spatiotemporal mode. To that end, we first prepare a single source atom in an excited Rydberg state. The source atom interacts with a large ensemble of ground-state atoms via a laser-mediated dipole-dipole exchange interaction. Using an adiabatic passage with a chirped laser pulse, we produce a spatially extended spin wave of a single Rydberg excitation in the ensemble, accompanied by the transition of the source atom to another Rydberg state. The collective atomic excitation can then be converted to a propaga…
The quadrupole interaction between the Rydberg electronic states of a Rydberg ion and the radio frequency electric field of the ion trap is analyzed. Such a coupling is negligible for the lowest energy levels of a trapped ion but it is important for a trapped Rydberg ion due to its large electric dipole moment. This coupling cannot be neglected by the standard rotating-wave approximation because it is comparable to the frequency of the trapping electric field. We investigate the effect of the quadrupole coupling by performing a suitable effective representation of the Hamiltonian. For a single…
Electromagnetically induced transparency (EIT) in a ladder system involving a Rydberg level is known to yield giant optical nonlinearities for the probe field, even in the few-photon regime. This enhancement is due to the strong dipole-dipole interactions between Rydberg atoms and the resulting excitation blockade phenomenon. In order to study such highly correlated media, ad hoc models or low-excitation assumptions are generally used to tackle their dynamical response to optical fields. Here, we study the behaviour of a cavity Rydberg-EIT setup in the non-equilibrium quantum field formalism, …
Fault-tolerant implementation of quantum gates is one of preconditions for realizing quantum computation. The platform of Rydberg atoms is one of the most promising candidates for achieving quantum computation. We propose to implement a controlled-$Z$ gate on Rydberg atoms where an amplitude-modulated field is employed to induce Rydberg antiblockade. Gate robustness against the fluctuations in the Rydberg-Rydberg interaction can be largely enhanced by adjusting amplitude-modulated field. Furthermore, we introduce a Landau-Zener-Stückelberg transition on the target atom so as to improve the gat…
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…
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…
We study the possibility to use interaction between a polar molecule in the ground electronic and vibrational state and a Rydberg atom to construct two-qubit gates between molecular qubits and to coherently control molecular states. A polar molecule within the electron orbit in a Rydberg atom can either shift the Rydberg state, or form Rydberg molecule. Both the atomic shift and the Rydberg molecule states depend on the initial internal state of the polar molecule, resulting in molecular state dependent van der Waals or dipole-dipole interaction between Rydberg atoms. Rydberg atoms mediated in…
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 our results on the experiments with cold Rb Rydberg atoms in a magneto-optical trap (MOT). Characteristic features of our experiment were the excitation of Rydberg atoms in a small volume within the cold atom cloud and sorting of the measured signals and spectra over the number of registered Rydberg atoms. We have measured the effective lifetime of the Rydberg state 37P, as well as its polarizability in a weak electric field. The results are in good agreement with the theoretical calculations. We have shown that localization of the small excitation volume around the zero-magnetic-fi…
Kramers-Kronig (KK) relation between the dispersion and absorption responses of a signal field can be mapped from the frequency domain into the space domain via the dipole-dipole interactions between a homogeneous sample of target atoms and a control atom. This is achieved by establishing an effective two-level configuration for the three-level target atoms in the single-photon far-detuned driving regime while maintaining a high Rydberg excitation for the three-level control atom in the single-photon resonant driving regime. We find in particular that it is viable to realize a dynamically tuna…
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.
