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International audience; We demonstrate the possibility to generate squeezed vacuum states of light by four wave mixing (FWM) enabled coherent population trapping in a metastable helium cell at room temperature. Contrary to usual FWM far detuned schemes, we work at resonance with an atomic transition. We investigate the properties of such states and show that the noise variances of the squeezed and anti-squeezed quadratures cannot be explained by the simple presence of losses. A specific model allows us to demonstrate the role played by spontaneous emitted photons, which experience squeezing while propagation inside of the cell. This theoretical model, which takes into account both residual absorption and spontaneous emission, leads to an excellent agreement with the experimental data without any adjusted parameter.

In this paper, we report on numerical calculations of the spontaneous emission rates and Lamb shifts of a $^{87}\text{Rb}$ atom in a Rydberg-excited state $\left(n\leq30\right)$ located close to a silica optical nanofiber. We investigate how these quantities depend on the fiber's radius, the distance of the atom to the fiber, the direction of the atomic angular momentum polarization as well as the different atomic quantum numbers. We also study the contribution of quadrupolar transitions, which may be substantial for highly polarizable Rydberg states. Our calculations are performed in the macroscopic quantum electrodynamics formalism, based on the dyadic Green's function method. This allows us to take dispersive and absorptive characteristics of silica into account; this is of major importance since Rydberg atoms emit along many different transitions whose frequencies cover a wide range of the electromagnetic spectrum. Our work is an important initial step towards building a Rydberg atom-nanofiber interface for quantum optics and quantum information purposes., 31 pages, 21 figures

International audience; We report on numerical simulations demonstrating the emergence of stroboscopic thermalisation in a chain of atoms submitted to a laser eld whose frequency is periodically modulated close to resonance with a transition towards a Rydberg state. We relate the conditions of equilibration of the Rydberg population to the spectrum of the Floquet Hamiltonian and suggest a possible experimental implementation.

The influence of an optical nanofiber on the spontaneous emission rates and Lamb shifts of a Rydberg rubidium atom in its close vicinity is investigated, in view of the implementation of a Rydberg-blockade-based quantum network.

We study the propagation and storage of a quantum field using ultra-narrow Coherent Population Oscillations (CPO) in a $\Lambda-$type atomic medium. The predictions for classical fields are checked experimentally in a metastable vapor at room temperature. We derive the evolution of its squeezing spectrum in the presence of a large classical pump field which enables CPO to exist. We show that the spontaneous emission of the residual population pumped into the excited state progressively destroys the quantum noise properties of the quantum field along propagation. The output quantum field therefore tends to be a coherent state, discarding the possibility to store quantum states of light with CPO., Comment: 9 pages, 4 figures, 2 appendices

International audience; We report on numerical calculations of the spontaneous emission rate of a Rydberg-excited sodium atom in the vicinity of an optical nanobre. In particular, we study how this rate varies with the distance of the atom to the bre, the bre's radius, the symmetry s or p of the Rydberg state as well as its principal quantum number. We nd that a fraction of the spontaneously emitted light can be captured and guided along the bre. This suggests that such a setup could be used for networking atomic ensembles, manipulated in a collective way due to the Rydberg blockade phenomenon.

We isolate a novel four-wave mixing process, enabled by Coherent Population Trapping (CPT), leading to efficient phase sensitive amplification. This process is permitted by the exploitation of two transitions starting from the same twofold degenerate ground state. One of the transitions is used for CPT, defining bright and dark states from which ultra intense four-wave mixing is obtained via the other transition. This leads to the measurement of a strong phase sensitive gain even for low optical densities and out-of-resonance excitation. The enhancement of four-wave mixing is interpreted in the framework of the dark-state polariton formalism., 5 pages, 4 figures, 1 supplemental material (2 pages)

In a previous Letter [A. Grankin et al., Phys. Rev. Lett. 117, 253602 (2016)] we studied the giant optical nonlinearities of a Rydberg atomic medium within an optical cavity, in the Schwinger-Keldysh formalism. In particular, we calculated the nonlinear contributions to the spectrum of the light transmitted through the cavity. In this article we spell out the essential details of this calculation and we show how it can be extended to higher input photon numbers and higher-order correlation functions. As a relevant example, we calculate and discuss the three-photon correlation function of the transmitted light and discuss its physical significance in terms of the polariton energy levels of the Rydberg medium within the optical cavity.

We theoretically study the propagation and storage of a classical field in a $\Lambda$-type atomic medium using coherent population oscillations (CPOs). We show that the propagation eigenmodes strongly relate to the different CPO modes of the system. Light storage in such modes is discussed by introducing a "populariton" quantity, a mixture of populations and field, by analogy to the dark state polariton used in the context of electromagnetically induced transparency light storage protocol. As experimentally shown, this memory relies on populations and is then - by contrast with usual Raman coherence optical storage protocols - robust to dephasing effects., Comment: 5 pages, 3 figures, Supplemental Material

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, and we obtain analytic expressions for elastic and inelastic components of the cavity transmission spectrum, valid up to higher excitation numbers than previously achieved. This allows us to identify and interpret a polaritonic resonance structure, to our knowledge unreported so far., Comment: 5 pages, 3 figures

In this paper, we propose a neutral atom implementation of the two-qubit conditional phase gate, based on the large Rydberg–Rydberg interaction induced energy shift. Contrary to previous proposals, this gate does not substantially populate the Rydberg levels. After describing the model in detail, we provide numerical simulations and discuss the performance of our gate. In particular we address the influence on the fidelity of spontaneous emission and atomic motion.

We report measurements of the time-dependent phases of the leak and retrieved pulses obtained in electromagnetically-induced-transparency storage experiments with metastable helium vapor at room temperature. In particular, we investigate the influence of the optical detuning at two-photon resonance and provide numerical simulations of the full dynamical Maxwell-Bloch equations, which allow us to account for the experimental results.

In this article, we theoretically study the quantum statistical properties of the light transmitted through or reflected from an optical cavity, filled by an atomic medium with strong optical non-linearity induced by Rydberg-Rydberg van der Waals interactions. Atoms are driven on a two-photon transition from their ground state to a Rydberg level via an intermediate state by the combination of a weak signal field and a strong control beam. By using a perturbative approach, we get analytic results which remain valid in the regime of weak feeding fields, even when the intermediate state becomes resonant. Therefore they allow us to investigate quantitatively new features associated with the resonant behaviour of the system. We also propose an effective non-linear three-boson model of the system which, in addition to leading to the same analytic results as the original problem, sheds light on the physical processes at work in the system.

We show that multidimensional Zeno effect combined with non-holonomic control allows to efficiently protect quantum systems from decoherence by a method similar to classical coding. Contrary to the conventional approach, our method is applicable to arbitrary error-inducing Hamiltonians and general quantum systems. We also propose algorithms of finding encoding that approaches the Hamming upper bound along with methods of practical realizations of the encodings. Two new codes protecting 2 information qubits out of 7 and 4 information qubits out of 9 against a single error with arbitrarily small probability of failure are constructed as an example.

We experimentally characterize the optical nonlinear response of a cold atomic medium placed inside an optical cavity, and excited to Rydberg states. The excitation to S and D Rydberg levels is carried out via a two-photon transition in an EIT (electromagnetically induced transparency) configuration, with a weak (red) probe beam on the lower transition, and a strong (blue) coupling beam on the upper transition. The observed optical nonlinearities induced by S states for the probe beam can be explained using a semi-classical model with van der Waals' interactions. For the D states, it appears necessary to take into account a dynamical decay of Rydberg excitations into a long-lived dark state. We show that the measured nonlinearities can be explained by using a Rydberg bubble model with a dynamical decay., Comment: 8 pages, 6 figures

A method is presented to transfer a system of two-level atoms from a spin coherent state to a maximally spin squeezed Dicke state, relevant for quantum metrology and quantum information processing. The initial state is the ground state of an initial linear Hamiltonian which is gradually turned into a final quadratic Hamiltonian whose ground state is the selected Dicke state. We use compensating operators to suppress diabatic transitions to unwanted states that would occur if the change were not slow. We discuss the possibilities of constructing the compensating operators by sequential application of quadratic Hamiltonians available in experiments., Comment: 10 pages, 10 figures. Replaced with published version

We theoretically investigate the quantum statistical properties of light transmitted through an atomic medium with strong optical non-linearity induced by Rydberg-Rydberg van der Waals interactions. In our setup, atoms are located in a cavity and non-resonantly driven on a two-photon transition from their ground state to a Rydberg level via an intermediate state by the combination of the weak signal field and a strong control beam. To characterize the transmitted light we compute the second-order correlation function $g^{\left(2\right)}\left(\tau\right)$. The simulations we obtained on the specific case of rubidium atoms suggest that the bunched or antibunched nature of the outgoing beam can be chosen at will by appropriately tuning the physical parameters., Comment: 20 pages, 3 figures

We numerically simulate the dynamics of atomic clusters aggregation deposited on a surface interacting with the growing island. We make use of the well-known DLA model but replace the underlying diffusion equation by the Smoluchowski equation which results in a drifted DLA model and anisotropic jump probabilities. The shape of the structures resulting from their aggregation-limited random walk is affected by the presence of a Laplacian potential due to, for instance, the surface stress field. We characterize the morphologies we obtain by their Hausdorff fractal dimension as well as the so-called external fractal dimension. We compare our results to previously published experimental results for antimony and silver clusters deposited onto graphite surface.

We propose and analyze a quantum repeater architecture in which Rydberg-blocked atomic ensembles inside optical cavities are linked by optical fibers. Entanglement generation, swapping, and purification are achieved through collective laser manipulations of the ensembles and photon transmission. Successful transmission and storage of entanglement are heralded by ionization events rather than by photon detection signals used in previous proposals. We demonstrate how the high charge detection efficiency allows for a shortened average entanglement generation time, and we analyze an implementation of our scheme with ensembles of Cs atoms.

International audience; In this paper, we review an open-loop evolution control method, called the nonholonomic control, based on the alternate application of only two physical perturbations for timings which play the role of adjustable control parameters. We present the algorithm which allows one to explicitly compute the pulse sequence achieving any arbitrarily prescribed unitary evolution in a nonholonomic system, i.e. a system subject to two physical perturbations which, together with the natural Hamiltonian of the system, span the entire Lie algebra u(N). We moreover expose two extensions of our method to open quantum systems which, respectively, aim at preserving the information stored in the system and safely processing this information. The first is based on a generalization of the quantum Zeno effect, while the second is inspired by decoupling pulse techniques. The most important feature of the methods presented here is their universality: they indeed do not rely on any specific assumption on the system, which in particular is not bound to be a collection of two-level systems, or the error model considered, as is usually the case in the literature. Numerical and physical applications of our techniques are also provided.

We propose to implement the Jaynes-Cummings model by coupling a few-micrometer large atomic ensemble to a quantized cavity mode and classical laser fields. A two-photon transition resonantly couples the single-atom ground state |g> to a Rydberg state |e> via a non-resonant intermediate state |i>, but due to the interaction between Rydberg atoms only a single atom can be resonantly excited in the ensemble. This restricts the state space of the ensemble to the collective ground state |G> and the collectively excited state |E> with a single Rydberg excitation distributed evenly on all atoms. The collectively enhanced coupling of all atoms to the cavity field with coherent coupling strengths which are much larger than the decay rates in the system leads to the strong coupling regime of the resulting effective Jaynes-Cummings model. We use numerical simulations to show that the cavity transmission can be used to reveal detailed properties of the Jaynes-Cummings ladder of excited states, and that the atomic nonlinearity gives rise to highly non-trivial photon emission from the cavity. Finally, we suggest that the absence of interactions between remote Rydberg atoms may, due to a combinatorial effect, induce a cavity-assisted excitation blockade whose range is larger than the typical Rydberg dipole-dipole interaction length., 9 pages, 6 figures

We propose a new physical approach for encoding and processing of quantum information in ensembles of multi-level quantum systems, where the different bits are not carried by individual particles but associated with the collective population of different internal levels. One- and two-bit gates are implemented by collective internal state transitions taking place in the presence of an excitation blockade mechanism which restricts the population of each internal state to the values zero and unity. 10-20 bit quantum computers can be built via this scheme in single trapped clouds of ground state atoms subject to the Rydberg excitation blockade mechanism, and the linear dependence between register size and the number of internal quantum states in atoms offers realistic means to reach larger registers., Comment: 4 pages, 4 figures

We propose to use a collective excitation blockade mechanism to identify errors that occur due to disturbances of single atoms in ensemble quantum registers where qubits are stored in the collective population of different internal atomic states. A simple error correction procedure and a simple decoherence-free encoding of ensemble qubits in the hyperfine states of alkali atoms are presented., 4 pages, 2 figures

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., Comment: 5 pages, 4 figures

In this paper, we propose a way to achieve protected universal computation in a neutral atom quantum computer subject to collective dephasing. Our proposal relies on the existence of a Decoherence Free Subspace (DFS), resulting from symmetry properties of the errors. After briefly describing the physical system and the error model considered, we show how to encode information into the DFS and build a complete set of safe universal gates. Finally, we provide numerical simulations for the fidelity of the different gates in the presence of time-dependent phase errors and discuss their performance and practical feasibility., 7 pages, 8 figures

In this paper, we show how the non-holonomic control technique can be employed to build completely controlled quantum devices. Examples of such controlled structures are provided.

In this paper, we present a coherence protection method based upon a multidimensional generalization of the Quantum Zeno Effect, as well as ideas from the coding theory. The non-holonomic control technique is employed as a physical tool which allows its effective implementation. The two limiting cases of small and large quantum systems are considered.

The protection of the coherence of open quantum systems against the influence of their environment is a very topical issue. A scheme is proposed here which protects a general quantum system from the action of a set of arbitrary uncontrolled unitary evolutions. This method draws its inspiration from ideas of standard error-correction (ancilla adding, coding and decoding) and the Quantum Zeno Effect. A pedagogical demonstration of our method on a simple atomic system, namely a Rubidium isotope, is proposed., Comment: 17 pages, 6 figures

In this paper, we present a universal control technique, the non-holonomic control, which allows us to impose any arbitrarily prescribed unitary evolution to any quantum system through the alternate application of two well-chosen perturbations.

In this paper, we present a realistic application of the coherence protection method proposed in the previous article. A qubit of information encoded on the two spin states of a Rubidium isotope is protected from the action of electric and magnetic fields.

Decay acceleration by frequent measurements (interruptions of the coupling), known as the anti-Zeno effect is argued to be much more ubiquitous than its inhibition in one- or two-level systems coupled to reservoirs (continua). In multilevel systems, frequent measurements cause accelerated decay by destroying the multilevel interference, which tends to inhibit decay in the absence of measurements.

We propose a technique that allows to simultaneously perform universal control of the evolution operator of a system and compensate for the first-order contribution of any Hermitian constant noise and the action of the environment. We show that, at least, a three-valued Hamiltonian is needed in order to protect the system against any such noise and propose an explicit algorithm for finding an appropriate control sequence. This algorithm is applied to numerically design a safe gate in an atomic qutrit.

We propose a novel scheme for high fidelity photonic controlled phase gates using Rydberg blockade in an ensemble of atoms in an optical cavity. The gate operation is obtained by first storing a photonic pulse in the ensemble and then scattering a second pulse from the cavity, resulting in a phase change depending on whether the first pulse contained a single photon. We show that the combination of Rydberg blockade and optical cavities effectively enhances the optical non-linearity created by the strong Rydberg interaction and thereby reduces the requirements for photonic quantum gates. The resulting gate can be implemented with cavities of moderate finesse which allows for highly efficient processing of quantum information encoded in photons. As a particular example of this, we show how the gate can be employed to increase the communication rate of quantum repeaters based on atomic ensembles., Comment: main manuscript 5 pages with 11 pages of supplementary information

We question the microcanonical hypothesis, often made to account for the thermalization of complex closed quantum systems, on the specific example of a chain of two-level atoms optically driven by a resonant laser beam and strongly interacting via Rydberg-Rydberg dipole-dipole interactions. Along its (necessarily unitary) evolution, this system is indeed expected to thermalize, i.e. observables, such as the number of excitations, stop oscillating and reach equilibrium-like expectation values. The latter are often calculated through assuming the system can be effectively described by a thermal-like microcanonical state. Here, we compare the distribution of excitations in the chain calculated either according to the microcanonical assumption or through direct exact numerical simulation. This allows us to show the limitations of the thermal equilibrium hypothesis and precise its applicability conditions., Comment: v2: Add comparison with Bettelli et al.'s Monte-Carlo simulation (App. A) + typo correction

We demonstrate both experimentally and theoretically a new form of light storage based on Coherent Population Oscillations. It is shown to be phase preserving and robust to dephasing effects.

We perform Electromagnetically Induced Transparency (EIT)-based storage in metastable helium at room temperature. An additional phase shift is shown to be imposed to the retrieved pulse when we detune the coupling and probe beams from the center of the Doppler profile.

In this thesis, we studied the behavior of rubidium 87 atoms excited in Rydberg states and placed near an optical nanofiber. This work is motivated by the prospect of atom-nanofiber interfaces using Rydberg blocking (e.g. for the manipulation of quantum information contained in atomic nodes).More precisely, we have focused on determining the part of spontaneous emission of a Rydberg atom towards the guided modes of the nanofiber, on calculating the energy displacement (Lamb shift) generated by the nanofiber on this atom and the (Casimir-Polder) force that derives from it. We then analyzed the modifications induced by the introduction of an optical nanofiber on the van der Waals interaction potential between two Rydberg atoms. In all cases, we sought to characterize the influence on our results of the atomic quantum state (principal quantum number, orbital kinetic moment, etc.) and of the geometrical configuration. In particular, we have considered atomic states that give rise to a chiral interaction with the field near the fiber and generate, among others, directional emission phenomena., Dans ce mémoire, nous avons étudions le comportement d'atomes de rubidium 87 excités dans des états de Rydberg et placés à proximité d'une nanofibre optique. Ce travail est motivé par la perspective d'interfaces atomes-nanofibre utilisant le blocage Rydberg (par exemple pour la manipulation de l'information quantique contenue dans les noeuds atomiques).Nous nous sommes plus précisément attachés à déterminer la part d'émission spontanée d'un atome de Rydberg vers les modes guidés de la nanofibre, à calculer le déplacement énergétique (Lamb shift) engendré par la nanofibre sur cet atome et la force (de Casimir-Polder) qui en dérive. Nous avons ensuite analysé les modifications induites par l'introduction d'une nanofibre optique sur le potentiel d'interaction de van der Waals entre deux atomes de Rydberg. Dans tous les cas, nous avons cherché à caractériser l'influence sur nos résultats de l'état quantique atomique (nombre quantique principal, moment cinétique orbital, etc.) et de la configuration géométrique. Nous avons, en particulier, considéré des états atomiques qui donnent lieu à une interaction chirale avec le champ à proximité de la fibre et engendrent, entre autres, des phénomènes d'émission directionnelle.