Classically, the dynamics of the chiral oscillator (CO) may be described by the Landau model (LM) through a well established mathematical procedure known as duality mapping. In this letter we show how this duality is broken in quantum mechanics due to the presence of a $Z_2$-anomaly in the CO. We give the theoretical basis for an experimental setup displaying the possibility to measure this global anomaly using cold Rydberg atoms.
Semiunitary transformation is applied to discuss supersymmetrization of cold Rydberg atoms. In the limit of vanishing kinetic energy the lowest angular momentum of the supersymmetric cold Rydberg atom is $3\hbar/2$. A possible experimental verification is suggested.
We report the creation of an interacting cold Rydberg gas of strontium atoms. We show that the excitation spectrum of the inner valence electron is sensitive to the interactions in the Rydberg gas, even though they are mediated by the outer Rydberg electron. By studying the evolution of this spectrum we observe density-dependent population transfer to a state of higher angular momentum l. We determine the fraction of Rydberg atoms transferred, and identify the dominant transfer mechanism to be l-changing electron-Rydberg collisions associated with the formation of a cold plasma.
We demonstrate a cooperative optical non-linearity caused by dipolar interactions between Rydberg atoms in an ultra-cold atomic ensemble. By coupling a probe transition to the Rydberg state we map the strong dipole-dipole interactions between Rydberg pairs onto the optical field. We characterize the non-linearity as a function of electric field and density, and demonstrate the enhancement of the optical non-linearity due to cooperativity.
We report on a versatile, highly controllable hybrid cold Rydberg atom fiber interface, based on laser cooled atoms transported into a hollow core Kagomé crystal fiber. Our experiments are the first to demonstrate the feasibility of exciting cold Rydberg atoms inside a hollow core fiber and we study the influence of the fiber on Rydberg electromagnetically induced transparency (EIT) signals. Using a temporally resolved detection method to distinguish between excitation and loss, we observe two different regimes of the Rydberg excitations: one EIT regime and one regime dominated by atom loss. T…
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.
We propose and analyze a scheme for realizing the quantum reflection of single photons in a cold Rydberg atomic gas via electromagnetically induced transparency, by which a deep and tunable attractive potential well can be prepared by using stored gate photons. Such a scheme is promising for designing dispersion-type single-photon switches, and may be taken as a quantum device for observing the wave and particle natures of photons simultaneously.
Interaction between Rydberg atoms can significantly modify Rydberg excitation dynamics. Under a resonant driving field the Rydberg-Rydberg interaction in high-lying states can induce shifts in the atomic resonance such that a secondary Rydberg excitation becomes unlikely leading to the Rydberg blockade effect. In a related effect, off-resonant coupling of light to Rydberg states of atoms contributes to the Rydberg anti-blockade effect where the Rydberg interaction creates a resonant condition that promotes a secondary excitation in a Rydberg atomic gas. Here, we study the light-matter interact…
We study electromagnetically induced transparency (EIT) of a weakly interacting cold Rydberg gas. We show that the onset of interactions is manifest as a depopulation of the Rydberg state and numerically model this effect by adding a density-dependent non-linear term to the optical Bloch equations. In the limit of a weak probe where the depopulation effect is negligible, we observe no evidence of interaction induced decoherence and obtain a narrow Rydberg dark resonance with a linewidth of <600 kHz, limited by the Rabi frequency of the coupling beam
The implementation of electromagnetically induced transparency (EIT) in a cold Rydberg gas provides an attractive route towards strong photon--photon interactions and fully deterministic all-optical quantum information processing. In this brief review we discuss the underlying principles of how large single photon non-linearities are achieved in this system and describe experimental progress to date.
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 report on a controllable, hybrid quantum system consisting of cold Rydberg atoms and an optical nanofiber interface. Using a two-photon ladder-type excitation in $^{87}$Rb, we demonstrate both coherent and incoherent Rydberg excitation at submicron distances from the nanofiber surface. The 780 nm photon, near resonant to the $5S \rightarrow 5P$ transition, is mediated by the cooling laser, while the 482 nm light, near resonant to the $5P \rightarrow 29D$ transition, is mediated by the guided mode of the nanofiber. The population loss rate of the cold atom ensemble is used to measure the Ryd…
The combination of electromagnetically induced transparency (EIT) with the nonlinear interaction between Rydberg atoms provides an effective interaction between photons. In this paper, we investigate the storage of optical pulses as collective Rydberg atomic excitations in a cold atomic ensemble. By measuring the dynamics of the stored Rydberg polaritons, we experimentally demonstrate that storing a probe pulse as Rydberg polaritons strongly enhances the Rydberg mediated interaction compared to the slow propagation case. We show that the process is characterized by two time scales. At short st…
Long-range interactions between cold Rydberg atoms, which are used in many important applications, can be enhanced using Förster resonances between collective many-body states controlled by an external electric field. Here we report on the first experimental observation of highly-resolved radio-frequency-assisted Förster resonances in a few cold Rb Rydberg atoms. We also observed radio-frequency-induced Förster resonances which cannot be tuned by a dc electric field. They imply an efficient transition from van der Waals to resonant dipole-dipole interaction due to Floquet sidebands of Rydberg …
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…
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…
In Rydberg dressed ultra-cold gases, ground state atoms inherit properties of a weakly admixed Rydberg state, such as sensitivity to long-range interactions. We show that through hyperfine-state dependent interactions, a pair of atom clouds can evolve into a spin and subsequently into a spatial Schrödinger's cat state: The pair, containing 20 atoms in total, is in a coherent superposition of two configurations, with cloud locations separated by micrometers. The mesoscopic nature of the superposition state can be proven with absorption imaging, while the coherence can be revealed though recombi…
In the last twenty years, Rydberg atoms have become a versatile and much studied system for implementing quantum many-body systems in the framework of quantum computation and quantum simulation. However, even in the absence of coherent evolution Rydberg systems exhibit interesting and non-trivial many-body phenomena such as kinetic constraints and non-equilibrium phase transitions that are relevant in a number of research fields. Here we review our recent work on such systems, where dissipation leads to incoherent dynamics and also to population decay. We show that those two effects, together …
We experimentally demonstrate an original method to measure very accurately the density of a frozen Rydberg gas. It is based on the use of adiabatic transitions induced by the long-range dipole-dipole interaction in pairs of nearest neighbor Rydberg atoms by sweeping an electric field with time. The efficiency of this two-body process is experimentally tunable, depends strongly on the density of the gas and can be accurately calculated. The analysis of this efficiency leads to an accurate determination of the Rydberg gas density, and to a calibration of the Rydberg detection. Our method does n…
The electric fields near the heterogeneous metal/dielectric surface of an atom chip were measured using cold atoms. The atomic sensitivity to electric fields was enhanced by exciting the atoms to Rydberg states that are 10^8 times more polarizable than the ground state. We attribute the measured fields to charging of the insulators between the atom chip wires. Surprisingly, it is observed that these fields may be dramatically lowered with appropriate voltage biasing, suggesting configurations for the future development of hybrid quantum systems.
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.
Atoms in highly excited (Rydberg) states have a number of unique properties which make them attractive for applications in quantum information. These are large dipole moments, lifetimes and polarizabilities, as well as strong long-range interactions between Rydberg atoms. Experimental methods of laser cooling and precision spectroscopy enable the trapping and manipulation of single Rydberg atoms and applying them for practical implementation of quantum gates over qubits of a quantum computer based on single neutral atoms in optical traps. In this paper, we give a review of the experimental and…
This work reports on the real-time detection of internal-state dynamics of cold Rb$^{87}$ atoms being excited to the $30D_{5/2}$ Rydberg state via two-photon excitation. A mesoscopic cloud of atoms is overlapped with the mode volume of a confocal optical cavity and optically pumped by two laser beams transverse to the cavity axis. The excitation to Rydberg states changes the collective atom-cavity coupling, which is detected by monitoring the light transmitted through the cavity while being weakly driven. In addition to the damped coherent excitation dynamics and the decay back to the ground s…
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 n…
We report on the direct measurement in real space of the effect of the van der Waals forces between individual Rydberg atoms on their external degrees of freedom. Clusters of Rydberg atoms with inter-particle distances of around 5 μm are created by first generating a small number of seed excitations in a magneto-optical trap, followed by off-resonant excitation that leads to a chain of facilitated excitation events. After a variable expansion time the Rydberg atoms are field ionized, and from the arrival time distributions the size of the Rydberg cluster after expansion is calculated. Our expe…
We provide a detailed theoretical and conceptual study of a planned experiment to excite Rydberg states of ions trapped in a Paul trap. The ultimate goal is to exploit the strong state dependent interactions between Rydberg ions to implement quantum information processing protocols and to simulate the dynamics of strongly interacting spin systems. We highlight the promises of this approach when combining the high degree of control and readout of quantum states in trapped ion crystals with the novel and fast gate schemes based on interacting giant Rydberg atomic dipole moments. We discuss antic…
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 have investigated formation of structures of Rydberg atoms excited from a disordered gas of ultracold atoms, using rate equations for two-photon Rydberg excitation in a single atom without eliminating the intermediate state. We have explored the validity range of these rate equations and defined a simple measure to determine, whether our model is applicable for a given set of laser parameters. We have applied these rate equations in Monte Carlo simulations of ultracold gases, for different laser beam profiles, and compared these simulations to experimental observations and find a general ag…
Quantum reflection refers to a non-vanishing reflection probability in the absence of a classically turning point. Much attention has been paid to such reflections due to their fundamental, intriguing physics and potential practical applications. Here we propose a scheme to realize a quantum reflection of nonlocal nonlinear optical beams in a cold Rydberg atomic gas via electromagnetically induced transparency working in a dispersion regime. Based on the long-range interaction between Rydberg atoms, we found that the system supports low-power nonlocal optical solitons. Such nonlocal solitons c…
The atom-based traceable standard for microwave electrometry shows promising advantages by enabling stable and uniform measurement. Here we theoretically propose and then experimentally realize an alternative direct International System of Units (SI)-traceable and self-calibrated method for measuring a microwave electric field strength based on electromagnetically induced absorption (EIA) in cold Rydberg atoms. Comparing with the method of electromagnetically induced transparency, we show that the equivalence relation between microwave Rabi frequency and Autler-Townes splitting is more valid a…
The collective effect of large amounts of atoms exhibit an enhanced interaction between light and atoms. This holds great interest in quantum optics, and quantum information. When a collective excited state of a group of atoms during Rabi oscillation is varying, the oscillation exhibits rich dynamics. Here, we experimentally observe a size-reduction effect of the Rydberg collective state during Rabi oscillation in cold atomic dilute gases. The Rydberg collective state was first created by the Rydberg quantum memory, and we observed a decreased oscillation frequency effect by measuring the time…
The resonant transfer of energy from the inversion sublevels in NH$_3$ to He atoms in triplet Rydberg states with principal quantum number $n=38$ has been controlled using electric fields below 15 V/cm in intrabeam collisions at translational temperatures of $\sim1$ K. The experiments were performed in pulsed supersonic beams of NH$_3$ seeded in He at a ratio of 1:19. The He atoms were prepared in the metastable 1s2s $^3$S$_1$ level in a pulsed electric discharge in the trailing part of the beams. The velocity slip between the heavy NH$_3$ and the lighter metastable He was exploited to perform…
We present a simplified version of a repeater protocol in a cold neutral-atom ensemble with Rydberg excitations optimized for two-node entanglement generation and describe a protocol for quantum teleportation. Our proposal draws from previous proposals [Zhao, {\sl et al.}, Phys. Rev. A {\bf 81}, 052329 (2010)] and [Han, {\sl et al.} Phys. Rev. A {\bf 81}, 052311 (2010)] who described efficient and robust protocols for long-distance entanglement with many nodes. Using realistic experimental values we predict an entanglement generation rate of $\sim$25 Hz and teleportation rate of $\sim$ 5 Hz. O…
Experiments on the spectroscopy of the Förster resonance Rb(37P)+Rb(37P) -> Rb(37S)+Rb(38S) and microwave transitions nP -> n'S, n'D between Rydberg states of cold Rb atoms in a magneto-optical trap have been performed. Under ordinary conditions, all spectra exhibited a 2-3 MHz line width independently of the interaction time of atoms with each other or with microwave radiation, although the ultimate resonance width should be defined by the inverse interaction time. Analysis of the experimental conditions has shown that the main source of the line broadening was the inhomogeneous electric fiel…
We devise a cold-atom approach to realizing a broad range of bi-linear quantum magnets. Our scheme is based on off-resonant single-photon excitation of Rydberg $P$-states (Rydberg-dressing), whose strong interactions are shown to yield controllable XYZ-interactions between effective spins, represented by different atomic ground states. The distinctive features of Förster-resonant Rydberg atom interactions are exploited to enhance the effectiveness of Rydberg-dressing and, thereby, yield large spin-interactions that greatly exceed corresponding decoherence rates. We illustrate the concept on a …
The coupling of weak light fields to Rydberg states of atoms under conditions of electromagnetically induced transparency (EIT) leads to the formation of Rydberg polaritons which are quasi-particles with tunable effective mass and long-range interactions. Confined to one spatial dimension their low energy physics is that of a moving-frame Luttinger liquid which due to the long-range character of the repulsive interaction can form a Wigner crystal. We calculate the Luttinger $K$ parameter using density-matrix renormalization group (DMRG) simulations and find that under typical slow-light condit…
Versatile controllability of interactions in ultracold atomic and molecular gases has now reached an unprecedented era where quantum correlations and unconventional many-body phases can be studied with no corresponding analogs in solid state systems. Recent experiments in Rydberg atomic gases have achieved exquisite control over non-local interactions, allowing novel quantum phases unreachable with the usual local interactions in atomic systems. Here, we study Rydberg dressed atomic fermions in a three dimensional optical lattice predicting the existence of hitherto unheard-of exotic mixed top…
We calculate properties of dipolar interacting ultracold molecules or Rydberg atoms in a semi-synthetic three-dimensional configuration -- one synthetic dimension plus a two-dimensional real space optical lattice or periodic microtrap array -- using the stochastic Green function Quantum Monte Carlo method. Through a calculation of thermodynamic quantities and appropriate correlation functions, along with their finite size scalings, we show that there is a second order transition to a low temperature phase in which two-dimensional `sheets' form in the synthetic dimension of internal rotational …
The spectral structure underlying excitonic energy transfer in ultra-cold Rydberg gases is studied numerically, in the framework of random matrix theory, and via self-consistent diagrammatic techniques. Rydberg gases are made up of randomly distributed, highly polarizable atoms that interact via strong dipolar forces. Dynamics in such a system is fundamentally different from cases in which the interactions are of short range, and is ultimately determined by the spectral and eigenvector structure. In the energy levels' spacing statistics, we find evidence for a critical energy that separates de…
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…
Feshbach resonances in ultra-cold atomic gases have led to some of the most important advances in atomic physics. They did not only enable ground breaking work in the BEC-BCS crossover regime [1], but are also widely used for the association of ultra-cold molecules [2], leading to the formation of molecular Bose-Einstein condensates [3,4] and ultra-cold dipolar molecular systems [5]. Here, we demonstrate the experimental realization of an optical Feshbach resonance using ultra-long range Rydberg molecules [6]. We show their practical use by tuning the revival time of a quantum many-body system…
A theory of Rydberg atom interactions is used to derive analytical forms for the spin wave pair correlation function in laser-excited cold-atom vapors. This function controls the quantum statistics of light emission from dense, inhomogeneous clouds of cold atoms of various spatial dimensionalities. The results yield distinctive scaling behaviors on the microsecond timescale, including generalized exponential decay. A detailed comparison is presented with a recent experiment on a cigar-shaped atomic ensemble [Y. Dudin and A. Kuzmich, Science 336, 887 (2012)], in which Rb atoms are excited to a …
Rydberg spin waves are optically excited in a quasi-one-dimensional atomic sample of Rb atoms. Pair-wise spin-wave correlations are observed by a spatially selective transfer of the quantum state onto a light field and photoelectric correlation measurements of the light. The correlations are interpreted in terms of the dephasing of multiply-excited spin waves by long-range Rydberg interactions.
We review Rydberg aggregates, assemblies of a few Rydberg atoms exhibiting energy transport through collective eigenstates, considering isolated atoms or assemblies embedded within clouds of cold ground-state atoms. We classify Rydberg aggregates, and provide an overview of their possible applications as quantum simulators for phenomena from chemical or biological physics. Our main focus is on flexible Rydberg aggregates, in which atomic motion is an essential feature. In these, simultaneous control over Rydberg-Rydberg interactions, external trapping and electronic energies, allows Born-Oppen…
Recent experiments have realized an all-optical photon transistor using a cold atomic gas. This approach relies on electromagnetically induced transparency (EIT) in conjunction with the strong interaction among atoms excited to high-lying Rydberg states. The transistor is gated via a so-called Rydberg spinwave, in which a single Rydberg excitation is coherently shared by the whole ensemble. In its absence the incoming photon passes through the atomic ensemble by virtue of EIT while in its presence the photon is scattered rendering the atomic gas opaque. An important current challenge is to pre…
We implement high-efficiency coherent excitation to a Rydberg state using stimulated Raman adiabatic passage in a cold atom electron and ion source. We achieve an efficiency of 60% averaged over the laser excitation volume with a peak efficiency of 82%, a 1.6 times improvement relative to incoherent pulsed-laser excitation. Using pulsed electric field ionization of the Rydberg atoms we create electron bunches with durations of 250 ps. High-efficiency excitation will increase source brightness, crucial for ultrafast electron diffraction experiments, and coherent excitation to high-lying Rydberg…
The possibility of testing spatial noncommutativity via Rydberg atoms is explored. An atomic dipole of a cold Rydberg atom is arranged in appropriate electric and magnetic field, so that the motion of the dipole is constrained to be planar and rotationally symmetric. Spatial noncommutativity leads to that the canonical angular momentum possesses fractional values. In the limit of vanishing kinetic energy, the dominate value of the lowest canonical angular momentum takes $\hbar/2$. Furthermore, in the limit of eliminating magnetic field, the dominate value of the lowest canonical angular moment…
We discuss laser dressed dipolar and Van der Waals interactions between atoms and polar molecules, so that a cold atomic gas with laser admixed Rydberg levels acts as a designed reservoir for both elastic and inelastic collisional processes. The elastic scattering channel is characterized by large elastic scattering cross sections and repulsive shields to protect from close encounter collisions. In addition, we discuss a dissipative (inelastic) collision where a spontaneously emitted photon carries away (kinetic) energy of the collision partners, thus providing a significant energy loss in a s…
We present a demonstrative application of the nonholonomic control method to a real physical system composed of two cold Cesium atoms. In particular, we show how to implement a CNOT quantum gate in this system by means of a controlled Stark field.
We study nonlinear optical effects in the laser excitation of Rydberg states. $5S_{1/2}$ and $5P_{3/2}$ levels of $^{85}$Rb are strongly coupled by a strong laser field and probed by a weak laser tuned to the $5P_{3/2} - 44D$ Rydberg resonance. We observe high contrast Autler-Townes spectra which are dependent on the pump polarization, intensity and detuning. The observed behavior agrees with calculations, which include the effect of optical pumping.
By mapping the strong interaction between Rydberg excitations in ultra-cold atomic ensembles onto single photons via electromagnetically induced transparency, it is now possible to realize a nonlinear optical medium which exhibits a strong optical nonlinearity at the level of individual photons. We review the theoretical concepts and the experimental state-of-the-art of this exciting new field, and discuss first applications in the field of all-optical quantum information processing.
