Atom counting statistics in ensembles of interacting Rydberg atoms

Large deviations in one-dimensional random sequential adsorption

In random sequential adsorption (RSA), objects are deposited randomly, irreversibly, and sequentially; attempts leading to an overlap with previously deposited objects are discarded. The process continues until the system reaches a jammed state when no further additions are possible. We analyze a class of lattice RSA models in which landing on an empty site in a segment is allowed when at least b neighboring sites on the left and the right are unoccupied. For the minimal model (b=1), we compute the full counting statistics of the occupation number. We reduce the determination of the full counting statistics to a Riccati equation that appears analytically solvable only when b=1. We develop a perturbation procedure which, in principle, allows one to determine cumulants consecutively, and we compute the variance of the occupation number for all b.

Electric Field Excitation Suppression in Cold Atoms

In this article, the atom excitation suppression is studied in two mechanisms. The first mechanism for excitation suppression is caused by an external DC electric field. The second mechanism is due to the energy shift caused by an electric field generated by free charges, which are created by ionizing atoms. The latter mechanism is known as the Coulomb blockade. Here, the Coulomb forces originate from ions created by ionizing atoms with a UV laser. The interaction, which causes the suppression, is treated theoretically as dipole–charge interactions. In the model, the charge is an ion, and the dipole is an atom. From measurements, we use 85Rb atoms. The valence electron and the ion core are the two poles of an electric dipole. The interaction potential energy between the ion and the atom is proportional to 1R2, and the frequency shift caused by this interaction is proportional to 1R4, where R is the distance between the ion and the dipole considered. This research is motivated by potential applications for quantum information storage, remote control, creating hot plasmas using cold atoms, as well as electronic devices.

Emergence of quantum correlations from interacting fibre-cavity polaritons

Over the past decade, exciton-polaritons in semiconductor microcavities have revealed themselves as one of the richest realizations of a light-based quantum fluid¹, subject to fascinating new physics and potential applications^2-6. For instance, in the regime of large two-body interactions, polaritons can be used to manipulate the quantum properties of a light field^7-9. In this work, we report on the emergence of quantum correlations in laser light transmitted through a fibre-cavity polariton system. We observe a dispersive shape of the autocorrelation function around the polariton resonance that indicates the onset of this regime. The weak amplitude of these correlations indicates a state that still remains far from a low-photon-number state. Nonetheless, given the underlying physical mechanism⁷, our work opens up the prospect of eventually using polaritons to turn laser light into single photons.

Towards polariton blockade of confined exciton-polaritons

Cavity-polaritons in semiconductor microstructures have emerged as a promising system for exploring non-equilibrium dynamics of many-body systems¹. Key advances in this field, including the observation of polariton condensation², superfluidity³, realization of topological photonic bands⁴, and dissipative phase transitions^5-7, generically allow for a description based on a mean-field Gross-Pitaevskii formalism. Observation of polariton intensity squeezing^8,9 and decoherence of a polarization entangled photon pair by a polariton condensate¹⁰, on the other hand, demonstrate quantum effects that show up at high polariton occupancy. Going beyond and into the regime of strongly correlated polaritons requires the observation of a photon blockade effect^11,12 where interactions are strong enough to suppress double occupancy of a photonic lattice site. Here, we report evidence of quantum correlations between polaritons spatially confined in a fibre cavity. Photon correlation measurements show that careful tuning of the coupled system can lead to a modest reduction of simultaneous two-polariton generation probability by 5%. Concurrently, our experiments allow us to measure the polariton interaction strength, thereby resolving the controversy stemming from recent experimental reports¹³. Our findings constitute an essential step towards the realization of strongly interacting photonic systems.

Rydberg interaction induced enhanced excitation in thermal atomic vapor

We present the experimental demonstration of interaction induced enhancement in Rydberg excitation or Rydberg anti-blockade in thermal atomic vapor. We have used optical heterodyne detection technique to measure Rydberg population due to two-photon excitation to the Rydberg state. The anti-blockade peak which doesn’t satisfy the two-photon resonant condition is observed along with the usual two-photon resonant peak which can’t be explained using the model with non-interacting three-level atomic system. A model involving two interacting atoms is formulated for thermal atomic vapor using the dressed states of three-level atomic system to explain the experimental observations. A non-linear dependence of vapor density is observed for the anti-blockade peak which also increases with increase in principal quantum number of the Rydberg state. A good agreement is found between the experimental observations and the proposed interacting model. Our result implies possible applications towards quantum logic gates using Rydberg anti-blockade in thermal atomic vapor.

Tunable phonon blockade in quadratically coupled optomechanical systems

We theoretically investigate the phonon statistics of a quadratically coupled optomechanical system, in which an effective second-order nonlinear interaction between an optical mode and a mechanical mode is induced by a strong optical driving field on two-phonon red-sideband resonance. We show that strong phonon antibunching can be observed even if the strength of the effective second-order nonlinear interaction is much weaker than the decay rates of the system, by driving the optical and mechanical modes with weak driving fields respectively. Moreover, the phonon statistics can be dynamically controlled by tuning the strengths and the phase difference of the weak driving fields. The scheme proposed here can be used to realize tunable single-phonon sources with quadratically optomechanical coupling.

Control of Spatial Correlations between Rydberg Excitations using Rotary Echo

We manipulate correlations between Rydberg excitations in cold atom samples using a rotary-echo technique in which the phase of the excitation pulse is flipped at a selected time during the pulse. The correlations are due to interactions between the Rydberg atoms. We measure the resulting change in the spatial pair correlation function of the excitations via direct position-sensitive atom imaging. For zero detuning of the lasers from the interaction-free Rydberg-excitation resonance, the pair-correlation value at the most likely nearest-neighbor Rydberg-atom distance is substantially enhanced when the phase is flipped at the middle of the excitation pulse. In this case, the rotary echo eliminates most uncorrelated (unpaired) atoms, leaving an abundance of correlated atom pairs at the end of the sequence. In off-resonant cases, a complementary behavior is observed. We further characterize the effect of the rotary-echo excitation sequence on the excitation-number statistics.

Sub-Poissonian Statistics of Jamming Limits in Ultracold Rydberg Gases

Several recent experiments have established by measuring the Mandel Q parameter that the number of Rydberg excitations in ultracold gases exhibits sub-Poissonian statistics. This effect is attributed to the Rydberg blockade that occurs due to the strong interatomic interactions between highly excited atoms. Because of this blockade effect, the system can end up in a state in which all particles are either excited or blocked: a jamming limit. We analyze appropriately constructed random-graph models that capture the blockade effect, and derive formulae for the mean and variance of the number of Rydberg excitations in jamming limits. This yields an explicit relationship between the Mandel Q parameter and the blockade effect, and comparison to measurement data shows strong agreement between theory and experiment.

Tuning ultracold chemical reactions via Rydberg-dressed interactions

We show that ultracold chemical reactions with an activation barrier can be tuned using Rydberg-dressed interactions. Scattering in the ultracold regime is sensitive to long-range interactions, especially when weakly bound (or quasibound) states exist near the collision threshold. We investigate how, by Rydberg dressing a reactant, one enhances its polarizability and modifies the long-range van der Waals collision complex, which can alter chemical reaction rates by shifting the position of near-threshold bound states. We carry out a full quantum mechanical scattering calculation for the benchmark system H(2)+D, and show that resonances can be moved substantially and that rate coefficients at cold and ultracold temperatures can be increased by several orders of magnitude.

Kinetic constraints, hierarchical relaxation, and onset of glassiness in strongly interacting and dissipative Rydberg gases

We show that the dynamics of a laser driven Rydberg gas in the limit of strong dephasing is described by a master equation with manifest kinetic constraints. The equilibrium state of the system is uncorrelated but the constraints in the dynamics lead to spatially correlated collective relaxation reminiscent of glasses. We study and quantify the evolution towards equilibrium in one and two dimensions, and analyze how the degree of glassiness and the relaxation time are controlled by the interaction strength between Rydberg atoms. We also find that spontaneous decay of Rydberg excitations leads to an interruption of glassy relaxation that takes the system to a highly correlated nonequilibrium stationary state. The results presented here, which are in principle also applicable to other systems such as polar molecules and atoms with large magnetic dipole moments, show that the collective behavior of cold atomic and molecular ensembles can be similar to that found in soft condensed-matter systems.

Emergence of spatial spin-wave correlations in a cold atomic gas

Rydberg spin-waves are optically excited in a quasi-one-dimensional atomic sample of Rb atoms. Pairwise 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.

Quantum nonlinear optics with single photons enabled by strongly interacting atoms

The realization of strong nonlinear interactions between individual light quanta (photons) is a long-standing goal in optical science and engineering, being of both fundamental and technological significance. In conventional optical materials, the nonlinearity at light powers corresponding to single photons is negligibly weak. Here we demonstrate a medium that is nonlinear at the level of individual quanta, exhibiting strong absorption of photon pairs while remaining transparent to single photons. The quantum nonlinearity is obtained by coherently coupling slowly propagating photons to strongly interacting atomic Rydberg states in a cold, dense atomic gas. Our approach paves the way for quantum-by-quantum control of light fields, including single-photon switching, all-optical deterministic quantum logic and the realization of strongly correlated many-body states of light.

Cooperative excitation and many-body interactions in a cold Rydberg gas

The dipole blockade of Rydberg excitations is a hallmark of the strong interactions between atoms in these high-lying quantum states [M. Saffman, T. G. Walker, and K. Mølmer, Rev. Mod. Phys. 82, 2313 (2010); D. Comparat and P. Pillet, J. Opt. Soc. Am. B 27, A208 (2010)]. 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 ultracold rubidium atoms both on and off resonance, which exhibit sub- and super-Poissonian counting statistics, respectively. We compare our results with numerical simulations using a novel theoretical model based on Dicke states of Rydberg atoms including dipole-dipole interactions, finding good agreement between experiment and theory.

Strongly interacting Rydberg excitations of a cold atomic gas

Highly excited Rydberg atoms have many exaggerated properties. In particular, the interaction strength between such atoms can be varied over an enormous range. In a mesoscopic ensemble, such strong, long-range interactions can be used for fast preparation of desired many-particle states. We generated Rydberg excitations in an ultra-cold atomic gas and subsequently converted them into light. As the principal quantum number n was increased beyond ~70, no more than a single excitation was retrieved from the entire mesoscopic ensemble of atoms. These results hold promise for studies of dynamics and disorder in many-body systems with tunable interactions and for scalable quantum information networks.

Interaction enhanced imaging of individual Rydberg atoms in dense gases

We propose a new all-optical method to image individual Rydberg atoms embedded within dense gases of ground state atoms. The scheme exploits interaction-induced shifts on highly polarizable excited states of probe atoms, which can be spatially resolved via an electromagnetically induced transparency resonance. Using a realistic model, we show that it is possible to image individual Rydberg atoms with enhanced sensitivity and high resolution despite photon-shot noise and atomic density fluctuations. This new imaging scheme could be extended to other impurities such as ions, and is ideally suited to equilibrium and dynamical studies of complex many-body phenomena involving strongly interacting particles. As an example we study blockade effects and correlations in the distribution of Rydberg atoms optically excited from a dense gas.

Many-body spin interactions and the ground state of a dense Rydberg lattice gas

We study a one-dimensional atomic lattice gas in which Rydberg atoms are excited by a laser and whose external dynamics is frozen. We identify a parameter regime in which the Hamiltonian is well approximated by a spin Hamiltonian with quasilocal many-body interactions which possesses an exact analytic ground state solution. This state is a superposition of all states of the system that are compatible with an interaction induced constraint weighted by a fugacity. We perform a detailed analysis of this state which exhibits a crossover between a paramagnetic phase with short-ranged correlations and a crystal. This study also leads us to a class of spin models with many-body interactions that permit an analytic ground state solution.

Thermalization in a coherently driven ensemble of two-level systems

We investigate the coherent quantum time evolution of a driven mesoscopic chain of two-level systems that interact via the van der Waals interaction in their excited state. The Hamiltonian is the sum of a classical lattice gas Hamiltonian and an off-diagonal driving term without classical counterpart. Starting from a product state we observe-beyond a certain interaction strength-thermalization of the system with respect to observables of the classical lattice gas. This transition can be studied experimentally with Rydberg atoms, ions, or polar molecules. We suggest how to experimentally determine the temperature of the thermal state which should allow for thermometry of the internal degrees of freedom of cold Rydberg gases whose external dynamics is frozen.

Evidence of antiblockade in an ultracold Rydberg gas

We present the experimental observation of the antiblockade in an ultracold Rydberg gas recently proposed by Ates et al. [Phys. Rev. Lett. 98, 023002 (2007)]. Our approach allows the control of the pair distribution in the gas and is based on a strong coupling of one transition in an atomic three-level system, while introducing specific detunings of the other transition. When the coupling energy matches the interaction energy of the Rydberg long-range interactions, the otherwise blocked excitation of close pairs becomes possible. A time-resolved spectroscopic measurement of the Penning ionization signal is used to identify slight variations in the Rydberg pair distribution of a random arrangement of atoms. A model based on a pair interaction Hamiltonian is presented which well reproduces our experimental observations and allows one to deduce the distribution of nearest-neighbor distances.

Efficient multiparticle entanglement via asymmetric Rydberg blockade

We present an efficient method for producing N particle entangled states using Rydberg blockade interactions. Optical excitation of Rydberg states that interact weakly, yet have a strong coupling to a second control state is used to achieve state dependent qubit rotations in small ensembles. On the basis of quantitative calculations, we predict that an entangled quantum superposition state of eight atoms can be produced with a fidelity of 84% in cold Rb atoms.

Breaking the dipole blockade: nearly resonant dipole interactions in few-atom systems

A dipole blockade, in which Rydberg-atom-Rydberg-atom interactions inhibit all but a single collective Rydberg excitation, has been proposed as a mechanism to store and manipulate quantum information in mesoscopic ensembles. We investigate the excitation dynamics of a collection of a few atoms and show that they undergo an unexpected, qualitative change when the number of atoms increases from two to three. In particular, the combined action of three atoms, each of which pairwise would produce a blockade, can break the dipole blockade.

Double-resonance spectroscopy of interacting Rydberg-atom systems

The energy level spectrum of a many-body system containing two shared, collective Rydberg excitations is measured using cold atoms in an optical dipole trap. Two pairs of independently tunable laser pulses are employed to spectroscopically probe the spectrum in a double-resonance excitation scheme. Depending on the magnitude of an applied electric field, the Rydberg-atom interactions can vary from resonant dipole-dipole to attractive or repulsive van der Waals, leading to characteristic signatures in the measured spectra. Our results agree with theoretical estimates of the magnitude and sign of the interactions.

Rydberg-Rydberg collisions: resonant enhancement of state mixing and penning ionization

In rubidium Rydberg states, the collision nD_(5/2)+nD_(5/2)-->(n-2)F_(7/2)+(n+2)P_(3/2) is nearly resonant in the vicinity of n=43. As a result, over a short range of n centered around n approximately 43 the Rydberg-Rydberg interaction potential is quite large and turns from repulsive to attractive [Phys. Rev. A 75, 032712 (2007)10.1103/PhysRevA.75.032712]. We use state-selective field ionization to investigate the effect of this resonance on instantaneous excitation of mixed two-particle states, state-mixing collisions, and Penning ionization. We find that these processes depend on the magnitude and sign of the two-particle interaction potential, and thus on n near the resonance. The large magnitude of the observed state mixing provides evidence for many-body effects.

Rabi oscillations between ground and Rydberg states with dipole-dipole atomic interactions

We demonstrate Rabi oscillations of small numbers of 87Rb atoms between ground and Rydberg states with n< or =43. Coherent population oscillations are observed for single atoms, 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.

Echo experiments in a strongly interacting Rydberg gas

When ground state atoms are excited to a Rydberg state, van der Waals interactions among them can lead to a strong suppression of the excitation. Despite the strong interactions the evolution can still be reversed by a simple phase shift in the excitation laser field. We experimentally prove the coherence of the excitation in the strong blockade regime by applying an "optical rotary echo" technique to a sample of magnetically trapped ultracold atoms, analogous to a method known from nuclear magnetic resonance. We additionally measured the dephasing time due to the interaction between the Rydberg atoms.

Evidence for coherent collective Rydberg excitation in the strong blockade regime

We report on strong van der Waals blockade in two-photon Rydberg excitation of ultracold magnetically trapped 87Rb atoms. The excitation dynamics was investigated for a large range of densities and laser intensities and shows a full saturation and a strong suppression with respect to single-atom behavior. The observed scaling of the initial increase with density and laser intensity provides evidence for coherent collective excitation. This coherent collective behavior, that was observed for up to several thousand atoms per blockade volume, is generic for all mesoscopic systems which are able to carry only one single quantum of excitation.

Electric-field induced dipole blockade with Rydberg atoms

High resolution laser Stark excitation of np (60<n<85) Rydberg states of ultracold 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 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 atoms agree with the experiments and indicate a major role of the nearest neighboring Rydberg atom.

Enhancement of Rydberg atom interactions using ac Stark shifts

The ac Stark effect was used to induce resonant energy transfer between translationally cold 85Rb Rydberg atoms. When a 28.5 GHz dressing field was set at specific field strengths, the two-atom dipole-dipole process 43d5/2+43d5/2-->45p3/2+41f was dramatically enhanced, due to induced degeneracy of the initial and final states. This method for enhancing interactions is complementary to dc electric-field-induced resonant energy transfer, but has more flexibility due to the possibility of varying the applied frequency.

Antiblockade in Rydberg excitation of an ultracold lattice gas

It is shown that the two-step excitation scheme typically used to create an ultracold Rydberg gas can be described with an effective two-level rate equation, greatly reducing the complexity of the optical Bloch equations. This allows us to efficiently solve the many-body problem of interacting cold atoms with a Monte Carlo technique. Our results reproduce the observed excitation blockade effect. However, we demonstrate that an Autler-Townes double peak structure in the two-step excitation scheme, which occurs for moderate pulse lengths as used in the experiment, can give rise to an antiblockade effect. It is most pronounced for atoms arranged on a lattice. Since the effect is robust against a large number of lattice defects it should be experimentally realizable with an optical lattice created by CO2 lasers.

Dipole blockade at Förster resonances in high resolution laser excitation of Rydberg states of cesium atoms

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.