We show that the resonance shifts in the fluorescence of a cold gas of rubidium atoms substantially differ from those of thermal atomic ensembles that obey the standard continuous medium electrodynamics. The analysis is based on large-scale microscopic numerical simulations and experimental measurements of the resonance shifts in a steady-state response in light propagation.
We analyze the temporal response of the fluorescence light that is emitted from a dense gas of cold atoms driven by a laser. When the average interatomic distance is smaller than the wavelength of the photons scattered by the atoms, the system exhibits strong dipolar interactions and collective dissipation. We solve the exact dynamics of small systems with different geometries and show how these collective features are manifest in the scattered light properties such as the photon emission rate, the power spectrum and the second-order correlation function. By calculating these quantities beyond…
We study the spectra of emission of a system composed by an atom, tightly confined inside a high-finesse resonator, when the atom is driven by a laser and is at steady state of the cooling dynamics induced by laser and cavity field. In general, the spectrum of resonance fluorescence and the spectrum at the cavity output contain complementary information about the dynamics undergone by the system. In certain parameter regimes, quantum interference effects between the scattering processes induced by cavity and laser field lead to the selective suppression of features of the resonance fluorescenc…
We investigate the behavior of the light pulse in $Lambda$-type cold atomic gases with two counterpropagating control lights with equal strength by directly simulating the dynamic equations and exploring the dispersion relation. Our analysis shows that, depending on the length $L_0$ of the stored wave packet and the decay rate $γ$ of ground-spin coherence, the recreated light can behave differently. For long $L_0$ and/or large $γ$, a stationary light pulse is produced, while two propagating light pulses appear for short $L_0$ and/or small $γ$. In the $γ\to 0$ limit, the light always splits int…
We study the emergence of a collective optical response of a cold and dense $^{87}$Rb atomic cloud to a near-resonant low-intensity light when the atom number is gradually increased. Experimental observations are compared with microscopic stochastic simulations of recurrent scattering processes between the atoms that incorporate the atomic multilevel structure and the optical measurement setup. We analyze the optical response of an inhomogeneously-broadened gas and find that the experimental observations of the resonance line shifts and the total collected scattered light intensity in cold ato…
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…
We present an analytical theory for the nonlinear optical response of a strongly interacting Rydberg gas under conditions of electromagnetically induced transparency. Simple formulae for the third order optical susceptibility are derived and shown to be in excellent agreement with recent experiments. The obtained expressions reveal strong nonlinearities, which in addition are of highly nonlocal character. This property together with enormous strength of the Rydberg-induced nonlinearities is shown to yield a unique laboratory platform for nonlinear wave phenomena, such as collapse-arrested modu…
We review experimental and theoretical work on cold, trapped metastable noble gases. We em- phasize the aspects which distinguish work with these atoms from the large body of work on cold, trapped atoms in general. These aspects include detection techniques and collision processes unique to metastable atoms. We describe several experiments exploiting these unique features in fields including atom optics and statistical physics. We also discuss precision measurements on these atoms including fine structure splittings, isotope shifts, and atomic lifetimes.
We experimentally investigate trap-loss spectra of the cesium 6S1/2(F=4)-71P3/2 Rydberg state by combining the cesium atomic magneto-optical trap with the narrow-linewidth, continuously-tunable 318.6 nm ultraviolet laser. That is, the atoms in the magneto-optical trap are excited to the Rydberg state due to the ultraviolet laser single-step Rydberg excitation, which leads to the reduction of atomic fluorescence. Based on the trap-loss spectroscopy technology, the Autler-Townes splitting due to strong cooling laser is observed, and the parameter dependence of the AT splitting interval of trap-l…
In this paper, we use steady-state measurements to obtain evidence of radiation trapping in an optically thick a cloud of cold rubidium atoms. We investigate the fluorescence properties of our sample, pumped on opened transitions. The intensity of fluorescence exhibits a non trivial dependence on the optical thickness of the media. A simplified model, based on rate equations self-consistently coupled to a diffusive model of light transport, is used to explain the experimental observations in terms of incoherent radiation trapping on one spectral line. Measurements of atomic populations and flu…
Ultracold quantum gases offer unique possibilities to study interacting many-body quantum systems. Probing and manipulating such systems with ever increasing degree of control requires novel experimental techniques. Scanning electron microscopy is a high resolution technique which can be used for in situ imaging, single site addressing in optical lattices and precision density engineering. Here, we review recent advances and achievements obtained with this technique and discuss future perspectives.
The effect of microwave radiation on the resonance fluorescence of a cloud of cold $^{85}Rb$ atoms in a magnetooptical trap is studied. The radiation frequency was tuned near the hyperfine splitting frequency of rubidium atoms in the 5S ground state. The microwave field induced magnetic dipole transitions between the magnetic sublevels of the 5S(F=2) and 5S(F=3) states, resulting in a change in the fluorescence signal. The resonance fluorescence spectra were recorded by tuning the microwave radiation frequency. The observed spectra were found to be substantially dependent on the transition und…
Cold, dense Rydberg gases produced in a cold-atom trap are investigated using spectroscopic methods and time-resolved electron counting. On the discrete Rydberg resonances we observe large trap losses and long lasting electron emission from the Rydberg gas (>30ms). Our observations are explained by quasi-elastic l-mixing collisions between Rydberg atoms and slow electrons that lead to the population of long-lived high-angular-momentum Rydberg states. These atoms thermally ionize slowly and with large probabilities, leading to the observed effects.
While many-particle entanglement can be found in natural solids and strongly interacting atomic and molecular gases, generating highly entangled states between weakly interacting particles in a controlled and scalable way presents a significant challenge. We describe here a one-step method to generate entanglement in a dilute gas of cold polar molecules. For molecules in optical traps separated by a few micrometers, we show that maximally entangled states can be created using the strong off-resonant pulses that are routinely used in molecular alignment experiments. We show that the resulting a…
The rapidly developing field of optomechanics aims at the combined control of optical and mechanical (solid-state or atomic) modes. In particular, laser cooled atoms have been used to exploit optomechanical coupling for self-organization in a variety of schemes where the accessible length scales are constrained by a combination of pump modes and those associated to a second imposed axis, typically a cavity axis. Here, we consider a system with many spatial degrees of freedom around a single distinguished axis, in which two symmetries - rotations and translations in the plane orthogonal to the …
We theoretically predict a novel type of synthetic Lorentz force for classical (cold) atomic gases, which is based on the Doppler effect and radiation pressure. A fairly uniform and strong force can be constructed for gases in macroscopic volumes of several cubic millimeters and more. This opens the possibility to mimic classical charged gases in magnetic fields, such as those in a tokamak, in cold atom experiments.
We study laser cooling of atomic gases by collisional redistribution of fluorescence. In a high pressure buffer gas regime, frequent collisions perturb the energy levels of alkali atoms, which allows for the absorption of a far red detuned irradiated laser beam. Subsequent spontaneous decay occurs close to the unperturbed resonance frequency, leading to a cooling of the dense gas mixture by redistribution of fluorescence. Thermal deflection spectroscopy indicates large relative temperature changes down to and even below room temperature starting from an initial cell temperature near 700 K. We …
Besides being a source of energy, light can also cool gases of atoms down to the lowest temperatures ever measured, where atomic motion almost stops. The research field of cold atoms has emerged as a multidisciplinary one, highly relevant, e.g., for precision measurements, quantum gases, simulations of many-body physics, and atom optics. In this focus article, we present the field as seen in 2015, and emphasise the fundamental role in its development that has been played by mastering.
Turbulent radiation flow is commonplace in systems with strong, incoherent, light-matter interactions. In astrophysical contexts, photon bubble turbulence is considered a key mechanism behind enhanced radiation transport, and its importance has been widely asserted for a variety of high energy objects such as accretion disks and massive stars. We demonstrate here that analogous conditions to those of dense astrophysical objects can be obtained in large clouds of cold atoms driven close to a sharp electronic resonance. By accessing the spatially-resolved atom density, we are able to identify a …
We study superconducting microtraps with rectangular shapes for cold atomic gases. We present a general argument why microtraps open, if brought close to the surface of the superconductor. We show that for a given width of the strips there exists an optimal thickness under which the closest distance of the microtrap from the superconductor can be achieved. The distance can be significantly improved, if the edge enhancement of the supercurrent near edges and corners is exploited. We compare numerical calculations with results from conformal mapping and show that conformal mapping can often give…
Recent success in manipulating ultra-cold atomic systems allows to probe different strongly correlated regimes in one-dimension. Regimes such as the (spin-coherent) Luttinger liquid and the spin-incoherent Luttinger liquid can be realized by tuning the inter-atomic interaction strength and trap parameters. We identify the noise correlations of density fluctuations as a robust observable (uniquely suitable in the context of trapped atomic gases) to discriminate between these two regimes. Finally, we address the prospects to realize and probe these phenomena experimentally using optical lattices…
We propose a novel scheme to efficiently tune the scattering length of two colliding ground-state atoms by off-resonantly coupling the scattering-state to an excited Rydberg-molecular state using laser light. For the s-wave scattering of two colliding ${^{87}}\mathrm{Rb}$ atoms, we demonstrate that the effective optical length and pole strength of this Rydberg optical Feshbach resonance can be tuned over several orders of magnitude, while incoherent processes and losses are minimised. Given the ubiquity of Rydberg molecular states, this technique should be generally applicable to homo-nuclear …
We investigate the scattering cross section of aligned dipolar molecules in low-temperature gases. Over a wide range of collision energies relevant to contemporary experiments, the cross section declines in inverse proportion to the collision speed, and is given nearly exactly by a simple semiclassical formula. At yet lower energies, the cross section becomes independent of energy, and is reproduced within the Born approximation to within corrections due to the s-wave scattering length. While these behaviors are universal for all polar molecules, nevertheless interesting deviations from univer…
We describe a simple and compact architecture for generating all optical frequencies required for the laser cooling, state preparation and detection of atoms in an ultracold rubidium-87 experiment from a single 780 nm laser source. In particular, repump light $\sim$ 6.5 GHz away from the cooling transition is generated by using a high-bandwidth fiber-coupled eletro-optical modulator (EOM) in a feedback loop configuration. The looped repump light generation scheme solves the problem of the limited power handling capabilities characteristics of fiber EOMs. We demonstrate the functionality of the…
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…
We report on the simultaneous observation from four directions of the fluorescence of single $^{87}$Rb atoms trapped at the common focus of four high numerical aperture (${\rm NA}=0.5$) aspheric lenses. We use an interferometrically-guided pick-and-place technique to precisely and stably position the lenses along the four cardinal directions with their foci at a single central point. The geometry gives right angle access to a single quantum emitter, and will enable new trapping, excitation, and collection methods. The fluorescence signals indicate both sub-Poissonian atom number statistics and…
Systems of three particles show a surprising feature in their bound state spectrum: a series of geometrically scaled states, known as Efimov states. These states have not yet been observed directly, but many recent experiments show indirect evidence of their existence via the so-called recombination process. The theories that predict the Efimov states also predicts either resonant enhancement of the recombination process or suppression by destructive interference, depending on the sign of the interaction between the particles. The theories predict universal features for the Efimov states, for …
We use single or few Cs atoms as thermometer for an ultracold, thermal Rb cloud. Observing the thermometer atoms' thermalization with the cold gas using spatially resolved fluorescence detection, we find an interesting situation, where a fraction of thermometer atoms thermalizes with the cloud while the other fraction remains unaffected. We compare release-recapture measurements of the thermometer atoms to Monte-Carlo simulations while correcting for the non-thermalized fraction, and recover the cold cloud's temperature. The temperatures obtained are verified by independent time-of-flight meas…
Ultra-cold atomic gases are unique in terms of the degree of controllability, both for internal and external degrees of freedom. This makes it possible to use them for the study of complex quantum many-body phenomena. However in many scenarios, the prerequisite condition of faithfully preparing a desired quantum state despite decoherence and system imperfections is not always adequately met. To path the way to a specific target state, we explore quantum optimal control framework based on Bayesian optimization. The probabilistic modeling and broad exploration aspects of Bayesian optimization is…
Photoexcitation rates for creation of ultralong-range Rydberg molecules (ULRM) with 31$\lesssim n \lesssim41$ in both ground and excited vibrational levels in cold ($T\sim900$~nK) gases of polarized and unpolarized $^{87}$Sr are presented. The measured production rates of the $ν=0, 1$ and 2 vibrational levels reveal rather different $n$ dependences which are analyzed by evaluating the Franck-Condon factors associated with excitation of the different vibrational levels and molecular rotational states. In particular, for gases of spin-polarized fermions, only Rydberg dimers with odd rotational q…
We review phase space techniques based on the Wigner representation that provide an approximate description of dilute ultra-cold Bose gases. In this approach the quantum field evolution can be represented using equations of motion of a similar form to the Gross-Pitaevskii equation but with stochastic modifications that include quantum effects in a controlled degree of approximation. These techniques provide a practical quantitative description of both equilibrium and dynamical properties of Bose gas systems. We develop versions of the formalism appropriate at zero temperature, where quantum fl…
Superradiance has been extensively studied in the 1970s and 1980s in the regime of superfluores-cence, where a large number of atoms are initially excited. Cooperative scattering in the linear-optics regime, or "single-photon superradiance" , has been investigated much more recently, and superra-diant decay has also been predicted, even for a spherical sample of large extent and low density, where the distance between atoms is much larger than the wavelength. Here, we demonstrate this effect experimentally by directly measuring the decay rate of the off-axis fluorescence of a large and dilute …
The collision cross section that controls thermalization of gas mixtures is the transport cross section $σ_η^{(1)}$ and not the elastic cross section $σ_{\rm el}$. The two are the same for pure s-wave scattering but not when higher partial waves contribute. We investigate the differences between them for prototype atomic mixtures and show that the distinction is important at energies above 100 $μ$K for LiYb and 3 $μ$K for RbYb and RbCs. For simple systems both $σ_η^{(1)}$ and $σ_{\rm el}$ follow universal energy dependence that depends only on the s-wave scattering length when expressed in red…
We study the effect of an external magnetic field on coherent backscattering of light from a cool rubidium vapor. We observe that the backscattering enhancement factor can be {\it increased} with $B$. This surprising behavior shows that the coherence length of the system can be increased by applying a magnetic field, in sharp contrast with ususal situations. This is mainly due to the lifting of the degeneracy between Zeeman sublevels. We find good agreement between our experimental data and a full Monte-Carlosimulation, taking into account the magneto-optical effects and the geometry of the at…
We observe the shift of Rydberg levels of rubidium close to a copper surface when atomic clouds are repeatedly deposited on it. We measure transition frequencies of rubidium to S and D Rydberg states with principal quantum numbers n between 31 and 48 using the technique of electromagnetically induced transparency. The spectroscopic measurement shows a strong increase of electric fields towards the surface that evolves with the deposition of atoms. Starting with a clean surface, we measure the evolution of electrostatic fields in the range between 30 and 300 \mum from the surface. We find that …
We use the standard fermionic and boson-fermion Hamiltonians to study the BCS-BEC cross-over near the 202 G resonance in a two-component mixture of fermionic 40K atoms employed in the experiment of C.A. Regal et al., Phys. Rev. Lett. 92, 040403 (2004). Our mean-field analysis of many-body equilibrium quantities shows virtually no differences between the predictions of the two approaches, provided they are both implemented in a manner that properly includes the effect of the highest excited bound state of the background scattering potential, rather than just the magnetic-field dependence of the…
We further examine a theory of phase contrast imaging (PCI) of cold atomic gases, first introduced by us in Phys. Rev. Lett. {\bf 112}, 233602 (2014). We model the PCI measurement by directly calculating the entangled state between the light and the atoms due to the ac Stark shift, which induces a conditional phase shift on the light depending upon the atomic state. By interfering the light that passes through the BEC with the original light, one can obtain information of the atomic state at a single shot level. We derive an exact expression for a measurement operator that embodies the informa…
Manifestations of dipole-dipole interactions in dilute thermal gases are difficult to sense because of strong inhomogeneous broadening. Recent experiments reported signatures of such interactions in fluorescence detection-based measurements of multiple quantum coherence (MQC) signals, with many characteristic features hitherto unexplained. We develop an original open quantum systems theory of MQC in dilute thermal gases, which allows us to resolve this conundrum. Our theory accounts for the vector character of the atomic dipoles as well as for driving laser pulses of arbitrary strength, includ…
The theory of continuous phase transitions predicts the universal collective properties of a physical system near a critical point, which for instance manifest in characteristic power-law behaviours of physical observables. The well-established concept at or near equilibrium, universality, can also characterize the physics of systems out of equilibrium. The most fundamental instance of a genuine non-equilibrium phase transition is the directed percolation universality class, where a system switches from an absorbing inactive to a fluctuating active phase. Despite being known for several decade…