Ultracold Atomic Clouds Research Articles

Sub-atom shot noise Faraday imaging of ultracold atom clouds

We demonstrate that a dispersive imaging technique based on the Faraday effect can measure the atom number in a large, ultracold atom cloud with a precision below the atom shot noise level. The minimally destructive character of the technique allows us to take multiple images of the same cloud, which enables sub-atom shot noise measurement precision of the atom number and allows for an in situ determination of the measurement precision. We have developed a noise model that quantitatively describes the noise contributions due to photon shot noise in the detected light and the noise associated with single atom loss. This model contains no free parameters and is calculated through an analysis of the fluctuations in the acquired images. For clouds containing atoms, we achieve a precision more than a factor of two below the atom shot noise level.

Preparation of Ultracold Atom Clouds at the Shot Noise Level.

We prepare number stabilized ultracold atom clouds through the real-time analysis of nondestructive images and the application of feedback. In our experiments, the atom number N∼10^{6} is determined by high precision Faraday imaging with uncertainty ΔN below the shot noise level, i.e., ΔN<sqrt[N]. Based on this measurement, feedback is applied to reduce the atom number to a user-defined target, whereupon a second imaging series probes the number stabilized cloud. By this method, we show that the atom number in ultracold clouds can be prepared below the shot noise level.

Single-shot imaging of trapped Fermi gas

Recently developed techniques allow for simultaneous measurements of the positions of all ultra-cold atoms in a trap with high resolution. Each such single-shot experiment detects one element of the quantum ensemble formed by the cloud of atoms. Repeated single-shot measurements can be used to determine all correlations between particle positions as opposed to standard measurements that determine particle density or two-particle correlations only. In this paper we discuss the possible outcomes of such single-shot measurements in the case of cloud of ultra-cold noninteracting Fermi atoms. We show that the Pauli exclusion principle alone leads to correlations between particle positions that originate from unexpected spatial structures formed by the atoms.

Measurement of Chern numbers through center-of-mass responses

Probing the center-of-mass of an ultracold atomic cloud can be used to measure Chern numbers, the topological invariants underlying the quantum Hall effects. In this work, we show how such center-of-mass observables can have a much richer dependence on topological invariants than previously discussed. In fact, the response of the center of mass depends not only on the current density, typically measured in a solid-state system, but also on the particle density, which itself can be sensitive to the topology of the band structure. We apply a semiclassical approach, supported by numerical simulations, to highlight the key differences between center-of-mass responses and more standard conductivity measurements. We illustrate this by analyzing both the two- and the four-dimensional quantum Hall effects. These results have important implications for experiments in engineered topological systems, such as ultracold gases and photonics.

Unifying Brillouin scattering and cavity optomechanics

So far, Brillouin scattering and cavity optomechanics were mostly disconnected branches of research -- although both deal with photon-phonon coupling. This begs for the development of a broader theory that contains both fields. Here, we derive the dynamics of optomechanical cavities from that of Brillouin-active waveguides. This explicit transition elucidates the link between phenomena such as Brillouin amplification and electromagnetically induced transparency. It proves that effects familiar from cavity optomechanics all have traveling-wave partners, but not vice versa. We reveal a close connection between two parameters of central importance in these fields: the Brillouin gain coefficient and the zero-point optomechanical coupling rate. This enables comparisons between systems as diverse as ultracold atom clouds, plasmonic Raman cavities and nanoscale silicon waveguides. In addition, back-of-the-envelope calculations show that unobserved effects, such as photon-assisted amplification of traveling phonons, are now accessible in existing systems. Finally, we formulate both circuit- and cavity-oriented optomechanics in terms of vacuum coupling rates, cooperativities and gain coefficients, thus reflecting the similarities in the underlying physics.

Energy Scaling of Cold Atom-Atom-Ion Three-Body Recombination

We study three-body recombination of Ba^{+}+Rb+Rb in the mK regime where a single ^{138}Ba^{+} ion in a Paul trap is immersed into a cloud of ultracold ^{87}Rb atoms. We measure the energy dependence of the three-body rate coefficient k_{3} and compare the results to the theoretical prediction, k_{3}∝E_{col}^{-3/4}, where E_{col} is the collision energy. We find agreement if we assume that the nonthermal ion energy distribution is determined by at least two different micromotion induced energy scales. Furthermore, using classical trajectory calculations we predict how the median binding energy of the formed molecules scales with the collision energy. Our studies give new insights into the kinetics of an ion immersed in an ultracold atom cloud and yield important prospects for atom-ion experiments targeting the s-wave regime.

Quantum Enhancement of the Index of Refraction in a Bose-Einstein Condensate.

We study the index of refraction of an ultracold bosonic gas in the dilute regime. Using phase-contrast imaging with light detuned from resonance by several tens of linewidths, we image a single cloud of ultracold atoms for 100 consecutive shots, which enables the study of the scattering rate as a function of temperature and density using only a single cloud. We observe that the scattering rate is increased below the critical temperature for Bose-Einstein condensation by a factor of 3 compared to the single-atom scattering rate. We show that current atom-light interaction models to second order of the density show a similar increase, where the magnitude of the effect depends on the model that is used to calculate the pair-correlation function. This confirms that the effect of quantum statistics on the index of refraction is dominant in this regime.

Interaction between Atoms and Slow Light: A Study in Waveguide Design

One path to quantum information processing involves light-matter interaction, such as light in a photonic-crystal waveguide coupled to a cloud of ultracold alkali atoms. However, to actually implement such a system, it is crucial to increase the coupling strength beyond what is presently achievable. The authors explain the design requirements to achieve large coupling by decreasing the group velocity of an edge mode in a hybrid-clad waveguide, allowing photons of ``slow light'' to interact with trapped cold atoms in a robust, chip-integrated setting.

Generalized BEC and Crossover Theories of Superconductors and Ultracold Bosonic and Fermionic Gases

The generalized Bose-Einstein condensation (GBEC) theory of superconductivity hinges on three distinct new ingredients: (a) treatment of Cooper pairs as real bosons, (b) inclusion of two-hole pairs on an equal footing with two-electron ones, and (c) insertion in the resulting ternary ideal boson-fermion gas of boson-fermion vertex interactions that drive formation/disintegration processes. Besides subsuming both BCS and BEC theories as well as the well-known crossover picture as special cases, GBEC leads to several-orders-of-magnitude enhancements in the critical superconducting temperature Tc. The crossover picture is applicable also to ultracold atomic clouds, both bosonic and fermionic. But known low-density expansions involving the interatomic scattering length a diverge term-by-term around the so-called unitary zone about the Feshbach resonance where a itself diverges. However, expanding a in powers of the attractive part of the interatomic potential renders smooth, divergence-free low-density expansions whose convergence can be accelerated with Pade approximants.

Hybrid synchronization in coupled ultracold atomic gases

We study the time evolution of two coupled many-body quantum systems one of which is assumed to be Bose condensed. Specifically, we consider two ultracold atomic clouds populating each two localized single-particle states, i.e. a two-component Bosonic Josephson junction. The cold atoms cloud can retain its coherence when coupled to the condensate and displays synchronization with the latter, differing from usual entrainment. We term this effect among the ultracold and the condensed clouds as {\it hybrid synchronization}. The onset of synchronization, which we observe in the evolution of average properties of both gases when increasing their coupling, is found to be related to the many-body properties of the quantum gas, e.g. condensed fraction, quantum fluctuations of the particle number differences. We discuss the effects of different initial preparations, the influence of unequal particle numbers for the two clouds, and explore the dependence on the initial quantum state, e.g. coherent state, squeezed state and Fock state, finding essentially the same phenomenology in all cases.

Detection of the clock transition in ultra-cold thulium atoms

The magnetic dipole transition between fine structure sublevels of the ground state of thulium atom has been directly excited in a cloud of ultra-cold atoms by a frequency-stabilised laser. This transition at the wavelength is planned to be used as the clock one in an optical frequency reference on laser-cooled thulium atoms.

Modeling spontaneous breaking of time-translation symmetry

We show that an ultra-cold atomic cloud bouncing on an oscillating mirror can reveal spontaneous breaking of a discrete time translation symmetry. In many-body simulations we illustrate the process of the symmetry breaking that can be induced by atomic losses or by a measurement of particle positions. The results pave the way for understanding and realization of the time crystal idea where crystalline structures form in the time domain due to spontaneous breaking of continuous time translation symmetry.

Vortex interactions in the collision of Bose–Einstein condensates

We investigate the effects of vortex interaction on the formation of interference patterns in a coherent pair of two-dimensional Bose condensed clouds of ultra-cold atoms traveling in opposite directions subject to a harmonic trapping potential. We identify linear and nonlinear regimes in the dipole oscillations of the condensates according to the balance of internal and centre-of-mass energies of the clouds. Simulations of the collision of two clouds each containing a vortex with different winding number (charge) are carried out in these regimes in order to investigate the creation of varying interference patterns. The interaction between different vortex types can be clearly distinguished by those patterns.

Optically measuring force near the standard quantum limit

The Heisenberg uncertainty principle sets a lower bound on the noise in a force measurement based on continuously detecting a mechanical oscillator's position. This bound, the standard quantum limit, can be reached when the oscillator subjected to the force is unperturbed by its environment and when measurement imprecision from photon shot noise is balanced against disturbance from measurement back-action. We applied an external force to the center-of-mass motion of an ultracold atom cloud in a high-finesse optical cavity and measured the resulting motion optically. When the driving force is resonant with the cloud's oscillation frequency, we achieve a sensitivity that is a factor of 4 above the standard quantum limit and consistent with theoretical predictions given the atoms' residual thermal disturbance and the photodetection quantum efficiency.

Measuring tiny forces with atomic clouds

Quantum Metrology For projects such as detecting gravity waves, physicists need to measure tiny forces precisely. Schreppler et al. developed an extremely sensitive method for force measurement. They applied a known force on a cloud of ultracold rubidium atoms in an optical cavity. The force caused

Ultrasensitive optomechanical magnetometry.

A cavity optomechanical magneto-meter operating in the 100 pT range is reported. The device operates at earth field, achieves tens of megahertz bandwidth with 60 μm spatial resolution and microwatt optical-power requirements. These unique capabilities may have a broad range of applications including cryogen-free and microfluidic magnetic resonance imaging (MRI), and investigation of spin-physics in condensed matter systems.

STE-QUEST—test of the universality of free fall using cold atom interferometry

The theory of general relativity describes macroscopic phenomena driven by the influence of gravity while quantum mechanics brilliantly accounts for microscopic effects. Despite their tremendous individual success, a complete unification of fundamental interactions is missing and remains one of the most challenging and important quests in modern theoretical physics. The spacetime explorer and quantum equivalence principle space test satellite mission, proposed as a medium-size mission within the Cosmic Vision program of the European Space Agency (ESA), aims for testing general relativity with high precision in two experiments by performing a measurement of the gravitational redshift of the Sun and the Moon by comparing terrestrial clocks, and by performing a test of the universality of free fall of matter waves in the gravitational field of Earth comparing the trajectory of two Bose–Einstein condensates of 85Rb and 87Rb. The two ultracold atom clouds are monitored very precisely thanks to techniques of atom interferometry. This allows to reach down to an uncertainty in the Eötvös parameter of at least 2 × 10−15. In this paper, we report about the results of the phase A mission study of the atom interferometer instrument covering the description of the main payload elements, the atomic source concept, and the systematic error sources.

Coherent versus incoherent excitation dynamics in dissipative many-body Rydberg systems

We study the impact of dephasing on the excitation dynamics of a cloud of ultracold two-level Rydberg atoms for both resonant and off-resonant laser excitation, using the wave function Monte Carlo (MCWF) technique. We find that while for resonant laser driving, dephasing mainly leads to an increase of the Rydberg population and a decrease of the Mandel Q parameter, at off-resonant driving strong dephasing toggles between direct excitation of pairs of atoms and subsequent excitation of single atoms, respectively. These two excitation mechanisms can be directly quantified via the pair correlation function, which shows strong suppression of the two-photon resonance peak for strong dephasing. Consequently, qualitatively different dynamics arise in the excitation statistics for weak and strong dephasing in off-resonant excitation. Our findings show that time-resolved excitation number measurements can serve as a powerful tool to identify the dominating process in the system's excitation dynamics.

Quantum shock waves and population inversion in collisions of ultracold atomic clouds

Using a time-dependent density matrix renormalization group (TDMRG) approach we study the collision of one-dimensional atomic clouds confined in a harmonic trap and evolving with the Lieb-Liniger Hamiltonian. It is observed that the motion is essentially periodic with the clouds bouncing elastically, at least on the time scale of the first few oscillations that can be resolved with high accuracy. This is in agreement with the results of the ``quantum Newton cradle'' experiment of Kinoshita et al. [Nature (London) 440, 900 (2006)]. We compare the results for the density profile against a hydrodynamic description, or generalized nonlinear Schr\"odinger equation, with the pressure term taken from the Bethe ansatz solution of the Lieb-Liniger model. We find that hydrodynamics can describe the breathing mode of a harmonically trapped cloud for arbitrary long times while it breaks down almost immediately for the collision of two clouds due to the formation of shock waves (gradient catastrophe). In the case of the clouds' collision TDMRG alone allows one to extract the oscillation period which is found to be measurably different from the breathing mode period. Concomitantly with the shock waves formation we observe a local energy distribution typical of population inversion, i.e., an effective negative temperature. Our results are an important step towards understanding the hydrodynamics of quantum many-body systems out of equilibrium and the role of integrability in their dynamics.

Dimensional confinement and Yang-Baxter integrability in cold-atom systems via optical lattices

Using two-dimensional optical lattices, it has recently become possible to split up clouds of ultra cold atoms into collections of parallel one-dimensional tubes in which the dynamics is restricted to the direction along their axis. Since the Feshbach-resonance interactions among atoms are short ranged, they can be approximated as contact interactions. It is thus possible to realize optical-trap versions of some classic integrable systems first studied by Lieb, Gaudin, Yang and others. Such systems can display exotic physics like spin-charge separation and unusual paired states. We focus on the study of systems of fermions in one-dimension. At finite temperatures, regimes such as the spin-coherent and the spin-incoherent Luttinger liquids can be realized by tuning the inter-atomic interaction strength and trap parameters. We identify the noise correlation of density fluctuations as a robust observable to discriminate between these two regimes. We also address the effects of spin imbalance for the case of attractive interactions, and study the one-dimensional analog of spatially modulated (FFLO) superconducting states. Our focus is on how the temperature affects the density profiles that are being measured in the experiments. The theoretical study of temperature effects in these systems is of experimental relevance for the problem of thermometry.