An obvious determination of the acceleration of gravity g can be deduced from the measurement of the velocity of falling atoms using a pi-pi pulses sequence of stimulated Raman transitions. By using a vertical standing wave to hold atoms against gravity, we expect to improve the relative accuracy by increasing the upholding time in the gravity field and to minimize the systematic errors induced by inhomogeneous fields, owing to the very small spatial amplitude of the atomic center-of-mass wavepacket periodic motion. We also propose to use such an experimental setup nearby a Watt balance. By exploiting the g/h (h is the Planck constant) dependence of the Bloch frequency, this should provide a way to link a macroscopic mass to an atomic mass.
We report an accurate measurement of the recoil velocity of Rb atoms based on Bloch oscillations in a vertical accelerated optical lattice. We transfer about 900 recoil momenta with an efficiency of 99.97 % per recoil. A set of 72 measurements of the recoil velocity, each one with a relative uncertainty of about 33 ppb in 20 min integration time, leads to a determination of the fine structure constant alpha with a statistical relative uncertainty of 4.4 ppb. The detailed analysis of the different systematic errors yields to a relative uncertainty of 6.7 ppb. The deduced value of 1/alpha is 137…
We use Bloch oscillations in a horizontal moving standing wave to transfer a large number of photon recoils to atoms with a high efficiency (99.5% per cycle). By measuring the photon recoil of $^{87}Rb$, using velocity selective Raman transitions to select a subrecoil velocity class and to measure the final accelerated velocity class, we have determined $h/m_{Rb}$ with a relative precision of 0.4 ppm. To exploit the high momentum transfer efficiency of our method, we are developing a vertical standing wave set-up. This will allow us to measure $h/m_{Rb}$ better than $10^{-8}$ and hence the fin…
We report on a trapped atom interferometer based on Bragg diffraction and Bloch oscillations with alkaline-earth-metal atoms. We use a Ramsey-Bordé Bragg interferometer with $^{88}$Sr atoms combined with Bloch oscillations to extend the interferometer time. Thanks to a long coherence time for Bloch oscillations of $^{88}$Sr atoms, we observed interference up to 1 s evolution time in the lattice. A detailed study of decoherence sources during the Bloch phase is also presented. While still limited in sensitivity by lattice lifetime and beam inhomogeneity this result opens the way to high contras…
We report the direct observation and characterization of position-space Bloch oscillations using an ultracold gas in a tilted optical lattice. While Bloch oscillations in momentum space are a common feature of optical lattice experiments, the real-space center-of-mass dynamics are typically too small to resolve. Tuning into the regime of rapid tunneling and weak force, we observe real-space Bloch oscillation amplitudes of hundreds of lattice sites, in both ground and excited bands. We demonstrate two unique capabilities enabled by tracking of Bloch dynamics in position space: measurement of th…
We simulate and analyze an experimental method of loading interacting ultracold atoms onto nontrivial quantum states such as nonlinear Bloch wave and soliton solutions in a 1-dimensional bichromatic lattice. Of standard bands, inverted bands, and bands with Dirac-like points permitted by a bichromatic lattice, we consider the case of an inverted band and examine the loading process in terms of nonlinear Bloch waves formed by an aggregate of ultracold atoms described by the mean-field model. Specifically, we solved the Gross-Pitaevskii equation numerically and found an appropriate standing wave…
The standard Bloch oscillation normally refers to the oscillatory tunneling dynamics of quantum particles in a periodic lattice plus a linear gradient. In this work we theoretically investigate the generalized form of the Bloch oscillation in the presence of additional higher order gradients, and demonstrate that the higher order gradients can significantly modify the tunneling dynamics, particularly in the spectrum of the density oscillation. The spectrum of the standard Bloch oscillation is composed of a single prime frequency and its higher harmonics, while the higher-order gradients in the…
We report new measurements and simulations of laser-induced fluorescence in ultracold neutral plasmas. We focus on the earliest times, when the plasma equilibrium is evolving and before the plasma expands. In the simulation, the ions interact via the Yukawa potential in a small cell with wrapped boundary conditions. We solve the optical Bloch equation for each ion in the simulation as a function of time. Both the simulation and experiment show the initial Bloch vector rotation, disorder-induced heating, and coherent oscillation of the rms ion velocity. Detailed modeling of the fluorescence sig…
We apply a Bloch-bands approach to the analysis of pulsed optical standing wave diffractive elements in optics and interferometry with ultracold atoms. We verify our method by comparison to a series of experiments with Bose-Einstein condensates. The approach provides accurate Rabi frequencies for diffraction pulses and is particularly useful for the analysis and control of diffraction phases, an important systematic effect in precision atom interferometry. Utilizing this picture, we also demonstrate a method to determine atomic band structure in an optical lattice through a measurement of phas…
We report on the use of an ultracold ensemble of $^{87}$Rb atoms trapped in a vertical lattice as a source for a quantum force sensor based on a Ramsey-Raman type interferometer. We reach spatial resolution in the low micrometer range in the vertical direction thanks to evaporative cooling down to ultracold temperatures in a crossed optical dipole trap. In this configuration, the coherence time of the atomic ensemble is degraded by inhomogeneous dephasing arising from atomic interactions. By weakening the confinement in the transverse direction only, we dilute the cloud and drastically reduce …
We develop a theoretical approach for the dynamics of Rydberg excitations in ultracold gases, with a realistically large number of atoms. We rely on the reduction of the single-atom Bloch equations to rate equations, which is possible under various experimentally relevant conditions. Here, we explicitly refer to a two-step excitation-scheme. We discuss the conditions under which our approach is valid by comparing the results with the solution of the exact quantum master equation for two interacting atoms. Concerning the emergence of an excitation blockade in a Rydberg gas, our results are in q…
We provide a one-to-one map between the spin correlations and certain three-dimensional shapes, analogous to the map between single spins and Bloch vectors, and demonstrate its utility. Much as one can reason geometrically about dynamics using a Bloch vector -- e.g. a magnetic field causes it to precess and dissipation causes it to shrink -- one can reason similarly about the shapes we use to visualize correlations. This visualization demonstrates its usefulness by unveiling the hidden structure in the correlations. For example, seemingly complex correlation dynamics can be described as simple…
When a gas of ultracold atoms is suddenly illuminated by light that is nearly resonant with an atomic transition, the atoms cannot respond instantaneously. This non-instantaneous response means the gas is initially more transparent to the applied light than in steady-state. The timescale associated with the development of light absorption is set by the atomic excited state lifetime. Similarly, the index of refraction in the gas also requires time to reach a steady-state value, but the development of the associated phase response is expected to be slower than absorption effects. Faraday rotatio…
We report on the observation of Bloch oscillations on the unprecedented time scale of severalseconds. The experiment is carried out with ultra-cold bosonic strontium-88 loaded into a vertical optical standing wave. The negligible atom-atom elastic cross section and the absence of spin makes $^{88}$Sr an almost ideal Bose gas insensitive to typical mechanisms of decoherence due to thermalization and to external stray fields. The small size enables precision measurements of forces at micrometer scale. This is a challenge in physics for studies of surfaces, Casimir effects, and searches for devia…
We propose a new kind of toroidal trap, designed for ultracold atoms. It relies on a combination of a magnetic trap for rf-dressed atoms, which creates a bubble-like trap, and a standing wave of light. This new trap is well suited for investigating questions of low dimensionality in a ring potential. We study the trap characteristics for a set of experimentally accessible parameters. A loading procedure from a conventional magnetic trap is also proposed. The flexible nature of this new ring trap, including an adjustable radius and adjustable transverse oscillation frequencies, will allow the s…
Ultracold atoms in optical lattices are a powerful tool for quantum simulation, precise measurement, and quantum computation. A fundamental problem in applying this quantum system is how to manipulate the higher bands or orbitals in Bloch states effectively. Here we mainly review our methods for manipulating high orbital ultracold atoms in optical lattices with different configurations. Based on these methods, we construct the atom-orbital qubit under nonadiabatic holonomic quantum control and Ramsey interferometry with trapped motional quantum states. Then we review the observation of the nov…
We propose and demonstrate a method to increase the momentum separation between the arms of an atom interferometer and thus its area and measurement precision, by using Bloch oscillations (BOs) in an excited band of a pulsed optical standing wave lattice. Using excited bands allows us to operate at particular "magic" depths, where high momentum transfer efficiency ($>99.4\%$ per $\hbar k$, where $\hbar k$ is the photon momentum) is maintained while minimizing the lattice-induced phase fluctuations ($<1\,$milliradian per $\hbar k$) that are unavoidable in ground-band BOs. We apply this method t…
We show that the timed Dicke states of a collection of three-level atoms can form a tight-binding lattice in momentum space. This lattice, coined the superradiance lattice (SL), can be constructed based on electromagnetically induced transparency (EIT). For a one-dimensional SL, we need the coupling field of the EIT system to be a standing wave. The detuning between the two components of the standing wave introduces an effective uniform force in momentum space. The quantum lattice dynamics, such as Bloch oscillations, Wannier-Stark ladders, Bloch band collapsing and dynamic localization can be…
The energy distribution of an ultracold rubidium ion beam, which is intended to be used as the source for a focused ion beam instrument, is measured with a retarding field analyzer. The ions are created from a laser-cooled and compressed atomic beam by two-step photoionization in which the ionization laser power is enhanced in a build-up cavity. Particle tracing simulations are performed to ensure the analyzer is able to resolve the distribution. The lowest achieved full width 50% energy spread is $\left(0.205\pm0.006\right)$ eV. The energy spread originates from the variation in the ionizatio…
Non-Abelian and non-adiabatic variants of Berry's geometric phase have been pivotal in the recent advances in fault tolerant quantum computation gates, while Berry's phase itself is at the heart of the study of topological phases of matter. The geometrical and topological properties of the phase space of spin$-1$ quantum states is richer than that of spin$-1/2$ quantum states and is relatively unexplored. For instance, the spin vector of a spin-1 system, unlike that of a spin$-1/2$ system, can lie anywhere on or inside the Bloch sphere representing the phase space. Recently, a generalization o…
We study the effects of high optical depth and density on the performance of a light-atom quantum interface. An in-situ imaging method, a dual-port polarization contrast technique, is presented. This technique is able to compensate for image distortions due to refraction. We propose our imaging method as a tool to characterize atomic ensembles for high capacity spatial multimode quantum memories. Ultracold dense inhomogeneous Rubidium samples are imaged and we find a resonant optical depth as high as 680 on the D1 line. The measurements are compared with light-atom interaction models based on …
We investigate the collective spin dynamics of a self-rephasing bosonic ensemble of $^{87}$Rb trapped in a 1D vertical optical lattice. We show that the combination of the frequency shifts induced by atomic interactions and inhomogeneous dephasing, together with the spin self-rephasing mechanism leads to the existence of a `magic density': \textit{i.e} a singular operating point where the clock transition is first-order insensitive to density fluctuations. This feature is very appealing for improving the stability of quantum sensors based on trapped pseudo-spin-1/2 ensembles. Ramsey spectrosco…
We demonstrate light-induced localization of Coulomb-interacting particles in multi-dimensional structures. Subwavelength localization of ions within small multi-dimensional Coulomb crystals by an intracavity optical standing wave field is evidenced by measuring the difference in scattering inside symmetrically red- and blue-detuned optical lattices and is observed even for ions undergoing substantial radial micromotion. These results are promising steps towards the structural control of ion Coulomb crystals by optical fields as well as for complex many-body simulations with ion crystals or fo…
We propose a method to characterize the ultra-narrow momentum distribution of atomic gases by employing a standing-wave light-pulse sequences beam-splitter. The mechanism of beam splitting is analyzed in detail, and the influence of a finite-width momentum distribution on the population of each diffraction order is given. The temperature of ultracold atomic gases can be calibrated by measuring the ratio of population in different diffraction orders after double standing-wave light-pulses. We obtain analytical expressions for two typical cases, and demonstrate phase space evolution in the whole…
In this work we consider the advantages and challenges of using free-standing two-dimensional electron gases (2DEG) as active components in atom chips for manipulating ultracold ensembles of alkali atoms. We calculate trapping parameters achievable with typical high-mobility 2DEGs in an atom chip configuration, and identify advantages of this system for trapping atoms at sub-micron distances from the atom chip. We show how the sensitivity of atomic gases to magnetic field inhomogeneity can be exploited for controlling the atoms with quantum electronic devices and, conversely, using the atoms t…
We have experimentally studied the magnetic-field dependence of the decay of a Bose-Einstein condensate of metastable 4He atoms confined in an optical dipole trap, for atoms in the m=+1 and m=-1 magnetic substates, and up to 450 G. Our measurements confirm long-standing calculations of the two-body loss rate coefficient that show an increase above 50 G. We demonstrate that for m=-1 atoms, decay is due to three-body recombination only, with a three-body loss rate coefficient of 6.5(0.4)(0.6)10^(-27)cm^6s^(-1), which is interesting in the context of universal few-body theory. We have also search…
Probing disorder-driven topological phase transitions via topological edge modes with ultracold atoms in Floquet-engineered honeycomb lattices
Max-Planck-Institut für Quantenoptik（马克斯·普朗克量子光学研究所）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Fakultät für Physik, Ludwig-Maximilians-Universität（慕尼黑大学物理学院）
The quasienergy spectrum of a Bloch electron affected by dc-ac fields is known to be a fractal function of the so-called electric matching ratio which is the ratio of the ac field frequency and the Bloch frequency. This paper studies a manifestation of the fractal spectrum in the system atom in a standing laser wave, which is a quantum optical realization of a Bloch electron. It is shown that for an appropriate choice of the system parameters the atomic survival probability (a quantity measured in laboratory experiments) develops a fractal structure as a function of the electric matching ratio…
We study off-resonant collective light scattering from ultracold atoms trapped in an optical lattice. Scattering from different atomic quantum states creates different quantum states of the scattered light, which can be distinguished by measurements of the spatial intensity distribution, quadrature variances, photon statistics, or spectral measurements. In particular, angle-resolved intensity measurements reflect global statistics of atoms (total number of radiating atoms) as well as local statistical quantities (single-site statistics even without an optical access to a single site) and pair …
We report on a high precision measurement of gravitational acceleration using ultracold strontium atoms trapped in a vertical optical lattice. Using amplitude modulation of the lattice intensity, an uncertainty $Δg /g \approx 10^{-7}$ was reached by measuring at the 5$^{th}$ harmonic of the Bloch oscillation frequency. After a careful analysis of systematic effects, the value obtained with this microscopic quantum system is consistent with the one we measured with a classical absolute gravimeter at the same location. This result is of relevance for the recent interpretation of related experime…
Simple models of interacting spins play an important role in physics. They capture the properties of many magnetic materials, but also extend to other systems, such as bosons and fermions in a lattice, systems with gauge fields, high-Tc superconductors, and systems with exotic particles such as anyons and Majorana fermions. In order to study and compare these models, a versatile platform is needed. Realizing such a system has been a long-standing goal in the field of ultracold atoms. So far, spin transport has only been studied in the isotropic Heisenberg model. Here we implement the Heisenber…
In this paper we show that the sensitivity of absorption imaging of ultracold atoms can be significantly improved by imaging in a standing-wave configuration. We present simulations of single-atom absorption imaging both for a travelling-wave and a standing-wave imaging setup, based on a scattering approach to calculate the optical density of a single atom. We find that the optical density of a single atom is determined only by the numerical aperture of the imaging system. We determine optimum imaging parameters, taking all relevant sources of noise into account. For reflective imaging we find…
Electron lattice potentials for ultracold atoms using circular Rydberg orbitals
Max-Planck Institut für Physik komplexer Systeme（马克斯·普朗克复杂系统物理研究所）；Joint Quantum Centre (JQC) Durham-Newcastle, Department of Chemistry, Durham University（杜伦大学化学系）；Physikalisches Institut and Center for Integrated Quantum Science and Technology, Universität Stuttgart（斯图加特大学第五物理研究所及综合量子科学技术中心）；Department of Physics and Astronomy, Purdue University（普渡大学物理与天文学系）
We experimentally investigate a scheme for studying lattice transport phenomena, based on the controlled momentum-space dynamics of ultracold atomic matter waves. In the effective tight-binding models that can be simulated, we demonstrate that this technique allows for a local and time-dependent control over all system parameters, and additionally allows for single-site resolved detection of atomic populations. We demonstrate full control over site-to-site off-diagonal tunneling elements (amplitude and phase) and diagonal site-energies, through the observation of continuous-time quantum walks,…
We report on the design and characterization of a cold atom source for strontium (Sr) based on a two-dimensional magneto-optical trap (MOT) that is directly loaded from the atom jet of a dispenser. We characterize the atom flux of the source by measuring the loading rate of a three-dimensional MOT. We find loading rates of up to $10^{8}$ atoms per second. The setup is compact, easy to construct, and has low power consumption. It addresses the long standing challenge of reducing the complexity of cold beam sources for Sr, which is relevant for optical atomic clocks and quantum simulation and co…
