In many experiments isolated atoms and ions have been inserted into high-finesse optical resonators for the study of fundamental quantum optics and quantum information. Here, we introduce another application of such a system, as the realization of cavity optomechanics where the collective motion of an atomic ensemble serves the role of a moveable optical element in an optical resonator. Compared with other optomechanical systems, such as those incorporating nanofabricated cantilevers or the large cavity mirrors of gravitational observatories, our cold-atom realization offers direct access to the quantum regime. We describe experimental investigations of optomechanical effects, such as the bistability of collective atomic motion and the first quantification of measurement backaction for a macroscopic object, and discuss future directions for this nascent field.
In this article we discuss and compare different ways to engineer an interface between ultracold atoms and micro- and nanomechanical oscillators. We start by analyzing a direct mechanical coupling of a single atom or ion to a mechanical oscillator and show that the very different masses of the two systems place a limit on the achievable coupling constant in this scheme. We then discuss several promising strategies for enhancing the coupling: collective enhancement by using a large number of atoms in an optical lattice in free space, coupling schemes based on high-finesse optical cavities, and …
The transmission probability of ultracold atoms through a micromaser is studied in the general case where a detuning between the cavity mode and the atomic transition frequencies is present. We generalize previous results established in the resonant case (zero detuning) for the mesa mode function. In particular, it is shown that the velocity selection of cold atoms passing through the micromaser can be very easily tuned and enhanced using a non-resonant field inside the cavity. Also, the transmission probability exhibits with respect to the detuning very sharp resonances that could define sing…
A promising route to novel quantum technologies are hybrid quantum systems, which combine the advantages of several individual quantum systems. We have realized a hybrid atomic-mechanical experiment consisting of a SiN membrane oscillator cryogenically precooled to 500 mK and optically coupled to a cloud of laser cooled Rb atoms. Here, we demonstrate active feedback cooling of the oscillator to a minimum mode occupation of n = 16 corresponding to a mode temperature of T = 200 μK. Furthermore, we characterize in detail the coupling of the membrane to the atoms by means of sympathetic cooling. B…
Current research on micro-mechanical resonators strives for quantum-limited detection of the motion of macroscopic objects. Prerequisite to this goal is the observation of measurement backaction consistent with quantum metrology limits. However, thermal noise presently dominates measurements and precludes ground-state preparation of the resonator. Here we establish the collective motion of an ultracold atomic gas confined tightly within a Fabry-Perot optical cavity as a system for investigating the quantum mechanics of macroscopic bodies. The cavity-mode structure selects a single collective v…
We present a new theoretical method to study a trapped gas of bosonic two-level atoms interacting with a single mode of a microwave cavity. This interaction is described by a trilinear Hamiltonian which is formally completely equivalent to the one describing parametric down-conversion in quantum optics. A system of differential equations describing the evolution, including the long-time behaviour, of not only the mean value but also the variance of the number of excited atoms is derived and solved analytically. For different initial states the mean number of excited atoms exhibits periodically…
We propose a scheme to probe quantum coherence in the state of a nano-cantilever based on its magnetic coupling (mediated by a magnetic tip) with a spinor Bose Einstein condensate (BEC). By mapping the BEC into a rotor, its coupling with the cantilever results in a gyroscopic motion whose properties depend on the state of the cantilever: the dynamics of one of the components of the rotor angular momentum turns out to be strictly related to the presence of quantum coherence in the state of the cantilever. We also suggest a detection scheme relying on Faraday rotation, which produces only a very…
Based on the developed quantum microscopic theory, the interaction of weak electromagnetic radiation with dense ultracold atomic clouds is described in detail. The differential and total cooperative scattering cross sections are calculated for monochromatic radiation as particular examples of application of the general theory. The angular, spectral, and polarization properties of scattered light are determined. The dependence of these quantities on the sample size and concentration of atoms is studied and the influence of collective effects is analyzed.
In this article, a method is proposed to spatially scale up a trapped ultracold gas while conserving the quantum correlations of the initial many-body state. For systems supporting self-similar dynamics, this is achieved by implementing a many-body finite-time frictionless quantum quench of the harmonic trap which acts as a quantum dynamical microscope.
We study the nonlinear dynamics of an ensemble of cold trapped atoms with a hyperfine transition magnetically coupled to a resonant microwave cavity mode. Despite the minute single atom coupling one obtains strong coupling between collective hyperfine qubits and microwave photons enabling coherent transfer of an excitation between the long lived atomic qubit state and the mode. Evidence of strong coupling can be obtained from the cavity transmission spectrum even at finite thermal photon number. The system makes it possible to study further prominent collective phenomena such as superradiant d…
Quantum simulations with ultracold atoms typically create atomic wavefunctions with structures at optical length scales, where direct imaging suffers from the diffraction limit. In analogy to advances in optical microscopy for biological applications, we use a non-linear atomic response to surpass the diffraction limit. Exploiting quantum interference, we demonstrate imaging with super-resolution of $λ/100$ and excellent temporal resolution of 500 ns. We characterize our microscope's performance by measuring the ensemble averaged wavefunction of atoms within the unit cells of an optical lattic…
The quantum optical response of high density ultracold atomic systems is critical to a wide range of fundamentally and technically important physical processes. These include quantum image storage, optically based quantum repeaters and ultracold molecule formation. We present here a microscopic analysis of the light scattering on such a system, and we compare it with a corresponding description based on macroscopic Maxwell theory. Results are discussed in the context of the spectral resonance structure, time-dependent response, and the light localization problem.
This article reviews the development in our laboratory of magnetic lattices comprising periodic arrays of magnetic microtraps created by patterned magnetic films to trap periodic arrays of ultracold atoms. Recent achievements include the realisation of multiple Bose-Einstein condensates in a 10 micron-period one-dimensional magnetic lattice; the fabrication of sub-micron-period square and triangular magnetic lattice structures suitable for quantum tunnelling experiments; the trapping of ultracold atoms in a sub-micron-period triangular magnetic lattice; and a proposal to use long-range interac…
Despite the unquestionable empirical success of quantum theory, witnessed by the recent uprising of quantum technologies, the debate on how to reconcile the theory with the macroscopic classical world is still open. Spontaneous collapse models are one of the few testable solutions so far proposed. In particular, the continuous spontaneous localization (CSL) model has become subject of an intense experimental research. Experiments looking for the universal force noise predicted by CSL in ultrasensitive mechanical resonators have recently set the strongest unambiguous bounds on CSL; further impr…
We report a technique that uses clouds of ultracold atoms as sensitive, tunable, and non-invasive probes for microwave field imaging with micrometer spatial resolution. The microwave magnetic field components drive Rabi oscillations on atomic hyperfine transitions whose frequency can be tuned with a static magnetic field. Readout is accomplished using state-selective absorption imaging. Quantitative data extraction is simple and it is possible to reconstruct the distribution of microwave magnetic field amplitudes and phases. While we demonstrate 2d imaging, an extension to 3d imaging is straig…
Chemical reactions at ultracold temperatures are expected to be dominated by quantum mechanical effects. Although progress towards ultracold chemistry has been made through atomic photoassociation, Feshbach resonances and bimolecular collisions, these approaches have been limited by imperfect quantum state selectivity. In particular, attaining complete control of the ground or excited continuum quantum states has remained a challenge. Here we achieve this control using photodissociation, an approach that encodes a wealth of information in the angular distribution of outgoing fragments. By phot…
We report on the local probing and preparation of an ultracold Fermi gas on the length scale of one micrometer, i.e. of the order of the Fermi wavelength. The essential tool of our experimental setup is a pair of identical, high-resolution microscope objectives. One of the microscope objectives allows local imaging of the trapped Fermi gas of 6Li atoms with a maximum resolution of 660 nm, while the other enables the generation of arbitrary optical dipole potentials on the same length scale. Employing a 2D acousto-optical deflector, we demonstrate the formation of several trapping geometries in…
We demonstrate coherent microwave control of rotational and hyperfine states of trapped, ultracold, and chemically stable $^{23}$Na$^{40}$K molecules. Starting with all molecules in the absolute rovibrational and hyperfine ground state, we study rotational transitions in combined magnetic and electric fields and explain the rich hyperfine structure. Following the transfer of the entire molecular ensemble into a single hyperfine level of the first rotationally excited state, $J{=}1$, we observe collisional lifetimes of more than $3\, \rm s$, comparable to those in the rovibrational ground state…
"Bottom-up" approaches to the many-body physics of fermions have demonstrated recently precise number and site-resolved preparations with tunability of interparticle interactions in single-well, SW, and double-well, DW, nano-scale confinements created by manipulating ultracold fermionic atoms with optical tweezers. These experiments emulate an analogue-simulator mapping onto the requisite microscopic hamiltonian, approaching realization of Feynman's vision of quantum simulators that "will do exactly the same as nature". Here we report on exact benchmark configuration-interaction computational …
We demonstrate a set of tools for microscopic control of neutral strontium atoms. We report single-atom loading into an array of sub-wavelength scale optical tweezers, light-shift free control of a narrow-linewidth optical transition, three-dimensional ground-state cooling, and high-fidelity nondestructive imaging of single atoms on sub-wavelength spatial scales. Extending the microscopic control currently achievable in single-valence-electron atoms to species with more complex internal structure, like strontium, unlocks a wealth of opportunities in quantum information science, including tweez…
Quantum mechanics predicts that our physical reality is influenced by events that can potentially happen but factually do not occur. Interaction-free measurements (IFMs) exploit this counterintuitive influence to detect the presence of an object without requiring any interaction with it. Here we propose and realize an IFM concept based on an unstable many-particle system. In our experiments, we employ an ultracold gas in an unstable spin configuration which can undergo a rapid decay. The object - realized by a laser beam - prevents this decay due to the indirect quantum Zeno effect and thus, i…
At ultralow energies, atoms and molecules undergo collisions and reactions that are best described in terms of quantum mechanical wave functions. In contrast, at higher energies these processes can be understood quasiclassically. Here, we investigate the crossover from the quantum mechanical to the quasiclassical regime both experimentally and theoretically for photodissociation of ultracold diatomic strontium molecules. This basic reaction is carried out with a full control of quantum states for the molecules and their photofragments. The photofragment angular distributions are imaged, and ca…
We investigate a hybrid quantum system consisting of a cavity optomechanical device optically coupled to an ultracold quantum gas. We show that the dispersive properties of the ultracold gas can be used to dramatically modify the optomechanical response of the mechanical resonator. We examine hybrid schemes wherein the mechanical resonator is coupled either to the motional or the spin degrees of freedom of the ultracold gas. In either case, we find an enhancement of more than two orders of magnitude in optomechanical cooling due to this hybrid interaction. Significantly, based on demonstrated …
We propose the use of periodic arrays of permanent magnetic films for producing magnetic lattices of microtraps for confining, manipulating and controlling small clouds of ultracold atoms and quantum degenerate gases. Using analytical expressions and numerical calculations we show that periodic arrays of magnetic films can produce one-dimensional (1D) and two-dimensional (2D) magnetic lattices with non-zero potential minima, allowing ultracold atoms to be trapped without losses due to spin flips. In particular, we show that two crossed layers of periodic arrays of parallel rectangular magnets …
We report on a class of configurations of permanent magnets on an atom chip for producing 1D and 2D periodic arrays of magnetic microtraps with non-zero potential minima and variable barrier height for trapping and manipulating ultracold atoms and quantum degenerate gases. We present analytical expressions for the relevant physical quantities and compare them with our numerical results and with some previous numerical calculations. In one of the configurations of permanent magnets, we show how it is possible by changing the angle between the crossed periodic arrays of magnets to go from a 1D a…
The standard experimental techniques usually adopted in the study of the behaviour of ultracold atoms in optical lattices involve extracting the atom density profile from absorption images of the atomic sample after trap release. Quantum mechanically this procedure is described by a generalized measure (POVM); interference patterns found in absorption images suggest a generalized measure based on fixed-phase, coherent-like states. We show that this leads to an average atomic density which differs from the usually adopted one, obtained as the expectation value of the atom density operator in th…
High-resolution imaging of ultracold atoms typically requires custom high numerical aperture (NA) optics, as is the case for quantum gas microscopy. These high NA objectives involve many optical elements each of which contributes to loss and light scattering, making them unsuitable for quantum back-action limited "weak" measurements. We employ a low cost high NA aspheric lens as an objective for a practical and economical-although aberrated-high resolution microscope to image ${^{87}\mathrm{Rb}}$ Bose-Einstein condensates. Here, we present a novel methodology for digitally eliminating the resu…
In this review, we discuss the properties of a few impurity atoms immersed in a gas of ultracold fermions, the so-called Fermi polaron problem. On one side, this many-body system is appealing because it can be described almost exactly with simple diagrammatic and/or variational theoretical approaches. On the other, it provides quantitatively reliable insight into the phase diagram of strongly interacting population imbalanced quantum mixtures. In particular, we show that the polaron problem can be applied to study itinerant ferromagnetism, a long standing problem in quantum mechanics.
Existing space-based cold atom experiments have demonstrated the utility of microgravity for improvements in observation times and for minimizing the expansion energy and rate of a freely evolving coherent matter wave. In this paper we explore the potential for space-based experiments to extend the limits of ultracold atoms utilizing not just microgravity, but also other aspects of the space environment such as exceptionally good vacuums and extremely cold temperatures. The tantalizing possibility that such experiments may one day be able to probe physics of quantum objects with masses approac…
Advances with trapped ultracold atoms intensified interest in simulating complex physical phenomena, including quantum magnetism and transitions from itinerant to non-itinerant behavior. Here we show formation of antiferromagnetic ground states of few ultracold fermionic atoms in single and double well (DW) traps, through microscopic Hamiltonian exact diagonalization for two DW arrangements: (i) two linearly oriented one-dimensional, 1D, wells, and (ii) two coupled parallel wells, forming a trap of two-dimensional, 2D, nature. The spectra and spin-resolved conditional probabilities reveal for …
The study of dynamical tunnelling in a periodically driven anharmonic potential probes the quantum-classical transition via the experimental control of the effective Planck's constant for the system. In this paper we consider the prospects for observing dynamical tunnelling with ultracold atoms in magnetic microtraps on atom chips. We outline the driven anharmonic potentials that are possible using standard magnetic traps, and find the Floquet spectrum for one of these as a function of the potential strength, modulation, and effective Planck's constant. We develop an integrable approximation t…
Preparing and manipulating quantum states of mechanical resonators is a highly interdisciplinary undertaking that now receives enormous interest for its far-reaching potential in fundamental and applied science. Up to now, only nanoscale mechanical devices achieved operation close to the quantum regime. We report a new micro-optomechanical resonator that is laser cooled to a level of 30 thermal quanta. This is equivalent to the best nanomechanical devices, however, with a mass more than four orders of magnitude larger (43 ng versus 1 pg) and at more than two orders of magnitude higher environm…
For exploration of quantum effects with hybrid atom-ion systems, reaching ultracold temperatures is the major limiting factor. In this work, we present results on numerical simulations of trapped ion buffer gas cooling using an ultracold atomic gas in a large number of experimentally realistic scenarios. We explore the suppression of micromotion-induced heating effects through optimization of trap parameters for various radio-frequency (rf) traps and rf driving schemes including linear and octupole traps, digital Paul traps, rotating traps and hybrid optical/rf traps. We find that very similar…
Hubbard models with ultracold shielded molecules in optical lattices
Institute for Molecules and Materials, Radboud University（分子与材料研究所，拉德堡德大学）；Department of Physics and Astronomy, Rice University（物理与天文系，莱斯大学）；Smalley-Curl Institute, Rice University（斯马利-柯尔研究所，莱斯大学）
All-optical bubble trap for ultracold atoms in microgravity
ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology（ICFO-光子科学研究所，巴塞罗那科学技术研究院）；LP2N, Laboratoire Photonique, Numérique et Nanosciences, Université de Bordeaux-IOGS-CNRS:UMR 5298（LP2N，光、数字与纳米科学实验室，波尔多大学-IOGS-CNRS）；Department of Physics and Astronomy, Bates College（贝茨学院物理与天文学系）；Dept. of Physics and Astronomy, University of Sussex（苏塞克斯大学物理与天文学系）
Photodissociation of a molecule produces a spatial distribution of photofragments determined by the molecular structure and the characteristics of the dissociating light. Performing this basic chemical reaction at ultracold temperatures allows its quantum mechanical features to dominate. In this regime, weak applied fields can be used to control the reaction. Here, we photodissociate ultracold diatomic strontium in magnetic fields below 10 G and observe striking changes in photofragment angular distributions. The observations are in excellent qualitative agreement with a multichannel quantum c…
Quantum mechanics is an inherently linear theory. However, collective effects in many body quantum systems can give rise to effectively nonlinear dynamics. In the present work, we analyze whether and to what extent such nonlinear effects can be exploited to enhance the rate of quantum evolution. To this end, we compute a suitable version of the quantum speed limit for numerical and analytical examples. We find that the quantum speed limit grows with the strength of the nonlinearity, yet it does not trivially scale with the ``degree'' of nonlinearity. This is numerically demonstrated for the pa…
The recent advances in single atom detection and manipulation in experiments with ultracold quantum gases are reviewed. The discussion starts with the basic principles of trapping, cooling and detecting single ions and atoms. The realization of single atom detection in ultracold quantum gases is presented in detail and the employed methods, which are based on light scattering, electron scattering, field ionization and direct neutral particle detection are discussed. The microscopic coherent manipulation of single atoms in a quantum gas is also covered. Various examples are given in order to hi…
Zero-point energy of a trapped ultracold Fermi gas at unitarity: squeezing the Heisenberg uncertainty principle and suppressing the Pauli principle to produce a superfluid state
Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma（俄克拉荷马大学霍默·L·道奇物理与天文学系）
We report the realization of a robust magnetic transport scheme to bring 3x10^8 ultracold 87Rb atoms into a cryostat. The sequence starts with standard laser cooling and trapping of 87Rb atoms, transporting first horizontally and then vertically through the radiation shields into a cryostat by a series of normal- and superconducting magnetic coils. Loading the atoms in a superconducting microtrap paves the way for studying the interaction of ultracold atoms with superconducting surfaces and quantum devices requiring cryogenic temperatures.
We report the trapping of ultracold neutral $ \text{Rb}$ atoms and $ \text{Ba}^+ $ ions in a common optical potential in absence of any radiofrequency (RF) fields. We prepare $ \text{Ba}^+ $ at $ 370 ~ μK $ and demonstrate efficient sympathetic cooling by $100 ~ μK $ after one collision. Our approach is currently limited by the $ \text{Rb}$ density and related three-body losses, but it overcomes the fundamental limitation in RF traps set by RF-driven, micromotion-induced heating. It is applicable to a wide range of ion-atom species, and may enable novel ultracold chemistry experiments and comp…
We examine off-resonant light scattering from ultracold atoms in the quantum Hall regime. When the light scattering is spin dependent, we show that images formed in the far field can be used to distinguish states of the system. The spatial dependence of the far-field images is determined by the two-particle spin-correlation functions, which the images are related to by a transformation. Quasiholes in the system appear in images of the density formed by collecting the scattered light with a microscope, where the quasihole statistics are revealed by the reduction in density at the quasihole posi…
The effect of conical intersections (CIs) on electronic relaxation, transitions from excited states to ground states, is well studied, but their influence on hyperfine quenching in a reactant molecule is not known. Here, we report on ultracold collision dynamics of the hydroxyl free-radical OH with Sr atoms leading to quenching of OH hyperfine states. Our quantum-mechanical calculations of this process reveal that quenching is efficient due to anomalous molecular dynamics in the vicinity of the conical intersection at collinear geometry. We observe wide scattering resonance features in both el…
A fundamental question in the study of chemical reactions is how reactions proceed at a collision energy close to absolute zero. This question is no longer hypothetical: quantum degenerate gases of atoms and molecules can now be created at temperatures lower than a few tens of nanoKelvin. In this work we consider the benchmark ultracold reaction between, the most-celebrated ultracold molecule, KRb and K. For the first time we map out an accurate ab initio ground state potential energy surface of the KRbK complex in full dimensionality and report numerically exact quantum-mechanical reaction dy…
We introduce a general method for designing tailored lattices of magnetic microtraps for ultracold atoms, on the basis of patterned permanently magnetized films. A fast numerical algorithm is used to automatically generate patterns which provide optimal atom confinement while respecting desired lattice symmetries and trap parameters. The algorithm can produce finite and infinite lattices of any plane symmetry; we focus specifically on square and triangular lattices which are of interest to future experiments. Typical trap parameters are discussed as well as the impact of realistic imperfection…
Trapping of single ultracold atoms is an important tool for applications ranging from quantum computation and communication to sensing. However, most experimental setups, while very precise and versatile, can only be operated in specialized laboratory environments due to their large size, complexity and high cost. Here, we introduce a new trapping concept for ultracold atoms in optical tweezers based on micrometer-scale lenses that are 3D printed onto the tip of standard optical fibers. The unique properties of these lenses make them suitable for both trapping individual atoms and capturing th…
Ultracold neutrons confined in the Earth's gravitational field display quantized energy levels that have been observed for over a decade. In recent resonance spectroscopy experiments [T. Jenke et al., Nature Phys. 7, 468 (2011)], the transition between two such gravitational quantum states was driven by the mechanical oscillation of the plates that confine the neutrons. Here we show that, by applying a sinusoidal modulation with slowly varying frequency (chirp), the neutrons can be brought to higher excited states by climbing the energy levels one by one. The proposed experiment should make it…
A complete physical approach to quantum information requires a robust interface among flying qubits, long-lifetime memory and computational qubits. Here we present a unified interface for microwave and optical photons, potentially connecting engineerable quantum devices such as superconducting qubits at long distances through optical photons. Our approach uses an ultracold ensemble of atoms for two purposes: quantum memory and to transduce excitations between the two frequency domains. Using coherent control techniques, we examine an approach for converting and storing quantum information betw…
Experiments using laser cooled atoms and ions show real promise for practical applications in quantum- enhanced metrology, timing, navigation, and sensing as well as exotic roles in quantum computing, networking and simulation. The heart of many of these experiments has been translated to microfabricated platforms known as atom chips whose construction readily lend themselves to integration with larger systems and future mass production. To truly make the jump from laboratory demonstrations to practical, rugged devices, the complex surrounding infrastructure (including vacuum systems, optics, …
Sympathetic cooling with ultracold atoms and atomic ions enables ultralow temperatures in systems where direct laser or evaporative cooling is not possible. It has so far been limited to the cooling of other microscopic particles, with masses up to $90$ times larger than that of the coolant atom. Here we use ultracold atoms to sympathetically cool the vibrations of a Si$_3$N$_4$ nanomembrane, whose mass exceeds that of the atomic ensemble by a factor of $10^{10}$. The coupling of atomic and membrane vibrations is mediated by laser light over a macroscopic distance and enhanced by placing the m…
Processes that break molecular bonds are typically observed with molecules occupying a mixture of quantum states and successfully described with quasiclassical models, while a few studies have explored the distinctly quantum mechanical low-energy regime. Here we use photodissociation of diatomic strontium molecules to demonstrate the crossover from the ultracold, quantum regime where the photofragment angular distributions strongly depend on the kinetic energy, to the energy-independent quasiclassical regime. Using time-of-flight velocity map imaging for photodissociation channels with millike…
Progress towards ultracold Sr for the AION project -- sub-microkelvin atoms and an optical-heterodyne diagnostic tool for injection-locked laser diodes
Wave-function microscopy: Derivation and anatomy of exact algebraic spinful wave functions and full Wigner-molecular spectra of a few highly correlated rapidly rotating ultracold fermionic atoms
Recent realizations of quantum gas microscope offer the possibility of continuous monitoring of the dynamics of a quantum many-body system at the single-particle level. By analyzing effective non-Hermitian Hamiltonians of interacting bosons in an optical lattice and continuum, we demonstrate that the backaction of quantum measurement shifts the quantum critical point and gives rise to a unique critical phase beyond the terrain of the standard universality class. We perform mean-field and strong-coupling-expansion analyses and show that non-Hermitian contributions shift the superfluid--to-Mott-…
