Precision measurement of small separations between two atoms or molecules has been of interest since the early days of science. Here, we discuss a scheme which yields spatial information on a system of two identical atoms placed in a standing wave laser field. The information is extracted from the collective resonance fluorescence spectrum, relying entirely on far-field imaging techniques. Both the interatomic separation and the positions of the two particles can be measured with fractional-wavelength precision over a wide range of distances from bout lambda/550 to lambda/2.
A few years ago, diffraction of atoms by double slits and gratings was achieved for the first time, and standard optical wave-theory provided an excellent description of the experiments. More recently, diffraction of weakly bound molecules and even clusters has been observed. Due to their size and to possible breakup processes optical wave-theory is no longer adequate and a more sophisticated approach is needed. Moreover, surface effects, which can modify the diffraction pattern of atoms and molecules, give rise to further complications. In this article a fully quantum mechanical approach to t…
We study the effects of time uncertainty in the interaction of atoms with a standing light wave. We discuss its physical origin and the possibility to observe intrinsic decoherence effects by measuring the atomic momentum distribution.
We formulate a wave atom optics theory of the Collective Atomic Recoil Laser, where the atomic center-of-mass motion is treated quantum mechanically. By comparing the predictions of this theory with those of the ray atom optics theory, which treats the center-of-mass motion classically, we show that for the case of a far off-resonant pump laser the ray optics model fails to predict the linear response of the CARL when the temperature is of the order of the recoil temperature or less. This is due to the fact that in theis temperature regime one can no longer ignore the effects of matter-wave di…
We review recent theoretical models and experiments dealing with the diffraction of neutral atoms from a reflection grating, formed by a standing evanescent wave. We analyze diffraction mechanisms proposed for normal and grazing incidence, point out their scopes and confront the theory with experiment.
We have built and operated an atom interferometer of the Mach-Zehnder type. The atomic wave is a supersonic beam of lithium seeded in argon and the mirrors and beam-splitters for the atomic wave are based on elastic Bragg diffraction on laser standing waves at 671 nm. We give here a detailed description of our experimental setup and of the procedures used to align its components. We then present experimental signals, exhibiting atomic interference effects with a very high visibility, up to 84.5 %. We describe a series of experiments testing the sensitivity of the fringe visibility to the main …
We report on a detailed investigation of the dynamics and the saturation of a light grating stored in a sample of cold cesium atoms. We employ Bragg diffraction to retrieve the stored optical information impressed into the atomic coherence by the incident light fields. The diffracted efficiency is studied as a function of the intensities of both writing and reading laser beams. A theoretical model is developed to predict the temporal pulse shape of the retrieved signal and compares reasonably well with the observed results.
Highly polarizable metastable He* ($\mathrm{2^3S}$) and Ne* ($\mathrm{2^3P}$) atoms have been diffracted from a 100 nm period silicon nitride transmission grating and the van der Waals coefficients $C_3$ for the interaction of the excited atoms with the silicon nitride surface have been determined from the diffraction intensities out to the 10th order. The results agree with calculations based on the non-retarded Lifshitz formula.
We propose a new approach to characterizing the depths of optical lattices, in which an atomic gas is given a finite initial momentum, which leads to high amplitude oscillations in the zeroth diffraction order which are robust to finite-temperature effects. We present a simplified model yielding an analytic formula describing such oscillations for a gas assumed to be at zero temperature. This model is extended to include atoms with initial momenta detuned from our chosen initial value, before analyzing the full finite-temperature response of the system. Finally we present a steady-state soluti…
A double cavity with a quantum mechanical and a classical field is located immediately behind of a double-slit in order to analyse the wave-particle duality. Both fields have common nodes and antinodes through which a three-level atom passes after crossing the double-slit. The atom-field interaction is maximum when the atom crosses a common antinode and path-information can be recorded on the phase of the quantum field. On other hand, if the atom crosses a common node, the interaction is null and no path-information is stored. A quadrature measurement on the quantum field can reveal the path f…
Molecular beams of rare gas atoms and D_2 have been diffracted from 100 nm period SiN_x transmission gratings. The relative intensities of the diffraction peaks out to the 8th order depend on the diffracting particle and are interpreted in terms of effective slit widths. These differences have been analyzed by a new theory which accounts for the long-range van der Waals -C_3/l^3 interaction of the particles with the walls of the grating bars. The values of the C_3 constant for two different gratings are in good agreement and the results exhibit the expected linear dependence on the dipole pola…
We present a scheme for eliminating the optical diffraction of slow-light in a thermal atomic medium of electromagnetically induced transparency. Nondiffraction is achieved for an arbitrary paraxial image by manipulating the susceptibility in momentum space, in contrast to the common approach, which employs guidance of specific modes by manipulating the susceptibility in real space. For negative two-photon detuning, the moving atoms drag the transverse momentum components unequally, resulting in a Doppler trapping of light by atoms in two dimensions.
We present an optical system designed to capture and observe a single neutral atom in an optical dipole trap, created by focussing a laser beam using a large numerical aperture N.A.=0.5 aspheric lens. We experimentally evaluate the performance of the optical system and show that it is diffraction limited over a broad spectral range (~ 200 nm) with a large transverse field (+/- 25 microns). The optical tweezer created at the focal point of the lens is able to trap single atoms of 87Rb and to detect them individually with a large collection efficiency. We measure the oscillation frequency of the…
We present a detailed study of the effects of imperfect atom-optical manipulation in Bragg-based light-pulse atom interferometers. Off-resonant higher-order diffraction leads to population loss, spurious interferometer paths, and diffraction phases. In a path-dependent formalism, we study numerically various effects and analyze the interference signal caused by an external phase or gravity. We compare first-order single and double Bragg diffraction in retroreflective setups. In double Bragg diffraction, phase imperfections lead to a beating due to three-path interference. Some effects of diffr…
We study the diffraction of quantum degenerate fermionic atoms off of quantized light fields in an optical cavity. We compare the case of a linear cavity with standing wave modes to that of a ring cavity with two counter-propagating traveling wave modes. It is found that the dynamics of the atoms strongly depends on the quantization procedure for the cavity field. For standing waves, no correlations develop between the cavity field and the atoms. Consequently, standing wave Fock states yield the same results as a classical standing wave field while coherent states give rise to a collapse and r…
We propose a super-resolution quantum lithography scheme based on coherent population trapping in lambda-type atoms coupled to temporally-cascaded standing-wave driving fields. By realizing effective multiplication of optical intensity profiles on an atomic state density distribution, the scheme enables an arbitrarily high degree of resolution enhancement without modifying the atomic level structure of the photographic medium or the light source configuration. It is also shown that the visibility of the super-resolution patterns is preserved under a significant atomic state decoherence rate.
A magnetic field gradient applied to an atom interferometer induces a $M$-dependent phase shift which results in a series of decays and revivals of the fringe visibility. Using our lithium atom interferometer based on Bragg laser diffraction, we have measured the fringe visibility as a function of the applied gradient. We have thus tested the isotopic selectivity of the interferometer, the velocity selective character of Bragg diffraction for different diffraction orders as well as the effect of optical pumping of the incoming atoms. All these observations are qualitatively understood but a qu…
Interference and diffraction of two-identical-particles are considered in the context of open quantum systems. This theoretical study is carried out within two approaches, the effective time-dependent Hamiltonian due to Caldirola-Kanai (CK) and the Caldeira-Leggett (CL) one where a master equation for the reduced density matrix is used under the presence of dissipation and temperature of the environment. Two simple but very illustrative examples are considered, diffraction by a single and two Gaussian slits by analyzing the mean square separation between particles, single-particle probability …
Diffraction of atoms by laser is a very important tool for matter wave optics. Although this process is well understood, the phase shifts induced by this diffraction process are not well known. In this paper, we make analytic calculations of these phase shifts in some simple cases and we use these results to model the contrast interferometer recently built by the group of D. Pritchard at MIT. We thus show that the values of the diffraction phases are large and that they probably contribute to the phase noise observed in this experiment.
We present here a new type of cold atom interferometry gravimeter based on Bragg diffraction, which is able to increase the gravity measurement sensitivity and stability of common Raman atom gravimeters significantly. By comparing with Raman transition, the principles and advantages of Bragg diffraction-based atom gravimeters have been introduced. The theoretical model for a time-domain Bragg atom gravimeter with atomic incident direction parallels to the wave vector of Bragg lasers has been constructed. Some key technical requirements for an nth-order Bragg diffraction-based atom gravimeter h…
We implement an estimator for determining the separation between two incoherent point sources. This estimator relies on image inversion interferometry and when used with the appropriate data analytics, it yields an estimate of the separation with finite-error, even when the sources come arbitrarily close together. The experimental results show that the technique has a good tolerance to noise and misalignment, making it an interesting consideration for high resolution instruments.
We propose a single-site addressing implementation based on the sub-wavelength localization via adiabatic passage (SLAP) technique. We consider a sample of ultracold neutral atoms loaded into a two-dimensional optical lattice with one atom per site. Each atom is modeled by a three-level Λ-system in interaction with a pump and a Stokes laser pulse. Using a pump field with a node in its spatial profile, the atoms at all sites are transferred from one ground state of the system to the other via stimulated Raman adiabatic passage, except the one at the position of the node that remains in the init…
A scheme is proposed to achieve substantial controllable phase modulation for a probe field propagating through a thermal atomic vapor in double-$Λ$ configuration. The phase modulation is based on the linear susceptibility of the probe field, paraxial diffraction is eliminated by exploiting the thermal motion of atoms, and residual absorption is compensated via an incoherent pump field. As a result, a strong controllable uniform phase modulation without paraxial diffraction is achieved essentially independent of the spatial profile or the intensity of the probe field. This phase shift can be c…
We show that far field diffraction image of spontaneously scattered Stokes photons can be used for detection of spin entanglement and for metrology of fields gradients in cold atomic ensembles. For many-body states with small or maximum uncertainty in spin-excitation number, entanglement is simply witnessed by the presence of a sharp diffraction peak or dip. Gradient vector of external fields is measured by the displacement of a diffraction peak due to inhomogeneous spin precessions, which suggests a new possibility for precision measurement beyond the standard quantum limit without entangleme…
A setup to frequency-convert an arbitrary image encoded in the spatial profile of a probe field onto a signal field using four-wave mixing in a thermal atom vapor is proposed. The atomic motion is exploited to cancel diffraction of both signal and probe fields simultaneously. We show that an incoherent probe field can be used to enhance the transverse momentum bandwidth which can be propagated without diffraction, such that smaller structures with higher spatial resolution can be transmitted. It furthermore compensate linear absorption with non-linear gain, to improve the four-wave mixing perf…
A practical scheme for entanglement creation between distant atoms located inside a single-mode optical cavity is discussed. We show that the degree of entanglement and the time it takes for the entanglement to reach its optimum value is a sensitive function the initial conditions and the position of the atoms inside the cavity mode. It is found that the entangled properties of the two atoms can readily be extracted from dynamics of a simple two-level system. Effectively, we engineer two coupled qubits whose the dynamics are analogous to that of a driven single two-level system. It is found th…
We consider photo ionization of an atom which, due to passing through a diffraction grating, is prepared in a multi-site state possessing a periodic space structure with alternating maxima and minima. It has been found that this process qualitatively differs from photo ionization of a 'normal' atom. In particular, the spectra of emitted electrons and recoil ions in this process display clear one- and two-particle interference effects. Moreover, there are also striking differences between the momentum distributions of these particles, which no longer mirror each other. The origin of all these f…
We propose a nonlinear atom-optics experiment to create diffraction catastrophes threaded by quantized vortex skeletons in Bose-Einstein condensed matter waves. We show how atom-optical aberrations induced in trapped Bose-Einstein condensates evolve into specific caustic structures due to imperfect focusing. Vortex skeletons, whose cross-sections are staggered vortex lattices, are observed to nucleate inside the universal diffraction catastrophes. Our observations shed further light on the structure and dynamics of Bose-novae and suggest applications of matter wave diffraction catastrophes, in…
Atom interferometry is the most successful technique for precision metrology. However, current interferometers using ultracold atoms allows one to probe the interference pattern only momentarily and has finite duty cycle, resulting in an aliasing effect and a low-bandwidth measurement -- also known as Dick effect. Interferometry with a continuous-wave atom laser shows promise in overcoming these limitations due a continuous monitoring of the interference pattern. In this work, we demonstrate a key step towards such an interferometry by demonstrating a diffraction of an `atom laser' in the Rama…
The use of retro-reflection in light-pulse atom interferometry under microgravity conditions naturally leads to a double-diffraction scheme. The two pairs of counterpropagating beams induce simultaneously transitions with opposite momentum transfer that, when acting on atoms initially at rest, give rise to symmetric interferometer configurations where the total momentum transfer is automatically doubled and where a number of noise sources and systematic effects cancel out. Here we extend earlier implementations for Raman transitions to the case of Bragg diffraction. In contrast with the single…
When a single two-level atom interacts with a pair of Laguerre-Gaussian beams with opposite helicity, this leads to an efficient exchange of angular momentum between the light field and the atom. When the radial motion is trapped by an additional potential, the wave function of a single localized atom can be split into components that rotate in opposite direction. This suggests a novel scheme for atom interferometry without mirror pulses. Also atoms in this configuration can be bound into a circular lattice.
We consider a method of high-fidelity, spatially resolved position measurement of ultracold atoms in an optical lattice. We show that the atom-number distribution can be nondestructively determined at a spatial resolution beyond the diffraction limit by tracking the progressive evolution of the many-body wavefunction collapse into a Fock state. We predict that the Pauli exclusion principle accelerates the rate of wavefunction collapse of fermions in comparison with bosons. A possible application of our principle of surpassing the diffraction limit to other imaging systems is discussed.
We study the diffraction of atoms and weakly-bound three-atomic molecules from a transmission grating at non-normal incidence. Due to the thickness of the grating bars the slits are partially shadowed. Therefore, the projected slit width decreases more strongly with the angle of incidence than the projected period, increasing, in principle, the experimental resolution. The shadowing, however, requires a revision of the theory of atom diffraction. We derive an expression in the style of the Kirchhoff integral of optics and show that the diffraction pattern exhibits a characteristic asymmetry wh…
We present a precision gravimeter based on coherent Bragg diffraction of freely falling cold atoms. Traditionally, atomic gravimeters have used stimulated Raman transitions to separate clouds in momentum space by driving transitions between two internal atomic states. Bragg interferometers utilize only a single internal state, and can therefore be less susceptible to environmental perturbations. Here we show that atoms extracted from a magneto-optical trap using an accelerating optical lattice are a suitable source for a Bragg atom interferometer, allowing efficient beamsplitting and subsequen…
In the waveguide quantum electrodynamics (QED) system, emitter separation plays an important role for its functionality. Here, we present a method to measure the deep-subwavelength emitter separation in a waveguide-QED system. In this method, we can also determine the number of emitters within one diffraction-limited spot. In addition, we also show that ultrasmall emitter separation change can be detected in this system which may then be used as a waveguide-QED-based sensor to measure tiny local temperature/strain variation.
Light transmission or diffraction from different quantum phases of cold atoms in an optical lattice has recently come up as a useful tool to probe such ultra cold atomic systems. The periodic nature of the optical lattice potential closely resembles the structure of a diffraction grating in real space, but loaded with a strongly correlated quantum many body state which interacts with the incident electromagnetic wave, a feature that controls the nature of the light transmission or dispersion through such quantum medium. In this paper we show that as one varies the relative angle between the ca…
German Aerospace Center (DLR), Institute of Quantum Technologies（德国航空航天中心量子技术研究所）；Institut des Sciences Moléculaires d’Orsay (ISMO), Centre national de la recherche scientifique (CNRS), University Paris-Sud, Université Paris-Saclay（奥赛分子科学研究所，法国国家科学研究中心，巴黎第十一大学，巴黎-萨克雷大学）；University of Vienna, Faculty of Physics（维也纳大学物理学院）
We have constructed an atom interferometer of the Mach-Zehnder type, operating with a supersonic beam of lithium. Atom diffraction uses Bragg diffraction on laser standing waves. With first order diffraction, our apparatus has given a large signal and a very good fringe contrast (74%), which we believe to be the highest ever observed with atom interferometers. This apparatus will be applied to high sensitivity measurements
Surface scattering of neutral helium beams created by supersonic expansion is an established technique for measuring structural and dynamical properties of surfaces on the atomic scale. Helium beams have also been used in Fraunhofer and Fresnel diffraction experiments. Due to the short wavelength of the atom beams of typically 0.1nm or less, Fraunhofer diffraction experiments in transmission have so far been limited to grating structures with a period (pitch) of up to 200nm. However, larger periods are of interest for several applications, for example for the characterization of photonic cryst…
Precise knowledge of optical lattice depths is important for a number of areas of atomic physics, most notably in quantum simulation, atom interferometry and for the accurate determination of transition matrix elements. In such experiments, lattice depths are often measured by exposing an ultracold atomic gas to a series of off-resonant laser-standing-wave pulses, and fitting theoretical predictions for the fraction of atoms found in each of the allowed momentum states by time of flight measurement, after some number of pulses. We present a full analytic model for the time evolution of the ato…
We have performed a precision atomic interferometry experiment on testing the universality of free fall (UFF) considering atoms' spin degree of freedom. Our experiment employs the Bragg atom interferometer with $^{87}$Rb atoms either in hyperfine state $\left| {F = 1,{m_F} = 0} \right\rangle $ or $\left| {F = 2,{m_F} = 0} \right\rangle $, and the wave packets in these two states are diffracted in one pair of Bragg beams alternatively, which can help suppress the common-mode systematic errors. We have obtained an E$\rm{\ddot{o}}$tv$\rm{\ddot{o}}$s ratio $η= \left( { 0.9 \pm 2.7} \right) \times …
Bohmian mechanics, widely known within the field of the quantum foundations, has been a quite useful resource for computational and interpretive purposes in a wide variety of practical problems. Here, it is used to establish a comparative analysis at different levels of approximation in the problem of the diffraction of helium atoms from a substrate consisting of a defect with axial symmetry on top of a flat surface. The motivation behind this work is to determine which aspects of one level survive in the next level of refinement and, therefore, to get a better idea of what we usually denote a…
We propose a method for measuring the temperature of fermionic atoms in an optical lattice potential from the intensity of the scattered light in the far-field diffraction pattern. We consider a single-component gas in a tightly-confined two-dimensional lattice, illuminated by far off-resonant light driving a cycling transition. Our calculations show that thermal correlations of the fermionic atoms generate fluctuations in the intensity of the diffraction pattern of light scattered from the atomic lattice array and that this signal can be accurately detected above the shot noise using a lens t…
We propose a novel scheme for asymmetric light diffraction of a weak probe field into a one-dimensional (1D) and two-dimensional (2D) lattice occupied with cold atoms. The atoms are driven into the double lambda-type configuration by a standing wave, two coupling laser fields and a probe. Our study suggests the proposed scheme is capable of forming an asymmetric diffraction as a result of inducing optical parity-time symmetry in both 1D and 2D lattices. Moreover it is demonstrated that the asymmetric pattern of diffraction can be dynamically manipulated by means of adjusting the relative phase…
Grazing incidence fast atom diffraction (GIFAD or FAD) is a sensitive tool for surface analysis, which strongly relies on the quantum coherence of the incident beam. In this article the influence of the incidence conditions and the projectile mass on the visibility of the FAD patterns is addressed. Both parameters determine the transverse coherence length of the impinging particles, which governs the general features of FAD distributions. We show that by varying the impact energy, while keeping the same collimating setup and normal energy, it is possible to control the interference mechanism t…
We experimentally demonstrate coherent light scattering from an atomic Mott insulator in a two-dimensional lattice. The far-field diffraction pattern of small clouds of a few hundred atoms was imaged while simultaneously laser cooling the atoms with the probe beams. We describe the position of the diffraction peaks and the scaling of the peak parameters by a simple analytic model. In contrast to Bragg scattering, scattering from a single plane yields diffraction peaks for any incidence angle. We demonstrate the feasibility of detecting spin correlations via light scattering by artificially cre…
