Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1409.8399 · Physical Review Letters

Diffraction-Unlimited Position Measurement of Ultracold Atoms in an Optical Lattice

Yuto Ashida, Masahito Ueda

Published Aug 26, 2015• 46 citations
arXivHTMLPDF

Abstract

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 wave function collapse into a Fock state. We predict that the Pauli exclusion principle accelerates the rate of wave function collapse of fermions in comparison with bosons. A possible application of our principle of surpassing the diffraction limit to other imaging systems is discussed.

DOI
10.1103/physrevlett.115.095301

Related papers

Quantum Gas Microscopy of Fermions in the Continuum

Tim de Jongh, Joris Verstraten, Maxime Dixmerias +3 more

Atom-based quantum simulators offer a unique platform that enables the imaging of each particle in a many-body system. Until now, however, this capability has been limited to quantum systems in discretized space such as optical lattices and tweezers, where spatial degrees of freedom are quantized. Here, we introduce a novel method for imaging atomic quantum many-body systems in the continuum, allowing for in situ resolution of every particle. We demonstrate the capabilities of our approach on a two-dimensional atomic Fermi gas. We probe the density correlation functions, resolving their full spatial functional form, and reveal the shape of the Fermi hole arising from Pauli exclusion as a function of temperature. Our method opens the door to probing strongly correlated quantum gases in the continuum with unprecedented spatial resolution, providing in situ access to spatially resolved correlation functions of arbitrarily high order across the entire system.

arXiv:2411.08776•Physical Review Letters•May 5, 2025•25 citations

Lattice-depth measurement using multipulse atom diffraction in and beyond the weakly diffracting limit

Benjamin T. Beswick, Ifan G. Hughes, S. A. Gardiner

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 atomic populations of the lowest momentum states, which is sufficient for a ``weak'' lattice, as well as numerical simulations incorporating higher momentum states for both relatively strong and weak lattices. Finally, we consider the situation where the initial gas is explicitly assumed to be at a finite temperature.

arXiv:1810.01376•Physical Review A•Jan 16, 2019•4 citations

Super-resolution microscopy of single atoms in optical lattices

Andrea Alberti, Carsten Robens, Wolfgang Alt +5 more

We report on image processing techniques and experimental procedures to determine the lattice-site positions of single atoms in an optical lattice with high reliability, even for limited acquisition time or optical resolution. Determining the positions of atoms beyond the diffraction limit relies on parametric deconvolution in close analogy to methods employed in super-resolution microscopy. We develop a deconvolution method that makes effective use of the prior knowledge of the optical transfer function, noise properties, and discreteness of the optical lattice. We show that accurate knowledge of the image formation process enables a dramatic improvement on the localization reliability. This allows us to demonstrate super-resolution of the atoms' position in closely packed ensembles where the separation between particles cannot be directly optically resolved. Furthermore, we demonstrate experimental methods to precisely reconstruct the point spread function with sub-pixel resolution from fluorescence images of single atoms, and we give a mathematical foundation thereof. We also discuss discretized image sampling in pixel detectors and provide a quantitative model of noise sources in electron multiplying CCD cameras. The techniques developed here are not only beneficial to neutral atom experiments, but could also be employed to improve the localization precision of trapped ions for ultra precise force sensing.

arXiv:1512.07329•New Journal of Physics•May 6, 2016•65 citations

Nanoscale Atomic Density Microscopy

Sarthak Subhankar, Yang Wang, T-C. Tsui +2 more

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/50 and excellent temporal resolution of 500 ns. We characterize our microscope's performance by measuring the ensemble averaged probability density of atoms within the unit cells of an optical lattice, and observe the dynamics of atoms excited into motion. This approach can be readily applied to image any atomic or molecular system, as long as it hosts a three-level system.

arXiv:1807.02871•Physical Review X•Apr 1, 2019•50 citations

Quantum gas magnifier for sub-lattice-resolved imaging of 3D quantum systems

Luca Asteria, Henrik P. Zahn, Marcel N. Kosch +2 more

Abstract Imaging is central to gaining microscopic insight into physical systems, and new microscopy methods have always led to the discovery of new phenomena and a deeper understanding of them. Ultracold atoms in optical lattices provide a quantum simulation platform, featuring a variety of advanced detection tools including direct optical imaging while pinning the atoms in the lattice1,2. However, this approach suffers from the diffraction limit, high optical density and small depth of focus, limiting it to two-dimensional (2D) systems. Here we introduce an imaging approach where matter wave optics magnifies the density distribution before optical imaging, allowing 2D sub-lattice-spacing resolution in three-dimensional (3D) systems. By combining the site-resolved imaging with magnetic resonance techniques for local addressing of individual lattice sites, we demonstrate full accessibility to 2D local information and manipulation in 3D systems. We employ the high-resolution images for precision thermodynamics of Bose–Einstein condensates in optical lattices as well as studies of thermalization dynamics driven by thermal hopping. The sub-lattice resolution is demonstrated via quench dynamics within the lattice sites. The method opens the path for spatially resolved studies of new quantum many-body regimes, including exotic lattice geometries or sub-wavelength lattices3–6, and paves the way for single-atom-resolved imaging of atomic species, where efficient laser cooling or deep optical traps are not available, but which substantially enrich the toolbox of quantum simulation of many-body systems.

arXiv:2104.10089•Nature•Nov 24, 2021•46 citations

Quantum theory of atomic position measurement using optical fields

John E. Thomas

A simple quantum theory of recently suggested optical techniques for ultrahigh-resolution position measurement and localization of moving atoms in beams is presented. Both the internal and center-of-mass motion are treated quantum mechanically so that the limitations on the ultimate position resolution due to atomic motion and wave-mechanical diffraction are included in the analysis. The techniques utilize a miniaturized form of Raman-induced resonance imaging in which optical fields are used to make transitions from a long-lived initial state to a long-lived final state. The final state is shifted by the spatially varying potential of an applied force field in order to correlate the atomic position with its resonance frequency. Spatially varying level shifts are obtainable by using very large Zeeman field gradients or spatially varying light shifts in a small interaction volume. This results in very high spatial resolution. The atomic transit time across the optical-field region is limited by focusing to an ideal diameter that minimizes the spatial resolution length. The results of the analysis show that nanometer spatial resolution of the initial-state position distribution is attainable. Under appropriate conditions, the final-state spatial wave function can take the form of a minimum-uncertainty Gaussian wave packet obeying \ensuremath{\Delta}x\ensuremath{\Delta}p=\ensuremath{\Elzxh}/2. Such states may prove useful in studying one-dimensional wave-packet motion in applied potentials.

Physical Review A•Nov 1, 1990•67 citations
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 wave function collapse into a Fock state. We predict that the Pauli exclusion principle accelerates the rate of wave function collapse of fermions in comparison with bosons. A possible application of our principle of surpassing the diffraction limit to other imaging systems is discussed.
Atom-based quantum simulators offer a unique platform that enables the imaging of each particle in a many-body system. Until now, however, this capability has been limited to quantum systems in discretized space such as optical lattices and tweezers, where spatial degrees of freedom are quantized. Here, we introduce a novel method for imaging atomic quantum many-body systems in the continuum, allowing for in situ resolution of every particle. We demonstrate the capabilities of our approach on a two-dimensional atomic Fermi gas. We probe the density correlation functions, resolving their full spatial functional form, and reveal the shape of the Fermi hole arising from Pauli exclusion as a function of temperature. Our method opens the door to probing strongly correlated quantum gases in the continuum with unprecedented spatial resolution, providing in situ access to spatially resolved correlation functions of arbitrarily high order across the entire system.
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 atomic populations of the lowest momentum states, which is sufficient for a ``weak'' lattice, as well as numerical simulations incorporating higher momentum states for both relatively strong and weak lattices. Finally, we consider the situation where the initial gas is explicitly assumed to be at a finite temperature.
We report on image processing techniques and experimental procedures to determine the lattice-site positions of single atoms in an optical lattice with high reliability, even for limited acquisition time or optical resolution. Determining the positions of atoms beyond the diffraction limit relies on parametric deconvolution in close analogy to methods employed in super-resolution microscopy. We develop a deconvolution method that makes effective use of the prior knowledge of the optical transfer function, noise properties, and discreteness of the optical lattice. We show that accurate knowledge of the image formation process enables a dramatic improvement on the localization reliability. This allows us to demonstrate super-resolution of the atoms' position in closely packed ensembles where the separation between particles cannot be directly optically resolved. Furthermore, we demonstrate experimental methods to precisely reconstruct the point spread function with sub-pixel resolution from fluorescence images of single atoms, and we give a mathematical foundation thereof. We also discuss discretized image sampling in pixel detectors and provide a quantitative model of noise sources in electron multiplying CCD cameras. The techniques developed here are not only beneficial to neutral atom experiments, but could also be employed to improve the localization precision of trapped ions for ultra precise force sensing.
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/50 and excellent temporal resolution of 500 ns. We characterize our microscope's performance by measuring the ensemble averaged probability density of atoms within the unit cells of an optical lattice, and observe the dynamics of atoms excited into motion. This approach can be readily applied to image any atomic or molecular system, as long as it hosts a three-level system.
Abstract Imaging is central to gaining microscopic insight into physical systems, and new microscopy methods have always led to the discovery of new phenomena and a deeper understanding of them. Ultracold atoms in optical lattices provide a quantum simulation platform, featuring a variety of advanced detection tools including direct optical imaging while pinning the atoms in the lattice1,2. However, this approach suffers from the diffraction limit, high optical density and small depth of focus, limiting it to two-dimensional (2D) systems. Here we introduce an imaging approach where matter wave optics magnifies the density distribution before optical imaging, allowing 2D sub-lattice-spacing resolution in three-dimensional (3D) systems. By combining the site-resolved imaging with magnetic resonance techniques for local addressing of individual lattice sites, we demonstrate full accessibility to 2D local information and manipulation in 3D systems. We employ the high-resolution images for precision thermodynamics of Bose–Einstein condensates in optical lattices as well as studies of thermalization dynamics driven by thermal hopping. The sub-lattice resolution is demonstrated via quench dynamics within the lattice sites. The method opens the path for spatially resolved studies of new quantum many-body regimes, including exotic lattice geometries or sub-wavelength lattices3–6, and paves the way for single-atom-resolved imaging of atomic species, where efficient laser cooling or deep optical traps are not available, but which substantially enrich the toolbox of quantum simulation of many-body systems.
A simple quantum theory of recently suggested optical techniques for ultrahigh-resolution position measurement and localization of moving atoms in beams is presented. Both the internal and center-of-mass motion are treated quantum mechanically so that the limitations on the ultimate position resolution due to atomic motion and wave-mechanical diffraction are included in the analysis. The techniques utilize a miniaturized form of Raman-induced resonance imaging in which optical fields are used to make transitions from a long-lived initial state to a long-lived final state. The final state is shifted by the spatially varying potential of an applied force field in order to correlate the atomic position with its resonance frequency. Spatially varying level shifts are obtainable by using very large Zeeman field gradients or spatially varying light shifts in a small interaction volume. This results in very high spatial resolution. The atomic transit time across the optical-field region is limited by focusing to an ideal diameter that minimizes the spatial resolution length. The results of the analysis show that nanometer spatial resolution of the initial-state position distribution is attainable. Under appropriate conditions, the final-state spatial wave function can take the form of a minimum-uncertainty Gaussian wave packet obeying \ensuremath{\Delta}x\ensuremath{\Delta}p=\ensuremath{\Elzxh}/2. Such states may prove useful in studying one-dimensional wave-packet motion in applied potentials.