Pulsed Ion Microscope to Probe Quantum Gases

The advent of the quantum gas microscope allowed for the in situ probing of ultracold gaseous matter on an unprecedented level of spatial resolution. However, the study of phenomena on ever smaller length scales, as well as the probing of three-dimensional systems, is fundamentally limited by the wavelength of the imaging light for all techniques based on linear optics. Here, we report on a high-resolution ion microscope as a versatile and powerful experimental tool to investigate quantum gases. The instrument clearly resolves atoms in an optical lattice with a spacing of 532 nm over a field of view of 50 sites and offers an extremely large depth of field on the order of at least $70\mu \mathrm{m}$. With a simple model, we extract an upper limit for the achievable resolution of approximately 200 nm from our data. We demonstrate a pulsed operation mode enabling 3D imaging and allowing for the study of ionic impurities and Rydberg physics.

Popular Summary

In the past decade, microscopy methods have allowed for the direct imaging of ultracold atoms loaded into optical lattices. The small depth of field and the limited resolution of typical optical microscopy schemes, however, have restricted most studies to essentially two dimensions and a spatial resolution on the order of $0.5\mu \mathrm{m}$. In this work, we present a high-resolution imaging method for ultracold gaseous matter that overcomes both of these limitations. Based on charged-particle optics, our approach enables the study of large 3D bulk quantum gases with a resolution better than 200 nm.

Our versatile technique relies on the imaging of ionized atoms onto a spatially resolving detector and permits the investigation of ground-state ensembles, ordered Rydberg excitations, and cold ion-atom hybrid systems. Furthermore, the method allows for the probing of fast dynamics on a submicrosecond timescale and for 3D imaging via the time-of-flight information of the particles. In experiments, our instrument clearly resolves atoms in an optical lattice with a lattice spacing of 532 nm and offers a depth of field of at least $70\mu \mathrm{m}$.

The presented concept paves the way for a whole range of new experiments and enables, for example, the detection of fine spatial structures in bulk Fermi gases or the exploration of strongly interacting impurities.

Figure 1

Concept of the pulsed ion microscope. Neutral atoms in a quantum gas (shown in a 1D periodic potential) are converted into ions at time $t=t_1$ via a suitable ionization process (e.g., near-threshold photoionization). After a variable wait time, an extraction field is pulsed on ($t=t_2$), and the ions are imaged onto a spatially resolving detector by means of an ion microscope consisting of three electrostatic lenses ($t=t_3$). The high time resolution of the multichannel plate detector (MCP) allows for the study of dynamical processes (e.g., in strongly interacting many-body systems) and 3D imaging via the time-of-flight information. The versatile nature of the concept enables the study of ground-state ensembles, Rydberg systems, and ionic impurities.

Figure 2

Ion microscope. The microscope column consists of three electrostatic lenses (main electrodes marked in red, drift sections in gray). Each lens is followed by an electrostatic quadrupole deflector (blue). (a) The object plane lies above a repeller electrode and below an extractor electrode (pale yellow), which, at the same time, are part of a six-plate electric field control (radial field plates marked in blue). The repeller hosts an indium-tin-oxide-coated aspheric optical lens. The extractor also acts as the lower lens electrode of the first lens. (b) Detailed view of the second lens and the following deflection stage. (c) Spatially resolved ion detection is achieved via a delay-line anode on top of an MCP stack. (d) Schematic representation of the electrode configuration. Imaging properties and magnification are determined by the extraction voltages ($V_{\mathrm{E}}$ and $V_{\mathrm{R}}$), the lens voltages ($V_1$ to $V_3$), and the drift-tube voltages ($V_{\mathrm{D}1}$ and $V_{\mathrm{D}2}$). The latter are referred to as $V_{\mathrm{D}}$ for all measurements for which $V_{\mathrm{D}1}=V_{\mathrm{D}2}$.

Figure 3

Tuning of the magnification. A large range of $M$ is achievable by tuning $V_2$ and $V_3$ ($V_{\mathrm{E}}=-V_{\mathrm{R}}=-500\mathrm{V}$, $V_1=-3.2\mathrm{kV}$, $V_{\mathrm{D}}=-2.4\mathrm{kV}$). (a) Result of numerical trajectory simulations for a test pattern with a line spacing of $L=100\mathrm{nm}$ (see inset) and parameters resembling the experimental situation. For the displayed data points, the line spacing is clearly resolved and low image distortion is present (see Appendix pp1 for details). Most values of $M$ are accessible by tuning only $V_2$. (b) Comparison between experiment and simulation along the dashed red line ($V_2=-250\mathrm{V}$) shown in panel (a). The atoms were loaded into a retroreflected 1064-nm lattice and photoionized in a crossed-beam configuration ($w_{780}\approx 26\mu \mathrm{m}$, $w_{479}\approx 5\mu \mathrm{m}$). (c) Comparison between experiment and simulation along the solid red line ($V_3=-110\mathrm{V}$) shown in panel (a). The 780-nm photoionization laser was spatially structured by projecting the diffraction pattern of a double slit onto the atoms (see Appendix pp5). As an example, the insets in panels (b) and (c) show a cutout of the postprocessed detector image along with the normalized magnitude of the fast Fourier transform (FFT) for one of the voltage configurations. The FFT corresponds to the integrated profile of the whole image in object coordinates. The values of $M$ are inferred from the period of the detected patterns. All experimental error bars (see Appendix pp5) are significantly smaller than the marker size.

Figure 4

Field of view. The FOV was investigated for the voltage configuration corresponding to the largest magnification shown in Fig. 3 ($M=1441$). (a) Measured data (sum over 1200 experimental cycles, object coordinates), corrected for a global phase ${\mathrm{\Phi }}_{\mathrm{g}}$ (drift of the lattice) and a local phase ${\mathrm{\Phi }}_{\mathrm{l}}$ (distortion). The marked region is enlarged in panels (b) (raw data) and (e) (phase-corrected data). Panel (c) shows ${\mathrm{\Phi }}_{\mathrm{g}}$ over time, and panel (d) shows ${\mathrm{\Phi }}_{\mathrm{l}}$ as a function of the spatial coordinates. The local phase ${\mathrm{\Phi }}_{\mathrm{l}}$ is extracted from the local deviation of the experimental data from the expected regular lattice structure.

Figure 5

Depth of field and resolution. (a) Imaging result for an increased depth of field limited only by the cloud size ($1/e$ diameter of $70\mu \mathrm{m}$). (b) Absolute value of the FFT corresponding to the integrated lattice profile shown in panel (a). (c) Magnitudes of the first- and second-order FFT peaks (here, as a function of $V_3$ and for a tightly confined ionization region) serving as a qualitative measure of the resolution. All experimental error bars (see Appendix pp6) are smaller than the marker size. The insets show the experimental data for $V_3=-150\mathrm{V}$. The solid line and the shaded area show the theoretical prediction for the upper bound of the second-order peak amplitude for a resolution of $200\pm 20\mathrm{nm}$. Experimental circumstances are detailed in the main text.

Figure 6

Pulsed operation mode. (a) Imaging result for $t_{\text{wait}}=0\mu \mathrm{s}$ and magnitude of the FFT corresponding to the integrated lattice profile. The clear signature of a second-order Fourier peak indicates a resolution on the order of half the lattice spacing (266 nm). (b) Decay of the first-order FFT peak, which serves as an indicator for the blurring of the lattice structure as a function of $t_{\text{wait}}$. The timescale of the decay reveals the low temperature of the produced ions in the few tens of microkelvin range. Error bars correspond to a conservative estimate of the statistical error (see Appendix pp6).

Figure 7

Three-dimensional imaging. (a) Transverse magnification for a reduced magnitude of $V_{\mathrm{D}1}$, boosting the axial resolution. All electrode voltages are given in the plot. (b) Proof-of-principle experiment to test the 3D imaging. The light field of the 479-nm photoionization laser is spatially structured by projecting the diffraction pattern of two crossed double slits onto the atoms. (c) Imaging result in detector coordinates ($xt$ plane) for an electrode voltage configuration corresponding to the red mark ($V_2=-50\mathrm{V}$, $V_3=-110\mathrm{V}$) shown in panel (a). The arrival time of the ions is corrected for an offset. As predicted from simulations, a curvature of the time of flight is observed. (d) Imaging result in object coordinates (all planes) after compensating for the curvature of the time of flight. In both panels (c) and (d), an integration of all ion counts is performed along the dimension not shown.

Figure 8

Example of the axial electrostatic potential. The curve shown corresponds to an electrode voltage configuration of $[V_{\mathrm{R}},V_{\mathrm{E}},V_1,V_2,V_3,V_{\mathrm{D}}]=[500,-500,-3200,-250,-110,-2400]\mathrm{V}$. The shaded regions mark the position of the main electrodes of the three lenses. The potential stays flat for the remaining distance to the detector, which is located at 1350 mm.