"First, FIG. 2 shows a hologram using a one-dimensional slit array having electrode pairs. This slit array is formed from a large plurality of slits 1 aligned in one row in silicon nitride (SiN) hologram substrate 3 having a thickness of 500 nm, slit 1 having a width of 1 micron and a length of 5 microns. In this embodiment a list array comprising 256 slits is employed, and at each slit an electrode pair 2 is arranged so as to generate an electric field orthogonal to the direction of the arrangement of the slit array and parallel to the surface of the hologram substrate. In addition, an electric potential can be impressed to the electrode pair of each slit independently to generate an electric field."

Double MOT apparatus for the 87Rb BEC experiment (Ken'ichi Nakagawa, Munekazu Horikoshi, Yusuke Suzuki, Kei-ichi Muraishi with former members Takayuki Iio, Masamichi Tamura, Yamao Nakajima, Osamu Uehara, Noritsugu Shiokawa) Toward coherent atom optics with BEC.

“Schematic of experimental setup. A beam of laser-cooled atoms generated in the source chamber (left) travels toward the magnetic guide between the source and detection chamber. Atoms enter the tracks and are guided around a barrier. After the guided atoms exit the tracks, they are ionized with a hot wire and ions are counted with a channeltron.”

Guiding neutral atoms around curves with lithographically patterned current-carrying wires (Dirk M¨uller, Dana Z. Anderson, Randal J. Grow, Peter D. D. Schwindt, Eric A. Cornell).

“We have developed an iron-core electromagnet and used it to trap neutral atoms. The magnetic field can be switched from a spherical quadrupole configuration to a Ioffe configuration within 2 ms. We load 2*10^7 87Rb atoms from a vapor into a Magneto-Optical Trap (MOT) and transfer them into the purely magnetic trap with an efficiency of 95%. A strong radial compression is possible since we can generate quadrupole gradients up to 0.1 T/cm with an excitation current of 10 A (400 W of power consumption).”

Iron-core electromagnetic trap for the use of trapping cold neutral atoms (B. Desruelle, V. Boyer, P. Bouyer, G. Birkl, M. Lecrivain (spelling), F. Alves, C.I. Westbrook, and A. Aspect)

"Central part of the vacuum system (technical drawing) with two quartz cells as experimental chambers and arrangement of the pumps (schematics). The two chambers are connected by a differential pumping hole. The lower chamber contains rubidium vapor up to 4*10^−7 mbar. In the upper ultra-high vacuum chamber a pressure lower than 3*10^−11 mbar is achieved."

`FIGURE 3.3: Ioffe-quadrupole magnetic trap. Left: View along the radial direction. Right: View along the horizontal symmetry axis. The magnetic field coils are made of water cooled copper tubes dissipating 5.4kW at 400 A. The thermally stable mount is designed like a bench system with four quartz rods.`

`FIGURE 3.5: Control circuit of the magnetic trap: The 8 coils of the trap carry currents up to 400 A. The currents are controlled by programming the power supplies and using the IGBT switches. The different paths A-E are used for the operation of the MOT, the compression of the magnetic trap and the compensation of the gravitational shift of the trap center.`

`FIGURE 3.7: Setup for absorption imaging: The atomic cloud creates a shadow in the center of the collimated detection beam. The confocal relay telescope creates an intermediate image of the cloud outside the vacuum cell. This allows the use of microscope objectives with short working distance. The magnified image is detected by a CCD camera. By inserting a phase-plate in the center of the telescope phase-contrast imaging can be applied.`

`FIGURE 4.1: Experimental setup: The rubidium vapor cell from which the atomic beam is extracted is located inside the four racetrack shaped magnetic field coils. These so called Ioffe-coils produce a two-dimensional quadrupolar magnetic field are used in the 2D-MOT and 2D+-MOT configurations. The anti-Helmholtz coils are used for the three-dimensional quadrupolar field necessary for the LVIS configuration. The vertical MOT-beams used for the 2D+-MOT and the LVIS are absent in the 2D-MOT case. After passing through an aperture in a 45 mirror into a ultrahigh vacuum chamber the atomic beam is detected by means of fluorescence.`

`FIGURE 5.1: Setup used for laser cooling and magnetic trapping: In the lower part the atomic beam source is shown. The atoms are recaptured from the atomic beam into a magneto-optical trap made of six laser beams and two pinch coils. The atomic cloud is at the same location loaded into the magnetic trap, which is made of the Ioffe, pinch, and compensation coils.`

`Figure 2.3: Laser frequency control for the three lasers in our experiment. For the less critical repump laser, the frequency modulation for the lock-in detection is applied to the laser frequency itself through current modulation. For the more critical trapping and probing beams, the frequency modulation is applied to the AOMs, and thus the frequency modulation is not on the light used on the atoms.`

`Figure 2.4: Vacuum system layout. The system is suspended with a series of clamps (not shown), so the center line of all the horizontal tubing is 18 cm above the optical table.`

`Figure 2.8: Picture of the vertical-beam optics for the MOT omitted from Fig. 2.7. Figure shows the location of the track (blue arrow) and the vertical MOT beams (red arrows). The coils of the MOT/quadrupole trap are translated left, towards the science cell, out of the field of view of this photograph.`

`Figure 2.9: Schematic of the MOT/Quadrupole trap servo circuit. The circuit has standard PI loop gain, where the proportional gain comes from the feedback from the closed-loop Hall current sensor. We use 2/0 gauge welding cable to carry 300 A from the power supply to the coils and MOSFETs. The three MOSFETs are mounted on a water cooled copper plate to remove the heat generated by the MOSFETs.`

`Figure 2.13: Science cell region showing the magnetic trap holder. Two stainless-steel endcaps on the ends of the Boron nitride form (white) are attached to a support structure behind the coil form. The microwave waveguide is shown on the left side of the picture directed towards the trapping region. Not shown is the objective lens on the back of the coil form.`

`Figure 2.14: Ioffe-Pritchard magnetic trap (end on view). The permanent magnets are at a 45 degree angle with respect to the horizontal axis so as to provide a magnetic field in the same direction as the magnetic field from the quadrupole trap used to transport the atoms. Four permanent magnets, magnetized through the thin dimension, will also work to provide a two dimensional quadrupole field with no field along the axial direction of the trap. However, using just two magnets magnetized through the thin direction will create a significant gradient along the axial direction of the trap.`

`Figure 2.15: Ioffe-Pritchard magnetic trap (side view) showing the permanent magnet and axial coil positions. Outer(inner) coils are each 20(10) turns of 18 gauge magnet wire and provide the axial confinement/bias.`

`Figure 2.20: Microwave frequency chain showing all of the components we use to produces variable frequency microwaves at 6.8 GHz. The solid arrows indicate transmission of 10 MHz signals. See text for further description.`

`A diagram of a three dimensional magneto-optical trap. Shown on the diagram are the three pairs of laser beams and the direction and the strength of the magnetic field along the axes in the trapping region [5].`

`Drawing of the vacuum system.The Rb getter is inside a stainless steel tube on the end of a vacuum feedthrough, cut-away view shown here. The ion pump is on the of a 25 cm long stainless steel pipe.`

`The project will follow the method described by Carl Wieman and Gwenn Flowers of University of Colorado and Sarah Gilbert of NIST, in a paper published in Am.J.Phys. 63(4), April 1995, and another paper by K. B. MacAdam, A. Steinbach, and C.Wieman of University of Colorado published in Am.J.Phys.60(12), December 1992. The two papers outline the method for obtaining narrow band tunable laser systems and trapping and cooling of Rb or Cs.`

Carl Wieman and Gwenn Flowers, Joint Institute for Laboratory Astrophysics and the Department of Physics, University of Colorado, Boulder, Colorado 80309, Sarah Gilbert National Institute of Standards and Technology, Boulder, Colorado 80303, Inexpensive laser cooling and trapping experiment for undergraduate laboratories, Am.J.Phys.63 (4), April 1995

`Figure 4.1: Schematic of the atomic beam line. (1) Fe source crucible. (2) Skimmer for differential pumping. (3) Laser cooling section. (4) Movable slit. (5) Deposition setup; only sample and mirror are shown. (6) Light sheet for atom beam imaging.`

`Figure 4.3: Fe source design. Heating current for graphite coil (4) comes through copper electrodes (1). Aperture (7) defines beam from expansion out of crucible (3). Water cooled oven (6) is isolated by 20 Ta foil radiation shields (5).`

`Figure 4.5: Left: sample holder. Right: Cross section of sample holder. The sample is clamped to a macor isolator that is screwed onto the steel frame. The mirror is pressed to the frame by a spring.`

`Left: Ag source. Water cooling through legs. Not shown: heating and thermocouple wires. Right: crucible design. (1) Tungsten crucible containing Ag; (2) Alumina spacer; (3) Ta filament; (4) Ta foil heat shields; (5) Mechanical shutter; (6) Thermocouple; (7) Water cooling.`

`Laser system for Fe atom lithography. Laser light at 744 nm is generated from multi-line green light in a tunable Ti:S laser. It is fed into a ring cavity with an LBO crystal in it. In the crystal, frequency doubled light at 372 nm is generated.`

`Polarization spectroscopy setup. Pump beam introduces birefringence in the iron discharge. The effect of this birefringence on the polarization of a counter propagating probe beam is analyzed using two photodiodes (right).`

`Experimental setup and results. (a) A collimated chromium beam impinges on a resonant standing light wave and subsequently hits a substrate. After deposition the substrate topography is analyzed with an atomic force microscope (AFM). (b) The Rabi frequency shows a spatial dependence due to the Gaussian laser beam profile along the y direction. Thus each individual substrate contains the whole intensity dependence of the atom-light interaction. (c) The AFM image and (d) cross sections reveal the light intensity dependence of the formed structures. For low intensity, peculiar periodic structures with feature spacings below λ/2 are observed.`

`Direct-write atom lithography schematic. Atoms are deflected and focused by the laser standing wave and follow the trajectories indicated. They are deposited onto the substrate, where a periodic structure is generated.`

`Figure 1 Schematic of a generic atom beam apparatus. In a vacuum chamber, heating a crucible containing the desired material produces atomic vapor. Atoms effuse through an orifice and are collimated by an aperture.`

`As the atoms emerge from the orifice, they fly in nominally straight lines across the vacuum system, eventually striking a substrate (or the vacuum chamber wall), where they stick or bounce depending on the local temperature and their particular chemical nature. If the pressure behind the orifice is not too high, so that few collisions occur as the atoms leave the aperture, the intensity distribution of the beam follows a cosine distribution, falling off as the cosine of the angle relative to the axis of the aperture.`

`The spontaneous force exerted by laser light on an atom. Photons incident from one direction only are absorbed and re-emitted by spontaneous emission in all directions. The result, on average, is a transfer of momentum to the atom.`

`Optical pumping. A laser is used to excite an atom from the ground state |g> to the excited state |e>. While the atom is in the excited state, there is some probability that it will fall into the metastable state |m> by spontaneous emission. Once in |m>, the atom can no longer interact with the laser.`

`Doppler cooling. Counterpropagating laser beams, tuned below the atomic resonance, interact with a population of atoms with random velocities. Those atoms with velocity components toward one of the laser beams will be Doppler shifted closer to resonance, and hence will feel a stronger spontaneous force from that laser. Thus atoms feel a velocity-dependent force, which reduces the velocity spread of the population.`

directions is produced by two coils with current I flowing in opposite directions (anti-Helmholtz configuration), and three pairs of oppositely-circularly-polarized laser beams counterpropagate through the center. (b) Energy of a J = 0 → J = 1 atom in the presence of the magnetic field of a MOT. The magnetic sublevels M = 1, 0, 1 are shifted in opposite directions on opposite sides of the center. When the laser frequency laser is tuned below resonance, atoms at negative positions are closer to resonance with the σ+ laser beam, while atoms at positive positions are closer to resonance with the σ laser beam. Thus all atoms feel a net spontaneous force toward the center.`

`While the dipole force seems a natural choice for high-resolution focusing, it is also possible to focus atoms with the spontaneous force. Such a lens has been demonstrated using four diverging near-resonant laser beams aimed transversely at a sodium atomic beam from four sides (Fig. 12)[64]. The approximately linear force dependence in this case comes from the fact that the laser beams are diverging as they propagate toward the atom beam. Atoms travelling through this light field experience a higher laser intensity the farther away from the axis they are, and so the spontaneous force is greater (as long as the atomic transition is not saturated). With this lens, it was possible to create an easily discernible image of a two-aperture atomic source, demonstrating the imaging capability of the technique. The two oven apertures were 0.5 mm in diameter and the resulting image spot sizes were 1.3 mm in diameter. The spot size was found to be limited by chromatic and spherical aberrations, and also by the random component of the spontaneous force.`

`Standing wave lens array. An above-resonance laser standing wave propagates parallel to and as close as possible to a surface. Collimated atoms, incident perpendicular to the surface, are focused in each of the nodes of the standing wave by the dipole force. Nanometer-scale focusing has been demonstrated with this lens (see section IV.A).`

`Perhaps the most dramatic demonstration of atom-optical diffraction has been the generation of a recognizable pattern by diffracting atoms through a computer-generated, microfabricated hologram[92,93]. In this demonstration, metastable neon atoms were first trapped in a MOT and then released by a push from a near-resonant laser beam. The atoms fell through a screen that had an array of 500 nm-scale holes cut into it by microlithography, arranged in a pattern calculated to be the hologram of a desired image. After diffracting from the screen, the atoms were detected by a microchannelplate in the far field, where a clear image was observed (see Fig. 17). The transverse and longitudinal coherences of the atoms were kept high in this case because the atoms were launched from a trap, where their transverse and longitudinal velocity spreads were highly reduced. This experiment shows that the possibility of holographically imaging atoms is real, and opens up the possibility of fabrication of an arbitrary nanoscale pattern in the future.`

`Figure 17 Image formed by diffraction of metastable Ne atoms passing through a computergenerated hologram fabricated as an array of 500 nm-scale holes in a 100 nm-thick silicon nitride film. The image was detected with a microchannelplate. (from M. Morinaga et al, Phys. Rev. Lett. 77, 802 [1996]).`

`Two basic approaches to nanofabrication with atom optics have evolved from the preliminary research in this area. In one method, atoms are manipulated during direct deposition, growing nanostructures by adding atoms to the surface in a specific pattern. In the other, atoms are manipulated as they impact and expose a resist, in what is referred to as neutral atom lithography. In the next two sections, we discuss some of the results that have been obtained with these two approaches.`

`Schematic view of the neon beam line. Six laser cooling sections are indicated starting from the source with the collimator, the first transverse Doppler cooler, the Zeeman slower, the second transverse Doppler cooler, the magnetooptical compressor and the sub-Doppler cooler.`

`Schematic view of the optical components necessary for the different laser cooling sections of the neon beam line. All laser cooling sections are operated with a single dye-laser which is locked 1.8Γ to the red of the Ne (3s) 3P2 ↔(3p) 3D3 transition by using saturated absorption spectroscopy. T: optical telescope , CT: cylindrical optical telescope, CB: cubic beam splitter, PCB: polarizing cubic beam splitter, PD: photo diode, AOM: acousto optic modulator, λ/2, λ/4: half and quarter waveplates.`

`Figure 3.3: Artist's impression of the neon beam line. The main laser cooling sections and the wire scanners for beam diagnostics are indicated. Table III gives a detailed overview of the position and the length of the different parts of the setup.`

`Artist's impression of the trapping chamber. On the left the last part of the neon beam-machine is visible (chapter 3). The amount of atoms entering the trapping chamber can be detected with a movable detection plate (detector). Not shown in this figure is a valve between the chamber of the beam machine and the differential chamber.`

`Top view of the trapping chamber with schematically a view of the optical components of the magneto-optical trap. The light for the six trapping beams all come from a single dye laser which is locked to the Zeeman-tuned Ne(3s)3P2↔(3p)3D3 transition by saturated absorbtion. The light for the extra Zeeman slower and the probe-beam come from the dye laser used for preparing the atomic beam (chapter 3). L: single lens, T: optical telescope, CB: cubic beamsplitter, PCB: polarizing cubic beam splitter, PD: photo diode, S: beam-shutter, AOM: acousto optical modulator, λ/2, λ/4: half and quarter wave plates.`

Hybrid apparatus for Bose-Einstein condensation and cavity quantum electrodynamics: Single atom detection in quantum degenerate gases (Anton ¨Ottl, Stephan Ritter, Michael K¨ohl, and Tilman Esslinger)

`Schematic sketch of the experimental setup illustrating the nested vacuum chambers, the short magnetic transport and the “science platform” bearing the ultrahigh finesse optical cavity on top of the vibration isolation system. The atomic cloud captured in the magneto-optical trap (MOT) is transferred through a differential pumping tube into the ultrahigh vacuum region and evaporatively cooled towards quantum degeneracy. We output couple a continuous atom laser from the BEC and direct it to the cavity mode where single atoms are detected.`

`Overview of the complete vacuum system showing the pumping sections for the two nested vacuum regions, high vacuum (HV) and ultrahigh vacuum (UHV), respectively. The overall length is close to 2m. The main tank offers multiple optical and electrical access and is sealed off by two CF 200 cluster flanges called “BEC production rig” and “science platform.”`

`Section through the UHV system illustrating the realization of the nested chambers design and revealing the details and objectives of the divers optical axes. The position of the BEC and cavity are marked by (•) and (), respectively. The high vacuum MOT chamber is suspended from the “BEC production rig” and sealed by a tight fit bushing against the UHV main tank. The “science platform” provides space for additional components such as the ultrahigh finesse optical cavity. [Note: For clarity in the illustration the magnet coil configuration (Fig. 5) and the optical cavity assembly (Fig. 8) are omitted in this figure.]`

`Section through the complete assembly inside the main vacuum chamber. It illustrates the arrangement of magnet coils, the inner chamber, and the cavity with respect to each other. Functional units of the magnet coil configuration are the two transport brackets that sandwich the inner chamber and the laterally mounted Ioffe frame (elements between dashed lines). These parts, including the top gradient coil, are fixed to each other and mounted from the top flange. The optical cavity on top of the vibration isolation system, the surrounding coils, and the bottom gradient coil are mounted on the science platform.`

`We clad the main vacuum chamber in a mu-metal shielding (Fig. 6) to minimize the influence of residual external magnetic field fluctuations on the cold atoms. A magnetically quiet environment is essential for stable continuous wave (cw) operation of the atom laser. Mu-metal is a magnetically soft nickel alloy with a very high magnetic permeability micro ~10^{^}⁵ which attenuates magnetic fields inside a cohesive enclosure. The screening effect depends very much on the completeness of the mu-metal box. Magnetic field lines penetrate an opening roughly as far as its diameter. Therefore we have attached a stub around the pumping tube of the main vacuum tank to attain a better aspect ratio at the position of the BEC. The design of the mu-metal hull was aided by computer simulations of the electromagnetic field. The mu-metal was machined and cured as recommended by the manufacturer.100 After demagnetization we have measured a dc magnetic extinction ratio of ~ 40 in the vertical and ~ 100 in the horizontal direction at the position of the BEC.`

`Elements of the optical cavity implementation. (a) Plane cut through the assembled cavity design where the arrows indicate optical access. (b) Photograph of the cavity setup. The electrical leads for the piezotube are pinched in a slotted Viton piece to efficiently decouple the cavity from the environment. (c) The cavity assembly resting on top of the vibration isolation stack which is positioned on the science platform. (d) Modeled frequency response of our vibration isolation stack.`