We discuss the application of spatial light modulators (SLMs) to the field of atom optics. We show that SLMs may be used to generate a wide variety of optical potentials that are useful for the guiding and dipole trapping of atoms. This functionality is demonstrated by the production of a number of different light potentials using a single SLM device. These include Mach-Zender interferometer patterns and the generation of a bottle-beam. We also discuss the current limitations in SLM technology with regard to the generation of both static and dynamically deformed potentials and their use in atom optics.
©2003 Optical Society of America
The application of optical fields in the area of atom optics is well established. Aside from the role of light beams in the standard cooling and trapping experiments that are routinely carried out in labs throughout the world they are also of interest for atom transport [1, 2], atom guiding [3, 4], evaporative cooling , dipole trapping [6, 7, 8, 9] and optical lattices .
There has also been significant progress in using magnetic fields to control and manipulate atoms, indeed magnetic trapping is a vital part of most realisations of Bose-Einstein Condensation . Most work on “atom-chip” devices is also reliant on the application of magnetic manipulation schemes [12, 13]. Such techniques have great power in that it is relatively straightforward to design fields that can move atoms in complicated, preordained geometries that are not conventionally possible with light fields. For instance, light fields cannot be bent in the manner of the magnetic work of Sauer et al . Magnetic fields have been used very successfully as atomic guides [12, 15, 16] and beamsplitters [17, 18] and it is predicted that they will be useful in interferometers [19, 20]. We note that the magnetic potentials used in the interferometer proposed in  need to be dynamically varied, something which is not as simple to do with light fields.
Despite the attractive possibilities of using magnetic potentials for atomic manipulation there do exist some drawbacks. Recent work by the Ketterle and Pritchard  group and the Zimmermann  group has shown that unexpected fragmentation of BECs occur when using magnetic guides due to geometric deformations of the current carrying wires and, possibly, other unexplained effects. Such deformations may pose limitations in atom-chip and magnetic waveguide physics. Other recent work has shown that there are limits for the coherent manipulation of atoms on atom chips due to the shot noise in current carrying wires .
Optical analogues to the magnetic atom chips have been proposed  which make use of evanescent waves produced by integrated optical waveguides. Evanescent waves have already been shown to be a useful tool in trapped atoms above surfaces . Other possibilities include the use of microfabricated optical elements to produce both individually addressable arrays of dipole traps  and optical guides with applications in interferometry . Using such micro-optical devices it is possible to create tailored light potentials that will have a whole range of applications, but there are some drawbacks. Use of predetermined optical chips or light patterns are just that - predetermined. They require a certain amount of experimental hardware for each application that they are required to be used for, thus there are difficulties in reconfiguring set-ups. Furthermore such systems are not always suited for dynamic deformation of light potentials which may be useful for guiding, manipulating and interfering samples of cold atoms. In the following article we show how spatial light modulators (SLMs) can be used as powerful, highly reconfigurable, dynamically controllable holograms and their applications in the field of atom optics. Such devices can produce light patterns that require no microfabrication and that can be projected into a vacuum system away from any surfaces. We demonstrate a number of light patterns that are difficult to generate using conventional micro-optical techniques but which can be made using etched holographic methods, although these lack the flexibility of the patterns generated using the SLM. These include a Mach-Zender interferometer, a Y-splitter, a bottle-beam and an array of dipole traps related to those generated by Dumke et al in . While such patterns can be generated using etched holograms, the SLM offers many advantages over such techniques.
2. Spatial Light Modulators
A spatial light modulator can be considered as a number of discrete pixels each acting as a variable waveplate. There are various types of device which act either as phase or amplitude modulators. In the following we will consider a phase-only modulator. The SLM can encode an input light beam with a phase such that it produces the desired light pattern. Hence the output from the SLM can be given by:
where A 0(r) is the complex amplitude of the beam incident on the SLM. The phase term that we modulate the incident beam with, ei ψ(r) can be calculated directly being, for example, in the case of a Laguerre-Gaussian, eil φ where l is the azimuthal index of the beam and φ is the azimuthal angle. Alternatively, for more complicated patterns, we may use an iterative algorithm such as the Gerchbech and Saxton algorithm . An example of the holograms from such a process is shown in Fig. 1. These methods have been used recently for the generation of complex patterns for use in optical tweezers . Such an implementation of an SLM can be used to realize a very powerful tool for the dynamic control of complex light potentials.
The generation of the hologram on the SLM is simply a matter of sending a precalculated image (the hologram) from a computer to the SLM. Current refresh rates for SLMs working in phase modulation mode allow images to be sent at around 30Hz, but work is in progress to increase this speed . Amplitude modulated devices can run at higher rates, up to 1kHz, but this comes at the expense of overall efficiency.
Current phase modulated SLMs offer resolutions of up to 1024×768 pixels and zero-order diffraction efficiencies of the order of 40 – 60%, which compares favorably with etched holograms produced lithographically. However SLMs offer a distinct advantage over normal holographic techniques in that they can be readily redesigned, prototyped and optimised on the computer. Such speed of adaptation is a great boon as many hundreds of holograms could be tried in a single experimental run, a facility that is not available with micro-fabricated devices. We also note that the quality of holograms produced by the SLM is in many cases far superior to that found in etched holograms. For instance the generation of Laguerre-Gaussian beams via the etched holographic method can be difficult since a focussed Laguerre-Gaussian beam has the tendency to break up into l vortices if the hologram is not perfectly made. Higher quality holograms that do not suffer from this vortex break-up can be easier to make with the SLM as it is a straightforward matter to tweak the design of the hologram and try again. This iterative “clean-up” is important for proposals that make use of Laguerre-Gaussian and high-order Bessel beams for atom focussing .
3. Experimental Results
We use a 512×512 nematic-SLM from Boulder Nonlinear Systems in the experimental set-up shown in Fig. 2. Our laser source is a Yb fibre laser (IPG Photonics) and typically we use an incident power of 500mW. The SLM can withstand powers of up to 2W without any external cooling being required (thermoelectric coolers are now a standard option). As examples of the flexibility of the SLM we generate four differing types of patterns, each with application in the field of atom optics.
3.1 Mach-Zender Interferometer
In Ref.  conventionally microfabricated optical components are used to create a light potential that can act as an interferometer. Atoms can be loaded into the light potential and then, due to intensity gradients within the light guides generated the atoms flow down the guides, subsequently being split and reformed. We are able to generate comparable potentials using the SLM and an example of a Mach-Zender interferometer-type structure is shown in cross-section in Fig. 3(a). We can image any pattern that we can generate into, say, a vacuum (as in ) allowing flexible manipulation of the optical potential realised within the trap.
One of the attractions of magnetic guiding is that it is possible to design guides with curved geometry in which the atom cloud can be adiabatically transported. This is not so simple using current optical guiding techniques. The SLM generated patterns may allow this adiabatic transport within the optical regime.
We are also able to make (as a simple extension of theMach-Zender pattern) a Y-splitter, which can be optimised to act as a 50:50 splitter (or indeed any other fraction). The splitter is shown in Fig. 3(b). A Y-splitter of this type is similar to that demonstrated in .
3.3 Blue-detuned Patterns
More difficult to create are hollow blue-detuned guides which would be useful as part of a blue-detuned interferometer, something not easily achievable using the micro-optics approach (although just as possible using etched holographic techniques).
A hollow Mach-Zender interferometer pattern is shown in Fig. 4(a). This is not explicitly generated as a pipe in three-dimensions, which is difficult using a phase only modulator, but it diffractively fills in, at least partially, on either side of the focus and hence forms an intensity null surrounded by high intensity barriers, necessary for a blue detuned guide. The filling process in this instance may not be enough however to constitute a stable atomic guiding potential, but such potentials should be possible with the inclusion of amplitude modulation effects, or with a more sophisticated holographic design technique.We estimate that the effective dipole potential of such a guide is 10mK (assuming a power of 100mW in the beam, a guide thickness of 0.01mm, a guide outer radius of 1.2mm and inner radius of 0.3mm. We also assume a guide detuning of 3GHz and that the atomic system in question is 85Rb with a decay rate of 2π×6.1Mhz). We note that the generated image lies in a plane orthogonal to the optical axis of the SLM. To generate an image where the entrance to the guide lies parallel to the optical axis is, again, difficult using a phase-only SLM. However, this is a problem that can be overcome using a suitable trap geometry.
3.4 Array of dipole traps
A grid of dipole traps formed with a conventionally microfabricated lens array has recently been observed in a MOT by the Ertmer group . The same group has also recently observed a similar configuration using VCSEL and microlens arrays , which allows the individual addressability of dipole traps. Such traps have applications in quantum computing. The use of SLMs has now begun to be established in colloidal physics [37, 32], where the creation of arrays of particles is of interest in the study of particle interactions, colloidal transport  and nanofabrication . Here we demonstrate an array of spots that can be used in a similar manner to the ones described above. The array produced is shown in Fig. 5. We see one of the problems of using an essentially diffractive optical element to create the light patterns in Fig. 5(a); that of the zero-order diffraction spot. This is due to the fact that we are not using an ideal continuous phase profile when we use an SLM, but a pixellated, or discrete implementation of such a profile. This problem can be addressed in several ways, first the spot can be spatially filtered from the desired image. Secondly the design of the pattern can take the position of the zero-order spot into account with, say the lattice structure such that the zero-order spot does not obscure any the the surrounding spots (Fig. 5(b)), or by moving the pattern offa xis (Fig. 5(c)).
With the SLM we are able to fully control the relative positions of the trap sites, either between experiments or dynamically, by changing the hologram supplied to the SLM. Hence the lattice constant of the array can be easily tuned, as can the shape of the array. It should also possible to control the position of each trap site in real time, and therefore each site can be turned on or off.
A bottle-beam is a localized dark space region that is surrounded by light. It can therefore be used as a blue-detuned dipole trap. Here we recreate the beam first shown by Arlt and Padgett , which is a superposition of two high-order Laguerre-Gaussian beams with their azimuthal indices l = 0 and their radial mode indices p = 0 and p = 2 respectively. Figure 6 shows the propagation of the generated bottle beam. Another problem of the SLM can be seen in some of the figures, that of spurious diffraction spots, these however have little of the beam power and can be filtered out by appropriate spatial filtering, or possibly with more careful hologram design.
This dynamical control is readily extended to any pattern we can generate on the SLM, thus we can envisage moving the focus of a beam in the manner of the transport of a BEC with optical tweezers , or generating movable patterns that mimic the optical conveyer belts studied by Kuhr et al .
4. Discussion and Conclusions
As can be seen from the examples above the SLM is a powerful tool for the generation of optical patterns. One of the major new avenues that is opened up by the SLM is that of dynamically deformed optical potentials. Such functionality is well illustrated in the work of Grier and Glückstad [37, 32] in optical tweezers. The dynamical control of optical potentials is already of interest in the field of atom optics in the transport of BECs  and optical conveyor belts  and we can envisage doing comparable experiments driven only by an SLM generated optical potential. The loading of such traps is also straightforward, but is dependant on the exact potential being used. Atoms can be dropped into a guiding potential, e.g. ref , an optical lattice, such as those shown in Fig. 5 can be loaded by superimposing the pattern onto pre-cooled atoms, such as in ref , as can an optical Bottle beam. There are however refresh rate issues associated with creating dynamically controlled dipole trapping potentials with an SLM. Dynamically changing the pattern at relatively low frame rates leads to a frame ‘bleed’ effect as the SLM moves from one image to the next. Hence the integrity of the generated optical potential is lost for, perhaps as much as, milliseconds. For stable dipole trapping refresh rates in excess of one kilohertz are necessary [38, 39], so obviously SLM technology is not up to this task as yet. It is, however, still a young technology and faster rates, ultimately limited by the inertia of the liquid crystal used in these devices, will be developed in the coming years. Faster rates are possible, however, using amplitude modulation SLMs. These devices do indeed have refresh rates at around the kilohertz level and therefore should already be suitable for applications such as those outlined in [38, 39]. Amplitude modulation devices, as their name suggests, offer the ability to fully control the amplitude of a beam (and thus can act as high speed beam steerers) but not the phase. This inability to fully control both the amplitude and phase is currently a limitation, but tricks are available that offer full complex field modulation, for instance by a two-pixel encoding method coupled with spatial filtering . Amplitude only modulators should be able to generate patterns such as the dipole trap arrays and optical guiding structures seen in  without any difficulty but at a cost to overall efficiency.
The combination of both amplitude and phase modulation would open up even greater possibilities. With the possibility of completely arbitrary light fields the atom optician will be able to realize any complex optical field that they can imagine. A simple but powerful example of these is related to our recent paper on optical guiding  in which we generate a hollow light field with a diffractively filling hole that is able to capture and hold atoms that are in an atomic beam that runs obliquely to the guide direction. To do this we imaged an obstruction into the beam. With a SLM capable of both phase and amplitude modulation such patterns should be relatively straightforward - indeed we need not stop at one hole, but could have as many as are allowed - limited only by the amount of information that can be encoded onto an SLM with a fixed number of pixels and phase levels.
Other limitations of these devices include their efficiency, since they have only a 40–60% diffraction efficiency into the zeroth order. This does, however, compare favorably with many commercially available etched holograms. Since the SLM is also inherently dependent on a pixel structure there are issues with diffraction noise while the ultimate resolution of the images produced also depends on this structure. This has not prevented other groups  carrying out sensitive measurements on the microscopic level however.
Other applications of SLM technology in cold atom optics are in the area of evanescent trapping, mirrors and manipulation (e.g. ). Here we envisage that light potentials tailored to a particular experiment can be written onto a surface as an evanescent field, which should allow far more versatile and sophisticated studies than are possible at present. For instance in the case of atomic mirrors we envisage light fields that can represent a variety of mirrors such as corrugated mirrors. Again, with care, dynamic fields can be introduced adding further scope for new experiments, such as changing the type of mirror that a group of atoms encounter on each bounce. Other applications include guiding of atoms on surfaces, by writing potentials with intensity graduations we should be able to move atoms loaded onto a trap, or dropped onto the surface and move them from place to place.
The aim of this article has been to introduce the concept of tailored light potentials for application in the field of atom optics. The generation of such fields is by means of a spatial light modulator, emerging technology that we believe will make a significant impact in this field. We have demonstrated the power of such devices by generating a number of light potentials that have use in atom optics and that are simpler to generate, or more rapid to generate than by conventional methods. The rapid and iterative nature of the prototyping of such light fields has also been emphasized. We have looked at the dynamic nature of holograms generated by SLMs and suggested uses for this functionality. We have discussed the benefits of the SLM, but also the current limitations. The SLM allows light fields to act with the flexibility of current carrying wire atomic manipulation while allowing all prototyping and light potential generation to done outwith the vacuum system.
This work is supported by the UK’s EPSRC and the Leverhulme Trust. G.C.S. is also supported by an award from the Research Corporation and by the National Science Foundation through Grant No. DMR-0216631.
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