FIG 3. Measurement of the electron beam current as a function of time after switching off the MOT. (a) The B-field from the DC-MOT is seen to switch to <10-7T (where electrons are detected without loss) in ~6000 microsec. (b) By contrast, the AC-MOT is seen to switch off in ~18 microsec, more than 300 times faster.

Figure 3 shows results for (a) the DC-MOT and (b) the AC-MOT operating at 5kHz, with an electron beam energy of 50eV. The Zeeman slower was also operating, so that all B-fields to cool and trap atoms were present when data were obtained. Decay of the B-field from the DC-MOT is seen to take ~6ms before reaching an acceptable level, whereas the field from the AC-MOT only takes ~18 microsec to reach the same condition. These results clearly demonstrate the striking advantages accrued by operating the atom trap as an AC-MOT.

The results agree well with predictions of the above model. Differences from an exponential decay for the DC-MOT are due to the 20mm entrance diameter of the Faraday cup, which could measure currents for the electron beam deflected by ~5°. The decay for the AC-MOT field matches the slew rate of the 2kW audio amplifier used to drive current through the coils, and is due to the driving voltage rapidly switching to zero after the 5kHz alternating current reaches zero at toff = 0s (figure 3b).

To test the electron spectrometer, a pulsed time of flight ion detector was installed to detect K+ ions created by electron impact with cold atoms. The spectrometer was initially commissioned using an atomic beam source in place of the MOT, so as to characterise the system. The Zeeman slower and AC-MOT were then adjusted to produce cold potassium atoms, and the experiment repeated. The AC-MOT was driven with two complete sine-waves (400 microsec duration) and then switched off for 200 microsec in each cycle (efficient trapping has been demonstrated with only a single sine-wave of 200 microsec duration, with an off time of 100 microsec). The ionizing electron beam was switched on 50 microsec after the AC-MOT field turned off, to ensure zero B-field from the coils (since atoms move <25 micrometres in this time, this does not significantly affect trapping). Ions produced from the collision were then extracted and accelerated to a channeltron detector using a pulsed electrode located 40mm from the interaction region. The resulting ion signal was displayed on an Ortec 914 Turbo-MCS multi-channel scalar.

As a rigorous test of the AC-MOT performance, time of flight spectra were collected for incident electron energies from ~2eV to 70eV. These data are presented in figure 4 as a 3D spectrum. The ionization cross section for 39K+ atoms is clearly seen from low energies (the 39K+ ionization potential is 4.34eV), whereas at energies above 31.6eV the second ionization cross section for 39K2+ is also observed. Little evidence of 39K3+ ions was seen (the ionization potential of this state is 45.7eV), which we attribute to a low cross section for electron impact ionization to this state.

FIG 4. Time of flight spectra from cold atoms held in the AC-MOT as a function of incident electron energy, showing the development of the first and second ionization states of the target as a function of electron impact energy.

The experiments performed here used an electron gun of relatively low resolution (~0.8eV), and the uncertainty in the electron beam energy was ~1eV. The AC-MOT cooling laser beams remained on during ionization, and so the measured cross sections include a contribution from laser excited atoms. At present we do not have the facilities to rapidly switch off the laser beams, however additional information on the ionization of laser excited targets could be obtained by adopting such techniques.

In this work we have demonstrated the considerable advantages that accrue by trapping atoms with an AC-MOT, rather than using a conventional DC-MOT. The technique is simple to instigate, and produces a trap equivalent to that of a conventional MOT. We have shown the trapping fields can be accurately controlled, and that experiments can be cycled more than 300 times faster than was possible previously. These methods should be equally effective for Zeeman-slowers, by switching the polarization of the cooling laser beam in synchronicity with driving alternating sinusoidal current through the coils. It should then be possible to switch off the Zeeman-slower B-field as rapidly as for the AC-MOT. Although the currents required for Zeeman-slowers are higher than for the AC-MOT, these can easily be delivered by high power sound reinforcement amplifiers at low cost. We are at present setting up experiments to investigate this.

These AC-techniques open up the possibility of performing new experiments using cold atoms. In particular, it now becomes possible to routinely combine the fields of cold atom physics and charged particle collision physics, which will add significant advantages to each. Further, existing experiments that suffer from eddy currents within their apparatus can adopt this new approach to eliminate these problems.

Finally, it should be possible to extend these ideas to switch the B-field generated by magnetic traps more rapidly than is presently possible. This would require the trapping fields to be controlled by fast alternating currents, to ensure losses due to Majorana spin flips were minimised as the field direction reversed. We have not yet attempted this, however since magnetic traps are inherently symmetric, this should be possible (eg by combining the techniques used in TOP traps [14] with an AC-driven QUIC trap [15]). AC-driven magnetic traps have been realised previously for trapping high-field seeking atoms [16], however they have not been used for the applications considered here. Such an AC-driven magnetic trap would allow ultra-cold physics to explore new directions including studies using charged particles, an area ripe for future theoretical and experimental study.

We would like to thank the University of Manchester for supporting this work, and the EPSRC UK for providing a studentship for one of us (MH).

FIG 2. (color online) The experimental apparatus, showing the source chamber, Zeeman slower and trapping chamber.

The apparatus used for these studies is shown in figure 2. A well collimated beam of 39K atoms produced from a re-circulating oven in the source chamber enters a Zeeman slower which cools and compresses the atomic beam to a velocity ~40ms-1 ± 1ms-1. These atoms enter the AC-MOT coils located centrally in the trapping chamber. Six orthogonal red-detuned circularly polarized laser beams operating at 766.7nm illuminate the MOT after passing through CF70 windows. The MOT coils are constructed from 184 turns of Kapton coated wire wound on split copper formers which produce a B-field gradient of ~1.5mT/cm in the trapping region. The system operates with a base pressure in the trapping chamber ~8 x 10-11 torr. The combination of oven, Zeeman slower and MOT produces a high density trap (~1011 atoms/cm3) which fills in <1s, atoms remaining in the trap for >400s. The temperature of atoms in the trap has been estimated as ~0.3mK using ballistic time of flight techniques. A set of Helmholtz coils surround the trapping chamber to eliminate external magnetic fields. Full details of the apparatus will be given in a future publication [12].

To test the viability of charged particle experiments with cold atoms, an electron gun is installed in the trapping chamber. This produces an electron beam with energy from 2eV to 100eV, and beam currents up to 12 microamps. For the present measurements the electron current was on for 800ns, this time being accurately controlled using custom built delay generators [13]. In this way the effects of the B-field due to the MOT coils were determined by monitoring the electron beam that passed through the interaction region in the centre of the MOT coils, on a Faraday cup located 450mm from the gun. Any deflection of the electron beam by the B-field was seen as a reduction in beam current, providing a sensitive probe of the effects of this field.

FIG 1. The switching configuration for the AC-MOT. The MOT is driven by an alternating supply, so that the net induced current in conductors surrounding the MOT coils is zero. The polarization of the six trapping laser beams is switched at the same rate as the MOT current, so as to maintain trapping. Experiments using charged particles are conducted during the time the MOT current is zero.

By adopting a sinusoidal current at a single frequency, the inductive and resistive characteristics of the MOT coils can be determined. Precise control of the driving current (delivered by a high power audio amplifier) is then possible, since the phase shift between driving voltage and delivered current is constant at a set frequency. This contrasts with a DC-MOT that is rapidly switched off, since the harmonic content of the switched current produces complex phase shifts between current and voltage as the field decays.

The main advantage the AC-MOT has compared to the DC-MOT is that for an appropriate choice of drive to the MOT coils, the B-field generated by eddy currents in the surrounding conductors can be eliminated when the MOT current is zero. This is possible since the B-field from each half cycle of the alternating MOT current induces currents of equal magnitude, but which are in opposite directions. Since equal numbers of positive and negative cycles are used, the net eddy current is then zero.

For a driving voltage from the amplifier given by V = V0sin(omega*t + phi), the induced eddy currents can be estimated by modelling the conductors as an inductance Li (which is coupled to the MOT B-field), in series with a resistance Ri so that taui = Li / Ri. Since the conductors are not close to the coils, the coupling Mi between conductors and coils is weak, so that the differential equations governing the system can be solved analytically. For coils whose transient response  tauMOT is much faster than that of the surrounding conductors, the induced current is then given by:  

A new type of atom trap is described using alternating current to generate the magnetic B-field, together with high-speed polarization switching of the damping laser field. This combination produces a trap as effective as a standard Magneto-Optical Trap, with the advantage that the average B-field is zero. No net current is hence induced in surrounding conductive elements, and the B-field produced by the AC-MOT is found to switch off >300 times faster than a conventional MOT. New experiments can hence be performed, including charged particle probing or detection of the cold target ensemble.

The process of atom cooling and trapping using a combination of six orthogonal damping laser fields and a spatially varying magnetic B-field was first successfully implemented in 1987 [1], and is known as a Magneto-Optical Trap (MOT). Since that time cold targets have been used in many atomic and condensed matter experiments, leading to new discoveries and applications [2]. Amongst these are the application of Bose Einstein Condensates produced from cold atoms held in a DC-MOT [3], through to measurements of fundamental physical constants. The field continues to grow as new applications are found which study and manipulate these cold ensembles.

An alternative research area in atomic physics is that of collision studies, where targets are probed by charged particles (such as ions, electrons or positrons) to ascertain the dynamics of the collision under study. Experiments include elastic scattering studies where the momentum of the charged particle varies without changing energy, through to excitation or ionization of the target [4]. In all cases, maximum information about the interaction is obtained by ensuring the momentum of the incident charged particle is well defined, and by determining the momentum and state of the outgoing products following the reaction. Detailed theories are formulated to explain the results, these models being refined as the body of experimental data increases [5]. Collision theories are now accurate at high impact energies, however at low to intermediate energies differences between experiment and theory have yet to be satisfactorily explained. It is in this energy regime that much of the effort is now concentrated [6].

Advantages can arise if the techniques in cold atom research are combined with collision studies. As an example, the efficient production of BEC’s has resulted directly from detailed understanding of Feshbach resonances which arise from cold atom collisions in a magnetic B-field. This is a direct application of methods studied in collision physics. Further, the application of charged particle detection methods in cold atom physics allows fundamental quantum effects to be studied by detecting electrons or ions that may result from experiment. For collision studies, cooling the target prior to collision increases the sensitivity of the interaction to the initial momentum of the target ensemble. This is key to experiments such as COLTRIMS, which have proven very successful in recent years [7]. These experiments use a supersonically cooled target beam, and the momentum of the target must be known for meaningful results to be determined. By adopting laser cooled targets, the sensitivity and accuracy of such methods could be markedly increased.

A further advantage arises using cold targets, since their very low velocity effectively eliminates Doppler effects that can reduce experimental sensitivity. This becomes particularly important when studying laser and electron interactions simultaneously (such as the super-elastic scattering studies in a magnetic field recently developed in Manchester [8]). For studies involving excited targets with long lifetimes, the finite Doppler profile of an effusive target beam markedly reduces the laser-excited population, making many experiments unfeasible. Cooling the atoms prior to laser preparation would effectively eliminate these constraints.

One of the main barriers to widespread adoption of cold target collision studies is that B-fields must be reduced to less than ~10-7 Tesla before low energy studies can be performed. Larger B-fields significantly alter the direction of electrons and ions in the experiment, and whereas a well controlled B-field may be used [8,9], it is essential to eliminate uncontrolled fields before experiments can be conducted reliably. The B-field arising from trapping cold atoms must therefore be removed before these studies are possible.

An additional complication arises since experiments must be conducted in metal chambers to eliminate charging of insulating surfaces, and any component ‘seen’ by the charged particles must be a conductor. The B-field from a MOT induces eddy currents in these components, and it is not possible to reduce these in the usual way (e.g. by slotting conductors to prevent current flow). Hence even for MOT currents rapidly switched to zero, the induced eddy currents continue to produce B-fields until they too reduce to zero.

In practice the B-field due to the MOT takes ~10ms to reduce to <10-7 Tesla, this time depending on the proximity of conductors to the coils, their shape and resistivity. During this time, a large fraction of trapped atoms escape, resulting in a cold atom density that rapidly falls to zero. Losses can be reduced by leaving the cooling lasers on to create an optical molasses (if this does not interfere with the experiment), however the loss problems remain. The comparatively long time taken for the B-field to decay also reduces data accumulation rates, since the repetition rate is then only ~50Hz.

It is clearly advantageous to eliminate these constraints. Several methods have been attempted, including shaping the DC-MOT driving current at switch off to try to cancel fields due to eddy currents [10]. This technique is complicated and requires different currents when spectrometer elements move (as occurs in most collision experiments). These limitations have prevented the wider adoption of charged particle studies to cold atoms.

Here we detail a new technique which has eliminated these problems. In this method, a sinusoidally varying current is applied to the MOT coils, ensuring the current starts and ends at zero in any given trapping cycle (figure 1). Since the direction of the B-field is reversed in each half-cycle, the polarization of the trapping laser beams is also switched from right hand circular (RHC) to left hand circular (LHC) so as to be in phase with the current. This is facilitated using an electro-optic modulator controlled by a Behlke HTS-61-03-GSM switch [11]. In the short time the B-field passes through zero the atoms no longer experience a restoring force, however since the lasers remain on at this time, the molasses field prevents atoms moving from the trap. By ensuring a rapid switching frequency (up to 6kHz has been used), the AC-MOT is found to deliver the same cooling and trapping performance as when operating as a DC-MOT. The trapping lifetime of the AC-MOT is also found to be the same as the DC-MOT for frequencies over 2kHz.

References.

[1] E L Raab et al, Phys Rev Lett 59, 2631 (1987).

[2] H J. Metcalf and P van der Straten  Laser Cooling and Trapping, HaroldSpringer, New York, (1999).

[3] M H Anderson et al, Science 269, 198 (1995).

[4] I E McCarthy and E Weigold Electron-atom collisions Cambridge University Press, UK (2005)

[5] N Andersen and K Bartschat Polarization, alignment and orientation in atomic collisions, Springer, New York (2001)

[6] A J Murray, Phys Rev A 72, 062711 (2005) and references therein

[7] R Dörner et al, Phys Rep 330, 95 (2000).

[8] M J Hussey et al, Phys Rev Lett 99, 133202 (2007).

[9] F H Read & J M Channing, Rev Sci Inst 67 2372 (1996)

[10] C J Dedman et al, Rev Sci Inst 72 4055 (2001).

[11] http://www.behlke.de/pdf/61-03-gsm.pdf

[12] M Harvey and A J Murray Phys Rev A (in preparation) (2008)

[13] A J Murray, and P Hammond, Meas Sci Tech, 10 225 (1998).

[14] W Petrich et al, Phys Rev Lett 74, 3352 (1995)

[15] T Esslinger et al, Phys Rev A 58, R2664 (1998)

[16] E A Cornell et al, Phys Rev Lett 67, 2439 (1991)

where the constant of proportionality depends on the coupling Mi and the driving voltage V0 [12].

By an appropriate choice of phase angle phi =tan-1(taui * omega) the transient exponential term in equation (1) is eliminated, so that the induced current is purely sinusoidal. By choosing an integral number of half-cycles of the driving voltage,  this choice of phase also eliminates transients at turn-off, so that the B-field induced by eddy currents is zero after the MOT current is turned off. 

To facilitate atom trapping while minimising extraneous B-fields, the RMS current in the AC-MOT was set equal to that in the DC-MOT, the laser detuning and intensity remaining unchanged. The characteristic lifetime of eddy current decay was found to be taue ~1ms, whereas the MOT current decay was tauMOT < 20 microsec, justifying the use of equation (1). The phase angle was then set to minimise net eddy currents as determined by the electron beam (see below).