The experimental realisation of gaseous Bose-Einstein condensation (BEC) in
1995 sparked considerable interest in this intriguing quantum fluid. Here we
report on progress towards the development of an 87Rb BEC experiment in a large
(~10cm diameter) toroidal storage ring. A BEC will be formed at a localised
region within the toroidal magnetic trap, from whence it can be launched around
the torus. The benefits of the system are many-fold, as it should readily
enable detailed investigations of persistent currents, Josephson effects, phase
fluctuations and high-precision Sagnac or gravitational interferometry.Comment: 5 pages, 3 figures (Figs. 1 and 2 now work

A. S. Arnold

ARNOLD A. S.

E. Riis

English

arXiv

The experimental realization of gaseous Bose-Einstein condensation (BEC) in 1995 sparked considerable interest in this intriguing quantum fluid. Here, progress towards the development of an 87Rb BEC experiment in a large (, 10cm diameter) toroidal storage ring is reported. A BEC will be formed at a localized region within the toroidal magnetic trap, from whence it can be launched around the torus. The benefits of the system are manifold, as it should readily enable detailed investigations of persistent currents, Josephson effects, phase fluctuations and high-precision Sagnac or gravitational interferometry

Arnold, A.S.

Riis, E.

University of Strathclyde Institutional Repository

Strathprints Institutional RepositoryArnold, A.S. and Riis, E. (2002) Bose-Einstein condensates in ’giant’ toroidal magnetic traps.Journal of Modern Optics, 49 (5-6). pp. 959-964. ISSN 0950-0340Strathprints is designed to allow users to access the research output of the University of Strathclyde.Copyright c© and Moral Rights for the papers on this site are retained by the individual authorsand/or other copyright owners. You may not engage in further distribution of the material for anyprofitmaking activities or any commercial gain. You may freely distribute both the url (http://strathprints.strath.ac.uk/) and the content of this paper for research or study, educational, ornot-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to Strathprints administrator:mailto:strathprints@strath.ac.ukhttp://strathprints.strath.ac.uk/  Arnold, A.S.* and Riis, E. (2002) Bose-Einstein condensates in 'giant' toroidal magnetic traps. Journal of Modern Optics, 49 (5-6). pp. 959-964. ISSN 0950-0340     http://eprints.cdlr.strath.ac.uk/2865/    This is an author-produced version of a paper published in Journal of Modern Optics, 49 (5-6). pp. 959-964. ISSN 0950-0340. This version has been peer-reviewed, but does not include the final publisher proof corrections, published layout, or pagination.  Strathprints is designed to allow users to access the research output of the University of Strathclyde. Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (http://eprints.cdlr.strath.ac.uk) and the content of this paper for research or study, educational, or not-for-profit purposes without prior permission or charge. You may freely distribute the url (http://eprints.cdlr.strath.ac.uk) of the Strathprints website.  Any correspondence concerning this service should be sent to The Strathprints Administrator: eprints@cis.strath.ac.uk  arXiv:cond-mat/0110295 v2   16 Oct 2001Bose-Einstein condensates in ‘giant’ toroidal magnetic trapsA. S. Arnold and E. RiisDepartment of Physics and Applied Physics, University of Strathclyde, 107 Rottenrow, Glasgow G4 0NG, UK∗Abstract. The experimental realisation of gaseous Bose-Einstein condensation (BEC) in 1995 [1] sparked consider-able interest in this intriguing quantum fluid [2]. Here we report on progress towards the development of an 87Rb BECexperiment in a large (≈ 10 cm diameter) toroidal storage ring. A BEC will be formed at a localised region within thetoroidal magnetic trap, from whence it can be launched around the torus. The benefits of the system are many-fold,as it should readily enable detailed investigations of persistent currents, Josephson effects, phase fluctuations andhigh-precision Sagnac or gravitational interferometry.The idea [3] of neutral atomic and molecular storage rings has only very recently been realised experimentally:fast polar molecules were stored in a 25 cm diameter electrostatic hexapole ring [4], and laser-cooled neutral 87Rbatoms have been confined in a 2 cm diameter two-wire toroidal magnetic guide with an ≈ 1 s lifetime [5]. We believeour ‘BEC-friendly’ approach to toroidal neutral atom storage will have additional advantages, ensuring that this newtechnology can also be used to perform coherent atom optics with BECs. Our storage ring will be highly adaptable,have a long (≈ 1minute) trapping lifetime, and have good optical access (for both imaging and manipulation). Inaddition, as the BEC will be prepared within the ring, coherently transferring the atoms into the ring from a separateBEC creation site is not necessary.A good atomic source can greatly lower the duration of BEC experiments. To this end we have realised an 87Rbmagneto-optical trap (MOT) [6] with a relatively large atom number (N = 2 × 109). The MOT was formed usinglow powers (40mW) of trapping light generated by a simple diode laser system [7]. The 780 nm 5s 2S1/2, F = 2 →5p 2P3/2, F = 3 trapping light is red-detuned by 20MHz and comprised of three retro-reflected two inch diameterlaser beams. The loading rate of the MOT is controlled by the current passing through SAES alkali metal dispensers[8]. This MOT, situated in the high pressure end of the differentially-pumped XHV vacuum chamber of Fig. 1, willbe used as a high-flux (≈ 1010 atoms/s) source to multiply-load [9] a second ‘low pressure’ MOT in another chamber.We note that our atomic source should yield comparable performance to a Zeeman slower [10], without the addedcomplexity.The ‘low pressure’ MOT will be formed within a ‘square donut’ quartz vacuum cell (Fig. 2). This MOT will bean elongated [11], forced dark [12] MOT which should decrease light-assisted losses. The high product of the MOTloading rate and lifetime will yield a large trapped atom population. Ex-vacuo coils will be used for subsequentmagnetic trapping of the atoms in a localised region of the toroidal magnetic trap illustrated in Fig. 3.The currents of our magnetic coils (Fig. 3) will be regulated by five water-cooled MOSFET banks [13], and allcurrents will originate from the same 5V, 500A power supply, ensuring optimal magnetic field noise cancellation [14]when the coils are connected in series configurations. Our magnetic coil design allows us to realise many differentmagnetic geometries. Quadrupolar toroidal confinement will be provided by the circular coils (Fig. 3), which havemean diameters of 7.5 and 12.5 cm. Each coil carries a current of 2 Iq = 0−2×500A, yielding a maximum quadrupolemagnetic field gradient of 227G/cm. An azimuthal bias field can be added at the minimum of the toroidal field usingthe black straight wire, preventing spin-changing Majorana flops [15] in a purely toroidal trap. The rectangular ‘pinch’coils in Fig. 3 localise atoms within the torus, and moreover they can be used in two distinct geometries, namelyquadrupole and Ioffe-Pritchard (IP) [16] configurations. The two left rectangular coils are hard-wired in series, asare the right pair of coils. These left and right pinch coil pairs carry currents of 4 Il = 0 − 4 × 500A (with Il ≤ Iq)and 4 Ir = ±4Il respectively. The geometry of the rectangular coils is such that if Il = Ir, then in conjunction withthe circular coils, an IP magnetic trap is formed. In contrast, if Il = −Ir then the rectangular coils are equivalent toanti-Helmholtz coils.In the IP configuration the rectangular coils are designed to provide axial curvature to the trap (up to 55G/cm2),whilst the axial bias field is minimised (≈ 0.9G). Thus the optimal axial and radial magnetic trapping frequencies are10Hz and 305Hz respectively – certainly adequate for condensate formation [17]. In the ‘anti-Helmholtz’ configurationthe rectangular coils yield a maximum axial gradient of −67G/cm (and the 227,−227G/cm radial gradients from thetoroidal quadrupole coils change to 207,−140G/cm).As the same coils are used for the MOT and the IP magnetic trap, the centres of the two magnetic fields overlap,and any possible ‘sloshing’ effects during transfers are eliminated. The adjustable nature of the axial magnetic fieldin both MOT and IP trap configurations also enables excellent mode-matching between the two traps.∗Electronic address: a.arnold@phys.strath.ac.uk; URL: http://www.photonics.phys.strath.ac.uk/People/Aidan/Aidan.html2FIG. 1: The vacuum system consists of a ‘high pressure’ conflat cross (right) where an N = 2× 109 atom 87Rb MOT is nowformed. This MOT will be used to multiply load the special toroidal ‘low pressure’ quartz vacuum cell (enlarged in Fig. 2)which already yields pressures less than 4× 10−11 torr.FIG. 2: The ‘square torus’ high optical quality quartz vacuum cell. The side-length of the square chamber is 12.5 cm.The coils will initially be set to Iq = Il = −Ir = 36A, yielding radial and axial magnetic field gradients of312.5 cmFIG. 3: The magnetic trap coils (to scale). Arrows indicate current directions in the various coils. The small elliptical cloudrepresents the axially elongated low pressure MOT/magnetic trap.approximately = 15,−10G/cm and −5G/cm respectively. This provides an optimal field [18] for creating the ‘lowpressure’ MOT. The aspect ratio of this MOT cloud will therefore be 0.7:1:1.2 (cf. 0.7:1:1 for a ‘standard’ MOT).Once this MOT contains a few 109 atoms, then the MOT can be elongated axially by reducing the current Il = −Irin the rectangular coils. Atoms will not be collected directly in the elongated MOT due to its shallow axial depthand short lifetime.The atoms in the elongated MOT will then be released into optical molasses for a few milliseconds, before beingoptically pumped into the |F,mF 〉 = |2, 2〉 weak-field seeking state. Due to the elongated geometry of the MOT,we expect that the atoms at this stage should have a temperature as low as 10µK, and a peak density of a few1011 cm−3. By reversing the current Ir, the atoms will then be rapidly (≪ 1ms) loaded into the IP-type magnetictrap (Iq = Il = Ir) described above.The magnetically trapped atoms can then be compressed by ramping up the current in the magnetic coils. Thisincreases the inter-atomic elastic collision rate to facilitate efficient (‘runaway’) radio-frequency evaporation, whichoccurs when the ratio of elastic:inelastic collisions is above ≈200:1 [13, 19]. The use of a ‘dark’ MOT will probably not4be necessary for reaching the runaway evaporation threshold [20], however it will increase the condensate population.If more magnetic compression is necessary, current can be passed through the vertical wire (Fig. 3), and the MOT canbe loaded into an IP trap with an (initially) large bias field. After implementing a suitable evaporation trajectory,condensation will occur in the Ioffe-Pritchard trap in essentially the same manner as in most alkali BEC experimentsto date.By ramping down the current in the magnetic trap’s pinch coils, atoms can subsequently access the entire torus,either by adiabatic expansion using the pinch coils followed by non-adiabatic expansion, or using a Bragg launchingscheme. An important issue which needs to be addressed is the coherence of the condensate. It can be shown [20]that the coherence length of a non-interacting isotropic BEC is given simply by the width of the condensate. Thisresult has also been seen experimentally along the ‘short’ dimension of a cigar-shaped interacting condensate [21].One might therefore na¨ıvely expect that both the physical and coherence lengths of an axially adiabatically expandingBEC would remain equal, especially as the ‘phase-space density’ of the condensate should remain well above one evenif the condensate is released non-adiabatically into the storage ring. However, recently attention has been drawn tothe issue of phase-fluctuations along the ‘long’ axis of cigar-shaped interacting BECs [22], and such phase-fluctuationshave now been seen experimentally [23]. We also hope to study phase-fluctuations, however their presence makesinterferometry somewhat difficult, and we will instead use a Bragg launching scheme (described below) to initiatetoroidal BEC motion.Second-order Bragg scattering [21, 24] will be used to (multiply) launch well-localised, phase-coherent atomic pulses(with very slowly decaying phase-space density) out of the BEC, very shortly after the pinch coils are turned off.One therefore avoids the large divergence of atomic orbits that occur if one simply releases the BEC at the top of avertically oriented storage ring. The Bragg-scattered condensate pulses will be launched in both directions aroundthe ring. Due to their initial velocity of 2.4 cm/s, one can only ‘lift’ the BEC packets h = 30µm vertically againstgravity (or up a magnetic field ‘hill’ of 45mG), and it is therefore important to form the BEC at the ‘high’ point ofthe toroidal potential. For this reason we will tilt the axis of the toroidal trap with respect to gravity, making therestrictions on magnetic field ripples less stringent. Even vertical orientations of the magnetic ring are possible, as itcontains all atoms travelling at < 1.6m/s.Our ‘open’ experimental geometry is well-suited to condensate investigation, in particular for imaging the atoms.The high degree of optical access will also facilitate the application of dipole force laser beams for manipulating theBEC in persistent current/Josephson effect experiments. The Sagnac rotational effect is proportional to the enclosedarea of the beams in an interferometer. The single-revolution enclosed area of our toroidal trap is ≈ 140cm2, whichis more than six hundred times the area of the state-of-the-art thermal atomic beam gyroscope [25]. Due to the longlifetime of our magnetic trap, we envisage that BEC pulses could rotate around the storage ring hundreds of times[5], further enhancing the interferometer’s sensitivity. Additionally, it is hoped that the minimum detectable phaseshift (δφ ≈ 1/√N) decreases to δφ ≈ 1/N [26] when coherent atoms such as BECs are used, and higher precisionSagnac effect measurement should therefore be possible. The magnetic trap will also provide a good testing groundfor investigations into the behaviour of one-dimensional quantum gases.Acknowledgments: ASA is supported by a Royal Society of Edinburgh/Scottish Executive Education and LifelongLearning Department research fellowship and the experiment is funded by the UK Engineering and Physical SciencesResearch Council.[1] Anderson, M. H., et al., 1995, Science, 269, 198; Davis, K. B., et al., 1995, Phys. Rev. Lett., 75, 3969; Bradley, C. C., etal., 1995, Phys. Rev. Lett., 75, 1687.[2] See for example the GSU BEC webpage: http://amo.phy.gasou.edu/bec.html/[3] Ketterle, W., and Pritchard, D. E., 1992, Appl. Phys. B, 54, 403.[4] Crompvoets, F. M. H., et al., 2001, Nature, 411, 174.[5] Sauer, J. A., Barrett, M. D., and Chapman, M. S., xxx.lanl.gov/abs/quant-phys/0108138.[6] Raab, E. L., et al., 1987, Phys. Rev. Lett., 59, 2631.[7] Arnold, A. S., Wilson, J. S., and Boshier, M. G., 1998, Rev. Sci. Instrum., 69, 1236.[8] Wieman, C., and Flowers, G., 1995, Am. J. Phys., 63, 317; Fortagh, J., et al., 1998, J. Appl. Phys., 84, 6499; Rapol, U.D., et al., 2001, Phys. Rev A, 64, 023402.[9] Gibble, K., Chang, S., and Legere, R., 1995, Phys. Rev. Lett., 75, 2666; Myatt, C. J., et al., 1996, Optics Lett., 21, 290.[10] Phillips, W. D., and Metcalf, H., 1982, Phys. Rev. Lett., 48, 596; Barrett, T. E., et al., 1991, Phys. Rev. Lett., 67, 3483.[11] Dudle, G., et al., 1996, J. Phys. B, 29, 4659.[12] Ketterle, W., et al., 1993, Phys. Rev. Lett., 70, 2253.[13] Arnold, A. S., 1999, PhD thesis, University of Sussex.[14] Mewes, M. O., et al., 1997, Phys. Rev. Lett., 78, 582.5[15] Petrich, W., et al., 1995, Phys. Rev. Lett., 74, 3352.[16] Pritchard, D. E., 1983, Phys. Rev. Lett., 51, 1336.[17] Arnold, A. S., MacCormick, C., and Boshier, M. G., submitted to Phys. Rev. Lett.[18] Lindquist, K., Stephens, M., and Wieman, C., 1992, Phys. Rev. A, 46, 4082.[19] Luiten, O. J., Reynolds, W. M., and Walraven, J. T. M., 1996, Phys. Rev. A, 53, 381.[20] Arnold, A. S., and Boshier, M. G., to be published.[21] Stenger, J. et al., 1999, Phys. Rev. Lett., 82, 4569.[22] Petrov, D. S., Shlyapnikov, G. V., and Walraven, J. T. M., 2001, Phys. Rev. Lett., 87, 050404.[23] Dettmer, S., et al., xxx.lanl.gov/abs/cond-mat/0105525.[24] Kozuma, M., et al., 1999, Phys. Rev. Lett., 82, 871.[25] Gustavson, T. L., et al., 1997, Phys. Rev. Lett., 78, 2046.[26] Jacobson, J., Bjo¨rk, G., and Yamamoto, Y., 1995, Appl. Phys. B, 60, 187.

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