approaching absolute zero

Spectrochimica Acta Part B 63 (2008) 104–114www.elsevier.com/locate/sab

Review

Approaching absolute zero☆,☆☆

Peter Hannaford

ARC Centre of Excellence for Quantum-Atom Optics and Centre for Atom Optics and Ultrafast Spectroscopy,Swinburne University of Technology, PO Box 218, Melbourne, 3122 Australia

Received 11 November 2007; accepted 18 November 2007Available online 4 December 2007

Abstract

We start with a brief background to the field of ultracold atoms and degenerate quantum gases and then review research in this field currently inprogress in our laboratory in Melbourne. Current experiments include the use of a permanent magnetic film atom chip to create a Bose–Einsteincondensate (BEC) of 87Rb atoms; the use of a periodic magnetic microstructure on an atom chip to produce a magnetic lattice for trappingultracold atoms and BECs; and the production of a BEC of 6Li2 molecules, comprising pairs of weakly bound fermionic 6Li atoms, and adegenerate Fermi gas of 6Li atoms in an optical dipole trap near a Feshbach resonance.© 2007 Elsevier B.V. All rights reserved.

Keywords: Ultracold atom; Degenerate quantum gas; Atom chip

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1042. Ultracold degenerate quantum gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1053. Bose–Einstein condensation on a magnetic film atom chip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

3.1. The magnetic film atom chip. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1063.2. Spatially resolved RF spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1073.3. Splitting of a BEC in an asymmetric double well . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1093.4. Permanent magnetic lattice on an atom chip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

4. Quantum degenerate lithium molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1125. Approaching absolute zero . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1126. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

☆ This article is published in a special issue dedicated to Jim Winefordner onthe occasion of his retirement, in recognition of his outstanding accomplish-ments in analytical atomic and molecular spectroscopy.☆☆ The material in this article is based on an updated version of the AustralianAcademy of Science Lloyd Rees Lecture The Golden Jubilee of AtomicAbsorption— Approaching Absolute Zero presented by the author in Melbourneon 22 September 2004.

E-mail address: [email protected].

0584-8547/$ - see front matter © 2007 Elsevier B.V. All rights reserved.doi:10.1016/j.sab.2007.11.025

1. Introduction

It is a great honor to be able to contribute to this special issue ofSpectrochimica Acta devoted to Professor JimWinefordner on theoccasion of his retirement after almost half a century of research atthe University of Florida. When I joined the field of atomicspectroscopy in 1967 Jim was already in full flight pioneeringflame atomic fluorescence for analytical spectroscopy usingconventional light sources [1]. It was another five years before I

mailto:[email protected]

http://dx.doi.org/10.1016/j.sab.2007.11.025

105P. Hannaford / Spectrochimica Acta Part B 63 (2008) 104–114

had the pleasure to meet Jim in person, when I visited his lab inGainesville en route to the Unite Kingdom to learn about the thennew tunable dye lasers. I have vivid memories and some lastingimpressions of that visit to Gainesville. It was the morning of 5September 1972, and Jim greeted me with great sadness with thehorrific news about the massacre at the Munich Olympics earlierthat day. I was deeply moved by Jim's humaneness. Later that day,in response to a question about his prolific research output, Jimexplained how he had been extremely fortunate to have had somany excellent young researchers working in his group. I wasstruck by his humility. The final thing that sticks in mymind aboutthat visit was the wonderful camaraderie and friendship betweenJim and members of his group. One of those excellent youngresearchers to whom Jimwas referring went by the name of NicoloOmenetto. I recall a long and lively discussion between the three ofus about the magic of the new tunable lasers and how they wereabout to revolutionize spectroscopy. Indeed Jim already had apaper in the pipeline on “Laser excited atomic fluorescence flamespectrometry as an analytical method” [2], with a further threepapers, with Nicolo, on laser excited atomic flame fluorescence tobe published the following year [3–5].

We remember Jim Winefordner for his pioneering work onatomic fluorescence and laser excited atomic fluorescence inhigh temperature flames [1–5]. In this paper we describe somecurrent research on atomic vapors at the opposite end of thetemperature scale. In particular, we will describe the use of lasercooling [6–8] and evaporative cooling techniques [9,10] to coola cloud of atoms down to temperatures within about a hundrednanokelvin of absolute zero, where the atoms are moving atspeeds of just a few mm/s. Excellent reviews on laser coolingcan be found in the Nobel lectures of Steve Chu [6], ClaudeCohen-Tannoudji [7] and Bill Phillips [8].

At temperatures as low as a hundred nanokelvin the atomsbehave as waves rather than particles, and quantum statistics playa crucial role. For a gas of ultracold atoms confined in a trap thewavepackets of the individual atoms begin to overlap and the gascan form a Bose–Einstein condensate (BEC) [11] if the atoms arebosons (integral total angular momentum) or a degenerate Fermigas [12] if the atoms are fermions (half-integral angularmomentum). In this paper we start with a brief background toultracold degenerate quantum gases and then review someresearch on ultracold gases of bosonic atoms and fermionicatoms currently in progress in our Centre for Atom Optics andUltrafast Spectroscopy at Swinburne University of Technology inMelbourne.

2. Ultracold degenerate quantum gases

In 1925 Einstein, inspired by a paper sent to him bySatyendra Bose, predicted that at low temperatures [bosonic]particles in a gas could all accumulate in the same quantum state[13]. In a letter to Paul Ehrenfest, he wrote “The theory is pretty,but is there also some truth to it?” [14].

In order to realize a Bose–Einstein condensate in a weaklyinteracting gas of bosonic atoms the temperature T of the atomsneeds to be sufficiently low and the atom densityn sufficiently highthat the wavepackets of the individual atoms overlap, i.e., we need

a phase space density of nλdB3 =2.6, where λdB=h / (2πM kB T)1/2

is the thermal de Broglie wavelength of the atoms. For a cloud ofn=109 87Rb atoms cm−3 at T=300 K, the phase space density isabout 10−18; so in order to realize a BEC one needs to increase thephase space density by 18 orders of magnitude. After laser coolingand trapping in a magneto-optical trap (MOT) to T≈30 µK andn≈1010 atoms cm−3, the phase space density is about 10−7. Toobtain the final 7 orders ofmagnitude the atom cloud is compressedin a magnetic trap to n≈1014 atoms cm−3 and further cooled byforced evaporative cooling to T≈500 nK. It took another 70 yearsafter Einstein's prediction for the first BEC in a weakly interactinggas to be realized [11], culminating in the award of the 2001Physics Nobel Prize to Eric Cornell, Wolfgang Ketterle and CarlWieman [9,10].

In a Bose–Einstein condensate the atoms all congregate inthe lowest quantum state of the trapping potential well (Fig. 1)and the atomic wavepackets behave as one giant coherentmatter wave, which can be described by a single macroscopicwavefunction, rather like the light waves in a single-mode laser.The BEC is a superfluid of weakly interacting particles andwhen rotated can exhibit quantized vortices [15,16]. Bose–Einstein condensation has to date been achieved for 9 elementsand 12 isotopes: 1H (nuclear spin I=1/2) [17], 4He (I=0)[18,19], 7Li (I=3/2) [20], 23Na (I=3/2) [21], 39K (I=3/2) [22],41K (I=3/2) [23], 52Cr (I=0) [24], 85Rb (I=5/2) [25], 87Rb(I=3/2) [11], 133Cs (I=7/2) [26], 170Yb (I=0) [27] and 174Yb(I=0) [28].

By contrast, in a degenerate Fermi gas the fermionic atoms inthe same spin state occupy different quantum states of thepotential well, on account of the Pauli exclusion principle, andthey sequentially fill up the various quantum states starting fromthe lowest state (Fig. 1). The first degenerate Fermi gas in a dilutegas was realized in 1999, in 40K, by Brian DeMarco andDeborah Jin [12]. Only a relatively small number of isotopes arefermions and these usually have a small natural abundance. Adegenerate Fermi gas has to date been produced in fourelements: 3He (natural abundance 0.00013%; I=1/2) [29], 6Li(7.59%; I=1) [30], 40K (0.012%; I=4) [12] and 173Yb (16.13%;I=5/2) [31]. Other promising candidates include 53Cr (9.55%;I=3/2), 171Yb (14.31%; I=1/2) and 87Sr (7.02%; I=9/2).

One of the remarkable properties of ultracold atoms is that itis possible to precisely tune the strength of the interactionbetween the atoms over a very wide range, and to change its sign,by means of a so-called Feshbach resonance. A Feshbachresonance occurs when a bound state of a closed channel of themolecule formed by two interacting atoms is tuned todegeneracy with the continuum of the open scattering channelusing an external magnetic field (Fig. 2 [32]). By varying themagnetic field, the strength of the interatomic interaction can beprecisely tuned from large and positive through to large andnegative.

In 2003 the group of Rudolf Grimm in Innsbruck succeeded inrealizing a Bose–Einstein condensate of stable, weakly bound 6Li2molecules comprising pairs of fermionic 6Li atoms in opposite spinstates confined in an optical dipole trap [33]. The molecules wereformed during evaporative cooling by three-body recombination ofa 50:50 spinmixture on the lowmagnetic field side of the Feshbach

Fig. 1. Schematic illustrating the behavior of ultracold bosonic atoms andfermionic atoms trapped in a potential well.

106 P. Hannaford / Spectrochimica Acta Part B 63 (2008) 104–114

resonancewhere the s-wave scattering length a is large and positive(Fig. 2). The weakly bound 6Li2 molecules, composed of pairs offermionic 6Li atoms, were found to be remarkably stable, withlifetimes of tens of seconds. This is in contrast with the situation formolecules composed of pairs of bosonic atoms, such as 23Na2,87Rb2 and

133Cs2, which have lifetimes of typically less than 1 ms,which is too short to allow production of a BEC. The high stabilityof the 6Li2 molecules against collisions is a consequence of thelarge separation of the weakly bound fermionic 6Li atoms, leadingto Pauli blocking of collisionswith other like fermionic atoms in thegas [34].At the same time as the experiment in Innsbruck, the groupof Deborah Jin in Boulder realized a BEC of stable, weakly bound40K2 molecules comprising pairs of fermionic 40K atoms [35].

After this major breakthrough the next step was to investigatethe 6Li system on the high field ab0 side of the Feshbachresonance, where it is predicted that at sufficiently lowtemperatures a Bardeen–Cooper–Schrieffer (BCS) superfluidof correlated, unbound Cooper pairs of fermionic 6Li atomsshould form, like the Cooper pairs of (fermionic) electrons insuperconductivity. In particular, there was intense interest inexploring the ‘cross-over’ from the superfluid molecular BEC

Fig. 2. Left: a Feshbach resonance occurs when a bound state of a closed channel ocontinuum of the open scattering channel using an external magnetic field. By varyituned from large and positive through to large and negative. Right: s-wave Feshbachstate. After Ref. [32].

(aN0) to the superfluid BCS state (ab0) [36–41]. The ‘smokinggun’ evidence of the realization of a superfluid BCS state camein 2005 when the group of Wolfgang Ketterle at MITdemonstrated that at suitably low temperature quantized vorticescontinue to be formed as the magnetic field is tuned from theaN0 molecular BEC side of the Feshbach resonance to theab0 side [42].

3. Bose–Einstein condensation on a magnetic film atom chip

In 2001 the groups of Claus Zimmermann in Tübingen andJakob Reichel in Munich reported the realization of a Bose–Einstein condensate of 87Rb atoms confined in a surface magneticmicrotrap created by current-carrying conductors on a substrate[43,44]. Such ‘atom chips’ can produce tightly confiningmagnetic potentials using modest electric currents, therebygreatly simplifying and speeding up the production of the BEC,and they also allow precise control of the motion and position ofthe condensate. They are also compact and relatively robust,making them attractive for BEC-based devices and applications.

Atom chips based on current-carrying conducting wires,however, have certain limitations. Current noise and currentinstabilities in the wires can limit the lifetime and coherenceproperties of the BEC, and high current densities can lead toexcessive heating and broken circuits [45]. In addition, anyimperfections in the conducting wires can lead to tiny spatialdeviations in the current flow which in turn can result infragmentation of the atom cloud [46,47]. Finally, thermal fluc-tuations associated with Johnson noise from nearby conductingsurfaces on the chip can lead to spin flips and a loss of atomsfrom the magnetic trap [48].

3.1. The magnetic film atom chip

In 2005 our group in Melbourne succeeded in realizing aBose–Einstein condensate on a permanent magnetic film atomchip [49,50], which was constructed from perpendicularly

f the molecule formed by two interacting atoms is tuned to degeneracy with theng the magnetic field the strength of the interatomic interaction can be preciselyresonance at 834 G resulting from the two lowest spin states of the 6Li ground


magnetized magneto-optical films previously developed for ouratom optics experiments [51–53]. Magnetic films can producehighly stable, tightly confining magnetic potentials without anyheating, and they can produce very fine-structured magneticpotentials, with characteristic size down to about 1 µm [51–53].Although the potentials from permanent-magnet films arenecessarily static, they can be combined with magneticpotentials from current-carrying conductors when time-depen-dent magnetic fields are required, for example, for initialtrapping of the ultracold atoms and for loading the atoms intothe magnetic film trap. BECs on permanent-magnet atom chipshave also recently been produced using videotape [54], aCoCrPt hard disk [55] and FePt films [56].

Our atom chip (Fig. 3) consists of a perpendicularly mag-netized 1 µm-thick TbGdFeCo magneto-optical film depositedon a glass substrate and mounted on a silver foil ‘circuit’, whichprovides time-dependent magnetic fields for initial trapping ofultracold atoms and loading into the magnetic film trap. Thesilver circuit has a U-shaped wire for producing a surfacemagneto-optical trap (MOT) [57], which is used for initialcooling and loading of atoms close to the surface of the chip,and a Z-shaped wire for producing a Ioffe–Pritchard magnetictrap (with non-zero potential minimum) [57], which is used formagnetic trapping and evaporative cooling to produce the BEC.The magnetic film microtrap is created by the magnetic fieldabove an edge of the film plus a bias field Bbias to provide tightradial confinement and two end-wires to provide weak axialconfinement [50] (Fig. 3).

The magneto-optical films are prepared in-house bymagnetron sputtering [53] and typically comprise six 150 nmlayers of Tb10Gd6Fe80Co4 separated by 100 nm layers of non-magnetic Cr. The films have high perpendicular anisotropy withexcellent magnetic homogeneity, high remanent magnetization(~3 kG), high coercivity (~6 kOe) and a nominally high Curietemperature (~300 °C). The films are coated with a reflectinggold film for use in the mirror MOT. The atom chip is mountedin the vacuum chamber with the magnetic film facing down.The vacuum is typically about 10−11 Torr.

Initially, about 2×108 87Rb atoms are collected and laser-cooled in the mirror MOT located about 5mm below the surface,optically pumped into the |F=2, mF=+2N low magnetic-field-seeking state and subsequently transferred to the Z-wire

Fig. 3. (a) Schematic, and (b) photograph of the

microtrap by turning on the current in the Z-wire. The atomsare then loaded into the magnetic film microtrap by slowlyramping the current in the Z-wire down to zero. Forced radio-frequency evaporative cooling of the atom cloud in the magneticfilm microtrap leads to a BEC with about 105 atoms [49,50](Fig. 4). Temperature measurements made by releasing theatoms from the trap and imaging the cloud after ballisticexpansion indicate a cloud temperature of about 200 nK at adistance of 210 µm from the surface and a heating rate of only3 nK s−1 in the magnetic film trap, compared with 270 nK s−1 inthe Z-wire trap. The trap lifetime was about 5 s, which is limitedby stray time-varying magnetic fields.

3.2. Spatially resolved RF spectroscopy

The small kinetic energies and small spatial extent of thecloud of ultracold atoms can provide a sensitive high resolution(∼5 µm) probe of corrugations in the magnetic potential fromthe magnetic film atom chip [58]. Precision RF spectroscopyplus high resolution imaging of trapped ultracold atoms areemployed to probe the magnetic-field topology along the edgeof the magnetic film [59].

The atom cloud is allowed to expand along the 5 mm edge ofthe magnetic film, by reducing the current in the two end-wires,and a ramped RF field is applied perpendicular to the trap axis toresonantly out-couple atoms to untrapped magnetic states atpositions where the RF frequency exactly matches the Zeemansplitting of the atoms. At the end of the ramp the resonant RFfrequency approaches a final cut-off frequency νf correspondingto the bottom of the trap.

Fig. 5 shows absorption images for a cold atom cloud in theelongated magnetic microtrap located 67 µm below the mag-netic film edge for several values of the RF cut-off frequency νf.For νfb1.3 MHz significant fragmentation of the atom cloud isobserved, and for νfb0.9 MHz well separated regions appearcorresponding to atoms in the lowest potential wells. Using aniterative procedure, values of ∣Bz,y(z)∣ are extracted to obtain thereconstructed magnetic-field profiles shown in Fig. 6 for anumber of trap heights [59]. The characteristic period of thecorrugations is about 390 µm for yN100 µm with additionalhigher frequency components appearing as the atom cloud isbrought closer to the film.

magnetic film atom chip. After Ref. [61].

Fig. 4. Absorption images (top) and optical density profiles (bottom) of a ballistically expanded 87Rb atom cloud. After truncating the evaporation ramp, the atoms areheld for 150 ms and ballistically expanded for 40 ms before imaging on a CCD camera. RF cut-off frequency νf of (a) 804 kHz (thermal cloud), (b) 788 kHz (partiallycondensed cloud), and (c) 760 kHz (almost pure Bose–Einstein condensate). After Ref. [50].


Measurements taken with the atom cloud positioned belowthe magnetic film at x=+100 µm from the edge (Fig. 3) showsignificant corrugation while those recorded below the non-magnetic (gold) film at x=−100 µm from the edge show almostno corrugation. This and other investigations indicate that thefragmentation results from spatial variations of the magnetiza-tion in the body of the magnetic film rather than fromfluctuations along the film edge [59].

After removing the magnetic film atom chip from the vacuumchamber, the magnetic corrugation was examined under a home-built magneto-resistance microscope. The magneto-resistancemeasurements (dotted lines in Fig. 6) show a remarkablecorrelation with the RF spectroscopy cold atom data [59],thereby verifying the validity of the RF spectroscopy cold atom

Fig. 5. Absorption images for an ultracold 87Rb cloud in the magnetic microtraplocated 67 µm below the edge of the magnetic film, for a RF cut-off frequency νfof (a) 1238 kHz, (b) 890 kHz, (c) 766 kHz and (d) 695 kHz. Trap parameters:Bbias =5.7 G, field offset B0=0.82 G, ωr =2π×1070 Hz. Initial cloudtemperature T=10 µK. After Ref. [59].

technique. The use of RF spectroscopy plus high resolutionimaging of the ultracold atoms thus provides a sensitive highresolution technique for mapping the magnetic topology of amagnetic film.

The observed magnetic inhomogeneity in the magnetic filmwas found to be caused by deterioration during vacuum bake-out of the magnetic film atom chip (140 °C for 4 days). Afterremagnetizing the film the level of inhomogeneity was reducedby about a factor of 10 [59]. In subsequent experiments care wastaken not to exceed a temperature of 100 °C during vacuumbake-out.

Fig. 6. Magnetic-field profiles Bz(z) measured using spatially resolved RFspectroscopy (solid lines) for various distances y below the edge of the magneticfilm. The dotted lines correspond to measurements of the magnetic film edgeusing a scanning magneto-resistance probe. The relative longitudinal offset hasbeen adjusted for optimal agreement. After Ref. [59].

Fig. 7. Top: dynamic splitting of a BEC in a double-well potential. Highresolution absorption images are shown as the BEC is slowly moved from170 µm below the film to 57 µm below the film. Bottom: characterization of thedouble-well potential as a function of trap-surface separation y is performedusing two-component clouds. The well separation λ, barrier height β and trapasymmetry Δ are shown schematically in (c). After Ref. [60].

Fig. 8. Fractional number difference versus asymmetry Δ of a double-wellpotential. The asymmetry is altered by changing the end-wire current imbalanceδI. The experimental points and line of best fit (dashed line) compare well with asimple analytic result (solid line). After Ref. [60].


3.3. Splitting of a BEC in an asymmetric double well

In the reconstructed magnetic-field profiles in Fig. 6, a double-well potential is identified in the region near z=0 when themagnetic trap is brought close to the surface of the film byincreasing Bbias in the x direction [60]. The double well originatesfrom higher spatial frequency components of the magnetizationinhomogeneity at distances close to the magnetic film.

Fig. 7 (top) shows a series of high resolution absorptionimages as a BEC is slowly brought from about 170 µm belowthe film, where the potential in the central region behaves as asingle well, to 57 µm below the film, where it behaves as adouble well. Under these conditions the BEC dynamicallysplits into two, with about equal numbers of atoms in eachwell. The double well was characterized by taking absorptionimages for various trap heights y and determining the wellseparation λ and barrier height β as a function of the trap-surface separation y (Fig. 7, bottom) [60]. A small asymmetryΔ in the double well can result in a marked difference in thenumber of atoms in the two wells when the barrier height β isless than the chemical potential µ. Slight tilts of the atomchip for example, produced by tiny movements of the opticaltable, were found to have a dramatic effect on the distributionof the condensate between the two wells. The gravitationalgradient could be cancelled by applying a small magnetic-field gradient provided by a current imbalance±δI betweenthe two end-wires on the chip.

Using a tailored double well located at y=155 µm, wherethe well separation λ≈70 µm and the barrier height β≈1/4µ,absorption images of the condensate were recorded as afunction of the current imbalance δI, and the fractional atomnumber difference (NR−NL) / (NR + NL)=ΔN /N was plottedagainst δI, and hence Δ. From the distribution of the data(Fig. 8) a single-shot sensitivity ΔSNR≈16 Hz was estimated,which is limited by the shot-to-shot variation in the number ofatoms in the BEC. From this result a single-shot sensitivity togravity gradients of δg /g≈2×10−4 is inferred. It should bepossible to enhance the sensitivity significantly by decreasingthe trap frequency, thereby lowering the chemical potential µ,and by using multiple double-well potentials on a single chip[60].

Fig. 9. (a)−(c) 1D periodic array of parallel magnets with perpendicular magnetization. (d)−(f) Calculated contour plots of the magnetic field in the central region in they0z plane with (d) no bias fields, (e) bias field B1y=−15 G, and (f) bias fields B1x=−20 G, B1y=−15 G. 1001 magnets, a=1 µm, t=0.05 µm, length lx=1000.5 µm,and magnetization 4πMz=3.8 kG. After Ref. [63].


3.4. Permanent magnetic lattice on an atom chip

Optical lattices produced by the interference of intersectinglaser beams are widely used to trap, manipulate and control smallclouds of ultracold atoms and BECs, for example, in quantumtunneling experiments [62]. Here, we describe the use ofmagneticlattices produced by permanent magnetic films [63] as analternative to optical lattices.

Magnetic lattices have a number of distinctive characteristics:(i) there can be no spontaneous emission; (ii) they are highlystable with low technical noise; (iii) they can have large andcontrollable barrier heights and large trap curvature leading tohigh trap frequencies; (iv) both 1D and 2D magnetic lattices canbe constructed; and (v) the atoms need to be prepared in lowmagnetic-field-seeking states in order to be trapped, allowing RFevaporative cooling in situ and the use of spatially resolved RFspectroscopy (Fig. 6). Thus magnetic lattices may be considered

Fig. 10. Left: 2D periodic array consisting of two crossed layers of parallel magnetmagnets, a=1 µm, t1=0.322 µm, t2=0.083 µm, lx= ly=1000.5 µm, 4πMz=3.8 kGpotential barrier height ΔUx/kB=ΔU

y/kB=485 µK, ΔUz/kB=307 µK, ωx=ωx=2π×

to be complementary to optical lattices, in much the same way asmagnetic traps are complementary to optical dipole traps.

We first consider a simple 1D magnetic lattice produced by asingle periodic array of parallel magnets with perpendicularmagnetization, period a, and bias fields B1x and B1y parallel andperpendicular to the grooves, respectively (Fig. 9) [63]. ForB1x=B1y=0 (Fig. 9(d)), the magnetic field falls off exponen-tially with distance z above the surface (for z >> a/4π),representing the case of a magnetic mirror for ultracold atoms[51,52]. For B1x=0, B1y=−15 G (Fig. 9(e)), the magnetic fielddevelops 2D microtraps; however these microtraps have zeropotential minima, which results in spin flips and hence loss ofatoms from the lattice, and thus are not suitable as a magneticlattice for ultracold atoms. For B1x=−20 G, B1y=−15 G (Fig. 9(f)), the magnetic field has 2D magnetic traps with non-zeropotential minima, and this configuration is suitable for amagnetic lattice. For an infinite 1D magnetic lattice, the

s with perpendicular magnetization. Right: 3D plot of the magnetic field. 1001, B1x=−4.08 G, B1y=−6.05 G, B1z=−0.69 G. Bmin=2.7 G, zmin=1.22 µm,232 kHz, ωz=2π×329 kHz. After Ref. [63].

Fig. 11. Transition to a 6Li2 molecular BEC in an elongated crossed dipole trap.The curves show integrated cross-sections along the weakest trapping axis700 µs after release from the trap at deceasing trap depths (bottom to top). Thedashed, dash-dotted and solid lines are fits to the Gaussian, Thomas–Fermi andcombined profiles showing the thermal and condensed molecules, respectively.A condensate fraction of 75% for a total of 12,000 molecules is observed.Images taken at 694 G after forced evaporation at 770 G. After Ref. [68].


potential minimum (Bmin), trap height (zmin), and barrier heights(ΔBy, ΔBz) are given by [63]

Bmin ¼ jB1xj; zmin ¼ a=2kð Þ ln B0y=jB1yj� �

DBy ¼ B21x þ 4B2

1y

� �1=2�jB1xj; DBz ¼ B2

1x þ B21y

� �1=2�jB1xj

where B0y=B0 (1−e− kt) ekt, k=2π /a, t is the thickness of themagnets, and here the z-axis is taken to be in the vertical

Fig. 12. In situ absorption images of (a) a 6Li2 molecular BEC, and (b) a 6Li degenevaporation at 770 G (imaging at 694 G), and (b) forced evaporation and imaging at 1is clearly evident in the density and size of the clouds. After Ref. [68].

direction (Fig. 9(b)) . The potential minima, trap height andbarrier heights can be controlled by varying the bias fields B1x

and B1y.We now consider a 2D magnetic lattice produced by two

crossed periodic arrays of parallel magnets separated by adistance s small compared with the period a, and with bias fieldsB1x, B1y (Fig. 10(a)). Fig. 10(b) shows the calculated magneticfield for the parameters given in the caption. For an infinitesymmetrical 2D magnetic lattice, the trap minimum, trap height,and barrier heights are given by [63]

Bmin ¼ c1jB1xj; zmin ¼ a=2kð Þ ln c2B0x=jB1xjð ÞDBx ¼ DBy ¼ c4jB1xj; DBz ¼ c5jB1xj

with the constraint B1y=c0 B1x for a symmetrical lattice. The ci'sare dimensionless constants [63] that involve geometrical constantsa, s, t1 and t2 of themagnetic arrays, andB0x=B0 (1−e−kt2) ek(s+t1+ t2).The potential minimum, trap position and barrier heights can becontrolled by varying the bias fields B1x and B1y. Otherconfigurations of 2D magnetic lattices have also been proposed[63–65].

We have constructed a 1D magnetic lattice with perioda=10 µm and dimensions 10 mm×10 mm using a six-layerstructure of perpendicularly magnetized TbGdFeCo magneto-optical films deposited on a grooved silicon wafer [66]. Themagnetic microstructure was mounted on an atom chip, similar tothat described above, but with a 30mm long Z-wire, in addition to a5 mm long Z-wire, perpendicular to the grooves for effectiveloading of ultracold atoms into the 10mm×10mmmagnetic lattice.

First, a BEC with about 2×105 87Rb atoms was produced inthe short (5 mm) Z-wire trap 250 µm from the chip surfacewhere the magnetic microstructure has a negligible effect. Thecurrent in the Z-wire was then slowly ramped down to bring thecondensate closer to the surface to interact with the magneticmicrostructure. Absorption images indicate that about 5×10587Rb atoms at 15 µK were successively transferred from the5 mm Z-wire trap into the 10 mm×10 mm magnetic lattice andthat atoms were trapped in about 150 of the 1000 lattice sites atb 5 µm from the surface, with a trap lifetime of about 0.3 s [66].By loading the long (30 mm) Z-wire trap and then transferringthe atoms to the lattice it should be possible to load atoms intoessentially all of the 1000 magnetic lattice sites.

erate Fermi gas in an identical crossed optical dipole trap following (a) forced100 G. The difference between the molecular BEC and the degenerate Fermi gas


We plan to use RF evaporative cooling on the trapped atomclouds to create and image BECs on individual sites of the10 µm-period magnetic lattice. We also plan to implement a 2Dmagnetic lattice on an atom chip and to construct magneticlattices with smaller periods (1–5 µm) in order to studyquantum tunneling in 1D and 2D magnetic lattices. In a veryrecent paper the group of Robert Spreeuw in Amsterdam hasreported the trapping of ultracold 87Rb atoms in a 2D FePtmagnetic lattice with a period of 20 µm [67].

4. Quantum degenerate lithium molecules

In April 2007 our group succeeded in producing a Bose–Einstein condensate of 6Li2 molecules, comprising pairs ofweakly bound fermionic 6Li atoms, in a low power (22 W)crossed optical dipole trap at 1030 nm. The crossed dipole trapused a versatile, variable geometry arrangement in which theaspect ratio could be varied over a wide range in order tomaximize the number of molecules at the relatively low poweravailable from our Versadisk YbYAG laser [68]. Evaporativecooling was achieved by reducing the power of the optical dipoletrap laser near the Feshbach resonance at 834 G. By tuning to thelowmagnetic field side (770G) of the Feshbach resonance, wherethe scattering length a is large and positive, molecules wereformed at sufficiently low temperatures through three-bodyrecombination. Fig. 11 shows integrated cross-sections along theweakest trapping direction for an elongated crossed dipole trap atvarious final trap depths. As the temperature falls below thecritical temperature for condensation (∼250 nK), a high densitypeak appears in the centre of the expanded clouds correspondingto the onset of Bose–Einstein condensation. Recently, a 100 Wfiber laser has been incorporated into the optical dipole trap and acondensate with more than 60,000 6Li2 molecules at a temper-ature of less than 50 nK was achieved.

By tuning to the high magnetic field side (1100 G) of theFeshbach resonance, where the scattering length a is large andnegative, we have also produced a degenerate Fermi gas of 6Liatoms [68]. Fig. 12 compares in situ absorption images of (a) atrapped molecular BEC on the aN0 (694 G) side of the Feshbachresonance and (b) a trapped degenerate Fermi gas on the ab0(1100G) side. The degenerate Fermi gas, on theab0 side, is widerand less dense than the molecular BEC due to the Fermi pressure.

The long term goal is to study the dissociation of 6Li2molecules in a molecular BEC as a source of strongly correlatedtwin atomic beams [69,70], which is the atom optics counterpartof parametric down-conversion with photons.

5. Approaching absolute zero

For a theoretical pure Bose–Einstein condensate the trappedatoms all occupy the same zero-momentum quantum state in thepotential well and the temperature is effectively zero. For apartially condensed atomic cloud, the ensemble consists of acondensate component and a thermal cloud, and the thermal cloudcan be used for temperature measurement in time-of-flightexpansion. The kinetic temperature of the ensemble is determinedby the velocity distribution of the thermal cloud and can only

approach absolute zero asymptotically [71]. The measuredtemperature is ultimately limited by factors such as collisionsand technical noise.

The lowest temperature achieved to date was reported by thegroup of Wolfgang Ketterle at MIT [71]. A partially condensedcloud of spin-polarized 23Na atoms was confined in a very weakgravito-magnetic trap, in which the condensate is levitated againstgravity by a current-carrying solenoid, and then further cooled byadiabatically decompressing the trapping potential to achieve amean trap frequency of just ϖ / 2π=1 Hz. The transitiontemperature, given byTC≈0.94 hϖN1/3 /2πkB, was then loweredby reducing the number of atoms in the trap to N=2500,corresponding to a peak condensate density of 5×1010 atomscm−3. This resulted in the entire cloud of atoms being cooled inthree dimensions to a kinetic temperature of just 450±80 pK,corresponding to a mean speed of about 0.7 mm s−1.

6. Summary

We have presented a review of experiments on ultracolddegenerate quantum gases currently in progress in ourlaboratory. First, we demonstrated the use of a permanentmagnetic film atom chip to create a Bose–Einstein condensate of87Rb atoms. Such an atom chip produces highly stable, tightlyconfining magnetic potentials with very low heating rate of theatoms (3 nK/s), and it can produce very fine-structured magneticpotentials, with characteristic size down to about 1 µm.Secondly, themagnetic chip has been usedwith RF spectroscopyand absorption imaging of the ultracold atoms as a sensitive highresolution probe to map the magnetic topology of a magneticfilm. Thirdly, the double-well potential created by the magneticfilm on the atom chip has been used as a sensitive probe ofpotential gradients, such as gravitational gradients. Fourthly, aperiodic magnetic film microstructure on the atom chip has beenused to produce a 1Dmagnetic lattice for manipulating ultracoldatoms and Bose–Einstein condensates. Finally, a Bose–Einsteincondensate of 6Li2 molecules, comprising pairs of weakly boundfermionic 6Li atoms, and a degenerate Fermi gas of 6Li atomshave been produced in a versatile, low-power optical dipole trapnear a Feshbach resonance.

Acknowledgments

The author would like to thank the following colleagues andPhD students who have contributed to the research presented inthis review: Andrei Sidorov, Brenton Hall, Shannon Whitlock,Russell Anderson, Mandip Singh, Michael Volk, AlexanderAkulshin, Russell McLean, Saeed Ghanbari, Wayne Rowlands,Chris Vale, Grainne Duffy, Jürgen Fuchs, Gopi Veeravalli andPaul Dyke. This work is supported by the ARC Centre ofExcellence for Quantum-Atom Optics (ACQAO) and aSwinburne University Strategic Initiative grant.

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approaching absolute zero

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