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A slow gravity compensated atom laser

A slow gravity compensated atom laser
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  Applied Physics B manuscript No. (will be inserted by the editor) A slow gravity compensated Atom Laser G. Kleine B¨uning 1 ⋆ , J. Will 1 , W. Ertmer 1 , C. Klempt 1 , J. Arlt 2 1 Institut f¨ur Quantenoptik, Leibniz Universit¨at Hannover, Welfengarten 1, D-30167 Hannover 2 QUANTOP, Danish National Research Foundation Center for Quantum Optics, Department of Physics and Astronomy,Aarhus University, Ny Munkegade 120, DK-8000 Aarhus CReceived: date / Revised version: date Abstract  We report on a slow guided atom laser beamoutcoupled from a Bose-Einstein condensate of   87 Rbatoms in a hybrid trap. The acceleration of the atomlaser beam can be controlled by compensating the grav-itational acceleration and we reach residual accelerationsas low as 0 . 0027 g. The outcoupling mechanism allowsfor the production of a constant flux of 4 . 5  ×  10 6 atomsper second and due to transverse guiding we obtain anupper limit for the mean beam width of 4 . 6  µ m. Thetransverse velocity spread is only 0 . 2 mm/s and thus anupper limit for the beam quality parameter is M 2 = 2 . 5.We demonstrate the potential of the long interrogationtimes available with this atom laser beam by measuringthe trap frequency in a single measurement. The smallbeam width together with the long evolution and inter-rogation time makes this atom laser beam a promisingtool for continuous interferometric measurements. 1 Introduction The conceptual similarities between the coherence of laser light and the coherence of Bose-Einstein condensedsamples has been a driving force for the field of coldquantum gases. Similarly to the laser, coherent matterwaves hold the promise of improving precision measure-ments and fundamental tests of quantum physics.However, there is a striking difference between thelaser and cold quantum gases that still has to be over-come. Current exponents with cold quantum gases relyon the technique of forced evaporative cooling to achievethe desired temperatures and densities. Since this cool-ing technique depends on collisions between the parti-cles, conservative magnetic or optical potentials are usedto confine the samples. While many similarities still ap-ply in this trapped case, the confinement impedes theproduction of a bright coherent matter wave output. ⋆ e-mail: It was realized soon after the production of the firstBose-Einstein condensates (BEC), that the mechanismfor forced evaporation could also be used as an outcou-pler for matter wave packets [1]. This technique also al-lowed for the production of long pulses [2,3], limited onlyby the size of the initial BEC. Due to the small momen-tum of the outcoupled atoms, this technique is howeverlimited by the inherent interaction with the remainingBEC fraction [4]. In a different approach Raman transi-tions were hence used to impart a larger momentum tothe outcoupled atoms [5,6] and it was shown that theseoutcouplers lead to a strongly improved output beamquality [7].All of these outcoupling techniques rely on the trans-fer of atoms to magnetically untrapped states. Yet manyrecent experiments use all optical or hybrid potentials toproduce BEC. Hence outcoupling techniques were alsodeveloped for samples confined in dipole potentials [8,9]and optical lattices [10].In addition to these techniques to produce coherentmatter wave beams, powerful analysis techniques havebeen developed to investigate their coherence proper-ties and both first and second-order coherence were con-firmed [11,12,13].Current experimental efforts focus on methods tocontinuously replenish a BEC while simultaneously out-coupling a coherent beam. Both the replenishment of a BEC in an optical dipole trap [14] and simultane-ous pumping and outcoupling [15] of limited durationwere demonstrated. However completely new experimen-tal approaches such as continuous condensation in abeam [16] or continuous loading of a trap [17] may benecessary to achieve this ambitious goal.The similarity between a laser beam and the atomlaser points at another major experimental challenge.While the internal degrees of freedom can be controlledprecisely in quantum gases, control of the external de-grees of freedom of an outcoupled beam poses a largerchallenge. The divergence of the beam and its modestructure have been investigated intensely [18,19,4,20,   a  r   X   i  v  :   1   0   0   5 .   3   9   6   4  v   1   [  c  o  n   d  -  m  a   t .  q  u  a  n   t  -  g  a  s   ]   2   1   M  a  y   2   0   1   0  2 G. Kleine B¨uning et al. Transport CoilsDispensersDifferential PumpingTubeQuadrupole CoilsScience CellMOTCellTo the PumpsTo the Pumpsz (a)(b) Fig. 1  Outline of the experimental apparatus. The vacuum system with the two glass cells is shown in (a). In the large MOTcell, the atoms are captured from the background vapor. Subsequently, they are trapped magnetically and transported intothe science cell with movable coils. This cell is designed in a L-shape to grant optical access along three axes. The evaporativecooling takes place in a hybrid trap (b). The trapping potential is provided by a dipole beam focused slightly underneath thecenter of a magnetic quadrupole field. 7,21]. First atom optical elements were developed us-ing inhomogeneous magnetic [22,12] and optical [23,24]potentials. Recently, guided atom lasers were realizedstarting from optically [9] and magnetically confined [25]samples.Within our work a particularly slow atom laser beamwas realized. By compensating the gravitational accel-eration with an inhomogeneous magnetic field, accelera-tions below 0 . 003 g can be achieved. Thus this atom laserallows for interrogation times of up to 500 ms primar-ily limited by the field of view of the detection system.These long interrogation times promise continuous inter-ferometric measurements in this system over relativelylong periods of time. Special emphasis is given to thenovel features of the experimental apparatus. 2 Experiment The investigation of slow atom laser beams is per-formed in an experimental apparatus based on a hy-brid trap [26]. To incorporate this trap, a two chambervacuum system shown in Fig. 1 is used. The two partsare separated by a differential pumping stage and allowfor efficient loading of a magneto-optical trap (MOT)from the background vapor and for long lifetimes of theatomic samples in the science cell. The transport of theatoms between the cells is realized with a movable pairof quadrupole coils [27,28]. The science cell is designedin a L-shape to provide outstanding optical access fromsix directions. 2.1 MOT and magnetic transport  To enable the use of large trapping beams, the MOT cellhas inner dimensions of 50 mm  ×  50 mm  ×  140 mm. Ru-bidium vapor is provided by commercial dispensers lo-cated approximately 20 cm from the MOT center withina direct line-of-sight. During dispenser operation thepressure reaches 5  ×  10 − 10 mbar in the MOT cell and1  ×  10 − 11 mbar in the science cell.For operating the  87 Rb MOT, a laser system provideslight at a wavelength around 780 nm. The cooling lighton the D2 transition  F   = 2  →  F  ′ = 3 is derived froma stabilized external cavity diode laser (ECDL). The re-pumping light on the transition  F   = 1  →  F  ′ = 2 isdelivered by a second ECDL which is referenced to thecooling laser with a frequency offset of 6 . 8 GHz. Bothbeams are amplified to a total power of 1 W in a singletapered amplifier [29] and delivered to the experimentin a polarization maintaining optical fiber. To operatethe MOT, the total available laser power of 350 mW isdivided into six beams which are then individually ex-panded to a diameter of 50 mm in Galilean telescopes.The large beams in combination with the large glasscell enable for efficient and fast loading from the Ru-bidium background vapor. The loading rate is furtherenhanced by the use of ultraviolet light-induced atomdesorption [30] at 395 nm which increases the atom num-ber by a factor of 2 after 10 s loading time, resultingin 3  ×  10 9 atoms. Once this atom number is reached,the MOT is turned off and the atoms are further cooledwithin an optical molasses phase and optically pumpedto the  | F,m F    = | 2 , 2   for further magnetic trapping.To transfer the atoms to the science cell, they aretransported over a distance of 60 cm within 1 . 2 s bya quadrupole magnetic field. The MOT coils are there-fore mounted on a movable translation stage. For thetransport, the current through these coils is increasedto 45 A. The corresponding magnetic field gradient of  B ′ = 165 G/cm (where  B ′ =  ∂B/∂z  denotes the gra-dient in the strongest, vertical direction) captures andcompresses the cold cloud. Once the translation stagereaches its final position at the science cell, the atomsare transferred over a distance of 4 . 5 cm into a secondpair of quadrupole coils, as shown in Fig. 1. We obtain2 × 10 8 atoms at a peak phase space density of 1 × 10 − 7 which provides an excellent starting condition for furthercooling in the hybrid trap. 2.2 Hybrid trap Since the typical phase space density after laser coolingis still far from quantum degeneracy, all BEC experi-ments to date employ evaporative cooling to reach the  A slow gravity compensated Atom Laser 3 0 25 50 12575 100 ms 2.3 mm (a) (b) Fig. 2  (a) BEC positions after time of flight in the presenceof a magnetic field gradient. Residual accelerations of 0 . 14 g,0 . 082 g, 0 . 018 g and 0 . 010 g (from left to right) are obtainedfrom fits to this data. The dashed line indicates free fall atan acceleration of 1 g. For the case of 0 . 018 g the srcinalabsorption images are shown (b). required temperatures. In most cases this is done eitherby forced radio-frequency evaporation in magnetic po-tentials or by lowering the trap depth in optical dipolepotentials. In our experiment we combine the two ap-proaches in a hybrid trap, profiting from the advantagesof both [26].The magnetic confinement is provided by a simplemagnetic quadrupole potential which initially allows forvery efficient evaporation. Additional optical confine-ment is realized with a single gaussian beam with a waistof 52  µ m, focused below the center of the quadrupole po-tential. We use a single-mode, single-frequency fiber laserat a wavelength of 1064 nm which provides a power of upto 7 W at the position of the atomic cloud. The power iscontrolled with an acousto-optic modulator, whose con-trol circuit is optimized for stability at low optical powerof a few milliwatts.After the transfer of 2 × 10 8 atoms to the quadrupoletrap we employ forced microwave evaporation on the  | 2 , 2   to  |  1 , 1  -transition. Simultaneously, we ramp themagnetic field gradient from  B ′ = 300 G/cm down to132 G/cm. The evaporation is stopped at 6 . 845 GHzwhich corresponds to a magnetic field of 5 G. After thisfirst evaporation step, 7  ×  10 7 atoms at a phase spacedensity of 2  ×  10 − 4 are obtained. If this evaporation inthe quadrupole potential is continued, the lifetime beginsto suffer from Majorana spin-flip losses.At this point, the atoms are therefore transferred intothe hybrid trap shown in Fig. 1. This is accomplished byincreasing the dipole beam power to 7 W while loweringthe magnetic gradient to B ′ c  =  m Rb g/ ( m F  g F  µ B ) = 15 G / cm  .  (1)Here,  m Rb  denotes the mass of   87 Rb,  g  the gravitationalacceleration,  g F   is the Land´e factor and  µ B  representsBohr’s magneton. During this process, the atoms sagunder the influence of gravity and are thus transferredinto the optical dipole potential. At the final value  B ′ c ,gravity is compensated and thus, the atoms are primarilyconfined by the dipole potential in radial direction. (a)(b) Fig. 3  (a) Horizontal oscillation frequency as a function of the vertical position below the quadrupole center. The dottedline shows the position of the hybrid trap 230  µ m below thequadrupole center, which results in an axial confinement of 16 Hz. (b) Oscillating BEC falling through the magnetic fieldwith a residual acceleration of 0 . 010 g. The solid line is asolution of the equation of motion with only starting velocityand position as the free parameters. To calibrate the exact magnetic field gradient, wemeasure the residual acceleration of BECs released fromthe hybrid trap in the presence of various field gradients.Figure 2 shows an exemplary series of absorption imagesand the positions of the BEC as a function of the timeof flight.In the axial direction, the dipole potential hardly pro-vides any confinement and the trap relies on the remain-ing magnetic field. The quadrupole potential is linear onaxes through the center, but it has a curvature every-where else. The quadrupole potential is given by U  ( x,y,z ) =  m F  g F  µ B B ′   ( x 2 + y 2 )/4 + z 2 ,  (2)where  x,y  are the horizontal coordinates and  z  is the ver-tical position. The horizontal oscillation frequency  ω x  isobtained by calculating the curvature at a displacement z  below the quadrupole center: ω x ( z ) =   m F  g F  µ B 4 m Rb B ′ z  (3)In the experiment, the dipole beam is focused  z  =230  µ m below the center to avoid Majorana spin-fliplosses and to obtain a harmonic confinement with a suf-ficiently high axial trap frequency of   ω x  = 2 π × 16 Hz.At positions below the hybrid trap the horizontal oscil-lation frequencies decrease as shown in Fig. 3. To analyzethis transverse confinement during the time of flight, wedisplace the BEC in the hybrid trap. It hence oscillateswith an axial frequency of 16 Hz before it is released andcontinues to oscillate while falling through the magneticfield. Figure 3 shows the horizontal position of BECs  4 G. Kleine B¨uning et al. (a)(b) Fig. 4  (a) Potential provided by the hybrid trap for resid-ual accelerations of 0.0010 g (dashed), 0.018 g (dotted) and0.082 g (solid) and the corresponding minimal dipole beampower needed to support a BEC. These values are shown in(b). Reducing the dipole beam power below these values leadsto outcoupling of atoms. The experimental values are com-pared to calculated powers for fixed trap depths of 100 nK(solid) and 250 nK (dashed). during this process. As the BEC falls into regions of smaller axial confinement, the oscillation frequency de-creases and the amplitude increases. All of these featuresare reproduced by solving the classical equation of mo-tion for a particle in the potential of Eq. (2).During the transfer into the hybrid trap, roughly twothirds of the atoms are lost, but one order of magnitudein phase space density is gained. This fortunate behav-ior is caused by ongoing evaporative cooling and by anadditional gain in peak phase space density due to thechange from the linear quadrupole potential to the har-monic hybrid trap [26].With an initial atom number of 2 × 10 7 and a phasespace density of 2 × 10 − 3 in the hybrid trap, BEC is easilyobtained by decreasing the dipole beam power and thuslowering the trap depth. At a laser power of 20 mWcorresponding to a trap depth of 600 nK BECs of up to1  ×  10 6 atoms are created.After producing a BEC in the hybrid trap by low-ering the trap depth, we can slowly ramp down thepower of the dipole beam even further. This results ina cigar shaped trap with radial frequencies of typically ω y  =  ω z  = 2 π × 30 Hz and an axial frequency (dominatedby the magnetic confinement) of   ω x  = 2 π × 16 Hz. Dur-ing this process, further evaporation purifies the BECand due to the adiabatic expansion into this very weaktrap, the temperature is additionally decreased. Figure 4shows this potential for values of the magnetic field gra-dient and the experimentally determined minimal laserpower needed to trap a BEC of 5 × 10 5 atoms. Thus low-ering the potential saddle can serve as an outcouplingmechanism for this hybrid trap. 3 Atom laser The distinctive features of the hybrid trap allow for theproduction and investigation of a gravity compensated,particularly slow atom laser beam. 3.1 Atom laser with gravity compensation  To produce an atom laser beam we reduce the dipolelaser power to a fixed value slightly below the thresholdvalues presented in Fig. 4. The threshold value is deter-mined by the chemical potential of the BEC which is setby the repulsive interaction of the Rubidium atoms andthe number of atoms in the trap. If the trap depth fallsbelow the chemical potential, the BEC becomes partiallyuntrapped and the trap leaks. The leak is situated at thelowest point of the condensate’s surface and the spatialsize of the leak scales with the difference between trapdepth and chemical potential. The atoms flow out of theleak and the repulsive interaction of the escaping atomslimits the leakage flow. For long outcoupling times, theloss of trapped atoms in the BEC decreases the chemicalpotential, reducing and eventually terminating the leak-age. The timescale of this decrease is large in the limitof large BECs and small leakage, since the chemical po-tential depends on the atom number  N   as  N  2 / 5 .The outcoupled atom laser beam propagates withinthe remaining magnetic quadrupole field. This field islinear in the vertical direction and compensates grav-ity. In the horizontal direction it provides a symmet-ric quadratic confinement along the whole length of thebeam.Figure 5 shows a set of absorption images of the atomlaser. These images were taken for a residual accelera-tion of 0 . 018 g and the outcoupling time was varied fromzero up to 200 ms. By choosing gradients even closer togravity compensation, atom laser beams were observedfor more then half a second at a residual acceleration of 0 . 0027 g. In this case a peak velocity of only 13 mm/s af-ter 500 ms of acceleration is reached. This demonstratesthe long interrogation times available in this system,which were in fact only limited by the field of view of the detection system.Despite of the long evolution, hardly any broadeningof the width of the atom laser beam is observed withinthe resolution of our imaging system. This is due to the  A slow gravity compensated Atom Laser 5 4 .7 mm 0 25 50 175125 20015075 100 ms Fig. 5  Absorption images of a gravity compensated atomlaser. The outcoupling time is increased from 0 ms to 200 msin steps of 25 ms. very low temperature of the BEC in the shallow hybridtrap and due to the horizontal confinement provided bythe magnetic potential. 3.2 Beam analysis  To evaluate the beam profile quantitatively, we analyzethe atom laser beam shown in Fig. 6. This beam was out-coupled for 30 ms at an residual acceleration of 0 . 14 g.At several positions within the beam the profile is aver-aged over 45  µ m slices in vertical direction. A gaussianfit is performed to obtain the width and the atom num-ber for each of these slices. Figure 6 shows the resultingatom number per  µ m, the calculated atomic flux and thewidth along the beam (limited by the resolution of ourdetection system). The atom number per slice decreasesalong the beam as expected, since it is stretched due tothe remaining acceleration. The flux remains constant atapproximately 4 . 5 × 10 6 atoms/s along the beam, show- (a)(b)(c) Fig. 6  Analysis of an atom laser beam coupled out of thehybrid trap at an acceleration of 0.14 g. A series of gaussianfits is performed well below the BEC over 45  µ m slices invertical direction. The atom numbers per  µ m (a) are used todetermine the flux (b). The atom beam has a mean width of 4.6  µ m (c). ing that a constant outcoupling mechanism was realized.This analysis is valid as long as the size of the BEC it-self diminishes only little during the outcoupling time.Note however, that the flux decreases for long outcou-pling times as the chemical potential for the BEC drops(see Fig. 5).In addition to the spatial distribution shown inFig. 6, the beam quality is determined by the transversevelocity distribution. To analyze this distribution, atomlaser beams were produced and then released in absenceof any external potential for times of flight up to 25 ms.This allows for an analysis of the broadening of the beamand thus a transverse velocity spread of 0 . 2 mm/s wasdetermined.Recent analyses of atom laser beams [4,20] determinethe beam quality factor  M  2 in analogy to optical lasers.This value is defined as  M  2 = (2 m Rb / ¯ h )  ∆x∆v x , where ∆x  denotes the beam width at the waist and  ∆v x  de-notes the horizontal velocity spread. For a mean widthof 4 . 6  µ m and the measured velocity spread we obtain anupper limit  M  2 = 2 . 5 for the gravity compensated atomlaser beam. This value surpasses the Heisenberg limit foran atom laser and competes with radio frequency out-coupling mechanisms [20,4]. 3.3 All-optical atom laser  To compare the performance of the gravity compensatedatom laser with an uncompensated freely propagatingatom laser, an all-optical atom laser was realized [8,9].The axial magnetic confinement in the hybrid trap issubstituted by a second dipole laser beam. This beamcrosses the first beam at an angle of 18 ◦ in the hori-zontal plane. In this configuration a power of 200 mWfocused to a waist of 70  µ m in the additional beam pro-vides an axial harmonic confinement with an oscillation
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