A multibeam atom laser: coherent atom beam splitting from a single far detuned laser
J. Dugué, G. Dennis, M. Jeppesen, M. T. Johnsson, C. Figl, N. P. Robins, J. D. Close
aa r X i v : . [ c ond - m a t . o t h e r] S e p A multibeam atom laser: coherent atom beam splitting from a single far detuned laser
J. Dugu´e,
1, 2
G. Dennis, M. Jeppesen, M. T. Johnsson, C. Figl, ∗ N. P. Robins, and J. D. Close Australian Research Council Centre Of Excellence for Quantum-Atom Optics,Department of Physics, The Australian National University, Canberra, ACT 0200, Australia Laboratoire Kastler Brossel, ENS, UPMC-Paris 6,CNRS, 24 rue Lhomond, 75231 Paris Cedex 05, France
We report the experimental realisation of a multibeam atom laser. A single continuous atomlaser is outcoupled from a Bose-Einstein condensate (BEC) via an optical Raman transition. Theatom laser is subsequently split into up to five atomic beams with slightly different momenta,resulting in multiple, nearly co-propagating, coherent beams which could be of use in interferometricexperiments. The splitting process itself is a novel realization of Bragg diffraction, driven by each ofthe optical Raman laser beams independently. This presents a significantly simpler implementationof an atomic beam splitter, one of the main elements of coherent atom optics.
PACS numbers: 03.75.Pp,03.75.Be
Diffraction of atoms from an optical grating has led toa wealth of insights into atomic physics, and to practicalapplications such as coherent beam splitting for precisionatom interferometry [1, 2, 3]. Bragg diffraction of ther-mal atomic beams has been done mostly under nearlynormal incidence to the optical grating [4, 5, 6, 7]. Inthese experiments, great care had to be taken to meetthe Bragg condition by precisely matching the angle ofthe optical grating to the velocity of the atoms. Withthe advent of dilute gas BEC [8, 9], a source of coldatoms emerged that is ideal for studying and utilizingatom/light interactions in a highly controllable way. In-vestigations of BEC diffraction with light centered ondiffraction at normal incidence using short light pulses,leading, among other results, to the observation of pe-riodic focusing, collimation and the atomic Talbot ef-fect [10, 11]. It was soon realised that controllable Braggdiffraction could be generated in a stationary condensateby applying an optical running wave [12]. Energy andmomentum conservation for diffraction are met by pre-cisely setting the energy (frequency) difference betweenthe two incident lasers. This is equivalent to satisfyingthe Bragg condition on the angle of incidence in atomicbeam experiments. Bragg and Raman diffraction fromtwo detuned optical beams became an immensely pow-erful tool. It has been used as a coherent beam splitterin interferometry [1, 2, 3], as a spectroscopic probe ofa BEC [13, 14], as the basis for demonstrating superra-diance and matter wave amplification [15, 16, 17, 18],as a tool to measure the relative phase between twoBECs [19], and as a mechanism for producing [20] andmanipulating [21, 22] an atom laser.In this article we present a mechanism for highly ef-ficient cw Bragg diffraction of a continuous atom laserunder non-normal incidence onto an optical grating. Asopposed to previous realisations of Bragg diffraction, thegratings are each produced from only a single far detunedoptical laser and its diffuse backreflection. In Figure 1(a)we show an absorption image of the system in operation. An atom laser beam outcoupled from a Rb BEC is seenin the centre and the diffracted beams off to the sides,falling under gravity. We outcouple the initial atom laserusing two optical beams that drive a two-photon Ramantransition [20, 23], coherently transfering atoms from themagnetically trapped | F = 1 , m F = − i to the magneti-cally untrapped | F = 1 , m F = 0 i state, forming a contin-uous atom laser beam [24, 25, 26]. The laser beams areroughly collimated and have a radius of around 500 µ m,much bigger than the BEC. The splitting, as opposed tothe output coupling, is induced by the subsequent inter-action of the atoms with the laser beams individually: FIG. 1: (a): Absorption image (360 µ m x 1100 µ m) of a multi-beam atom laser derived from 20ms continuous Raman out-put coupling (b): Experimental setup showing optical lasers,BEC (not to scale), and magnetic coils (c), (d): Absorptionimage of a pulsed RF atom laser, exposed to the upward (c)or downward (d) propagating Raman laser only. Image sizeis 540 µ m x 320 µ m, and θ = 15 ◦ the upward (downward) propagating laser imparts a mo-mentum into (against) the laser direction resulting in theatom beam on the left (right) as illustrated in Figure 1(c) and (d) where we illuminated an rf-outcoupled atomlaser pulse with only one of the laser beams. After 20 msof free fall an absorption image of the pulse reveals twomomentum components.The source for the atom laser is a BEC of 5 × atoms.We use a highly stable, water cooled QUIC magnetic trap(axial frequency ω y = 2 π ×
13 Hz and radial frequency ω ρ = 2 π ×
130 Hz, with a bias field of B = 2 G). Theorientations of our magnetic coils and the optical Ramanbeams are shown in Figure 1 (b). The two laser beamspropagate under an angle θ to the horizontal in the planeof gravity and the magnetic trap bias field. They areproduced by a 700 mW diode laser red-detuned by 300GHz from the D2 transition in Rb. We turn the laserpower on or off in less than 200 ns using a fast switchingacousto-optic modulator (AOM) in a double pass config-uration. After the switching AOM, the light is split andsent through two separate AOMs, each again in a dou-ble pass configuration. The frequency difference betweenthe AOMs corresponds to the Zeeman plus kinetic energydifference between the initial and final states of the two-photon Raman transition. We stabilize the frequency dif-ference by running the 80 MHz function generators driv-ing the AOMs from a single oscillator. The beams arethen coupled via single mode, polarization maintainingoptical fibers directly to the BEC through a collimatinglens and waveplate, providing a maximum intensity of2500 mW/cm per beam at the BEC. The polarizationof the beams is optimized to achieve maximum outcou-pling, maximizing π polarization for the downward prop-agating beam and σ − for the upward propagating beam.Continuously applying the Raman output coupler to thecondensate produces the image in Figure 1(a); a con-tinuous atom laser coherently split into three (or more)co-propagating momentum states. As we will show, thesplitting is caused by Bragg diffraction from two opticalstanding wave gratings.In our setup, we do not align a second laser beam to setup a grating for the Bragg diffraction. Also, we can ruleout a direct back reflection of the beam from the geom-etry of the set up, and a careful measurement searchingfor a direct back reflection of the input beam has notrevealed any measurable effect. However, the beams hitthe magnetic coils, giving rise to diffuse backscattering.For a small range of angles, the beam can pass throughthe atoms without clipping on the apparatus. In such asituation, we observe no measurable transfer into the mo-mentum side-mode. But deliberately placing black card-board as a diffuse scatterer in the path of the laser, afterit has passed through the glass cell, brings the diffractionback. We estimate that in our experimental setup, de-pending on θ , determining the distance of the scattererto the interaction region, the backscattered intensity to be between 0.01% and 0.06% of the incoming intensity.It might seem surprising at first that such a small frac-tion of reflected light induces an efficient transfer intohigher order momentum modes. From Raman outcou-pling experiments, where both lasers are applied to thecondensate, we have calibrated the 2-photon Rabi fre-quency, Ω = Ω Ω ∆ , where Ω , are the one-photonRabi frequencies. With maximum laser intensity we canachieve a maximum of Ω = 2 π ×
40 kHz. Thus, we es-timate the combination of the incident laser and the dif-fuse backscattered light to be able to drive a maximumtwo photon Rabi frequency of Ω ≈ π × (Ω t ). For a1 ms laser pulse, this results in a diffraction efficiency ofmore than 70%. The estimate makes it plausible that theseemingly small amount of backscattered light gives riseto efficient coupling.There are a few characteristic properties of Braggdiffraction that we can expect in the experiment. Diffrac-tion from a standing wave grating occurs from absorptionand emission of a photon, leading to a momentum trans-fer to the atom of 2¯ h k . The kinetic energy of the atom,however, must remain unchanged since the energy of theabsorbed and the emitted photon are the same and theatoms stays in the same internal state. This condition isonly fullfilled when the atom is traveling with the reso-nance velocity v res = ± ¯ hk/m sin ( θ ) , (1)where m is the atomic mass, and ( π/ − θ ) is the angleof the laser beam with the velocity of the atom. This iswhen Bragg diffraction can occur.In order to investigate the mechanism responsible forthe coherent splitting and to test it against the Braggcharacteristics, we separated the outcoupling mechanismfrom the splitting. We release the complete BEC byswitching off the magnetic trap. Upon trap switch-off,the atoms are accelerated upwards, resulting in a launchvelocity of 1.1 cm/s [27]. Thus, for θ > o , the atomsgo through two velocity resonances: the first diffractionoccurs when the atoms are traveling upwards, the secondwhen they travel downwards. Since the resonance veloc-ity increases with decreasing θ , for θ < o the atomsmove upwards too slowly to be diffracted. After a vari-able delay time we pulse only one of the Raman laserson. We then allow the atoms with the different momen-tum components to separate in free fall before taking anabsorption image 22 ms after the magnetic trap switch-off. From the images, we calculate the total number oftransmitted and diffracted atoms. FIG. 2: Number of diffracted atoms as a function of pulsedelay relative to trap switch off. Visible are the two possiblevelocity resonances, for atoms traveling upwards (circles) andthen traveling downwards (crosses). Pulse duration is 300 µs (the delay is given from the start of the pulse), and θ = 70 o .The insets show the corresponding images, each 460 µ m x890 µ m. The lines are interpolants to guide the eye.FIG. 3: Diffraction efficiency as a function of laser intensityfor fixed pulse duration of 2ms and θ = 15. First, we vary the pulse delay while keeping the laserpower and pulse duration fixed, for a few different angles.The results of one of these measurements, for θ = 70 o ,are shown in the main plot of Figure 2: We observe tworesonance structures at delay times which match the res-onance velocities. The width of the resonance is consis-tent with the energy spread of the trapped BEC. For allmeasurements, the momentum transfer to the diffractedatoms as well as the timing of the resonance is consistentwith Bragg diffraction.Second, fixing the delay time, angle and pulse dura-tion, we measure the diffraction efficiency as a functionof the laser intensity (Figure 3). For a 2 ms laser pulsewith the delay to the trap switch off chosen such as to ad-dress the resonance velocity, and θ = 15 o , we measure atransfer efficiency of up to 60% into the momentum side-mode, consistent with our simple estimate of diffractionefficiency above.This simple picture, however, does not take into ac-count the velocity selectivity of the process. A more ac- FIG. 4: a) Resonances in momentum space. Diffraction canoccur where the atom momentum trajectory intersects withthe dashed line. b) Avoided crossing for θ = 90 o . c) GPsimulation results (symbols). Solid lines are the predictedLandau-Zener transition probabilities. θ = 15 o curate description of the process results in a situationequivalent to an avoided crossing between the diffractedand undiffracted atoms. If we consider the transfer ofatoms during the diffraction process, the diffracted atomscan be considered to be in a distinct state from theundiffracted atoms because their momentum difference,2¯ h k , is significantly greater than the momentum widthof the falling atoms, see Figure 4(a) for an illustration ofthe resonances in this system. The diffracted ( | i ) andundiffracted ( | i ) atom states are coupled by the diffrac-tion grating leading to an avoided crossing in momentumspace, as shown in Figure 4(b). As the atoms are in freefall, their momentum, and hence the energy difference be-tween the two levels will vary linearly in time, enablingthe Landau-Zener theory [28, 29] to be applied. In thissituation, the Landau-Zener theory gives the diffractionprobability as P = 1 − exp (cid:18) − π Ω | k · g | (cid:19) , (2)where Ω is the two-photon Rabi frequency, k is the wavevector of the photons and g is the acceleration due togravity. Hence, for a sufficiently high two-photon Rabifrequency, this model predicts a perfect transfer of atoms FIG. 5: Spatial modulations occuring for large θ and highlight intensities. Size of the image is 480 µ m x 620 µ m. from the undiffracted state to the diffracted state. We donot consider a second diffraction of the diffracted pulse orthe diffraction into higher orders because they occur atdifferent resonance velocities which are not reached whilethe optical grating is present.We have verified the validity of the Landau-Zenermodel by solving the Gross-Pitaevskii equation (in twodimensions) for the diffracted and undiffracted atomicstates, including the effect of s-wave scattering betweenthe atoms. The results from both approaches agree verywell and are shown in Figure 4 (c). For high Rabi fre-quencies, it can be seen that the transition probabilitydecreases from the result from Landau-Zener theory dueto power broadening causing the state changing to begincloser to the BEC. Here, the inter-particle interactionsare non-negligible. The theoretical results reproduce thegeneral shape of the experimental data, in particular theplateau towards high Rabi frequencies. However, thereis some discrepancy in the maximum transfer probabilitywhich we attribute to the fact that the diffuse natureof the reflection is not taken into account in the cal-culations. The simulations confirm the estimate of thereflected light intensity and the resulting Rabi frequency.We would like to mention one observation that we can-not explain at this point. We observe the appearance ofstrong density modulation of both the condensate andthe diffracted pulse when the angle θ and the light inten-sity become large as shown in Figure 5. The wavelengthof the modulation is several 10 µ m. Interestingly, thestructure of the diffracted pulse is out of phase with thestructure on the BEC. At this point, we do not knowif the spatial structure is related at all to the splittingmechanism and we consider taking more data to illumi-nate the nature of the underlying physics.To the best of our knowledge, high efficiency atomicdiffraction from a single laser and its own diffusebackscattering has not been previously observed. Themethod presents a novel, experimentally simple and ver-satile tool for atom optics, and we have used it to producea multibeam atom laser. Compared to previous atomicbeam splitters which are based on two (usually counter-propagating) optical laser beams, our method presents asignificant experimental simplification. In vacuum sys-tems which do not allow optical access from two sides itmay be the only possibility to implement an atomic beamsplitter. The direction of the momentum transfer can be controlled, together with the resonance velocity and thusthe resonance position, by the angle of the incoming laserbeam. Future applications can be envisaged in coherentatom interferometry with a separated paths interferom-eter. For this purpose, a Raman outcoupled atom laserbeam is perfectely suited, e.g. offering a larger bright-ness, and a good beam profile [23]. Our results show thatit is possible to run the output coupling laser beams in aregime where they serve at the same time as two beamsplitters thus significantly simplifying the experimentaldemands.This work was supported by the APAC National Su-percomputing Facility and by the Alexander von Hum-boldt Foundation. We acknowledge very fruitful discus-sions with Peter Drummond. ∗ Electronic address: cristina.fi[email protected];URL: [1] J. B. Fixler et al. , science
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