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Counting atoms in a deep optical microtrap Matthew McGovern, Andrew J. Hilliard, Tzahi Grünzweig, and Mikkel F. Andersen* Jack Dodd Centre for Quantum Technology, Department of Physics, University of Otago, New Zealand *Corresponding author: [email protected] Received November 23, 2010; revised February 2, 2011; accepted February 17, 2011; posted February 18, 2011 (Doc. ID 138655); published March 16, 2011 We demonstrate a method to count small numbers of atoms held in a deep, microscopic optical dipole trap by collecting fluorescence from atoms exposed to a standing wave of light that is blue detuned from resonance. While scattering photons, the atoms are cooled by a Sisyphus mechanism that results from the spatial variation in light intensity. The use of a small blue detuning limits the losses due to light-assisted collisions, thereby making the method suitable for counting several atoms in a microscopic volume. © 2011 Optical Society of America OCIS codes: 020.1335, 020.3320, 020.7010, 110.0180, 110.2970, 140.7010. Atoms in optical microtraps provide a versatile platform for fundamental studies of quantum mechanics at the individual event level and have potential for application in quantum information processing. Recent progress in these fields includes demonstrations of many body quan- tum states at the single atom level [1] and a controlled- NOT quantum gate [2]. A key challenge in this field is the ability to determine the number of atoms in the optical microtrap. A contem- porary technique to achieve this is to collect fluores- cence from the atoms when exposed to polarization gradient cooling (PGC) light [1,3,4]. However, these PGC beams induce atom loss through light-assisted colli- sions, often prohibiting the counting of more than one atom [1,3,4]. These beams are also largein size and cov- er all directions, making it hard to eliminate stray light. Here we demonstrate a method to fluorescence image and count small numbers of atoms held in a deep optical microtrap. This is achieved by exposing 85 Rb atoms to a laser beam that is blue detuned from the D1 line at 795 nm and retroreflected to form a standing wave. The use of blue detuned light limits the energy gained in in- elastic light-assisted collisions [5], such that several atoms can be counted. The optical standing wave induces a spatial modulation of the imaging beam intensity, lead- ing to a form of Sisyphus cooling [6]. Unlike other forms of blue detuned cooling [7], this mechanism does not pump the atom(s) into optically dark states, making it suitable for fluorescence imaging. Finally, using a dedi- cated imaging beam detuned several nanometers from the light used for laser cooling means that standard op- tical filters can be used to remove stray light. To prepare small numbers of atoms, we load a cloud of atoms from a magneto-optical trap (MOT) into a micro- scopic dipole trap. The MOT operates on the F ¼ 3 to F 0 ¼ 4 transition of the D2 line in 85 Rb at 780 nm. The atoms are further cooled through 5 ms PGC, leaving 50 atoms in the microscopic dipole trap [8]. The dipole trap is formed by focusing a Gaussian beam with wave- length 828 nm by a high NA lens (NA ¼ 0:55) to a spot size of w 0 ¼ 1:8 μm. Figure 1(a) is a schematic of the set- up. We use 37:0 mW dipole trap power, producing a trap of depth U 0 ¼ h × 105 MHz. Figure 1(b) shows calculated spatially varying light shifts induced by the optical dipole trap. In the following, we quote detunings for an atom at the center of the dipole trap. To reduce the number of trapped atoms, we induce light-assisted collisions [8]. To image and count small numbers of trapped atoms, we induce fluorescence with a retroreflected beam at 795 nm and collect a portion of the light with the high NA lens. The standing-wave imaging beam has a Gaus- sian intensity profile with waist w 0 ¼ 92 μm at the posi- tion of the atoms. It is linearly polarized and blue detuned by δ ¼ 20 MHz from the D1 F ¼ 2 to F 0 ¼ 3 transition [Fig. 1(b)]. The light is applied as a 10 ms pulse, with a rectangular pulse envelope. The D1 line does not have a cycling transition, so an excited atom can decay to either of the two ground state manifolds. An atom that spontaneously decays to the F ¼ 3 ground state is pumped back to the F ¼ 2 ground state with a 795 nm D1 F ¼ 3 to F 0 ¼ 2 repump beam and the PGC beams, which the AC Stark shift of the trap shifts near to the D2 F ¼ 3 to F 0 ¼ 3 resonance. The D1 repump beam in- creases the detected fluorescence by 80%, given that only 795 nm light is detected, but this beam can be omitted. The D1 repump beam is mode matched to the imaging beam, tuned to resonance with a power of 10 μW. Each PGC beam has diameter of 8 mm and peak intensity of 2:1 mW cm -2 . Because of the light shift of the dipole trap, the PGC beams cool atoms on the D2 F ¼ 3 to F 0 ¼ 4 transition in the traps wings. Approximately half the light collected by the high NA lens is reflected Fig. 1. (Color online) (a) Schematic of the experimental setup. (b) Calculated spatially dependent light shifts of the F ¼ 2 to F 0 ¼ 3 D1 transition along the tight dimension of the trap. The blue double-headed arrow indicates the frequency of the standing-wave imaging light. April 1, 2011 / Vol. 36, No. 7 / OPTICS LETTERS 1041 0146-9592/11/071041-03$15.00/0 © 2011 Optical Society of America

Counting atoms in a deep optical microtrap

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Counting atoms in a deep optical microtrapMatthew McGovern, Andrew J. Hilliard, Tzahi Grünzweig, and Mikkel F. Andersen*

Jack Dodd Centre for Quantum Technology, Department of Physics, University of Otago, New Zealand*Corresponding author: [email protected]

Received November 23, 2010; revised February 2, 2011; accepted February 17, 2011;posted February 18, 2011 (Doc. ID 138655); published March 16, 2011

We demonstrate a method to count small numbers of atoms held in a deep, microscopic optical dipole trap bycollecting fluorescence from atoms exposed to a standing wave of light that is blue detuned from resonance. Whilescattering photons, the atoms are cooled by a Sisyphus mechanism that results from the spatial variation in lightintensity. The use of a small blue detuning limits the losses due to light-assisted collisions, thereby making themethod suitable for counting several atoms in a microscopic volume. © 2011 Optical Society of AmericaOCIS codes: 020.1335, 020.3320, 020.7010, 110.0180, 110.2970, 140.7010.

Atoms in optical microtraps provide a versatile platformfor fundamental studies of quantum mechanics at theindividual event level and have potential for applicationin quantum information processing. Recent progress inthese fields includes demonstrations of many body quan-tum states at the single atom level [1] and a controlled-NOT quantum gate [2].A key challenge in this field is the ability to determine

the number of atoms in the optical microtrap. A contem-porary technique to achieve this is to collect fluores-cence from the atoms when exposed to polarizationgradient cooling (PGC) light [1,3,4]. However, thesePGC beams induce atom loss through light-assisted colli-sions, often prohibiting the counting of more than oneatom [1,3,4]. These beams are also “large” in size and cov-er all directions, making it hard to eliminate stray light.Here we demonstrate a method to fluorescence image

and count small numbers of atoms held in a deep opticalmicrotrap. This is achieved by exposing 85Rb atoms to alaser beam that is blue detuned from the D1 line at795 nm and retroreflected to form a standing wave. Theuse of blue detuned light limits the energy gained in in-elastic light-assisted collisions [5], such that severalatoms can be counted. The optical standing wave inducesa spatial modulation of the imaging beam intensity, lead-ing to a form of Sisyphus cooling [6]. Unlike other formsof blue detuned cooling [7], this mechanism does notpump the atom(s) into optically dark states, making itsuitable for fluorescence imaging. Finally, using a dedi-cated imaging beam detuned several nanometers fromthe light used for laser cooling means that standard op-tical filters can be used to remove stray light.To prepare small numbers of atoms, we load a cloud of

atoms from a magneto-optical trap (MOT) into a micro-scopic dipole trap. The MOT operates on the F ¼ 3 toF 0 ¼ 4 transition of the D2 line in 85Rb at 780 nm. Theatoms are further cooled through 5ms PGC, leaving∼50 atoms in the microscopic dipole trap [8]. The dipoletrap is formed by focusing a Gaussian beam with wave-length 828 nm by a high NA lens (NA ¼ 0:55) to a spotsize of w0 ¼ 1:8 μm. Figure 1(a) is a schematic of the set-up. We use 37:0mW dipole trap power, producing a trapof depth U0 ¼ h × 105MHz. Figure 1(b) shows calculatedspatially varying light shifts induced by the optical dipoletrap. In the following, we quote detunings for an atom atthe center of the dipole trap. To reduce the number oftrapped atoms, we induce light-assisted collisions [8].

To image and count small numbers of trapped atoms,we induce fluorescence with a retroreflected beam at795 nm and collect a portion of the light with the highNA lens. The standing-wave imaging beam has a Gaus-sian intensity profile with waist w0 ¼ 92 μm at the posi-tion of the atoms. It is linearly polarized and blue detunedby δ ¼ 20MHz from the D1 F ¼ 2 to F 0 ¼ 3 transition[Fig. 1(b)]. The light is applied as a 10ms pulse, with arectangular pulse envelope. The D1 line does not havea cycling transition, so an excited atom can decay toeither of the two ground state manifolds. An atom thatspontaneously decays to the F ¼ 3 ground state ispumped back to the F ¼ 2 ground state with a 795 nmD1 F ¼ 3 to F 0 ¼ 2 repump beam and the PGC beams,which the AC Stark shift of the trap shifts near to theD2 F ¼ 3 to F 0 ¼ 3 resonance. The D1 repump beam in-creases the detected fluorescence by ∼80%, given thatonly 795 nm light is detected, but this beam can beomitted. The D1 repump beam is mode matched to theimaging beam, tuned to resonance with a power of10 μW. Each PGC beam has diameter of 8mm and peakintensity of 2:1mWcm−2. Because of the light shift of thedipole trap, the PGC beams cool atoms on the D2 F ¼ 3to F 0 ¼ 4 transition in the trap’s wings. Approximatelyhalf the light collected by the high NA lens is reflected

Fig. 1. (Color online) (a) Schematic of the experimental setup.(b) Calculated spatially dependent light shifts of the F ¼ 2 toF 0 ¼ 3 D1 transition along the tight dimension of the trap.The blue double-headed arrow indicates the frequency of thestanding-wave imaging light.

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by a polarizing beam splitter (PBS) located just outsidethe vacuum chamber. This light passes through opticalfilters, before an infinity corrected lens forms an imageon an electron-multiplying CCD (EMCCD) camera. To re-move dipole trap and PGC light, we use a 795 nm band-pass filter and a notch filter at 830 nm. Room light isfurther suppressed using shields. The high NA lens col-lects 10% of the fluorescence, and the combined trans-mission of the PBS, filters and additional optics is 37%.The EMCCD has a measured quantum efficiency of60%, so that the total photon detection efficiency is 2.3%.Integrating the image reveals that we collect ∼330photons per atom in a 10ms exposure.Using blue detuned light for imaging allows us to count

several atoms in the microtrap. Figure 2(a) shows a his-togram of integrated signal for 2000 experimental runs.Broadly, there are two mechanisms that allow us to de-tect more than one atom. The first is “optical shielding”:high intensity blue detuned light shields atom pairs frompossible inelastic collisions [5], reducing the overall in-elastic collision rate. Second, if an atom pair undergoesan inelastic light-assisted collision, the total energygained by the pair is limited to the detuning δ, whichis less than the trap depth, enforcing the need for multi-ple collisions to induce atom loss [9]. Given that the col-lision rate scales as NðN − 1Þ, where N is the number ofatoms, the loss due to light-assisted collisions increasessharply for higher numbers of atoms. This reduces thesurvival probabilities of multiple atoms (e.g., 0.72 forpairs), as shown in Fig. 2(b), which displays the resultof a second image, taken 20ms after the first. Takingtwo images allows us to reject realizations in which losshas occurred during imaging, and can be seen in Fig. 2(c).The major contributions to the peak widths are Poisso-nian photon statistics, readout noise, and excess noiseassociated with the EMCCD gain [10]. The zero atompeak has equal contributions from camera readout noiseand stray light. The peak widths in Fig. 2(c) are smallerthan those in Figs. 2(a) and 2(b) as using two images ef-fectively doubles the exposure time.Inducing fluorescence in atoms with blue detuned

laser light may cause Doppler heating as the atoms pre-ferentially pick up the recoil momentum of absorbed

copropagating photons. Heating leads to a loss of atomsfrom the microtrap, thereby prohibiting imaging andatom counting. To counteract Doppler heating, we em-ploy a variation of the Sisyphus cooling mechanism de-scribed in [6,11,12]. It relies on two atomic levels, in ourcase, the 52S1=2 F ¼ 2 ground state and the D1 52P1=2F 0 ¼ 3 excited state coupled by a blue detuned standingwave. The eigenstates of the Schrödinger equation for atwo-level atom in a near-detuned light field are usuallydescribed in terms of the “dressed states” j1; ni andj2; ni of the atom–light system [6]. n is the total numberof photons in the laser field, and, in the absence of light,j1i corresponds to the atomic ground state and j2i to theexcited state. When an atom moves in the standing wave,the dressed state energy and, hence, its center-of-masskinetic energy varies spatially with the local light inten-sity. The positions of lowest kinetic energy correspond tothe highest admixture of excited state in both dressedstates, leading to these positions having the highest prob-ability of spontaneous transition between dressed states.This creates a Sisyphus effect, where the atom is predo-minately moving up potential hills, as illustrated inFig. 3(a). The minimum kinetic energy reached by sucha cooling mechanism is equal to the depth of the wellscreated by the standing wave [12]. Unlike other blue de-tuned laser cooling mechanisms, such as gray molasses[7], where the atoms are pumped into optically darkstates, here atoms can scatter many photons and remaintrapped.

In our case, there is an additional complication to themodel considered in [6,11]. Because the transition weoperate on is not closed, a spontaneous emission eventcan cause an atom to decay into the 52S1=2 F ¼ 3 groundstate, as indicated in Fig. 3(b). The PGC beams will

Fig. 2. (Color online) (a) Histogram of the integrated analog-to-digital units (adu) from a small number of atoms in the micro-trap. The red curve is a fit of five Gaussians. (b) Result from asecond image taken 20ms after the first. (c) Average adu fromsuccessive images that were correlated to within �3000 adu.

Fig. 3. (Color online) (a) Spontaneous transitions betweendressed states effect Sisyphus cooling. (b) Atoms that decayto the F ¼ 3 ground state are pumped back into the cooling cy-cle by the D2 PGC beams (green straight arrow). (c) Survivalprobability for a single atom as a function of standing-wavepower for δ ¼ 1MHz (crosses) and δ ¼ 20MHz (circles). (d) In-tegrated fluorescence collected for these two detunings.(e) 2:5 s exposure image of a single atom.

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optically pump the atoms back to the cooling cycle withno preference to position along the standing wave. There-fore, this does not qualitatively change the above picture.The temperature of an atom during imaging depends

on the balance between Sisyphus cooling and Dopplerheating, and, thereby, the intensity and detuning of lightused to form the standing wave. The energy increase perphoton scattered in Doppler heating is independent ofthe light intensity. On the other hand, the Sisyphus en-ergy loss per photon depends on the magnitude of thepotential hills the atom climbs. Sisyphus cooling, there-fore, predominates at high intensities, leading to an in-creased probability of atom retention during imaging.We now investigate the luminosity and “survival prob-

ability” of the atom as a function of standing-wave param-eters. Here we omit the D1 repump beam to isolate therole of the blue detuned standing wave. In 200 repetitionsof a control experiment, we prepared single atoms, andtook two 10ms exposure images, 30ms apart with δ ¼20MHz and a power of 30 μW for the standing wave. Thisyielded a probability of detecting an atom in the final im-age (F), conditioned on it being detected in the initial im-age (I) of: PcðF jIÞ ¼ 0:97. To test the detuning and powerdependence of imaging, we took three 10ms exposureimages of single atoms 10ms apart, where the firstand last images were taken under the same conditionsas in the control experiment, and the standing-wave pa-rameters for the second image were varied. We define thesurvival probability as PxðF jIÞ=PcðF jIÞ, where PxðF jIÞis the probability of having an atom in the final imageconditioned on having it present in the initial image.Figure 3(c) shows the survival probability as a functionof power for two detunings. For δ ¼ 1MHz, we see a lowsurvival probability at low powers. which we attribute toDoppler heating dominating over Sisyphus cooling. Forhigher powers, the survival probability increases, as Si-syphus cooling becomes dominant. For powers above75 μW, the depth of the standing-wave wells becomescomparable to the depth of the dipole trap. As the atom’stypical external energy is set by the depth of the standing-wave wells, this leads to atom loss and manifests itself inthe decreasing survival probability observed. A similartrend is observed for δ ¼ 20MHz, but the trapped atomhas a high survival probability for a larger range ofpowers. Figure 3(d) shows the integrated fluorescencecounts from the second image from the runs where an

atom remained in all three images. The fluorescencecounts for δ ¼ 1MHz are higher than the counts for δ ¼20MHz because it is closer to resonance. Therefore, onemust compromise between high fluorescence and atomloss. δ ¼ 20MHz and a power of 50 μW comprise a usefulparameter set with a survival probability of 99% andrelatively high fluorescence, allowing long exposureimages, as shown in Fig. 3(e).

In conclusion, by using a dedicated blue detunedstanding wave to induce fluorescence, we reduce the en-ergy released in light-assisted collisions between atoms,making it possible to count several atoms in an opticalmicrotrap. Our work may open new avenues in few bodyphysics with neutral atoms.

This work is supported by the New Zealand Founda-tion for Research, Science and Technology (NZ-FRST)Contract No. NERF-UOOX0703 and a University of OtagoResearch Grant.

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