Measurements on release-recapture of cold Rb-85 atoms using an optical nanofibre in a magneto-optical trap
MMeasurements on release-recapture of cold Rb atomsusing an optical nanofibre in a magneto-optical trap
L. Russell a,b,c , R. Kumar a,b,c , V. B. Tiwari a,b,d , S. Nic Chormaic a,c,e a Physics Department, University College Cork, Cork, Ireland b Tyndall National Institute, Lee Maltings, Propsect Row, Cork, Ireland c Light-Matter Interactions Unit, OIST Graduate University, 1919-1 Tancha, Onna-son,Okinawa 904-0495, Japan d Laser Physics Applications Section, Raja Ramanna Centre for Advanced Technology,Indore 452013, India e School of Chemistry and Physics, University of Kwa-Zulu Natal, Durban 4001, SouthAfrica
Abstract
We have performed release-recapture temperature measurements of laser-cooled Rb atoms using an optical nanofibre (ONF) in a magneto-opticaltrap (MOT). The effects of changing the cooling laser light-shift parameter onthe temperature of the cold atoms and spring constant of the trap are studied.By varying the cold atom number density near the ONF, the onset of themultiple scattering regime is observed without the need for an estimation ofthe atom cloud size. Moreover, this sensitive ONF assisted release-recapturetechnique is easily able to detect any optical misalignment of the coolinglaser beams in the MOT.
Keywords: laser cooling, optical nanofiber, rubidium, release-recapture, temperature
1. Introduction
Temperature is undeniably one of the most important characteristics ofa laser-cooled sample of atoms that one can measure. By experimentallydetermining the ensemble temperature, T , quantities such as spring constantand diffusion coefficient can be estimated [1, 2], temperature and density Email address: [email protected] (L. Russell)
Preprint submitted to Optics Communications July 6, 2018 a r X i v : . [ phy s i c s . a t o m - ph ] A ug egimes can be mapped out [3], and a wealth of information regarding theefficiency of the trapping, cooling and compression scheme can be revealed[4, 5]. Although there now exist many temperature measurement techniques,for example [6, 7], the most commonly-implemented methods use the thermalexpansion of the cloud – time-of-flight (TOF) measurements – to estimate T [8, 9]. In this paper, we focus on the release-recapture (RR) which issensitive to the velocity distribution of the cloud. For temperatures at theDoppler limit (144 µ k for Rb) and above, as is the case in this work, theRR method is well-suited. At temperatures siginificantly below the Dopplerlimit, gravity begins to play a role in the thermal expansion of a cold cloudof atoms because the initial velocity of the atoms becomes small comparedto the velocity acquired due to gravity during the expansion phase.An optical nanofibre (ONF) [10, 11] is generally made from standardoptical fibre which is heated and simultaneously pulled to produce a sub-wavelength diameter fibre. ONFs can be used to couple light into opticalresonators [12, 13, 14, 15] and for characterising and guiding particles [16, 17].Spontaneous emission into the guided modes of an optical nanofiber is en-hanced [18], making it an ideal high-sensitivity tool for channeling atomicfluorescence to a detector. Thus, in recent years, ONFs have also beenshown to act as a measurement tool and delivery platform for cold atoms[19, 20, 21, 22, 23, 24, 25, 26] and atomic vapours [27, 28].Here, the RR method is performed by positioning a cold cloud of Rbatoms centrally around an ONF. Previous works show that, despite the pres-ence of the hot ONF surface in the cloud of cold atoms, sub-Doppler tem-peratures can still be obtained with large red-detunings of the cooling laserbeams [25].
2. Background
If a spherical cloud of atoms, with a Gaussian velocity distribution, isallowed to expand homogeneously from an initial finite diameter, the fractionof atoms, f r , remaining after the release time, ∆ t , is given by f r = 1 π / (cid:90) v c /v T e − u u du. π, (1)where u du. π is the spherical polar coordinate for velocity. The thermalvelocity of the atoms in the MOT at a temperature T is v T = (cid:112) k B T /m and v c = R c / ∆ t is the velocity at which the atoms just reach a position R c
2n the time interval ∆ t . The capture region is characterised by the radiusof the MOT beams, R c . Integrating Equation 1 yields: f r = − e − v cv T v c √ πv T + Erf (cid:20) v c v T (cid:21) . (2)Equation 2 describes f r as a function of ∆ t . This equation is fitted tothe experimental data by taking R c as known and v T is the fitting parameter.
3. Experiment
The cold Rb atom cloud is formed with a standard MOT configurationof three orthogonal, counter-propagating cooling beams intersecting at thecentre of an inhomogeneous magnetic field. The cooling laser is locked tothe crossover peak, S / F g = 3 → P / F e = (2 , co and then red-detunedfrom the cooling transition using an acousto-optical modulator (AOM). Thisdetuning is controlled by the frequency input (0–10 V) to the AOM driver.Each beam has a maximum diameter of 24 mm (controlled via an aperture).The repumping laser is locked to the crossover peak, S / F g = 2 → P / F e =(1 , co . The magnetic field is created by a pair of coils, each carrying currentsof ∼ and 10 atoms are trappedin the MOT depending on experimental parameters.To fabricate the ONF, the usual heat-and-pull-technique [29] is used withFibercore SM750 fibre. For these experiments, the transmission of the ONFwas ∼
60% and the waist diameter was ∼ µ m (as determined with a scanningelectron microscope). Further details about the experimental characteristicsof an ONF can be found in [22]. The fibre pigtails are coupled into andout of the UHV chamber using a Teflon feed-through [30] and one end isconnected to a single photon counting module (SPCM ). The cloud is alignedcentrally around the ONF using imaging techniques and optimisation of thefluorescence coupling into the fibre guided modes is detected by the SPCM.Final adjustments to cloud position are made with magnetic coil currents. Perkin and Elmer single photon counting module; model: SPCM-AQR-14; dark count= 100 counts s − ; quantum efficiency = 60% at 780 nm .1. Procedure The cooling laser beams were switched on and off with an AOM in orderto achieve the desired loading, release and recapture sequence (see Figure1). A recapture time, ∆ t , of 50 ms was used to ensure that no backgroundvapour atoms are recaptured by the MOT. The loading time of the MOT istypically ∼ Time 1. Load MOT for time Δ t
2. Release cloud (switch off MOT beams) for time Δ t
1. Recapture cloud for 50 ms (Δ t ) 0 t ONF Atom cloud
Figure 1: Illustration of the release and recapture sequence as a function of time. Thecloud is positioned centrally around the ONF. The cloud is loaded for a time ∆ t and thenreleased from the trap for a time ∆ t . ∆ t is varied from sequence to sequence to buildup a profile of the velocity of the atoms in the MOT. The recapture time, ∆ t , is set to 50ms. The cloud is then released once more for 50 ms, before repeating the entire sequence. To perform a temperature measurement, the cloud of atoms was loadedfor 10 seconds (∆ t ) to ensure a steady-state number of atoms was reached.Then, the cooling laser was switched off using the AOM for a time ∆ t toallow the cloud to expand freely. ∆ t is varied each time the sequence isrepeated: ∆ t = 5 ms, 10 ms, 20 ms, ... 150 ms. After the release timehas passed, the cooling laser is switched on for ∆ t =50 ms to recapture thecloud. The cooling beams are switched off again with the AOM for 50 ms4 N F ONF Cold Rb cloud Sequenced MOT beams +1-order to MOT beams Beamstop for 0-order RF signal (detuning)
RR sequence off on
Figure 2: Illustration of the experimental setup. The 1 st -order beam from an AOMis expanded and split into three equal-intensity cooling beams for the MOT. The Rbcloud is positioned centrally around the ONF. The cooling beams are switched on and offaccording to the sequence shown here with an AOM. Beam detuning is controlled via thetunable RF input on the AOM. to provide a suitable contrast between the signal from the recaptured atomsand the background level. The sequence is recommenced for the next value5f ∆ t . An image of the cloud is recorded using a CMOS camera and imageanalysis is performed to estimate the cloud radius.Following this release and recapture process, fast atoms escape the MOTafter a short release time and slower atoms are lost only after longer releasetimes. To estimate the temperature of the atoms, the fraction of remainingatoms is calculated as a function of ∆ t . This is proportional to the fluo-rescence coupled into the nanofibre. This method is sensitive to the velocitydistribution of the cloud.
4. Results and discussion
Temperatures approaching the Doppler limit have been observed at mod-erate detunings when the alignment of MOT beams has been particularlygood. For example, for a detuning of -2.6Γ (where Γ = 2 π × . S / → P / transition in Rb) with a coolinglaser intensity per beam, I beam , of 2.9 I s (where I s =1.6 mW/cm for σ ± -polarised light on the Rb cooling transition), T is estimated to be 167 µ K(Figure 3). Poor MOT beam alignment would mean that atoms may leavethe capture region in a non-isotropic way, the signature of which is an im-mediate and sharp decrease in recaptured atoms. The importance of preciseoptical alignment and power equalisation in the MOT beams is well known[31, 32]. For example, [31] reports a temperature and associated variationof (147 ± µK depending on the alignment of the laser beams. By usingthe ONF as the detection tool, the effect of beam misalignment and powermismatching is detectable with a greater sensitivity than for fluorescenceimaging techniques.The temperature of the cold atoms as a function of I beam was investigated(Figure 4) and measurements show that a span of a few hundred µ K can beobserved when varying I beam from 2.5 mW/cm to 6.7 mW/cm at a constantcooling laser red-detuning of ∼ R c is the quantity with the greatest uncertainty. A smallchange in R c ( ∼ . 0 0 0 . 0 1 0 . 0 2 0 . 0 3 0 . 0 4 0 . 0 5 0 . 0 6 0 . 0 70 . 00 . 20 . 40 . 60 . 81 . 0 4 5 . 0 4 5 . 5 4 6 . 0 4 6 . 505 0 01 0 0 01 5 0 02 0 0 02 5 0 03 0 0 0 Fraction of recaptured atoms
R e l e a s e t i m e , D t ( s ) B e s t f i t o f e x p e r i m e n t a l r e l e a s e - r e c a p t u r e c u r v e E x p e r i m e n t a l d a t a
B a c k g r o u n d l e v e l = 4 8 5 c o u n t s 7 3 % r e c a p t u r e d
Counts/s
T i m e ( s )
Figure 3: Fraction of recaptured atoms estimated from the fluorescence data obtainedfrom an optical nanofibre placed near the cold cloud of atoms. For a release time, ∆ t , of50 ms, 73% of the expanded cloud was recaptured with δ =-2.6Γ and cooling laser intensityof 2.9 I s (4.6 mW/cm ) per beam. igure 4: Temperature as a function of cooling laser intensity normalised to the saturationintensity, I s ( δ =-2Γ). The solid red line is a linear fit to the experimental data. Temperature ( m K) T o t a l c o o l i n g l a s e r i n t e n s i t y / s a t u r a t i o n i n t e n s i t y , I / I s T values whichhave been estimated with each method agree more strongly. Lower valuesof red-detuning were not easily examined with the ONF used for RR asthe sacrifice in N A was sufficient to lower the fluorescence coupling signalsiginificantly. Method
Red Detuning TemperatureΓ mK
Release recapture ± ± ± Forced oscillation ± ± ± ± Table 1: Variation of temperature with cooling laser red detuning in units of the naturallinewidth using two different measurement techniques. I beam was approximately 2.2 I s forrelease-recapture and 1.3 I s for forced oscillation. Forced oscillation data is taken directlyfrom [25]. From Figure 5, it is clear that temperatures obtained with the RR tech-nique increase linearly with the light-shift parameter, Ω / | δ | Γ, as expected[2]. The spring constant, κ , can be inferred from these temperature values. κ describes the restoring force in the MOT and is a particularly relevant quan-tity in relation to compressing atoms to high density. To determine κ it isassumed that, in thermal equilibrium, the atom cloud has a thermal energygiven by k B T = κ (cid:104) r (cid:105) = m (cid:104) v (cid:105) , where T is the experimentally-determinedcold atom cloud temperature, k B is Boltzmann’s constant, r is the radiusof the atom cloud, and (cid:104) v (cid:105) is the mean square atomic velocity [1, 4]. Foreach value of red-detuning, the cloud radius is estimated using image anal-ysis. Figure 6 shows that the spring constant increases with intensity atlow intensity or detuning values and then levels off at some critical value ofthe light-shift parameter. Wallace et al . [2] report that the spring constantis not independent of I beam until a moderately high value of the light-shiftparameter is reached. It is interesting to observe that, as evident in Figure6, κ levels off above light-shift parameter values of ≈
1. As the most dense9art of the cloud is being studied with the ONF, this may be an interestingobservation when compared to measurements done with photodiodes.
Temperature ( m K) L i g h t - s h i f t p a r a m e t e r , W / | d | G Figure 5: Temperature of the cloud as measured with RR plotted against the dimensionlesslight-shift parameter Ω / | δ | Γ (black circles) and a linear fit (red line) to the data.
As atom number is increased in the MOT, the regime of operation transi-tions from temperature-limited (TL) to multiple-scattering (MS) [34, 35, 36].In the TL regime, the cold atoms are essentially non-interacting because N A is small (typically less than 10 ) and the density is low. The cloud acts asan ideal gas in this regime, and, as more atoms are loaded into the trap, thesize of the cloud remains the same while the density increases linearly and itsdistribution remains Gaussian [37]. For larger N A ( ≥ ) the cloud beginsoperating in the MS regime and the density becomes largely independent of N A [38]. Two effects are seen in this regime. Firstly, repulsive forces causedby the re-absorption of scattered photons lead to an increase in the cloudsize while the density remains constant. This radiation trapping effect de-termines the density and temperature of cold atoms [3, 39]. For example, at N A ∼ the cloud density is maintained and the optical thickness is suchthat, on average, each photon absorbed from the cooling laser beams will,after re-emission, scatter no more than once on its way out of the cloud. This10 . 6 0 . 8 1 . 0 1 . 2 1 . 4 1 . 6 1 . 8 2 . 00 . 05 . 0 x 1 0 - 2 1 - 2 0 - 2 0 - 2 0 Spring Constant, k (N m-1) L i g h t - s h i f t p a r a m e t e r , W / | d | G Figure 6: Spring constant against dimensionless light-shift parameter Ω / | δ | Γ (black cir-cles) with a fit for a guide to the eye (red, solid line). determines the spatial growth of the cloud as N A increases beyond 10 [40].The second effect is due to an attenuation force which arises from the inten-sity gradients in the MOT beams and the absorption of such by the atoms[38, 41]. This results in spatial compression of the cloud and a small reduc-tion in spring constant of the trap [42]. When the MOT transitions from theTL to the MS regime, the atom distribution may or may not change fromGaussian to flat-topped. Thus, at higher cloud densities, cloud images maynot be a direct indicator of density. Measurements using an ONF negate theuse of imaging analysis to estimate cloud volume (for example, [39]) makingit simpler to observe regime-change in the MOT via fluorescence coupling.By considering an observation volume surrounding the ONF, cloud den-sity can be studied as the light-shift parameter is varied. It is assumed thatatoms within a hollow observation cylinder with an outer radius equal to theONF radius + 300 nm are most likely to emit fluorescence into the guidedmode of the ONF [19, 22]. This number of effective atoms, n eff , can beestimated at one end of the ONF using n eff = 2 C P /R sc η ONF Qη QD where R sc is the atomic scattering rate, η ONF is the average coupling efficiency ofphotons into the guided ONF mode in one direction (estimated at 2% using11revious work based on
Cs [43]), Q is the ONF transmission from the mid-dle of the ONF waist to the detector (the transmission through the entirelength of fibre is 60% so Q =77% for half the fibre length), and η QD is thequantum efficiency of the SPCM (60%). The quantity C P is the fluorescentcount rate obtained by the SPCM and is obtained from the RR raw data.The scattering rate, R sc is described by [35] R sc = Γ2 C Ω tot / δ + Γ / C Ω tot / . (3)Here, Ω tot is the Rabi frequency for all MOT beams and is taken to besix times that of any one of the trapping beams. C and C are averageClebsch-Gordan co-efficients. The values of C and C are assumed to beequal due to optical pumping among the Zeeman sublevels in the presenceof strong coupling between atoms and the radiation field [35].If n eff is plotted as a function of light-shift parameter, saturation of theatom number commences from Ω / | δ | Γ ∼
5. Outlook and conclusion
The temperature of a cold ensemble of Rb atoms has been measuredusing the RR method with an ONF. The RR sequence was applied to anAOM allowing the MOT beams to be switched off rapidly. The results pre-sented here agree with those found by the forced oscillation method [25] andagain reinforce the viability of placing the ONF in yet colder atomic sam-ples. This work has highlighted the sensitivity of the cloud temperature tosmall changes in beam misalignment, detunings, and intensities, and demon-strates the ability to detect these temperature changes with the ONF. Asthe detector can be positioned anywhere in the cloud of atoms, a systematictemperature measurement, while exploring the entire parameter space, canbe performed.Free-space RR measurements show that, with the same variation in lasercooling intensity as we have used, a few hundred µ K span can be observed.The results here display this trend and, additionally, provide detailed infor-mation about the velocity distribution of the atom cloud. In particular, withthe ONF-based RR method, the system is sensitive to atoms near the fibre12 . 5 0 0 . 7 5 1 . 0 0 1 . 2 5 1 . 5 0 1 . 7 5 2 . 0 0 2 . 2 50 . 0 00 . 2 50 . 5 00 . 7 51 . 0 01 . 2 51 . 5 01 . 7 52 . 0 0 neff
L i g h t - s h i f t p a r a m e t e r , W / | d | G Figure 7: Estimation of effective atom-number, n eff , with increasing dimensionless light-shift parameter Ω / | δ | Γ (black circles) with two linear fits to indicate the change in slopearound a light-shift parameter 1.2. surface and, using data analysis, it is possible to generate a decay curve thatshows how those near-surface atoms with a high velocity leave the captureregion quickly and do not continue to contribute to the signal detected viathe ONF.Values for the springs constant of the MOT, inferred from temperatureresults, increase with cooling laser intensity until some critical value of thelight-shift parameter is reached ( ≈
1) and then begin to level out. Further, byexamining coupling signal strengths while varying the light-shift parameter,the density regime in which the MOT is operating can be identified.13 . Acknowledgements
The authors wish to thank W. Cotter for help in creating the AOM se-quencing programme. This work is partially supported by Science Founda-tion Ireland under grant no.s 07/RFP/PHYF518 and 08/ERA/I1761 throughthe NanoSci-E+ Project NOIs, OIST Graduate University and the HigherEducation Authority via the INSPIRE programme. LR acknowledges sup-port from IRCSET under the Embark Initiative.
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