ULTRACOLD METASTABLE HELIUM-4 AND HELIUM-3 GASES

ULTRACOLD METASTABLE HELIUM-4 AND HELIUM-3 GASES W. VASSEN, T. JELTES, J.M. MCNAMARA, A.S. TYCHKOV, W. HOGERVORST Laser Centre Vrije Universiteit Amsterdam, The Netherlands K.A.H. VAN LEEUWEN Dept. of Applied Physics, Eindhoven Univ. of Technology, The Netherlands V. KRACHMALNICOFF, M. SCHELLEKENS, A. PERRIN, H. CHANG, D. BOIRON, A. ASPECT, C.I. WESTBROOK Lab. Charles Fabry de l Institut d Optique, Univ. Paris-Sud, Palaiseau, France We discuss our work to obtain a condensate containing more than 10 7 atoms and the first degenerate Fermi gas in a metastable state. Sympathetic cooling with Helium-4 is used to cool 10 6 Helium-3 atoms to a temperature T/T F < 0.5. The ultracold bosonic and fermionic gases have been used to observe the Hanbury Brown and Twiss effect for both isotopes, showing bunching for the bosons and antibunching for the fermions. A proposal for high resolution spectroscopy at 1.557 μm, connecting both metastable states directly, is discussed at the end. 1. Introduction Helium in the metastable 2 3 S 1 state has been Bose condensed in 2001 by two French groups [1,2]. Since then research on ultracold metastable helium gases has been concentrated on determining the scattering length, measuring loss processes, studies of the hydrodynamic regime and producing longrange molecules. In 2005 two other groups realized BEC in metastable helium [3,4]. Studies of atom-atom correlations in ultracold clouds of 4 He bosons were started around that time as well, exploiting the unique detection properties of metastable atoms [5]. In this contribution we will discuss experiments performed in Amsterdam. We will discuss the setup in which a BEC containing over 10 7 atoms and a degenerate Fermi gas (DFG) of metastable 3 He containing over 10 6 atoms was realized. Next we discuss experiments where the Amsterdam and Orsay/Palaiseau groups joined forces measuring the Hanbury Brown and Twiss effect both for a gas of ultracold 1

2 bosons and a cloud of ultracold fermions, demonstrating atom bunching for 4 He and atom antibunching for 3 He. 2. Helium level structure and relevant parameters Relevant energy levels are shown in Fig. 1. The helium atom is strongly LScoupled effectively leading to two spectra, that of parahelium, where the electron spins are antiparallel and that of orthohelium where the spins are parallel. The ground state of orthohelium (1s2s 3 S 1 or He*) can be laser cooled with laser light of 1083 nm exciting the 1s2s 3 S 1 1s2p 3 P (2 3 S 2 3 P) transition. The 2 3 S 1 state, populated in a DC discharge, has a lifetime of ~8000 s which is infinite for all practical purposes. Its 20 ev internal energy provides the unique detection possibilities: (almost) everything a He* atom hits gets ionized and the released electron can be counted with high efficiency using electron multipliers or microchannel plate (MCP) detectors. metastable state: 1s2s 3 S 1 ( 4 He*) F= 1/2,3/2 ( 3 He*) Figure 1: Level scheme showing the relevant energy levels for laser cooling and trapping of 4 He in the 2 3 S 1 state (M J =+1 in a magnetic trap). The 2 3 S state is split in a F=3/2 and a F=1/2 state (ΔE=6740 MHz) in the case of 3 He. The F=3/2 state has the lowest energy and is used for cooling and trapping (M F =+3/2 in the magnetic trap).

3 Losses in ultracold He* gases, either in a magneto optical trap (MOT) or a magnetic trap, are mainly due to two-body inelastic Penning ionization where one ion and one ground state atom are produced in a collision. The loss rate constant for this process in an unpolarized gas is quite large: ~1 10-10 cm 3 /s in the dark and ~4 10-9 cm 3 /s in the light of a MOT [6,7]. When the atoms are in a fully stretched state (as in a magnetic trap) these losses are suppressed in first order and the rate constant drops to ~1 10-14 cm 3 /s. In the fully stretched state of 4 He* ( J,M J >= 1,+1>) Penning losses are therefore acceptable and a BEC can be realized. The 4 He*- 4 He* scattering length a 44 that determines many properties of a BEC has recently been measured with high accuracy: a 44 (exp)= +7.5105 (25) nm [8]. Recent ab initio calculations of the molecular potential have allowed an astonishing accuracy in the calculation of a 44 as well and approach the experimental accuracy: a 44 (theory)= +7.562 (28) nm [9]. Mass scaling of the potential then provides a theoretical value of a 34 (theory)= +27.1 (5) nm for the scattering length determining the collision rate between spin-polarized 3 He* and 4 He* atoms [9]. 3. The experimental apparatus Laser cooling and trapping of He* atoms is performed at a wavelength of 1083 nm. As the isotope shift is 33 GHz we use two separate laser systems, each laser locked to the cycling transition of the relevant isotope in a DC discharge cell. The experimental setup is shown in Figs. 2 and 3. We use a liquid nitrogen cooled DC discharge source, which uses recycling of helium atoms from the turbo pump exhaust via molecular sieves. + 1 deflection Figure 2: Schematic of the experimental setup used to trap 3 He* and 4 He* atoms. The collimation section (two-dimensional) significantly improves the MOT loading. A deflection zone (in the horizontal plane) prevents ground state atoms entering the 2 m long Zeeman slower.

4 J. M c Namara Turbo Pump 1 Turbo Pump 2 Figure 3: Schematic of one-dimensional Doppler cooling in the cloverleaf magnetic trap (left) and UHV chamber (right; the arrow indicates the absorption imaging beam). The coils are located in plastic boxes positioned inside the re-entrant window flanges. We typically load 2 10 9 4 He* atoms or 1 10 9 3 He* atoms in 1 s in a MOT at a temperature of 1 mk. After a short spin polarization pulse the atoms are loaded into a spherical cloverleaf trap matching the MOT cloud. The high (24 G) bias magnetic field in this geometry allows efficient 1-dimensional Doppler cooling to a temperature of 0.15 mk (in 2 s), shrinking the cloud considerably and increasing the phase space density about a factor 600 to a value around 10-4 - 10-5 [3]. In another 2 s the cloud is compressed at small bias field (~3 G). The trap lifetime is 2 3 minutes (either 3 He or 4 He). To produce a BEC we perform a 15 s rf evaporative cooling ramp realizing a BEC containing (1.5 4) 10 7 4 He* atoms [3]. We monitor the BEC applying absorption imaging at 1083 nm (not very efficient due to the low efficiency of CCD cameras at 1083 nm) or on an MCP detector mounted directly under the trap (see Fig. 4). The latter technique is very sensitive allowing us to monitor a BEC after up to 75 s trapping inside the magnetic trap. To monitor the growth of a condensate we use a second MCP detector that attracts all ions produced by Penning ionization. As soon as the condensate starts to grow a dense cloud forms and the ion signal suddenly increases [3]. The lifetime of our condensate is about 1 s. We studied this as a function of the thermal fraction and found that a large thermal fraction reduces the lifetime of the condensate considerably. We attribute this to transfer of condensate atoms to the thermal cloud during condensate decay. A simple model that assumes thermal equilibrium during the decay confirms this and allows extraction of the two- and three-body loss rate constants [3,10].

5 4 He* 3 He* 3 He*+ 4 He* Figure 4: Time-of-flight pictures of a BEC (upper figure), a DFG (middle figure) and a mixture (lower figure). The upper figure shows three plots, each with a slightly different end rf frequency, showing a thermal cloud above the BEC temperature, a mixture of BEC and thermal cloud, and a pure BEC with the typical inverted parabola shape. In the middle figure a fit to a Fermi-Dirac distribution is shown from which we extract a temperature T=0.45 T F. In the lower figure the dashed-dotted line shows the BEC contribution to the signal and the dashed line the DFG contribution.

6 m=+1 B m=0 BEC B 0 Figure 5: He* atom laser, realized by repeatedly output coupling of a fraction of the BEC in 250 MHz/s ramps. The time-of-flight signal shows the effects of mean-field repulsion. We can couple out a small fraction of the atoms from a condensate applying an rf ramp as shown in Fig. 5. We applied repeatedly a 250 MHz/s rf ramp to couple atoms out of the condensate showing a typical atom laser pulse shape, revealing mean-field repulsion. To produce a degenerate Fermi gas a we load a MOT with both isotopes [3,6,7,11,12]. With an equal number of both isotopes in our gas reservoir we trap 1 10 9 4 He* atoms and 7 10 8 3 He* atoms in a MOT. However, we can not cool so many fermions and therefore reduce the number of fermions to 1-10% of the number of bosons. The large heteronuclear scattering length provides almost ideal conditions for sympathetic cooling and we obtain a DFG containing 2 10 6 3 He* atoms at T/T F =0.45 (Fig. 4) as well as a degenerate mixture (also Fig. 4). Three-body losses probably limit the lifetime of this mixture to ~10 ms [12]. 4. Hanbury Brown and Twiss experiments In 2005 the atomic analogon of the Hanbury Brown and Twiss (HBT) effect was demonstrated for metastable 4 He* atoms released from a cloverleaf magnetic trap very similar to the one in Amsterdam [5]. The HBT effect, first demonstrated for light in the fifties of the 20 th century [13], represents the measurement of the two-body second-order correlation function * r * r r r r r ( ) ( ) (2) r r E ( ) E ( ) E( ) E( ) I I g (, ) = * r r = 2 r 2 E ( ) E( ) I( ) displaying the joint probability of detecting two atoms (or photons) at locations r and r. For incoherent sources this function equals 1 for large separations and will tend to 2 for bosons and 0 for fermions, for detector

7 separations smaller than the correlation length l: bosons bunch and fermions antibunch. In the Amsterdam experiments we demonstrated bunching for 4 He* and antibunching for 3 He* trapped in identical traps at the same temperature [14]. For this purpose the position sensitive detector (PSD) of the Orsay (now Palaiseau) group was transported to Amsterdam and mounted under the Amsterdam UHV chamber (which is shown in Fig. 3). The detection part of the setup is shown in Fig. 6, showing on the left the PSD and on the right a schematic of the measurement. The correlation function for a measurement of atoms released from a harmonic trap is given by [14] 2 2 2 (2) Δx Δy Δz g + + th ( Δx, Δy, Δz) = 1± ηexp - lx ly lz ht with correlation lengths in each of the three spatial directions li = msi 2 where s k T mω, m the mass of the atom, T the temperature, t the i = B i drop time and ω i the trap frequency. The contrast η (0-1) depends on the detector resolution in all three spatial dimensions. This two-particle detector resolution is 6 nm in the vertical (z-) direction and 500 μm in the horizontal plane of the detector. As the correlation length in the x-direction is much smaller than the detector resolution in that direction (we have a cigar-shaped trap with long axis in the x-direction) η is on the order of 1/15. Figure 6: Position-sensitive MCP detector and schematic of the experiment. The inset of the figure on the right conceptually shows the two 2-particle amplitudes that interfere to give bunching or antibunching.

8 As the detector resolution is very good in the vertical plane, we plot the measured correlation function along the z-direction in Fig. 7. This plot was obtained by averaging over about 1000 clouds per isotope, with ~10 4 detector points per shot. The temperature was 0.5 μk. We also measured the correlation function along the y-direction, however with substantial broadening along the horizontal axis due the 500 μm resolution in the x-y plane [14]. Fig. 7 clearly demonstrates antibunching for fermions and bunching for bosons, over a macroscopic distance of ~1 mm. The measured ratio of the correlation lengths is 1.3 ± 0.2, which is as expected, realizing that the cloud sizes of both isotopes in the trap are equal, the drop times are equal and the mass ratio is 4/3. Also the individual correlations lengths agree very well with the formula l z = ħ t / m s z. We observe a small discrepancy in the amount of contrast for both isotopes. There are two possible experimental imperfections that affect the bosons and fermions differently and that may explain this, i.e. the non-sudden trap switch-off and the determination of the detector resolution function. 4 He * - boson 3 He * - fermion Figure 7: Normalized correlation functions for 4 He* in the upper plot and 3 He* in the lower plot, measured in the same trap at the same temperature of 0.5 μk. Error bars correspond to the square root of the number of pairs in each time bin. The line is a fit to a Gaussian function. Correlation lengths of 0.75 ± 0.07 mm and 0.56 ± 0.08 mm for fermions and bosons, respectively, are extracted.

9 Figure 8: Measured temperature dependence of correlation length and contrast. The curves are calculations and describe the measurements reasonably well. We took data for fermions at 0.5 μk, 1.0 μk and 1.4 μk. The fit results for l z and η are shown in Fig. 8 together with the calculated results. The limited resolution in the horizontal plane can be circumvented by using a negative atom lens, reducing the apparent size of the cloud in the horizontal plane. This does not affect the correlation length in the vertical plane but does affect the contrast via the correlation length l y, which increases. To implement this we focused a 300 mw laser beam, with elliptical waist and 300 GHz blue detuned from the 1083 nm transition, for 0.5 ms through the expanding 3 He* cloud after switching off the magnetic trap. The results are shown in Fig. 9 and qualitatively agree with expectations. without lens with lens Figure 9: Normalized correlation functions along the z (vertical) axis for 3 He*, demonstrating the effect of a diverging atomic lens in the x-y plane. The light circles are without lens and the dark squares with lens. The dip is deeper with the lens because the correlation length in the y- direction is increased which affects the contrast (and not the correlation length in the z- direction).

10 Figure 10: Raw data of an atomic lens experiment with fermions. The data show the numbers of pairs measured for a 25 μs time bin (1 ms corresponds to a vertical separation of 3.5 mm). They are averaged over 1000 shots. We wish to emphasize that the antibunching effect in Fig. 7 is big enough that significant processing of the data is not necessary. Fig. 10 shows the raw data of one of our runs before normalizing the data. Normalization (to get the data of Figs. 7 and 9) is done by dividing the raw data by the autoconvolution of the sum of the 1000 single-particle distributions. Therefore the raw data show the antibunching effect as well as the Gaussian spatial distribution of the cloud. 5. Proposed metrology experiment As one of the possible applications of samples of ultracold 4 He* and 3 He* atoms we envision to excite the forbidden 2 3 S 1 2 1 S 0 transition at 1.557 μm [15]. This transition is only magnetic-dipole (M1) allowed with an Einstein A-coefficient of 6.1 10-8 s -1 [16]. The high-resolution potential is very large as the natural linewidth of the transition is 8 Hz, fully determined by the 20 ms lifetime of the 2 1 S 0 metastable state due to two-photon (2E1) decay to the ground state. Measuring this transition will directly link the orthohelium and parahelium system (see also Fig. 1). The absolute frequency (for both isotopes) will provide sensitive tests of atomic theory for twoelectron systems, measuring QED contributions which are large for S-states. Measuring the isotope shift, the main theoretical inaccuracy is in the difference in mean nuclear charge radius of the 4 He and 3 He nucleus.

11 To measure the transition we theoretically investigated two setups: (1) spectroscopy with a laser-cooled and collimated atomic beam as provided from the Zeeman-slower and (2) spectroscopy in a one-dimensional optical lattice, loaded from a magnetically trapped and evaporatively cooled cloud. For both situations we solved the optical Bloch equations simplifying the model neglecting the decay from 2 1 S to 2 3 S as well as the decay from 2 3 S to 1 1 S (see Fig. 11). For the beam experiment we assume a 100 m/s Zeemanslowed atomic beam, transversely cooled to twice the Doppler limit. With an atomic beam intensity of 10 11 atoms per second, a 2 W 100 khz laser beam (1cm 1cm excitation region) will provide an on-resonance Rabi frequency Ω= 61 s -1, which for an excitation time of 100 μs will lead to an excited state population ρ 22 =4.6 10-7. A considerable flux of 5 10 3 atoms per second in the 2 1 S state then may be expected. Figure 11: Relevant energy levels for 2 3 S 1 2 1 S 0 spectroscopy and decay rates. The expected spectroscopic linewidth is 400 khz in this case, limited by Doppler broadening. Using 1083 nm light resonant with the 2 3 S 1 2 3 P 2 transition the nonexcited atoms can simply be deflected realizing a (hopefully) zero-background signal on a metastable atoms detector. A schematic view of the proposed setup, with three laser-atomic-beam crossings depicted, is shown in Fig. 12. Fig. 12: Schematic of the proposed setup to measure the 2 3 S 1 2 1 S 0 transition in a beam.

12 The one-dimensional lattice has more potential to achieve high accuracy. In the experiments described in Section 4 an ultracold cloud at temperatures around 1 μk of 3 He*, 4 He*, or a mixture was presented. Such a cloud may be transferred to a far off-resonance dipole trap (FORT). When a single retroreflected beam is used a one-dimensional lattice results which, when a wavelength of 1.557 μm is used, can easily trap a cloud from our cloverleaf trap at a temperature of a few μk. The experiment may be performed using the same 2 W laser as discussed in the beam experiment as the trapping potential is insensitive to the wavelength on a scale of an experiment on the forbidden transition. A narrower linewidth laser, though, is useful here as the width of the spectroscopy signal will now be limited by the laser linewidth as Doppler broadening is suppressed by Lamb-Dicke narrowing. Detection is now more challenging as the 2 1 S atoms are anti-trapped and slow. Photo ionization, or detection of ions due to Penning ionization with trapped 2 3 S atoms, are then options to consider. The accuracy of the spectroscopy in the lattice will be limited by how well the AC Stark shift due to the lattice potential can be controlled and measured. Calculations predict a 2 MHz shift of the transition at the maximum of the potential (the atoms are trapped in the light as the 1.557 μm wavelength is red detuned from the 1083 nm transition). The best experiment therefore will be to trap at a magic wavelength (where the AC Stark shifts of the metastable states are equal), which will not be easy as the highest magic wavelength available is 410 nm at which wavelength very high laser power is required to trap He* atoms. A second magic wavelength occurs at 351 nm and may be more suitable for spectroscopy on this forbidden transition. References 1. A. Robert, O. Sirjean, A. Browaeys, J. Poupard, S. Nowak, D. Boiron, C. Westbrook, A. Aspect, Science 292, 461 (2001). 2. F. Pereira Dos Santos, J. Léonard, J. Wang, C.J. Barrelet, F. Perales, E. Rasel, C.S. Unnikrishnan, M. Leduc, C. Cohen-Tannoudji, Phys. Rev. Lett. 86, 004359 (2001). 3. A.S. Tychkov, T. Jeltes, J.M. McNamara, P.J.J. Tol, N. Herschbach, W. Hogervorst, W. Vassen, Phys. Rev. A 73, 031603(R) (2006). 4. R.G. Dall, A.G. Truscott, Opt. Comm. 270, 255 (2007). 5. M. Schellekens, R. Hoppeler, A. Perrin, J.V. Gomes, D. Boiron, A. Aspect, C.I. Westbrook, Science 310, 648 (2005).

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