PHYSICAL REVIEW LETTERS

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1 PHYSICAL REVIEW LETTERS VOLUME JULY 1998 NUMBER 3 Searated-Path Ramsey Atom Interferometer P. D. Featonby, G. S. Summy, C. L. Webb, R. M. Godun, M. K. Oberthaler, A. C. Wilson, C. J. Foot, and K. Burnett Clarendon Laboratory, Deartment of Physics, University of Oxford, Parks Road, Oxford, OX1 3PU, United Kingdom (Received 12 March 1998) We demonstrate a novel tye of cesium atom interferometer which uses a combination of a microwave ground state transition and momentum changing adiabatic transfer light ulses as the atom otical comonents. It is the first atom interferometer where the mechanism which forms the internal suerosition lays no art in satially slitting the atomic wave ackets. The coherence length of the atom source is found by measuring the satial correlation between the two interferometer arms. This allows us to determine the temerature of the atomic ensemble. [S (98) ] PACS numbers: Dg, Lg, q, Vk In the ast few years atomic matter wave interferometry has become a valuable tool for robing rocesses such as accelerations, scattering amlitudes, and fundamental quantum henomena [1]. These exeriments work by forming a closed loo interferometer in which a wave acket is coherently slit into two aths which eventually overla so that interference can occur. In this Letter we resent results from an atomic interferometer of a unique design in which the internal and external states of a cesium atom are maniulated searately to roduce such a closed loo. The foundation of our exeriment is the well-known Ramsey interferometer [2] shown in Fig. 1(a). This consists of two searated oscillatory field interactions which create suerositions of the internal states. To observe the interference fringes we change the hase of the final interaction so that the accumulated hase difference between the internal states is transformed into a difference in oulation. The fringes from such an exeriment can be seen in Fig. 2(a). The closed loo Mach-Zehnder-tye interferometer, shown in Fig. 1(b), is created by taking the basic Ramsey configuration and maniulating the external state of each internal suerosition comonent in turn. This is done in a way such that the two internal states have the same final external state and can be recombined. Results from this exeriment are shown in Fig. 2(b), where the oulation of one internal state is lotted as a function of the hase of the last interaction which internally maniulates the atom. Exerimentally, the searated oscillatory fields are roduced by microwaves and the external state (atomic momentum) is controlled using adiabatic transfer (AT) light ulses. Figure 3 shows the sequence of interactions used to create the interferometer. This scheme has the advantage that the mechanism forming the coherent suerosition and the rocess slitting the aths are indeendent. This facilitates a greater amount of exerimental control. We erformed an exeriment to examine the deendence of the interference fringe visibility and hase on the final satial overla of the wave functions in the two arms. A major feature of this exeriment was the reduction in visibility as the searation between the outut wave functions was increased. Measuring the loss of visibility allowed us to extract the satial correlation function and from this the one-dimensional temerature of the atomic ensemble in the direction of the interferometer arm searation. Temerature measurements using an alternative aroach for determining the satial correlation function have also been recently reorted by Saubaméa et al. [3]. The use of AT in atom otics has been described by a number of different authors [4]. The essence of the method is to use a light field configuration for which a articular suerosition of the atomic ground states cannot coule to the excited state. If the light field is changed adiabatically [5], an atom which is initially decouled remains decouled by adjusting its ground state (3) 495(5)$ The American Physical Society 495

2 FIG. 1. Exerimental configurations used to observe interference, with oen and solid circles tracing the dynamics of the atomic oulation. The hashed circles at the outut reresent the uncertainty in determining which ath the oulation has taken. In (a) we see the sequence of microwave 2 ulses used for the Ramsey scheme. The setu for the searated ath interferometer can be seen in ( b). The main difference between these two exeriments was the introduction of two AT ulses to searate the wave ackets. Since AT light could only interact with atoms in the F 4 level, an additional microwave ulse was also alied to make the searated-ath interferometer symmetric. The width and length of this interferometer was aroximately 1 and 40 mm, resectively. configuration according to the state of the field. When the atom is in this dark state, sontaneous emission is suressed and the coherence of the atom is reserved. Our dark state scheme involves orthogonally roagating light fields of linear () and circular (s 1 ) olarizations which are resonant with the D 1 6S 1 2, F 4! 6P 1 2, F 0 4 transition. With this configuration the ground state oulation can be transferred from F 4, m 0 to F 4, m 14. If the oulation is initially in F 4, m 0, all of the light must start in the linearly olarized beam for the atom to be dark. After all of the intensity has been slowly transferred into the circularly olarized beam the atom is found in the m 4 state. The atom is dark at the start and finish of this interaction by the diole selection rules alone. At intermediate times the atom is in a suerosition of the magnetic substates between m 0 and m 4 which is dark because of the destructive interference of the excitation amlitudes from the substates. Since this rocess is coherent, the atom absorbs four hotons from the s 1 beam and emits four hotons into the beam, roducing a total momentum change of 4 2 hk. FIG. 2. Fringes from (a) Ramsey (visibility 95%) and ( b) searated ath interferometers (visibility 35%). The final oulation of the F 4 state is lotted against the hase of the last 2 microwave ulse. In (b), the reresents data obtained using two AT ulses ( large final satial overla) and the shows results with only the second AT ulse (no final satial overla). The solid line is a sinusoidal fit to the data. Error bars are of the same order as the oint size. It is undesirable to leave the atomic oulation in m 4 because magnetic fields may introduce unwanted hase shifts. Thus, once m 4 is reached, the AT is reversed in time so that the oulation is returned to m 0. Although the net momentum transfer of such a rocess is zero, FIG. 3. Sequence of events for the searated ath exeriment starting from the alication of the first microwave ulse. The Ramsey interferometer was realized by only erforming the two 2 microwave ulses. The final satial overla was varied by changing the duration of the last AT rocess t 2, while the first AT length t 1 was ket constant. The hashed AT ulse could also be omitted, as was done in the data of Fig. 2(b). 496

3 a small dislacement is roduced because of the finite momentum of the atom during the ulse. With this out and back sequence it is ossible to realize dislacements of aroximately 1 mm in a ulse time of 100 ms. This technique can be extended to a method for beam slitting into two aths by initially creating a suerosition of the m 0 comonents of the F 3 and F 4 ground levels with a 2 ulse of microwaves. The momentum of the F 4 comonent of the suerosition can then be maniulated with the 2s 1 2AT sequence [6] so that the F 3 and F 4 levels satially searate. Our atomic source consisted of a magneto-otic tra (MOT) of aroximately 10 7 atoms which was cooled in an otical molasses. The temerature of these atoms, measured with a time of flight technique, was found to be aroximately 3 mk. After the molasses beams were turned off, the atoms fell and were otically umed into the F 3 ground state by a ulse of resonant F 4! F 0 4 light. The atoms then underwent the sequence of microwave and AT ulses which constituted the interferometer. The microwave source was formed by a iece of X-band waveguide with a 1 cm hole located half a wavelength from its blanked-off end. When the atoms exerienced the microwaves they were aroximately 2.5 cm above the waveguide hole. A weak bias field of 10 mg was alied in the z direction to set u a quantization axis for the atoms and lift the degeneracy of the Zeeman substates to allow discrimination of the various microwave transitions by frequency. Thus we could be certain of exciting only the m 0! m 0 transition. Light for the AT was generated by a Ti:sahire laser locked to the F 4! F 0 4 transition of the D 1 line at 894 nm. Each AT ulse had an efficiency of aroximately 60%. Our Ramsey fringe and searated ath interferometry schemes both started with the alication of a 2 ulse of the microwaves to create an equal suerosition of the F 3, m 0 and F 4, m 0 states. To observe the Ramsey fringes of Fig. 2(a) we alied an additional microwave ulse with a 2 configuration. Ramsey fringes are normally obtained by changing the frequency of the microwave field; however, in our exeriment we scanned the hase of the final 2 ulse and ket the frequency constant so that our fringes were not modulated by the line shae of the microwave transition. The final signal was obtained by measuring the oulation of the F 4 state via the absortion of robe light resonant with the 6S 1 2, F 4! 6P 3 2, F 0 5 transition. The full interferometer shown in Fig. 1( b) was realized by modifying the Ramsey scheme so that AT was carried out immediately after the first and just before the last microwave ulse. The first AT was used to slit the aths and the second reestablished the satial overla between the comonents of the suerosition. After the first AT, a ulse of microwaves was alied to swa the F 3 and F 4 comonents of the suerosition. This reserved the overall symmetry of the interferometer and also obviated the need for the second AT to be carried out with laser beams in the oosite direction. Both AT ulses were erformed with the same two orthogonal laser beams which had a diameter of 2 cm and a tyical intensity of 10 mw cm 2. The final stage of the interferometer sequence was a 2 ulse of microwaves which recombined the states of the suerosition. Tyical fringes from this setu can be seen in Fig. 2( b). In this figure we also show data obtained using the same exerimental arameters for the AT, but with the critical difference that only the second AT ulse was alied. This searated the aths of the interferometer without having the additional reoverlaing ulse. The result of this exeriment was that fringes were no longer observed. This is interreted as being the effect of the searation between the arms becoming greater than the transverse coherence length of the source. We now discuss a method for estimating the temerature of the atomic source based uon a measurement of its coherence length. Our robe beam detected an absortion signal S, roortional to the final oulation of the F 4 state. This can be written as S ~ jc i x j 2 dx, (1) where c i x f i x 1 g i x 2 a, and the F 4 wave functions in the two arms f i x ; g i x 2 a are searated by a distance a. We have also summed over the contributions of all N atoms in our ensemble. If S max and S min reresent the maximum and minimum values observed in an interference signal, then a general exression for the fringe visibility is V S max 2 S min S max 1 S min. (2) Using this definition, it can be shown that the visibility of the fringes formed by scanning the hase of the final microwave ulse is roortional to the sum of the satial correlations of the wave functions found in the exansion of Eq. (1). That is, V a ~ Re f i x g i x 2 a dx. (3) Taking the Fourier transform of Eq. (3), we obtain V a e 2ika da ~ Re Fi k G i k, (4) where F i k and G i k reresent the momentum distributions of the ith wave acket and are the Fourier transforms of f i x and g i x. Assuming that F i k and G i k are roortional [7], the sum in Eq. (4) becomes the momentum distribution of the atomic ensemble, from which a determination of the temerature can be made. 497

4 We now discuss the exeriment we erformed to measure the visibility function V a. To create various arm searations a, both aths of the interferometer exerienced AT ulses of slightly different durations. After a single AT ulse of length t, the exectation value of the wave function osition is x 2 2 y recoil t, where y recoil is the recoil velocity due to the absortion of one hoton. We have assumed that during the AT ulse the atom has an average momentum of 2 and 22 hoton recoils in the direction of the s 1 and beams, resectively [8]. If the AT ulses exerienced by each arm are the same, then erfect satial overla at the outut of the interferometer is assured. However, if the ulse lengths are slightly different, we then create a satial searation a given by a 2 2 y recoil t 2 2t 1, (5) where t 1 and t 2 are the durations of the first and second AT rocesses, resectively. Exerimentally there are two imortant oints to consider. Firstly, the velocity selection caused by the AT should be very similar for each ulse. Secondly, the effects of light induced decoherence should remain relatively constant as different length AT rocesses are used. This can be achieved by adding an extra comensating eriod of olarized light when an AT is shortened, so that the total duration of exosure to the light is conserved. This is exlained schematically in Fig. 3. With these oints in mind, we measured the visibility and fringe hase shift as a function of the time difference between first and second AT rocesses. The results dislayed in Fig. 4 were obtained by maintaining the first AT duration at 25 ms while changing the length of the second ulse. As we exected, the visibility fell off as the difference between the ulses increased because the satial overla of the wave functions was reduced. We have fitted a Gaussian to this data and then alied Eq. (5) to find the visibility function V a. With Eq. (4) it is ossible to determine the half width at 1 e of the momentum distribution in k sace, Dk. We can equate this to a temerature [9] which, for the data of Fig. 4, is found to be mk. This is a little colder than the value found using the time of flight technique, but is consistent with the AT being slightly velocity selective. In Fig. 4( b) the hase of the fringes is lotted for different values of t 2 2t 1.These results are exlained well by a consideration of kinetic energy. During an AT ulse of length t, the wave function exeriences a kinetic energy hase shift, w 1 2 M Cs h 2 2 y recoil 2 t t. (6) This function is lotted in Fig. 4(b) (solid line) and rovides an excellent fit to the data. In rincile, the gradient of this line could be used to determine h M Cs. FIG. 4. (a) Visibility and ( b) hase shift as a function of the ulse length difference between the first and second AT rocesses t 2 2t 1. The Fourier transform of the Gaussian fit gives the momentum distribution and allows a determination of the atomic temerature to be made. In (b) the solid line reresents calculated results (with no adjustable arameters) for the hase shift due to the kinetic energy [Eq. (6)]. In this Letter we have resented the first results from a new tye of searated ath matter wave interferometer for cesium atoms. The interferometer used a sequence of ground state microwave interactions and otical adiabatic transfer ulses. The microwaves were used to create a suerosition of the ground hyerfine levels, and the adiabatic transfer then selectively maniulated the momentum of the F 4 comonent of this suerosition. We have demonstrated interference between satially searated aths and have develoed a method for measuring the temerature of our atomic ensemble. The future of this interferometer design seems romising. We are working towards using an AT scheme that will allow larger satial searations to be realized. This can be achieved by modifying the current technique so that when the atom reaches the m 4 state the laser beam directions are reversed and the atom is transferred back to m 0 with a net change in its momentum of 8 2 hk. Since the atom can be ket in this state without significant magnetic field interactions, it should be ossible to achieve searations between the arms of the interferometer of a macroscoic size. This work was suorted by the UK EPSRC and the EU as art of the TMR Coherent Matter Wave Interactions network, Contract No. EBRFMRXCT

5 [1] For an overview of the subject, see Atom Interferometry, edited by P. Berman (Academic Press, San Diego, 1997). [2] Molecular Beams, edited by N. F. Ramsay (Oxford University Press, Oxford, 1986). [3] B. Saubaméa et al., Phys. Rev. Lett. 79, 3146 (1997). [4] P. Marte, P. Zoller, and J. Hall, Phys. Rev. A 44, R4118 (1991); P. Pillet et al., Phys. Rev. A 48, 845 (1993); J. Lawall and M. Prentiss, Phys. Rev. Lett. 72, 993 (1994); L. Goldner et al., Phys. Rev. Lett. 72, 997 (1994); M. Weitz, B. Young, and S. Chu, Phys. Rev. Lett. 73, 2563 (1994); P. Featonby et al., Phys. Rev. A 53, 373 (1996). [5] J. Kuklinski et al., Phys. Rev. A 40, 6741 (1989). [6] This rocess is what is meant by the term AT for the remainder of this Letter. [7] This is a valid aroximation as long as the AT causes no velocity selection. A model of the 2s 1 2AT that we have develoed indicates that velocity selection for a 3 mk samle of atoms is only significant when the ulse length is greater than aroximately 20 ms. We have also confirmed this exerimentally. [8] This has been verified by the theory alluded to in Ref. [7]. [9] The temerature T is defined via k B T h 2 Dk 2 M Cs, where M Cs is the mass of a cesium atom.vadjust 499