Requirements for coherent atom channeling 1

Size: px

Start display at page:

Download "Requirements for coherent atom channeling 1"

Magnus Powell
5 years ago
Views:

25 May 2000 Ž. Optics Communications 179 2000 129 135 www.elsevier.

1 25 May 2000 Ž. Optics Communications Requirements for coherent atom channeling 1 Claudia Keller a,b,), Jorg Schmiedmayer b, Anton Zeilinger a,b a Institut fur Experimentalphysik, UniÕersitat Wien, Boltzmanngasse 5, A-1090 Wien, Austria b Institut fur Experimentalphysik, UniÕersitat Innsbruck, Technikerstraße, 25 A-6020 Innsbruck, Austria Received 30 September 1999; received in revised form 19 January 2000; accepted 24 January 2000 Abstract The evolution of atomic de Broglie waves inside strong periodic potentials can be described as channeling and exhibits both particle and wave effects. Using a beam of metastable Argon atoms interacting with an intense standing light wave we detect an interference pattern arising from the coherent guiding of the atoms through the light channels. In analogy to light optics these interference effects are only visible, if certain requirements for longitudinal and transverse coherence are fulfilled. We experimentally study the influence of the velocity selection and the collimation of the Argon atoms. As well as an another factor determining the coherence of the evolution the spontaneous emission. q 2000 Elsevier Science B.V. All rights reserved. PACS: qq; Be; Kb; Dg 1. Introduction The interaction of waves with periodic potentials is an extensively studied subject. In the case of long interaction times, the evolution inside the potential cannot be neglected. This arises particularly for X-ray and neutron diffraction at solid crystals. There the coupling between the incident wave and the periodic potential is small and the typical phenomenon of Bragg diffraction is observed. For special incidence angles Bragg diffraction is observed and in general ) Corresponding author. claudia.keller@univie.ac.at 1 This paper is dedicated to Professor Marlan O. Scully at the occasion of his 60th birthday. only one diffracted peak is observed. This regime can also be realized with atoms in standing light waves and has already been studied in detail w1 3 x. Using the interaction of an atomic beam with near resonant light in a standing light wave it is possible to increase the coupling strength enormously, far beyond anything possible for X-rays or neutrons. The potential height for the atoms is proportional to the intensity of the light field and inversely proportional to the detuning of the light from the atomic resonance. If the coupling is very strong the atoms can no longer pass over the potential maxima, as in the case of Bragg diffraction, and are confined between the maxima of the light potential. In each such channel they have to evolve independently. This evolution is analogous to the behaviour of light in an r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. Ž. PII: S

2 130 C. Keller et al.roptics Communications optical glass fiber, but now for the atoms in waveguides of light. First experiments in the channeling regime showed the localization of the atoms at the potential minima wx 4, guiding effects in a curved standing wave wx 5 and the influence of boundary conditions of the light crystal, which lead to adiawx 6. batic evolution To describe this so-called channeling regime, the dimensionless parameter q s VmaxrEG has to be con- sidered, where Vmax is the maximal potential and EG s" 2 G 2 r2 m is a characteristic energy associated with the periodic structure ŽG grating vector and m atomic mass.. For q-1 Bragg diffraction happens and only one additional interference order arises. For q)1 channeling effects are visible. In this regime there are two typical, quite independent effects visible. First there is nearly classical behaviour of the atoms in the single channels, they start to oscillate like balls on a corrugated surface. This leads to damped focusing and defocusing both in the space and in the momentum distributions. This effect determines the envelope of the momentum distribution in the far field wx 9. After a long interaction time, the oscillations dephase because of anharmonicities in the guiding potential. Eventually both momentum and position distributions stay constant and are guided through the potential. Secondly, because the evolution along the different channels is nearly identical and the channel exits are arranged in a row, there is an interference pattern arising from the different point like sources at the back face of the potential. But these interesting effects are only visible for certain coherence properties of the incident wave and for coherent evolution inside the potential. Calculations of the classical and of the quantum mechanical model for this regime are given in w7,8 x. In the present paper we report experimental verifications. In the reminder of the paper we will first describe the experimental setup and explain then separately the different influences of longitudinal and transverse coherence. To show that not only the coherence properties of the incoming beam are important, spontaneous emission, by which the coherence is destroyed in the interaction region, is also studied. At the end we will explain the importance of these results for further applications. 2. Experimental setup In our experimental setup we use a beam of metastable argon atoms interacting with a near resonant standing light wave Ž see Fig. 1.. For an interaction with laser light in the near infrared Ž 812 nm. it is necessary to first excite the argon atoms in a gas discharge to a metastable state Ž lifetime ; 40 s.. Next, the atoms exiting the source, with an average velocity of 720 mrs and a nearly thermal distribution of 50% width are collimated with two slits arranged at a distance of 1.55 m. The width of the first slit, important for the transverse coherence, can be varied from 0 to 60 mm with piezo actuators. The height of this slit is 4 mm. The second slit serving as an aperture in front of the standing light wave has a constant width of 5 mm and is also 4 mm high. This second slit is wider than the transverse coherence, and is only important to ensure a good momentum resolution and that the detector position is already in the far field of the diffraction. It is important to be in the far field in order to have sufficiently separated momenta associated with the various diffraction orders at the detector. In the experiment this requires that both the distance L between the slits and the distance between the standing wave and the detector have to be larger than a 2 rl, where a is the width of the second slit and l the de Broglie wave length. In our case a 2 rl is 1.8 m for our center wavelength of 14 pm and the condition is fulfilled for most of the spec- Fig. 1. Setup: A beam of metastable argon atoms excited in a gas discharge is collimated with two slits. The interference pattern is detected behind the periodic potential of the standing light wave with a space and time sensitive detector.

3 C. Keller et al.roptics Communications trum, only for fast atoms with a shorter wavelength the interference peaks are not completely separated. Directly behind the second collimation slit the periodic potential is realized by retroreflection of a wide laser beam at a mirror Ž flatness lr10. with a diameter of 5 cm located in the vacuum chamber. The mirror surface is almost parallel to the atomic beam passing at a distance of a few hundred mm. The exact incidence angle of the beam on the standing light wave can be adjusted by rotating the mirror with motors and piezo actuators in the vacuum. A typical length of the periodic potential is 4 cm, which leads to interaction times much larger than typical evolution times in the potential. The light is produced with an intensity of up to 2 W by an external-cavity-stabilized Titanium-Sapphire laser. The important parameter q at the maximum of the periodic potential can be calculated through the relation qs0.088pird directly from measured paramew10 x, where I is the incident intensity in ters mwrcm 2 and d the detuning from the atomic resonance in GHz. If the detuning from the atomic resonance is too small, a second process is possible: absorption and spontaneous emission of a photon. But this process can be avoided using large enough detuning, in our case of about 1 GHz. Behind the interaction zone free evolution over 1.25 m changes the periodic atom distribution in space into a momentum distribution of the atoms in the far field. This distribution is detected with a space and time sensitive detector. The detector is an assembly of three microchannel plates and a resistive anode w11 x. It allows easy detection of the metastable atoms with a very high efficiency and low background rate, because of their high internal energy of 12 ev. The channeling experiments are strongly dependent on the interaction time, that means for our case, on the longitudinal atomic velocity. Therefore it is necessary to have a very narrow velocity distribution or to select the different velocity components of the incident beam in a time of flight measurement. This is realized by pulsing the gas discharge with a pulse length of 80 ms and a repetition rate of 120 Hz. Using the gas discharge pulse as a start trigger, the arrival time of the atoms at the detector determines the flight time. Typically the flight time is about 4 ms for the length of our beam line of 2.94 m. In the gas discharge two metastable levels are populated, but the interaction with the light crystal is only possible with one of these species Ž 80% in 1s. 3. Our detection scheme is not state sensitive, and atoms in the wrong metastable state would produce background. The background can be reduced by pumping the atoms in the wrong metastable state with light of an open transition at 795 nm to the ground state. This light from an actively stabilized diode laser with an intensity of 5 mw interacts with the atomic beam directly behind the first collimation slit. 3. Longitudinal coherence The characteristic momentum exchange with a periodic potential is given by "G determined by the grating vector G s 2prd Ž d distance between two maxima of the potential.. This is analogous to the standard situation of light diffraction at a phase grating or an absorptive grating. For matter waves the diffraction angle for the different orders is given by sinqsnp"grž mõ., where ns0,"1,"2... is the number of the interference order. The angle Q depends, because of the de Broglie relation Žl s hrmõ., on the velocity of the atom corresponding to the wavelength of the incident atoms. Therefore the distance between interference orders in the far field increases for ensembles with larger wavelengths. In the interference pattern the different velocity components of the atomic beam add incoherently, since there is no phase relation between the components produced from the source. The resulting interference pattern smears out and if the velocity distribution is too wide, the pattern is no longer visible. It is important to notice that this effect amplifies at higher interference orders and broadens the interference maxima in higher orders more and more. In the literature this effect is described as a lack of longitudinal coherence. Analogous to normal light optics the longitudinal coherence length is given by w12x l 2 0 llcoh s, Ž 1. Dl where l0 is the center wavelength and Dl the width of the distribution. This length means that interference is visible as long as the path length differences

4 132 C. Keller et al.roptics Communications in interferometric experiments are shorter than l lcoh. In our situation this implies that the possible path length difference between different paths, which for example for the first interference order is equal to l 0 Ž condition for constructive interference., is smaller than l lcoh. Without velocity selection in our experiment the longitudinal coherence length is 7.7 pm. In the interference pattern Ž l s 14 pm. 0 only first order diffracted atoms are visible, all higher orders are not resolvable Ž see Fig. 2a.. In this measurement the potential had a height of qs15 and a length of 3 cm. The standing light wave was realized with an intensity of 136 mwrcm 2 and a detunig of 0.8 GHz to higher frequencies. But using a very fine velocity selection in the same experimental situation, Õ s 584 "6 mrs corresponding to a wavelength of 16.1" 0.2 pm, the longitudinal coherence length is 1.3 nm. In this case, as may be seen in Fig. 2b, many interference maxima are clearly visible. Theoretically it should be possible to observe up to 80 interference orders. In these experiments the collimation slit widths were 10 mm and 5 mm. This collimation configura- Fig. 2. Interference pattern for different longitudinal coherence lengths. Without velocity selection Ž. a the longitudinal coherence length is very short and only first order diffracted atoms are visible, higher orders are washed out. For a good velocity selection Ž. b but otherwise unchanged conditions many diffraction orders are visible because of the large coherence length. tion does not significantly reduce the visibility of the interference pattern. 4. Transverse coherence The transverse coherence determines the width over which the position of the incident atom at the potential is not determined. In our case this gives the number of coherently illuminated channels, i.e. through how many different channels of the periodic potential the atom can move without knowing the path it took. These different possibilities are necessary for the atoms to interfere and to show the characteristic pattern. A transverse coherence of arbitrarily large width is only possible with a point source. If the source is placed at infinite distance one would obtain plane wavefronts. But in the experiment this is not possible, for reasonable count rates one has to use an extended source in a certain distance. The extension is defined by the width of the first collimation slit. In addition it is necessary to select with the second collimation slit only a certain angle to have a well defined beam profile at the detector. Every point of the source produces an interference pattern at the detector and because the different points have no phase relation they add incoherently to the whole interference pattern. But, because of the different incident angle, every pattern has a slightly different position. Therefore, depending on the size of the source, the interference pattern has only a finite visibility in the experiment. This broadening effect of the interference orders does not increase in higher interference orders. In the experiment a compromise collimation has to be found which results in high enough count rate and good enough interference fringe visibility. The calculation of the transverse coherence length analogous to standard light optics w12 x. 1 l ltcoh s P, Ž 2. 2 a where a is the angle under which the source is visible from the interaction region. The factor 1r2 arises because we use a slit and not a pinhole in the experiment.

5 C. Keller et al.roptics Communications A useful compromise for the experiment are two slits of 10 mm and 5 mm in a distance of 1.55 m as shown in the sketch above Ž Fig. 2b.. There the divergence is 10 mrad, which for a de Broglie wave of 14 pm corresponds to a transverse coherence length of 1.1 mm. This implies that about three channels Ž lateral distance 406 nm. are illuminated coherently. Thus an interference pattern resulting from the coherent superposition of amplitudes emerging from three neighboring channels becomes visible. For large transverse coherence, i.e. for large distance between potential and detector an ideal pattern would have narrower peaks. To study the influence of the collimation in the experiment in more detail we varied the width of the first collimation slit between 5 and 60 mm. This means that we vary the transverse coherence width for our de Broglie wave with l s 18.6" 0.7 pm from 2.9 mm to 240 nm. In Fig. 3 the result is shown for different slit widths and for a potential height qs7 and length ls3 cm. One clearly sees that the visibility decreases for larger and larger slit widths. For the case that the transverse coherence length is below the width of one channel Ž 6th graph. only a broad envelope is visible because interference between different channels is no longer possible. Up to now we studied the influence of the coherence of the incoming beam on the resulting interference pattern. In the cases described above interference vanishes because of the incoherent sum of the different source points or different wavelength components. The periodic potential was only necessary to exchange a certain momentum and to observe the interference effect. This will change in the situation described below, where the coherence of every atom is destroyed inside the potential. 5. Spontaneous emission Fig. 3. Interference patterns for different transverse coherence lengths: Increasing the width of the first collimation slit, the interference pattern looses more and more visibility Žthe corresponding slit widths and transverse coherence widths are given in the graphs.. Only a broad envelope can be observed once the coherence length is smaller than the width of the single channel with 406 nm Ž last picture.. If an atom scatters a photon the two particles become entangled with each other. In the case of maximal entanglement measuring one particle determines the state of the second. The photon carries therefore information about the position of the atom. The mere possibility that the atom can be localized is enough to destroy the interference between its different paths. The accuracy of the localization is determined by the wavelength of the scattered photon. In a rough estimate the localization is of the order of half the wavelength of the photon. These effects have been demonstrated in w13 15 x. One possibility in our experiment to have photon scattering is to use absorption and spontaneous emission of photons used to create the guiding potential. This is possible by just decreasing the detuning. The corresponding scattering rate is connected with the potential and the detuning of the light field via q g Scats990P, Ž 3. d where d is again in GHz. This gives the number of scattered photons per second at the maximum of the potential. The scattering rate also depends on where

6 134 C. Keller et al.roptics Communications in the light potential the atoms mainly propagate during their caustic oscillations. For red detuning this is at the maxima of the light field and for blue detuning at the minima of the intensity. In the case of blue detuning the scattering rate is therefore decreased. To determine the real scattering rate in the experiment this effect has to be considered. In our experiment we thus can destroy the coherent evolution in the channels if we increase the rate of spontaneous emission by reducing the detuning of the light field. A scattered photon of 812 nm can localize the atom in one channel Ž 406 nm. and the interference pattern is destroyed by just one spontaneous emission. It is important to notice that the scattering of photons at the transition of 812 nm has no influence on their detection efficiency because the transition is closed and the atoms are still metastable. In the experiment we compared the two situations for a potential of qs11 realized in Fig. 4a with 1 GHz blue detuned and in Fig. 4b with y0.5 GHz red detuned. These settings would correspond to a probability of 35% and 70% respectively for an atom at the maximum of the light field to scatter a photon during the interaction time. But because of the different detunings atoms are located at different regions in the potential and these rates change. In the case of the blue detuned light crystal the effective scattering rate decreases to below 10% and for red detuning it increases to above one. In the two graphs it is clearly visible that, if the scattering rate is above one there is no interference anymore. Only a broad envelope is visible. It is interesting to notice that the width of the envelope stays the same, as may be expected because it is only determined by the potential height and the interaction time, which are similar in both situations. 6. Conclusion and outlook We demonstrated experimentally the influence of the longitudinal and of the transverse coherence on the interference patterns created by coherently guided atoms. Theses effects are only determined by the corresponding velocity distributions in longitudinal and transverse direction of the incidence beam. A totally different effect is visible if photons are scattered during the interaction and interference is destroyed directly inside the potential. Interference in this situation does not vanish because of incoherent addition but because the atom is entangled with the photon which carries away path information. Detailed knowledge of such behavior is important for realizing a coherent waveguide for atoms using light potentials. A tool like this could be useful for atom interferometers with a large enclosed area which would be very sensitive for example to rotational and gravitational phenomena. Acknowledgements Fig. 4. Interference patterns for different photon scattering rates: Ž. a a scattering probability below 10% shows nearly no influence on the interference pattern, Ž. b in contrast, when the scattering rate is above one, no interference is visible anymore. We thank S. Bernet, M.A. Horne and I. Jex for useful discussions and M. Berry and D. O Dell also for drawing our attention to the interesting propagation phenomena in strong sinusoidal potentials. This work was supported by the Austrian Science Foundation Ž FWF., projects S06504 and F1505, the Euro-

7 C. Keller et al.roptics Communications pean Union TMR-Network Coherent Matter-Wave Interactions, and the US National Science Foundation Grant No. PHY References wx 1 P.J. Martin, B.G. Oldaker, A.H. Miklich, D.E. Pritchard, Phys. Rev. Lett. 60 Ž wx 2 St. Durr, G. Rempe, Phys. Rev. A 59 Ž wx 3 M.K. Oberthaler, R. Abfalterer, S. Bernet, C. Keller, J. Schmiedmayer, A. Zeilinger, Phys. Rev. A 60 Ž wx 4 C. Salomon, J. Dalibard, A. Aspect, H. Metcalf, C. Cohen- Tannoudji, Phys. Rev. Lett. 59 Ž wx 5 V.I. Balykin, V.S. Letokhov, Y.B. Ovchinnikov, A.I. Sidorov, S.V. Shul ga, Opt. Lett. 13 Ž wx 6 C. Keller, J. Schmiedmayer, A. Zeilinger, T. Nonn, S. Durr, G. Rempe, Appl. Phys. B 69 Ž wx 7 M.V. Berry, The Diffraction of Light by Ultrasound, Academic Press, London, wx 8 M. Horne, I. Jex, A. Zeilinger, Phys. Rev. A 59 Ž wx 9 Recently with a BEC it was possible to demonstrate some of these phenomena: Y.B. Ovchinnikov, J.H. Muller, M.R. Doery, E.J.D. Vredenbregt, K. Helmerson, S.L. Rolston, W.D. Philips, Phys. Rev. Lett. 83 Ž w10x D.O. Chudesnikov, V.P. Yakovlev, Laser Phys. 1 Ž w11x Ch. Kurtsiefer, J. Mlynek, Appl. Phys. B 64 Ž w12x E. Hecht, Optik, Addison-Wesley Publishing Company, 2nd ed., Bonn, w13x T. Pfau, S. Spalter, Ch. Kurtsiefer, C.R. Ekstrom, J. Mlynek, Phys. Rev. Lett. 73 Ž w14x J.F. Clauser, S. Li, Phys. Rev. A 50 Ž w15x M.S. Chapman, T.D. Hammond, A. Lenef, J. Schmiedmayer, R.A. Rubenstein, E. Smith, D.E. Pritchard, Phys. Rev. Lett. 75 Ž

Dynamical diffraction of atomic matter waves by crystals of light

$Dynamical diffraction of atomic matter waves by crystals of light$ PHYSICAL REVIEW A VOLUME 60, NUMBER 1 JULY 1999 Dynamical diffraction of atomic matter waves by crystals of light M. K. Oberthaler, 1,2 R. Abfalterer, 1 S. Bernet, 1 C. Keller, 1 J. Schmiedmayer, 1 and