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Thermal atom beam splitting by an evanescent standing wave
cm .__
l!iid
15 March 1996
‘t-3
ELSEYIER
OPTICS COMMUNICATIONS Optics Communications124 (1996) 448-451
Thermal atom beam splitting by an evanescent standing wave R. Brow-i a, R. Asimov a, M. Gorlicki a, S. Feron a, .T.Reinhardt a, V. Lorent a, H. Haberland b ’ Laboratoire de Physique des Lasers, Laboratoire associe’au CNRS (MA 282), ZnstitutGalilb, Universite’Paris-Nerd, avenue J.-B. Cl.&nent, F-93430 Villetaneuse, France b Fakulttitfiir Physik, Hermann Herder Strasse, 3, D-3800 Freiburg, Germany
Received25 August 1995;accepted14 November 1995
Abstract We report the first experimental observation of the diffraction of a thermal supersonic beam of metastable atoms by a partially standing evanescent wave. The geometry of our experiment reduces the Doppler shift, and leads to an important atomic population diffracted in the first even order. PACS:
03.75.Be; 42.50.Vk
1. Introduction Interaction of atoms with quasi-resonant electromagnetic waves is now of common use as a device to perform atom optics experiments. Atomic lens and mirror effects are now well established [ l-41. The coherent splitting of an atomic beam has been also achieved, using many methods: splitting a running wave [ 51 or by stimulated Raman transitions [6], optical SternGerlach effect [ 71, magneto-optical beam splitter [ 81, and modulated atomic mirror [ 91. Diffraction of an atomic beam crossing perpendicularly a standing wave has been given particular interest [ lo]. The angular separations between the diffracted orders (typically lop4 rad) created by that kind of transmitting grating are related to the number of photon momenta r2k,rt that are transversaly transferred to the atomic momentum. In order to increase these angles, Hajnal and Opat proposed in 1989 [ 111 the use, at a grazing incidence, of a reflecting light grating produced by a standing evanescent wave. An atomic beam inci0030.4018/96/$12.00 0 1996Elsevier Science B.V. All rights reserved X?DZ0030-4018(95)00703-2
dent on such a device is expected to be diffracted at angles 10 to 500 times larger than the previous ones. An equivalent picture in terms of an optical wave diffracted by a material grating may be given for the even atomic diffraction orders, which imply even numbers of exchanged photons with the evanescent light. The couplings between these channels involve Ramanlike two-photon transitions, which are out of resonance by twice the Doppler shift. One way to overcome this gap consists in using an appropriate bi-chromatic evanescent wave, in order to create a grating moving at the atomic velocity [ 121. However, this method yields very small angular separations between the diffracted orders, that cannot be resolved experimentally. Actually, the non-resonant character of the Raman transition is here necessary to produce atomic spatial splitting. A central issue is then the relative population emerging in the diffraction orders. That question has been addressed in Ref. [ 11) and by Deutschmann et al. [ 131, by means of one-dimensional quantum mechanical treatments. A critical condition to get appreciable dif-
R. Brouri et al. /Optics
Communications
fracted populations concerns the ratio between the a.c. Stark splitting and the Doppler shift, which should be as large as possible, and, by the least, significantly larger than 1, With the laser intensities currently available, this condition is out of reach for atomic beams of thermal energies. One way to reach this regime consists in slowing down the atomic velocity. This has been demonstrated by Christ et al. [ 141, who obtained a three percent ratio between the populations in the first even order (y1= - 2) and in the zeroth order (specular reflection) _ In this letter we present a different approach to make up a situation where a thermal atom diffraction is possible. In order to reduce the Doppler shift A, =k,,,*p/ M, the incident plane of the matter wave is rotated at an angle with respect to the direction of propagation of the evanescent wave k,, (in the present experiment this angle in tuned to 8 1” (see Fig. 1) ) . The result may be described as a quasi-resonant evanescent grating with a periodicity much larger than half the optical wavelength. Moreover, in order to yield high a.c. Stark splitting, the evanescent wave is enhanced by exciting a surface plasmon wave [4]. This combination has finally provided the first observation of a thermal atomic beam diffraction by a standing evanescent wave grating with a large population ratio.
2. Experiment The experimental set-up is described in Figs. la, b. A metastable neon (Ne*(3P,) ) beam is produced by electron bombardment of a supersonic beam at room temperature. The longitudinal velocity of the atoms is 780 m/s with a selection spread of 7%. Two slits collimate the beam to an overall angular spread of 1 mrad. The deflected atomic population is analysed by a moving 75 pm slit in front of a secondary electron multiplier located at 28 cm beyond the evanescent mirror surface. The angular distribution of the Ne* beam is recorded with a resolution of 0.2 mrad by translating this latter slit, with a step of 50 pm. The evanescent wave is produced by coupling a laser wave (stemming from a ring dye laser tuned around the 1ss3P, e 2pg3D, transition at hopt = 640.2 nm) with a surface plasmon guide mode in the Kretschmann configuration [ 151. The total internal reflection of the TMpolarized laser beam, incident at 42.8” on the silver
124 (1996) 448-451
449
E.L.G.
(b)
Fig. 1. The experimental set-up. (a) Overview of the apparatus. N: nozzle, sk: skimmer, e.b.: electron bombardment, S, and Sz: 50 pm collimating slits, Ne*: supersonic beam of men&able neon atoms, E.L.G.: evanescent light grating, S.E.M.: secondary electron multiplier screened by a translating 75 pm slit (S,). The specularly reflected atomic beam is n=O, while n= -2 is the first “evendiffracted” population. (b) L: incident laser beam, G: evanescent light grating, the surface plasmon wave has an evanescent profile in the Y direction with a decay length of 0.6&r,, and is partially stationary in the Z direction, A: atomic beam axis tilted with respect to the grating direction (Z) by an angle f3= n/2 - 0’ with 6’ = 9”, cu,: angle of atomic beam incidence, P: atomic plane of incidence.
layer ( - 40 nm thickness), is reduced to 5%. A similar coupling with the surface plasmon wave was used in previous experiments [4] for which an enhancement factor of the evanescent wave intensity was found to be 100. An optical device creates a partially stationary surface wave (Fig. lb). The TM-polarized part of the incident light excites the principal plasmon wave that propagates in the -2 direction. The TE-polarized part, which is totally reflected at the dielectric-silver interface, is reflected back through a X/4 plate, which excites a surface wave propagating in the + z^direction. The stationarity of the evanescent field is controlled with a h/2 plate placed at the output of the light source. In the reported experiment, the standing wave ratio p of the surface wave amplitude was 0.4. The spot diameter of the plasmon wave was 0.5 X 0.7 mm*; in these
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124 (1996) 448-451
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Fig. 2. Angular distribution of the atomic population respectively reflected (peak A) and diffracted (peak B) by the evanescent wave grating. The angular scale refers to the atomic incidence direction. The reflected population is located at 3.2 mrad (twice the incidence angle) whereas the diffracted population is centred at 7 mrad (the incidence angle plus the diffraction angle). The laser detuning is 1.62 GHz. The laser power is 160 mW (a) or 120 mW (b) The overall angular distribution of the “specular + diffracted” atom populations (peak A plus peak B ) has a FWHM width of 5 mrad, whereas the angular width of the reflected population distribution is 2 mrad (see insert). Assuming the same angular distribution for both peaks. a comparison between their respective areas gives a ratio diffraction/reflection of 40%/60% (a) and 25%/75% (b) Insert: Specularly reflected atomic population obtained at a lower laser power (60 mW)
conditions, about 1% of the incident atomic beam interacts with the light grating. The electric field created by this method is evanescent in the direction (Oy) , perpendicular to the silver layer, and has a standing wave profile in the (Oz)direction given by E(r, t) =e^ E, exp( -y/t) x [cos(wt-k”,p)
+p
(z? p) = 81” ‘, which leads to a reduced Doppler shift A,, = (k,,,plM) cos 19=200 MHz, compared to 1.25 GHz for 8= 0 (see Fig. lb). Since the internal state of the atom is not modified after the exchange of an even number of photons between the two counter-propagating surface waves, the atomic kinetic energy EC is conserved. Therefore, the angle of deflection CI~of the nth even diffraction order (in the plane perpendicular to the prism surface) is given, for grazing angles, by
c0s(wt+k,,,z)1 ,
where &is the polarisation unit vector, c= 0.6h,,, is the attenuation length of the evanescent wave, and kc>,,= 2371&,pl is the propagating part of the wave vector. The important point of our device lies in its geometrical features. The prism is rotated so that the angle between the longitudinal component pZ of the atomic momentum and the evanescent wave grating be 8=
’ In a preliminary study the laser frequency was swept around the atomic transition, and the moving slit was positioned at twice the angle of incidence (2 X 1.6 mrad) in order to observe the specularly reflected atomic population. As the dipole force repels the atomic beam from the prism surface only for blue detunings of the laser field, the frequency dependence of the specularly reflected signal yields an experimental determination of the Doppler shift. A, was found in agreement with the 200 MHz value corresponding to the angle 0= 81” between the evanescent wave grating and the axis of the atomic beam.
R. Brouri et al. /Optics Communications 124 (1996) 448-451
%
z
d +
nA
D
-tn2S2 R ,
(n
even)
EC
where 8, is the (small) recoil shift. In our experimental conditions, the angle of incidence was CY; = 1.6 mrad, which yields for the n = - 2 order an angle (Y-~ = 5.4 mrad. Fig. 2a exhibits the angular distribution of the atomic population, for a laser frequency tuned in the blue side at 1.62 GHz from the atomic resonance, and a laser power of 160 mW. These profiles are obtained from differences between collected data recorded with and without the presence of the laser, which eliminates various non-significant contributions, such as specularly reflected UV photons. Since the zero of the angular scale refers to the incident atomic beam direction, the reflected population (A) is located at twice the angle of incidence (2 X 1.6 mrad). A second peak (B) clearly appears at 7 mrad, which is in fair agreement with the expected value ( (Y~ + 5.4 mrad) for then = - 2 order diffracted atomic population. This latter peak (B) corresponds to about 40% the Ne* population which interacts with the surface plasmon wave. In Fig. 2b, the laser power is reduced to 120 mW. The diffracted atomic population (B) is decreased whereas the specular peak (A) is enlarged, corresponding to a (75%25%) splitting. However, we have checked that the overall deflected population (A) + (B) remains unchanged within a few percent.
3. Conclusion We have shown that an evanescent wave grating can be used as an efficient atomic beam-splitter. As a byconsequence of this geometry compared to the original one proposed by Hajnal and Opat [ 111, the angular separations between the diffracted orders is narrower
451
than the one observed in Ref. [ 141. Still, speaking in terms of momentum transfer between the specular reflection direction and the diffraction direction, it represents an equivalent of 96 photon momenta. It should also be noted that, as a direct consequence of energymomentum conservation, the diffraction plane does not merge with the atomic plane of incidence. The angle between these two planes is less than 10P4 rad. However, one should be awared of this fact when this evanescent wave grating is used as a beam-splitter in the construction of an atomic interferometer.
References [ 11 J.E. Bjorkholm,R.R. Freeman, A. Ashkin and D.B. Pearson, Phys. Rev. Len. 41 (1978) 1361. 121 R.J. Cook and R.K. Hill, Optics Comm. 43 ( 1982) 258. 131 V.I. Balykin, VS. Letokhov, Yu.B. Ovchinnikov and A.I. Sidorov, JETP Lett. 45 (1987) 353. [41 S. Feron, J. Reinhardt, S. Le Boiteux, 0. Gorceix, J. Baudon, M. Ducloy, J. Robert, Ch. Miniatura, S. Nit Chormaic, H. Haberland and V. Lorent, Optics Comm. 102 (1993) 83. [5] Ch.J. Borde, N. Courtier, F. du Burck, A.N. Goncharov and M. Gorlicki, Phys. Lett. A 188 (1994) 187. [6] M. Kasevich and S. Chu, Phys. Rev. Lett. 67 (1991) 181. [ 71 T. Sleator, T. Pfau, V. Balykin, 0. Carnal and J. Mlynek, Phys. Rev. Lett. 68 ( 1992) 1996. [ 81 T. Pfau, Ch. Kurtsiefer, C.S. Adams, M. Sigel and J. Mlynek, Phys. Rev. Lett. 71 (1993) 3427. [9] A. Steane, P. Szriftgiser, P. Desbiolles and J. Dalibard, Phys. Rev. L&t. 74 ( 1995) 4972. [ 101 P.J. Martin, P.L. Gould, B.G. Oldaker, A.H. Miklich and D.E. Pritchard, Phys. Rev. A 36 (1987) 2495. [ 111 J.Y. Hajnal and G.I. Opat, Optics Comm. 71 ( 1989) 119. [ 121 B.W. Stenlake, I.C.M. Littler, H.-A. Bachor and K.G.H. Baldwin, Phys. Rev. A 49 (1994) R16. [ 131 R. Deutschmann, W. Ertmer and H. Wallis, Phys. Rev. A 47 (1993) 2169. [ 141 M. Christ, A. Scholz, M. Schiffer, R. Deutschmann and W. Ertmer, Optics Comm. 107 ( 1994) 211. [ 151 E. Kretschmann, 2. Phys. 241 (1971) 313.
l!iid
15 March 1996
‘t-3
ELSEYIER
OPTICS COMMUNICATIONS Optics Communications124 (1996) 448-451
Thermal atom beam splitting by an evanescent standing wave R. Brow-i a, R. Asimov a, M. Gorlicki a, S. Feron a, .T.Reinhardt a, V. Lorent a, H. Haberland b ’ Laboratoire de Physique des Lasers, Laboratoire associe’au CNRS (MA 282), ZnstitutGalilb, Universite’Paris-Nerd, avenue J.-B. Cl.&nent, F-93430 Villetaneuse, France b Fakulttitfiir Physik, Hermann Herder Strasse, 3, D-3800 Freiburg, Germany
Received25 August 1995;accepted14 November 1995
Abstract We report the first experimental observation of the diffraction of a thermal supersonic beam of metastable atoms by a partially standing evanescent wave. The geometry of our experiment reduces the Doppler shift, and leads to an important atomic population diffracted in the first even order. PACS:
03.75.Be; 42.50.Vk
1. Introduction Interaction of atoms with quasi-resonant electromagnetic waves is now of common use as a device to perform atom optics experiments. Atomic lens and mirror effects are now well established [ l-41. The coherent splitting of an atomic beam has been also achieved, using many methods: splitting a running wave [ 51 or by stimulated Raman transitions [6], optical SternGerlach effect [ 71, magneto-optical beam splitter [ 81, and modulated atomic mirror [ 91. Diffraction of an atomic beam crossing perpendicularly a standing wave has been given particular interest [ lo]. The angular separations between the diffracted orders (typically lop4 rad) created by that kind of transmitting grating are related to the number of photon momenta r2k,rt that are transversaly transferred to the atomic momentum. In order to increase these angles, Hajnal and Opat proposed in 1989 [ 111 the use, at a grazing incidence, of a reflecting light grating produced by a standing evanescent wave. An atomic beam inci0030.4018/96/$12.00 0 1996Elsevier Science B.V. All rights reserved X?DZ0030-4018(95)00703-2
dent on such a device is expected to be diffracted at angles 10 to 500 times larger than the previous ones. An equivalent picture in terms of an optical wave diffracted by a material grating may be given for the even atomic diffraction orders, which imply even numbers of exchanged photons with the evanescent light. The couplings between these channels involve Ramanlike two-photon transitions, which are out of resonance by twice the Doppler shift. One way to overcome this gap consists in using an appropriate bi-chromatic evanescent wave, in order to create a grating moving at the atomic velocity [ 121. However, this method yields very small angular separations between the diffracted orders, that cannot be resolved experimentally. Actually, the non-resonant character of the Raman transition is here necessary to produce atomic spatial splitting. A central issue is then the relative population emerging in the diffraction orders. That question has been addressed in Ref. [ 11) and by Deutschmann et al. [ 131, by means of one-dimensional quantum mechanical treatments. A critical condition to get appreciable dif-
R. Brouri et al. /Optics
Communications
fracted populations concerns the ratio between the a.c. Stark splitting and the Doppler shift, which should be as large as possible, and, by the least, significantly larger than 1, With the laser intensities currently available, this condition is out of reach for atomic beams of thermal energies. One way to reach this regime consists in slowing down the atomic velocity. This has been demonstrated by Christ et al. [ 141, who obtained a three percent ratio between the populations in the first even order (y1= - 2) and in the zeroth order (specular reflection) _ In this letter we present a different approach to make up a situation where a thermal atom diffraction is possible. In order to reduce the Doppler shift A, =k,,,*p/ M, the incident plane of the matter wave is rotated at an angle with respect to the direction of propagation of the evanescent wave k,, (in the present experiment this angle in tuned to 8 1” (see Fig. 1) ) . The result may be described as a quasi-resonant evanescent grating with a periodicity much larger than half the optical wavelength. Moreover, in order to yield high a.c. Stark splitting, the evanescent wave is enhanced by exciting a surface plasmon wave [4]. This combination has finally provided the first observation of a thermal atomic beam diffraction by a standing evanescent wave grating with a large population ratio.
2. Experiment The experimental set-up is described in Figs. la, b. A metastable neon (Ne*(3P,) ) beam is produced by electron bombardment of a supersonic beam at room temperature. The longitudinal velocity of the atoms is 780 m/s with a selection spread of 7%. Two slits collimate the beam to an overall angular spread of 1 mrad. The deflected atomic population is analysed by a moving 75 pm slit in front of a secondary electron multiplier located at 28 cm beyond the evanescent mirror surface. The angular distribution of the Ne* beam is recorded with a resolution of 0.2 mrad by translating this latter slit, with a step of 50 pm. The evanescent wave is produced by coupling a laser wave (stemming from a ring dye laser tuned around the 1ss3P, e 2pg3D, transition at hopt = 640.2 nm) with a surface plasmon guide mode in the Kretschmann configuration [ 151. The total internal reflection of the TMpolarized laser beam, incident at 42.8” on the silver
124 (1996) 448-451
449
E.L.G.
(b)
Fig. 1. The experimental set-up. (a) Overview of the apparatus. N: nozzle, sk: skimmer, e.b.: electron bombardment, S, and Sz: 50 pm collimating slits, Ne*: supersonic beam of men&able neon atoms, E.L.G.: evanescent light grating, S.E.M.: secondary electron multiplier screened by a translating 75 pm slit (S,). The specularly reflected atomic beam is n=O, while n= -2 is the first “evendiffracted” population. (b) L: incident laser beam, G: evanescent light grating, the surface plasmon wave has an evanescent profile in the Y direction with a decay length of 0.6&r,, and is partially stationary in the Z direction, A: atomic beam axis tilted with respect to the grating direction (Z) by an angle f3= n/2 - 0’ with 6’ = 9”, cu,: angle of atomic beam incidence, P: atomic plane of incidence.
layer ( - 40 nm thickness), is reduced to 5%. A similar coupling with the surface plasmon wave was used in previous experiments [4] for which an enhancement factor of the evanescent wave intensity was found to be 100. An optical device creates a partially stationary surface wave (Fig. lb). The TM-polarized part of the incident light excites the principal plasmon wave that propagates in the -2 direction. The TE-polarized part, which is totally reflected at the dielectric-silver interface, is reflected back through a X/4 plate, which excites a surface wave propagating in the + z^direction. The stationarity of the evanescent field is controlled with a h/2 plate placed at the output of the light source. In the reported experiment, the standing wave ratio p of the surface wave amplitude was 0.4. The spot diameter of the plasmon wave was 0.5 X 0.7 mm*; in these
450
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o
2
4
angle
6
8
10
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Communications
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of reflection (mrad)
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124 (1996) 448-451
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angle
6
8
10
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14
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Fig. 2. Angular distribution of the atomic population respectively reflected (peak A) and diffracted (peak B) by the evanescent wave grating. The angular scale refers to the atomic incidence direction. The reflected population is located at 3.2 mrad (twice the incidence angle) whereas the diffracted population is centred at 7 mrad (the incidence angle plus the diffraction angle). The laser detuning is 1.62 GHz. The laser power is 160 mW (a) or 120 mW (b) The overall angular distribution of the “specular + diffracted” atom populations (peak A plus peak B ) has a FWHM width of 5 mrad, whereas the angular width of the reflected population distribution is 2 mrad (see insert). Assuming the same angular distribution for both peaks. a comparison between their respective areas gives a ratio diffraction/reflection of 40%/60% (a) and 25%/75% (b) Insert: Specularly reflected atomic population obtained at a lower laser power (60 mW)
conditions, about 1% of the incident atomic beam interacts with the light grating. The electric field created by this method is evanescent in the direction (Oy) , perpendicular to the silver layer, and has a standing wave profile in the (Oz)direction given by E(r, t) =e^ E, exp( -y/t) x [cos(wt-k”,p)
+p
(z? p) = 81” ‘, which leads to a reduced Doppler shift A,, = (k,,,plM) cos 19=200 MHz, compared to 1.25 GHz for 8= 0 (see Fig. lb). Since the internal state of the atom is not modified after the exchange of an even number of photons between the two counter-propagating surface waves, the atomic kinetic energy EC is conserved. Therefore, the angle of deflection CI~of the nth even diffraction order (in the plane perpendicular to the prism surface) is given, for grazing angles, by
c0s(wt+k,,,z)1 ,
where &is the polarisation unit vector, c= 0.6h,,, is the attenuation length of the evanescent wave, and kc>,,= 2371&,pl is the propagating part of the wave vector. The important point of our device lies in its geometrical features. The prism is rotated so that the angle between the longitudinal component pZ of the atomic momentum and the evanescent wave grating be 8=
’ In a preliminary study the laser frequency was swept around the atomic transition, and the moving slit was positioned at twice the angle of incidence (2 X 1.6 mrad) in order to observe the specularly reflected atomic population. As the dipole force repels the atomic beam from the prism surface only for blue detunings of the laser field, the frequency dependence of the specularly reflected signal yields an experimental determination of the Doppler shift. A, was found in agreement with the 200 MHz value corresponding to the angle 0= 81” between the evanescent wave grating and the axis of the atomic beam.
R. Brouri et al. /Optics Communications 124 (1996) 448-451
%
z
d +
nA
D
-tn2S2 R ,
(n
even)
EC
where 8, is the (small) recoil shift. In our experimental conditions, the angle of incidence was CY; = 1.6 mrad, which yields for the n = - 2 order an angle (Y-~ = 5.4 mrad. Fig. 2a exhibits the angular distribution of the atomic population, for a laser frequency tuned in the blue side at 1.62 GHz from the atomic resonance, and a laser power of 160 mW. These profiles are obtained from differences between collected data recorded with and without the presence of the laser, which eliminates various non-significant contributions, such as specularly reflected UV photons. Since the zero of the angular scale refers to the incident atomic beam direction, the reflected population (A) is located at twice the angle of incidence (2 X 1.6 mrad). A second peak (B) clearly appears at 7 mrad, which is in fair agreement with the expected value ( (Y~ + 5.4 mrad) for then = - 2 order diffracted atomic population. This latter peak (B) corresponds to about 40% the Ne* population which interacts with the surface plasmon wave. In Fig. 2b, the laser power is reduced to 120 mW. The diffracted atomic population (B) is decreased whereas the specular peak (A) is enlarged, corresponding to a (75%25%) splitting. However, we have checked that the overall deflected population (A) + (B) remains unchanged within a few percent.
3. Conclusion We have shown that an evanescent wave grating can be used as an efficient atomic beam-splitter. As a byconsequence of this geometry compared to the original one proposed by Hajnal and Opat [ 111, the angular separations between the diffracted orders is narrower
451
than the one observed in Ref. [ 141. Still, speaking in terms of momentum transfer between the specular reflection direction and the diffraction direction, it represents an equivalent of 96 photon momenta. It should also be noted that, as a direct consequence of energymomentum conservation, the diffraction plane does not merge with the atomic plane of incidence. The angle between these two planes is less than 10P4 rad. However, one should be awared of this fact when this evanescent wave grating is used as a beam-splitter in the construction of an atomic interferometer.
References [ 11 J.E. Bjorkholm,R.R. Freeman, A. Ashkin and D.B. Pearson, Phys. Rev. Len. 41 (1978) 1361. 121 R.J. Cook and R.K. Hill, Optics Comm. 43 ( 1982) 258. 131 V.I. Balykin, VS. Letokhov, Yu.B. Ovchinnikov and A.I. Sidorov, JETP Lett. 45 (1987) 353. [41 S. Feron, J. Reinhardt, S. Le Boiteux, 0. Gorceix, J. Baudon, M. Ducloy, J. Robert, Ch. Miniatura, S. Nit Chormaic, H. Haberland and V. Lorent, Optics Comm. 102 (1993) 83. [5] Ch.J. Borde, N. Courtier, F. du Burck, A.N. Goncharov and M. Gorlicki, Phys. Lett. A 188 (1994) 187. [6] M. Kasevich and S. Chu, Phys. Rev. Lett. 67 (1991) 181. [ 71 T. Sleator, T. Pfau, V. Balykin, 0. Carnal and J. Mlynek, Phys. Rev. Lett. 68 ( 1992) 1996. [ 81 T. Pfau, Ch. Kurtsiefer, C.S. Adams, M. Sigel and J. Mlynek, Phys. Rev. Lett. 71 (1993) 3427. [9] A. Steane, P. Szriftgiser, P. Desbiolles and J. Dalibard, Phys. Rev. L&t. 74 ( 1995) 4972. [ 101 P.J. Martin, P.L. Gould, B.G. Oldaker, A.H. Miklich and D.E. Pritchard, Phys. Rev. A 36 (1987) 2495. [ 111 J.Y. Hajnal and G.I. Opat, Optics Comm. 71 ( 1989) 119. [ 121 B.W. Stenlake, I.C.M. Littler, H.-A. Bachor and K.G.H. Baldwin, Phys. Rev. A 49 (1994) R16. [ 131 R. Deutschmann, W. Ertmer and H. Wallis, Phys. Rev. A 47 (1993) 2169. [ 141 M. Christ, A. Scholz, M. Schiffer, R. Deutschmann and W. Ertmer, Optics Comm. 107 ( 1994) 211. [ 151 E. Kretschmann, 2. Phys. 241 (1971) 313.