jeanflop/post_ocr_correction2 huggingface dataset:
produire pour l'atome de césium des vitesses dans la gamme du µm/s et améliorer encore les performances de telles horloges. La possibilité d'obtenir des atomes refroidis par laser avec des températures dans la microkelvin range a stimulé une large variété d'applications allant de la métrologie et de la spectroscopie à haute résolution jusqu'à l'optique non linéaire, ou à l'interférométrie atomique [1]. Dans de nombreux cas, on tire parti de la longue durée d'observation des atomes rendue possible par leurs faibles vitesses (~cm/s), beaucoup plus petites que les temperatures ambiante (1 km/s). Pour des particules libres, la gravité de la Terre impose une limite sévère à cette durée d'observation et à l'utilité des plus basses températures atteintes. Considérons par exemple des atomes de césium laser refroidis à 2,5 µK avec une vitesse moyenne de 12 mm/s [2]. Après un second de libre chute, ces atomes ont descendu 5 m et leur vitesse a augmenté de 103. Une solution élégante à ce problème dans le contexte des réfères de temps et de fréquence a été proposée par Zacharias en 1953 [3] et réalisée seulement très récemment grâce aux avancées dans les techniques de refroidissement laser ([4], [5]). Elle consiste à utiliser une fontaine atomique dans laquelle des atomes sont lancés vers le haut et interactionnt deux fois avec un champ lumineux, une fois en montant et une fois en descendant. Des temps d'observation de l'ordre de 0,25 s ont été atteints dans ces conditions, une amélioration de 50 fois par rapport aux réfères de Cs existants. Dans une fontaine de hauteur H, le temps d'observation ne varie que comme H1/2 et des temps de l'ordre de 1 s seront devenus techniquement difficiles à obtenir. Une approche plus radicale est alors de "switcher" l'effet de la gravité, c'est-à-dire de faire que l'expérience se déroule dans un référentiel en chute libre, qui permettrait d'observer pendant plusieurs secondes. Dans cette Note, nous rapportons les premiers résultats obtenus dans cette direction. Nous avons produit et piégé des atomes de césium laser refroidis dans un référentiel avec une gravité réduite. Nous montrons que lorsque ces atomes libres
fontaine atomique dans laquelle des atomes sont lancés vers le haut et interactionnt deux fois avec un champ lumineux, une fois en montant et une fois en descendant. Des temps d'observation de l'ordre de 0,25 s ont été atteints dans ces conditions, une amélioration de 50 fois par rapport aux réfères de Cs existants. Dans une fontaine de hauteur H, le temps d'observation ne varie que comme H1/2 et des temps de l'ordre de 1 s seront devenus techniquement difficiles à obtenir. Une approche plus radicale est alors de "switcher" l'effet de la gravité, c'est-à-dire de faire que l'expérience se déroule dans un référentiel en chute libre, qui permettrait d'observer pendant plusieurs secondes. Dans cette Note, nous rapportons les premiers résultats obtenus dans cette direction. Nous avons produit et piégé des atomes de césium laser refroidis dans un référentiel avec une gravité réduite. Nous montrons que lorsque ces atomes libres sont lâchés pendant 0,2 s à ~20 µK, environ 10% d'entre eux (soit ~3. 107 atomes) encore restent dans un volume de 1 cm3. Ce temps d'observation est plusieurs ordres de grandeur supérieur au temps d'observation d'un faisceau atomique au temperature ambiante. Le référentiel en chute libre est fourni par un avion Caravelle [6] exécutant des vol paraboliques entre 7,500 et 8,000 m pendant lesquels le niveau de gravité est réduit à moins de 2x 10-2 g pour environ 20 s. Vingt et un successifs paraboles sont effectués durant un vol de 3 heures, pour 3 jours consécutifs. Les atomes laser refroidis et piégés sont produits à l'aide d'un piège magnéto-optique (MOT) dans une cellule à très basse pression ([7], [8]). L'ensemble expérimental (fig. 1) se monte sur une table de 200 kg, 1 m × 1,2 m, fixée au plancher par des systèmes anti-vibratoires. Soigneuse attention a été portée à l'emploi de composants stables optiquement, dont les dérivations angulaires durant les transitions 2 g --+ 0 g --+ 2 g n'avaient pas de plus de 10-4 rad. La cellule au césium avait un volume de 0,5 l et ses six parois étaient faites de quartz poli, à travers desquelles
un avion Caravelle [6] exécutant des vol paraboliques entre 7,500 et 8,000 m pendant lesquels le niveau de gravité est réduit à moins de 2x 10-2 g pour environ 20 s. Vingt et un successifs paraboles sont effectués durant un vol de 3 heures, pour 3 jours consécutifs. Les atomes laser refroidis et piégés sont produits à l'aide d'un piège magnéto-optique (MOT) dans une cellule à très basse pression ([7], [8]). L'ensemble expérimental (fig. 1) se monte sur une table de 200 kg, 1 m × 1,2 m, fixée au plancher par des systèmes anti-vibratoires. Soigneuse attention a été portée à l'emploi de composants stables optiquement, dont les dérivations angulaires durant les transitions 2 g --+ 0 g --+ 2 g n'avaient pas de plus de 10-4 rad. La cellule au césium avait un volume de 0,5 l et ses six parois étaient faites de quartz poli, à travers desquelles passaient les trois faisceaux de lasers de refroidissement. La température du gaz était de l'ordre de 5× 10-9 Torr. Two coils provide a 10 G/cm magnetic field gradient at the centre of the cell and of the trapping beams. The plane had no fixed direction with respect to the Earth's magnetic field, the cell was surrounded by a µ-metal shield in order to avoid any displacement of the magnetic field zero and therefore of the trap during the parabolas. The residual field inside the shield was <10 mG. Three lasers are used to produce the trapping. First a single-mode low power DBR diode, chosen for its narrow free running emission linewidth (4 MHz FWHM), is frequency locked to the Doppler induced crossover at mid-distance between the g, F = 4, e, F'=5 and the g, F = 4, → e, F' = 4 saturated absorption peaks in an auxiliary cesium cell. Using a FM technique (10 MHz modulation frequency) and sending the error signal on the diode current provides a unity gain bandwidth of 300 kHz sufficient to compensate the effect of the plane's low frequency vibrations. This laser stayed frequency-locked during take-off as well as during the 30 consecutive
magnetic field, the cell was surrounded by a µ-metal shield in order to avoid any displacement of the magnetic field zero and therefore of the trap during the parabolas. The residual field inside the shield was <10 mG. Three lasers are used to produce the trapping. First a single-mode low power DBR diode, chosen for its narrow free running emission linewidth (4 MHz FWHM), is frequency locked to the Doppler induced crossover at mid-distance between the g, F = 4, e, F'=5 and the g, F = 4, → e, F' = 4 saturated absorption peaks in an auxiliary cesium cell. Using a FM technique (10 MHz modulation frequency) and sending the error signal on the diode current provides a unity gain bandwidth of 300 kHz sufficient to compensate the effect of the plane's low frequency vibrations. This laser stayed frequency-locked during take-off as well as during the 30 consecutive parabolas and landing of the plane. After double path in an acousto-optic modulator (AOI) where its frequency is up-shifted by 190 MHz, this low power (3 mW) beam injects a high power (150 mW) laser diode which provides the trapping beams. The injection-locked diode thus acquires the narrow emission linewidth of the D.B.R. laser and can easily be tuned by tuning the AO frequency. The trap beam is then downshifted by 80 MHz in A02 which acts also as a fast beam shutter. This beam is then detuned at δ = 15 MHz below the g, F = 4 → e, F = 5 cesium transition. It is further expanded to 12 mm 1/e2 diameter before entering the cell. The laser intensity per beam was To = 8 mW corresponding to a Rabi frequency Ω = 2Γ where Γ/2 π = 5.3 MHz is the 6P3/2 natural width. A third diode laser tuned to g, F = 3 → e, F' = 4 is mixed to the 3 trapping beams and prevents from optically pumping the atoms into the g, F = 3 state. The fluorescence emitted by the trapped atoms was monitored by a CCD camera and tape recorded.
of the D.B.R. laser and can easily be tuned by tuning the AO frequency. The trap beam is then downshifted by 80 MHz in A02 which acts also as a fast beam shutter. This beam is then detuned at δ = 15 MHz below the g, F = 4 → e, F = 5 cesium transition. It is further expanded to 12 mm 1/e2 diameter before entering the cell. The laser intensity per beam was To = 8 mW corresponding to a Rabi frequency Ω = 2Γ where Γ/2 π = 5.3 MHz is the 6P3/2 natural width. A third diode laser tuned to g, F = 3 → e, F' = 4 is mixed to the 3 trapping beams and prevents from optically pumping the atoms into the g, F = 3 state. The fluorescence emitted by the trapped atoms was monitored by a CCD camera and tape recorded. A 50 mm diam. lens (f= 120 mm) also collected the fluorescence and imaged a 1 cm3 volume around the trap onto a 1 cm2 Si photodiode. Fig. 2. Release and recapture method. (a) Time sequence: intensity of the trapping beams (I) and magnetic field (Bo) vs time. (b) Fluorescence of the atoms and residual accelerations vs time at 0 g. The ratio f of fluorescence just after Toff to fluorescence just before Toff indicates the fraction of atoms which remained in the 1 cm3 observation volume. Here Toff = 0.1 s and f=25%. (c) Same as (b) but at 1 g. There is no signal from the trapped atoms which have fallen 5 cm below the trap. Note the slight rise of the signal after Toff due to the loading of the optical molasses from the vapour cell Fig. 2. La méthode Relâche et Recapture. (a) Séquence temporelle : intensité des faisceaux pièges (I) et champ magnétique (B) en fonction du temps. (b) Fluorescence des atomes et accélérations résiduelles en fonction du temps, à 0 g. Le rapport f de la fluorescence après coupure sur la fluorescence avant coupure donne la fraction d'atomes restants dans le volume d'observation 1
of the atoms and residual accelerations vs time at 0 g. The ratio f of fluorescence just after Toff to fluorescence just before Toff indicates the fraction of atoms which remained in the 1 cm3 observation volume. Here Toff = 0.1 s and f=25%. (c) Same as (b) but at 1 g. There is no signal from the trapped atoms which have fallen 5 cm below the trap. Note the slight rise of the signal after Toff due to the loading of the optical molasses from the vapour cell Fig. 2. La méthode Relâche et Recapture. (a) Séquence temporelle : intensité des faisceaux pièges (I) et champ magnétique (B) en fonction du temps. (b) Fluorescence des atomes et accélérations résiduelles en fonction du temps, à 0 g. Le rapport f de la fluorescence après coupure sur la fluorescence avant coupure donne la fraction d'atomes restants dans le volume d'observation 1 cm3. Ici f= 25% pour Toff = 0.1 s. (c) Même signal à 1 g. Le signal dû aux atomes initialement piégés disparaît car ils sont tombés ~5 cm en dessous du piège. La légère croissante après Toff est due au chargement de la mélasse optique par les atomes lents de la cellule. With this experimental set-up, the trap worked continuously during the three flights and contained typically 3 × 108 atoms at a density of 5 × 1010 at/cm3. Temperature measurements in micro-gravity were performed using the release and recapture (RR) Fig. 3. Fraction of atoms remaining in the 1 cm3 volume as a function of the atom free flight time Toff at g = 1, V molasses intensity I = I0, o : I = I0/2. (a) At 1 g. (b) At 0 g. The continuous line is a calculated decay at 0 g with a temperature of 18 µK i.e. a.r.m.s. velocity of 3 cm/s. Fig. 3. Fraction d'atomes restants dans le cm3 d'observation en fonction du temps de vol libre Toff pour g = 1, V: intensité des faisceaux de mélasse I = 10, a : I = 10/2. (a) 1 g. (b) 0 g. La
de la cellule. With this experimental set-up, the trap worked continuously during the three flights and contained typically 3 × 108 atoms at a density of 5 × 1010 at/cm3. Temperature measurements in micro-gravity were performed using the release and recapture (RR) Fig. 3. Fraction of atoms remaining in the 1 cm3 volume as a function of the atom free flight time Toff at g = 1, V molasses intensity I = I0, o : I = I0/2. (a) At 1 g. (b) At 0 g. The continuous line is a calculated decay at 0 g with a temperature of 18 µK i.e. a.r.m.s. velocity of 3 cm/s. Fig. 3. Fraction d'atomes restants dans le cm3 d'observation en fonction du temps de vol libre Toff pour g = 1, V: intensité des faisceaux de mélasse I = 10, a : I = 10/2. (a) 1 g. (b) 0 g. La ligne continue est issue d'un modèle simple d'expansion isotrope à 0 g d'un gaz à une température de 18 µK soit une vitesse quadratique moyenne de 3 cm/s. method [10] which is particularly simple and efficient in reduced gravity (fig. 2). First, the atoms are loaded into the MOT from the cesium vapour for 1.5 sec. The trapping magnetic field is then switched off in less than 0.5 ms and the laser intensity is reduced to cool down the atoms. The atoms diffuse slowly away in optical molasses over 40 ms while cooling down. The atoms are then released in free flight by switching off the trapping beams with A02 and a mechanical shutter. The time constant of the intensity turn-off was optimized and set to 50 fs to minimize the atom temperature. After an adjustable delay Toff (0-300 ms), the molasses beams are turned on again and the ratio fluorescence before turn-off to fluorescence immediately after turn-on indicates the fraction of atoms which stayed in the observation volume during Toff. These atoms then slowly diffuse out of the molasses volume with a decay time constant of 0.2 sec. and the fluorescence signal reaches a baseline. Interestingly, by repeating these
the cesium vapour for 1.5 sec. The trapping magnetic field is then switched off in less than 0.5 ms and the laser intensity is reduced to cool down the atoms. The atoms diffuse slowly away in optical molasses over 40 ms while cooling down. The atoms are then released in free flight by switching off the trapping beams with A02 and a mechanical shutter. The time constant of the intensity turn-off was optimized and set to 50 fs to minimize the atom temperature. After an adjustable delay Toff (0-300 ms), the molasses beams are turned on again and the ratio fluorescence before turn-off to fluorescence immediately after turn-on indicates the fraction of atoms which stayed in the observation volume during Toff. These atoms then slowly diffuse out of the molasses volume with a decay time constant of 0.2 sec. and the fluorescence signal reaches a baseline. Interestingly, by repeating these measurements without magnetic field gradient or equivalently at 1 g for long Toff, we found that this baseline was actually the sum of the fluorescence of the fast atoms from the cell and of the fluorescence of cold atoms being collected by the a+ <7~ molasses (fig. 2c). This signal was typically 3-5% of the fluorescence signal just before turn-off. We thus measured this contribution for each set of parameters Toff, I, δ and corrected for it. Simultaneous recordings of the residual accelerations along Ox, Oy, Oz on the optical table were made to reject the data where these accelerations were larger than ±2× 10-2 g. Typically 7 successive R-R measurements with the same laser parameters were made during each low gravity parabola. In the 2 min. interval between parabolas, Toff was changed as well as the trap parameters. All usable data for which the accelerations were low enough are reported in figure 3, representing about 40% of the total reduced gravity time. This figure illustrates the dramatic benefit of the reduced gravity for the residence time of the cold atoms in the small observation volume. Whereas at 1 g, all atoms have escaped the 1 cm3 volume in 50
was typically 3-5% of the fluorescence signal just before turn-off. We thus measured this contribution for each set of parameters Toff, I, δ and corrected for it. Simultaneous recordings of the residual accelerations along Ox, Oy, Oz on the optical table were made to reject the data where these accelerations were larger than ±2× 10-2 g. Typically 7 successive R-R measurements with the same laser parameters were made during each low gravity parabola. In the 2 min. interval between parabolas, Toff was changed as well as the trap parameters. All usable data for which the accelerations were low enough are reported in figure 3, representing about 40% of the total reduced gravity time. This figure illustrates the dramatic benefit of the reduced gravity for the residence time of the cold atoms in the small observation volume. Whereas at 1 g, all atoms have escaped the 1 cm3 volume in 50 ms, at 0 g 10% of them still remain in this volume after a free flight of 0.2 sec. The maximum time at which we were able unambiguously to detect atoms was 350 ms (I of the initial number). The temperature of the atoms was determined by fitting the data in figure 3, using a simple model of a gaussian atomic cloud expanding freely and isotropically at temperature T during Toff. The measured temperature at δ = 15 MHz was 18 µK (± 10), corresponding to an rms velocity along any axis of 3 cm/s. This temperature is within a factor of 2 of the lowest achieved temperature in cr + (y molasses at this detuning [11] and the uncertainty comes mostly from geometrical effects. Note that this temperature could still be lowered by 8 by working at much larger laser detuning or by using optical molasses with linear polarizations for which the temperature can reach~ 2.5 µK [2]. This would enable one to observe a larger fraction of atoms to be detected at Toff≧0.3 sec., but the residual plane accelerations would then become the main limit. To summarize, we have produced cold cesium atoms in a reduced gravity environment
in figure 3, using a simple model of a gaussian atomic cloud expanding freely and isotropically at temperature T during Toff. The measured temperature at δ = 15 MHz was 18 µK (± 10), corresponding to an rms velocity along any axis of 3 cm/s. This temperature is within a factor of 2 of the lowest achieved temperature in cr + (y molasses at this detuning [11] and the uncertainty comes mostly from geometrical effects. Note that this temperature could still be lowered by 8 by working at much larger laser detuning or by using optical molasses with linear polarizations for which the temperature can reach~ 2.5 µK [2]. This would enable one to observe a larger fraction of atoms to be detected at Toff≧0.3 sec., but the residual plane accelerations would then become the main limit. To summarize, we have produced cold cesium atoms in a reduced gravity environment and demonstrated a dramatic increase in the residence time of the atoms in a small volume. We believe that these experimental techniques have become simple enough to consider developing cold atom satellite clocks. Compared to the fountain, a gain of 10 in the resonance width seems a reasonable goal. Similarly, the accuracy of such a clock will benefit from both the compactness of the set-up made possible by the 0 g environment and the cm/s velocities of the atoms. Further cooling below the photon recoil energy [13] which, when applied to cesium, would produce atomic velocities in the mm/s range may also increase considerably the performance of such a 0 g satellite clock. We acknowledge useful discussions with C. Cohen-Tannoudji, J. Dalibard, Y. Castin, A. Clairon and the ENS Laser Cooling group. The technical support of ORBITICS and of the Bretigny-sur-Orge flight center is also gratefully acknowledged. This work was supported by CNES under contracts 900271, 910414 by DRET (89214) and Collège de France. Laboratoire de Spectroscopie Hertzienne is associated with CNRS (URA 18) and Université Pierre-et-Marie-Curie. Note remise le 4 janvier 1993, acceptée le 20 janvier 1993. REFERENCES [1] See for instance, C. COHEN-TANNOUDJI and W. PHILLIPS, Physics Today,
the accuracy of such a clock will benefit from both the compactness of the set-up made possible by the 0 g environment and the cm/s velocities of the atoms. Further cooling below the photon recoil energy [13] which, when applied to cesium, would produce atomic velocities in the mm/s range may also increase considerably the performance of such a 0 g satellite clock. We acknowledge useful discussions with C. Cohen-Tannoudji, J. Dalibard, Y. Castin, A. Clairon and the ENS Laser Cooling group. The technical support of ORBITICS and of the Bretigny-sur-Orge flight center is also gratefully acknowledged. This work was supported by CNES under contracts 900271, 910414 by DRET (89214) and Collège de France. Laboratoire de Spectroscopie Hertzienne is associated with CNRS (URA 18) and Université Pierre-et-Marie-Curie. Note remise le 4 janvier 1993, acceptée le 20 janvier 1993. REFERENCES [1] See for instance, C. COHEN-TANNOUDJI and W. PHILLIPS, Physics Today, oct. 1990, p. 33 and special issue of J. Opt. Soc. Am., 6, 1989, S. CHU and C. WIEMAN Eds., and Laser Manipulation of Atoms and Ions, E. ARIMONDO and W. D. PHILLIPS Eds, Varenna Summer School, 1991, North-Holland, Amsterdam, 1993. [2] C. SALOMON, J. DALIBARD, W. D. PHILLIPS, A. CLAIRON and S. GUELLATI, Europhys. Lett., 12, 1990, p. 683. [3] J. R. ZACHARIAS, Unpublished, 1953. See, for instance N. RAMSEY, Molecular beams, Oxford University Press. Oxford. 1985. [4] M. KASEVICH, E. RIIS, S. CHU and R. DE VOE, Phys. Rev. Lett., 63, 1989, p. 612. [5] A. CLAIRON, C. SALOMON, S. GUELLATI and W. D. PHILLIPS, Europhys. Lett., 16, 1991, p. 165. [6] This plane is operated by the French National Center for spatial Studies, CNES. [7] C. MONROE, W. SWANN, H. ROBINSON and C. WIEMAN, Phys. Rev. Lett., 65, 1990, p. 1571. [8] D. GRISON, B. LOUNIS, C. SALOMON, J. Y. COURTOIS and G. GRYNBERG, Europhys. Lett., 15, 1991, p. 149. [9] We gratefully thank the OMTEC laboratories for providing us with their DBR diodes. [10] S. CHU, L. HOLLBERG, J. BJORKHOLM, A. CABLE and A. ASHKIN, Phys. Rev. Lett., 55, 1985, p. 48. [11] A. CLAIRON, Ph.
CLAIRON and S. GUELLATI, Europhys. Lett., 12, 1990, p. 683. [3] J. R. ZACHARIAS, Unpublished, 1953. See, for instance N. RAMSEY, Molecular beams, Oxford University Press. Oxford. 1985. [4] M. KASEVICH, E. RIIS, S. CHU and R. DE VOE, Phys. Rev. Lett., 63, 1989, p. 612. [5] A. CLAIRON, C. SALOMON, S. GUELLATI and W. D. PHILLIPS, Europhys. Lett., 16, 1991, p. 165. [6] This plane is operated by the French National Center for spatial Studies, CNES. [7] C. MONROE, W. SWANN, H. ROBINSON and C. WIEMAN, Phys. Rev. Lett., 65, 1990, p. 1571. [8] D. GRISON, B. LOUNIS, C. SALOMON, J. Y. COURTOIS and G. GRYNBERG, Europhys. Lett., 15, 1991, p. 149. [9] We gratefully thank the OMTEC laboratories for providing us with their DBR diodes. [10] S. CHU, L. HOLLBERG, J. BJORKHOLM, A. CABLE and A. ASHKIN, Phys. Rev. Lett., 55, 1985, p. 48. [11] A. CLAIRON, Ph. LAURENT, A. NADIR, M. DREWSEN, D. GRISON, B. LOUNIS and C. SALOMON, Proc. of the 4th European Time and Frequency Forum, J. J. HUNT Ed., ESA SP 340, 1992, and to be published. [12] P. LETT, R. WATTS, C. WESTBROOK, W. PHILLIPS, P. GOULD and H. METCALF, Phys. Rev. Lett., 61, 1988, p. 169. [13] M. KASEVICH and S. CHU, Phys. Rev. Lett., 69, 1992, p. 1741. Laboratoire de Spectroscopie Hertzienne de l'École Normale Supérieure, 24, rue Lhomond, 75005 Paris, France. Physique de la matière condensée/Condensed Matter Physics Paramètre critique de transition microphase d'une solution de copolymères Mustapha BENMOUNA Résumé Le paramètre critique de transition microphase pour une solution de copolymères est obtenu à partir de l'équation de la spinodale généralisée déduite de la fonction de diffusion. Le cas d'un mélange de copolymères et d'homopolymères est aussi considéré. Critical parameter of microphase transition in copolymer solutions Abstract — The critical parameter above which a copolymer solution undergoes a microphase transition is calculated from the generalized spinodal equation which is obtained from the scattering function. The case of a mixture of copolymers and homopolymers is also considered. Abridged English Version The scattering intensity for a diblock copolymer AB in solution or