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Application of a very long cavity laser to atom slowing down and optical pumping
Volume 50, number 6
OPTICS COMMUNICATIONS
15 July 1984
APPLICATION OF A VERY LONG CAVITY LASER TO ATOM SLOWING DOWN AND OPTICAL PUMPING L. MOI * Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Received 10 January 1984 Revised manuscript received 10 May 1984
A method to slow down an atomic beam with a counter-propagating resonant laser beam is proposed. The laser radiates across the full Doppler profile of the atomic beam with a longitudinal mode separation which is slightly less than the homogeneous linewidth of the atoms. This allows the atoms to come to rest without the need for frequency tuning or laser chirping. The required mode separation can be obtained from a very long-cavity laser. The application to optical pumping will be also discussed.
As the proceedings o f a recent conference show, there is high interest in developing techniques for cooling and trapping isolated atoms [1]. The recent success in decelerating an atomic beam o f sodium with resonant laser light by Prodan et al. [2] is a major step toward the trapping o f neutral atoms. The use o f a monochromatic laser, however, requires some method to keep the atomic resonance in tune as the atoms decelerate. Prodan et al. [2] employed a spatially varying magnetic field to compensate the Doppler shift with a Zeeman shift. Another approach, originally proposed by Letokhov and his colleagues [3], and recently demonstrated b y Prodan and Phillips [4], employs a frequency chirped laser to track the resonance as the atoms slow. We propose here another alternative which has potential advantages in efficiency and simplicity. By using light from a very long multimode laser, the spectrum can be tailored to match the full Doppler profile o f the atomic beam, therel~y avoiding the need to tune the spectrum to follow each atom as it slows down. The method require higher power since many modes must operate simultaneously, *Permanent address: Istituto di Fisica Atomica e MolecolareC.N.R., via De1 Giardino 7, 56100 Pisa, Italy. 0 030-4018/84/$03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
but the overall power requirement appears to be reasonable. Furthermore, the method should also be useful for optical pumping of a dense vapor. To explain the method, we consider the problem of decelerating atoms b y laser light. The laser deceleration makes use of the momentum imparted to an atom when it absorbs a photon. The change in velocity is (1)
A V = hvMc ,
where v is the photon frequency and M is the atomic mass. If an atom is irradiated by counter propagating resonant laser light, it undergoes unidirectional absorption recoil followed by isotropic emission recoil. The result is a net transfer o f momentum from the light to the atom. The number o f absorptions to bring an atom with velocity V t o rest is
N=McV/h,,.
(2)
More exactly the atomic velocity can be confined around V = 0 with a spread given b y A V = cAr H/~',
(3)
where AvH = homogeneous linewidth o f the atom, and with a transversal velocity component
349
Volume 50, number 6
VT = x/
dM<
OPTICS COMMUNICATIONS
O)
caused by the random reradiation. These velocities correspond, if they are calculated for sodium atoms, to a kinetic temperature T ~ 0.05 K. Previous experiments have employed single mode tunable lasers. In order to stay tuned as the atom is retarded, the frequency matching condition must be maintained: VL = VO(I + V/C).
(5)
However, if the laser is not monochromatic but has a spectrum which spans the full Doppler profile of the beam &v L = v 0 VIe
(6)
then frequency matching occurs naturally. Such a spectrum can be simulated by operating the laser in a multimode regime for which the mode separation is less than or comparable to the homogeneous linewidth of the atom, AvH . Under this condition the atom "sees" a continuous spectrum. The length of the required laser cavity is L = c/2Av H .
(7)
For optimal operation the power in each mode should be high enough to saturate the transition. The method can work with lower power, but at the cost of a longer deceleration path. If higher power is available the linewidth can be power broadened, allowing the use of a shorter laser with broader mode spacing. The saturated linewidth is AVH = A v 0 (1 + P / P s ) 1 / 2 ,
(8)
where e S = 2rrhcA/X3r
(9)
is the saturatien power through the cross-section A for a two level system (5). r is the spontaneous lifetime for the transition. Optical pumping effects can be troublesome with light from a single mode laser. The proposed method avoids these, however, since the entire spectrum is continually excited. The dynamics of slowing down an atomic beam with light from a very long multimode laser is relatively straightforward, to a first approximation every atom experiences a constant retarding force irrespective of its speed. A sharp high. frequency cutoff will avoid to the atoms to be 350
15 July 1984
pushed back and a very narrow peak around the zero value of the axial velocity will be produced. This sharp cutoff may be realized, for example, by using a second atomic beam which crosses the laser cavity and absorbs the cavity light at resonance center. To illustrate the method, we give the order of magnitude of the parameters for retarding magnesium and sodium. Magnesium from an oven at 1000 K has a speed V ~ 105 cm s - 1 . Using the principal transition at X = 285 rim, the required number of photons is N = 1.6 × 104. The radiation lifetime is r = 2 ns. In the saturation regime the deceleration is a = 1.5 × 109 cm s - 2 and the atoms are brought to rest in about 3 cm. The required laser cavity length isL ~ 190 cm; and the total bandwidth is A v E = v 0 V/c = 3.3 GHz. The saturating laser power density, according to eq. (9), is PS "" 2.7 W c m - 2 for each laser mode. The total laser power density over the full bandwidth is PT ~ 1 I0 W c m - 2 : The power requirement can be lowered by stopping the atoms over a longer path. For example, ifa path of I m is available, the power can be reduced by a factor of about 30. The laser light can be obtained by frequency doubling the output of a Rhd 6G dye laser. For sodium, the parameters are: V " 105 cm s -1, X= 589 nm, N = 3 X 104 photons, r = 16 ns, a ~ 108 cm s - 2 ; stopping distance ~50 cm, AvL ~ 3 GHz, by considering the hyperfine structure, L ~ 15 m. The saturation power density calculated from eq. (9) isP s = 38 mW cm - 2 a n d P T ~-- 12.7 W cm - 2 . A 15 m laser cavity is feasible, but by operating the laser at 40 W c m - 2 the homogeneous linewidth is broadened by a factor of about 2 and the cavity length is reduced of the same factor. A long laser is easier to operate than one might at first expect. The long lasers can be easily achieved simply by moving the output mirror of a commercial c.w. dye laser and introducing positive lenses or spherical mirrors into the cavity in order to compensate for a small misalignment and for losses produced by diffraction. We have operated in the long cavity configuration a commercial linear dye laser (Coherent Radiation 599) and have achieved cavity lengths up to about 7 m, with power losses of the order of 30-40% with respect to the normal configuration. The obtained length and the power losses were mainly due to the lack of suitable tables and mirrors. Longer length and
Volume 50, number 6
OPTICS COMMUNICATIONS
lower losses should be easily achieved by adopting a folded configuration with appropriate spherical mirrors. The laser intensity is quite stable. The spectral width has been modified by inserting one or two etaIons in the cavity. With two intracavity etalons the laser oscillated over few modes, allowing the use of a 300 FSR spectrum analyzer. The obtained spectra show the expected frequency mode separation and do not exhibit, at first insight, peculiar features due to the longer cavity length. At the moment no quantitative data are available about the mode competition and the mode jitter of these cavities. However to reduce any possible mode competition, in according with the calculations made by Hertel et al. [6], it may be desirable to adopt a different configuration in which the dye jet is at the center of the cavity ("Z" configuration [7]). In this case there would be a complete superposition of the cavity modes and the "mirror-to-jet" mode, and the mode flipping should occur with a characteristic time of a few ns, fast enough to have negligible effect on the cooling process. Another approach, which would assure that each mode operates continuoUsly with the desired power, is to use a mode locked laser. The width of the pulse Tp would be controlled with an etalon so that the spectral width of the laser App = 1/2 rrTp satisfies App = APD. The repetition rate lJr is adjusted to match the homogeneous width ur = 1/r. This solution allow. ing higher peak power, is usefull when the doubling of the laser wavelength is necessary. A hasty and tentative test of a 6 m long cavity laser on a 2 m sodium beam showed a significative modification in the Doppler profile of the atomic beam. The power was about 350 mW, and the laser beam was first expanded to a diameter of 1 cm and then focused on the beam nozzle. The laser consisted of a Coherent 599 in which the end mirror was replaced by one spherical mirror (2 m focal length), one plane mirror and one spherical output coupler in the given order. The mirrors were located at about 2--4 and 6 m from the dye jet, and aligned in order to get almost normal incidence. A second single mode dye laser was used to check the induced modification on the atomic Doppler profile [2]. These results provide unambiguous evidence for the validity of the proposed cooling method and indicate that mode competition, if it occurs, may not be serious, even in the simplest laser configuration. A complete and deft-
15 July 1984
nitive experiment is now in progress. The very long cavity laser method is potentially quite general. The cooling process, which involves all the atoms in the beam, is not affected by collisions though, of course, collisions increase atomic beam divergence. Frequency jitter, which is usually a problem in a long laser, has no effect and can even help. The construction of a long cavity is straigthforward, requiring only a conventional optical table and standard components. Finally we point out that long cavity lasers may also be very useful for the optical pumping of dense vapors or of high flow rate atomic beams for producing polarized ion beam and for other applications. Recently Cusma and Anderson [8] reported unexpected high efficiency in optically pumping sodium when their dye laser operated multimode with a 200 MHz spacing. The pumping efficiency increased about 12% compared to operation with a 400 MHz spacing. A further improvement in optical pumping efficiency should be possible with a very long cavity laser which can pump simultaneously every atom regardless of its velocity. Furthermore the saturation intensity for optical pumping is reduced compared to saturation of the free transition by the factor 21"/T, where T is the optical pumping relaxation time [9]. Consequently, the absorption line can be easily broadened, allowing a shorter laser or a larger light beam. In summary, very long multimode lasers are relatively simple to operate and have important potential benefits for atom cooling and pumping. The author thanks the M.I.T. Regional Laser Facility for help in carrying out preliminary experimental work, and R.S. Dasari, M.M, Kash and R.G. Hulet for assistance. He also thanks J.V. Prodan, H. Metcalf and W.D. Phillips for offering their assistance in testing the application of a long cavity laser to the cooling of a sodium beam. The author wishes to thank T.I). Hansch for pointing out the possible ad. vantage of using a mode locked laser, D. Kleppner, S. Haroche and C. Cohen-Tannoudji for helpful discussions and for assistance in preparing the manuscript. This work was partially supported by the Office of Naval Research, Grant NR393-039, and the National Science Foundation, Grant 8210486-A01.PHY.
351
Volume 50, number 6
OPTICS COMMUNICATIONS
References [ 1] Laser cooled and trapped atoms, Proc. Workshop on Spectroscopic application of slow atomic beams, NBS, Gaithersburg, MD, April 1983, ed. W.D. Phillips, NBS Special Publication 653. [2] J.V. Prodan, W.D. Phillips and H. Metcalf, Phys. Rev. Lett. 49 (1982) 1149. [3] S. Letokhov, V.G. Minogin and B.D. Pavlik, Optics Comm. 19 (1976) 72. [4] J.V. Prodan and W.D. Phillips, Cooled and trapped atoms, Proc. Workshop on Spectroscopic applications of slow atomic beams, NBS, Gaithersburg, MD, April 1983, ed., W.D. Phillips, NBS Special Publication 653, p. 137.
352
15 July 1984
[5] K. Shhnoda, High resolution laser spectroscopy, ed. K. Shimoda (Springer-Verlag 1976) p. 16-19. [6] I.V. Hertel, W. Muller and W. Stoll, IEEE J. Quantum Electron. QE13 (1977) 6. [7] C.T. Pike, Optics Comm. 10 (1974) 14. [8] J.T. Cusma and L.W. Anderson, Phys. Rev. Lett. 28 (1983) 1195. [9] M.S. Feld, M.M. Bums, T.U. Kuhl, P.G. Pappas and D.E. Murnick, Optics Lett. 5 (1980) 79.
OPTICS COMMUNICATIONS
15 July 1984
APPLICATION OF A VERY LONG CAVITY LASER TO ATOM SLOWING DOWN AND OPTICAL PUMPING L. MOI * Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Received 10 January 1984 Revised manuscript received 10 May 1984
A method to slow down an atomic beam with a counter-propagating resonant laser beam is proposed. The laser radiates across the full Doppler profile of the atomic beam with a longitudinal mode separation which is slightly less than the homogeneous linewidth of the atoms. This allows the atoms to come to rest without the need for frequency tuning or laser chirping. The required mode separation can be obtained from a very long-cavity laser. The application to optical pumping will be also discussed.
As the proceedings o f a recent conference show, there is high interest in developing techniques for cooling and trapping isolated atoms [1]. The recent success in decelerating an atomic beam o f sodium with resonant laser light by Prodan et al. [2] is a major step toward the trapping o f neutral atoms. The use o f a monochromatic laser, however, requires some method to keep the atomic resonance in tune as the atoms decelerate. Prodan et al. [2] employed a spatially varying magnetic field to compensate the Doppler shift with a Zeeman shift. Another approach, originally proposed by Letokhov and his colleagues [3], and recently demonstrated b y Prodan and Phillips [4], employs a frequency chirped laser to track the resonance as the atoms slow. We propose here another alternative which has potential advantages in efficiency and simplicity. By using light from a very long multimode laser, the spectrum can be tailored to match the full Doppler profile o f the atomic beam, therel~y avoiding the need to tune the spectrum to follow each atom as it slows down. The method require higher power since many modes must operate simultaneously, *Permanent address: Istituto di Fisica Atomica e MolecolareC.N.R., via De1 Giardino 7, 56100 Pisa, Italy. 0 030-4018/84/$03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
but the overall power requirement appears to be reasonable. Furthermore, the method should also be useful for optical pumping of a dense vapor. To explain the method, we consider the problem of decelerating atoms b y laser light. The laser deceleration makes use of the momentum imparted to an atom when it absorbs a photon. The change in velocity is (1)
A V = hvMc ,
where v is the photon frequency and M is the atomic mass. If an atom is irradiated by counter propagating resonant laser light, it undergoes unidirectional absorption recoil followed by isotropic emission recoil. The result is a net transfer o f momentum from the light to the atom. The number o f absorptions to bring an atom with velocity V t o rest is
N=McV/h,,.
(2)
More exactly the atomic velocity can be confined around V = 0 with a spread given b y A V = cAr H/~',
(3)
where AvH = homogeneous linewidth o f the atom, and with a transversal velocity component
349
Volume 50, number 6
VT = x/
dM<
OPTICS COMMUNICATIONS
O)
caused by the random reradiation. These velocities correspond, if they are calculated for sodium atoms, to a kinetic temperature T ~ 0.05 K. Previous experiments have employed single mode tunable lasers. In order to stay tuned as the atom is retarded, the frequency matching condition must be maintained: VL = VO(I + V/C).
(5)
However, if the laser is not monochromatic but has a spectrum which spans the full Doppler profile of the beam &v L = v 0 VIe
(6)
then frequency matching occurs naturally. Such a spectrum can be simulated by operating the laser in a multimode regime for which the mode separation is less than or comparable to the homogeneous linewidth of the atom, AvH . Under this condition the atom "sees" a continuous spectrum. The length of the required laser cavity is L = c/2Av H .
(7)
For optimal operation the power in each mode should be high enough to saturate the transition. The method can work with lower power, but at the cost of a longer deceleration path. If higher power is available the linewidth can be power broadened, allowing the use of a shorter laser with broader mode spacing. The saturated linewidth is AVH = A v 0 (1 + P / P s ) 1 / 2 ,
(8)
where e S = 2rrhcA/X3r
(9)
is the saturatien power through the cross-section A for a two level system (5). r is the spontaneous lifetime for the transition. Optical pumping effects can be troublesome with light from a single mode laser. The proposed method avoids these, however, since the entire spectrum is continually excited. The dynamics of slowing down an atomic beam with light from a very long multimode laser is relatively straightforward, to a first approximation every atom experiences a constant retarding force irrespective of its speed. A sharp high. frequency cutoff will avoid to the atoms to be 350
15 July 1984
pushed back and a very narrow peak around the zero value of the axial velocity will be produced. This sharp cutoff may be realized, for example, by using a second atomic beam which crosses the laser cavity and absorbs the cavity light at resonance center. To illustrate the method, we give the order of magnitude of the parameters for retarding magnesium and sodium. Magnesium from an oven at 1000 K has a speed V ~ 105 cm s - 1 . Using the principal transition at X = 285 rim, the required number of photons is N = 1.6 × 104. The radiation lifetime is r = 2 ns. In the saturation regime the deceleration is a = 1.5 × 109 cm s - 2 and the atoms are brought to rest in about 3 cm. The required laser cavity length isL ~ 190 cm; and the total bandwidth is A v E = v 0 V/c = 3.3 GHz. The saturating laser power density, according to eq. (9), is PS "" 2.7 W c m - 2 for each laser mode. The total laser power density over the full bandwidth is PT ~ 1 I0 W c m - 2 : The power requirement can be lowered by stopping the atoms over a longer path. For example, ifa path of I m is available, the power can be reduced by a factor of about 30. The laser light can be obtained by frequency doubling the output of a Rhd 6G dye laser. For sodium, the parameters are: V " 105 cm s -1, X= 589 nm, N = 3 X 104 photons, r = 16 ns, a ~ 108 cm s - 2 ; stopping distance ~50 cm, AvL ~ 3 GHz, by considering the hyperfine structure, L ~ 15 m. The saturation power density calculated from eq. (9) isP s = 38 mW cm - 2 a n d P T ~-- 12.7 W cm - 2 . A 15 m laser cavity is feasible, but by operating the laser at 40 W c m - 2 the homogeneous linewidth is broadened by a factor of about 2 and the cavity length is reduced of the same factor. A long laser is easier to operate than one might at first expect. The long lasers can be easily achieved simply by moving the output mirror of a commercial c.w. dye laser and introducing positive lenses or spherical mirrors into the cavity in order to compensate for a small misalignment and for losses produced by diffraction. We have operated in the long cavity configuration a commercial linear dye laser (Coherent Radiation 599) and have achieved cavity lengths up to about 7 m, with power losses of the order of 30-40% with respect to the normal configuration. The obtained length and the power losses were mainly due to the lack of suitable tables and mirrors. Longer length and
Volume 50, number 6
OPTICS COMMUNICATIONS
lower losses should be easily achieved by adopting a folded configuration with appropriate spherical mirrors. The laser intensity is quite stable. The spectral width has been modified by inserting one or two etaIons in the cavity. With two intracavity etalons the laser oscillated over few modes, allowing the use of a 300 FSR spectrum analyzer. The obtained spectra show the expected frequency mode separation and do not exhibit, at first insight, peculiar features due to the longer cavity length. At the moment no quantitative data are available about the mode competition and the mode jitter of these cavities. However to reduce any possible mode competition, in according with the calculations made by Hertel et al. [6], it may be desirable to adopt a different configuration in which the dye jet is at the center of the cavity ("Z" configuration [7]). In this case there would be a complete superposition of the cavity modes and the "mirror-to-jet" mode, and the mode flipping should occur with a characteristic time of a few ns, fast enough to have negligible effect on the cooling process. Another approach, which would assure that each mode operates continuoUsly with the desired power, is to use a mode locked laser. The width of the pulse Tp would be controlled with an etalon so that the spectral width of the laser App = 1/2 rrTp satisfies App = APD. The repetition rate lJr is adjusted to match the homogeneous width ur = 1/r. This solution allow. ing higher peak power, is usefull when the doubling of the laser wavelength is necessary. A hasty and tentative test of a 6 m long cavity laser on a 2 m sodium beam showed a significative modification in the Doppler profile of the atomic beam. The power was about 350 mW, and the laser beam was first expanded to a diameter of 1 cm and then focused on the beam nozzle. The laser consisted of a Coherent 599 in which the end mirror was replaced by one spherical mirror (2 m focal length), one plane mirror and one spherical output coupler in the given order. The mirrors were located at about 2--4 and 6 m from the dye jet, and aligned in order to get almost normal incidence. A second single mode dye laser was used to check the induced modification on the atomic Doppler profile [2]. These results provide unambiguous evidence for the validity of the proposed cooling method and indicate that mode competition, if it occurs, may not be serious, even in the simplest laser configuration. A complete and deft-
15 July 1984
nitive experiment is now in progress. The very long cavity laser method is potentially quite general. The cooling process, which involves all the atoms in the beam, is not affected by collisions though, of course, collisions increase atomic beam divergence. Frequency jitter, which is usually a problem in a long laser, has no effect and can even help. The construction of a long cavity is straigthforward, requiring only a conventional optical table and standard components. Finally we point out that long cavity lasers may also be very useful for the optical pumping of dense vapors or of high flow rate atomic beams for producing polarized ion beam and for other applications. Recently Cusma and Anderson [8] reported unexpected high efficiency in optically pumping sodium when their dye laser operated multimode with a 200 MHz spacing. The pumping efficiency increased about 12% compared to operation with a 400 MHz spacing. A further improvement in optical pumping efficiency should be possible with a very long cavity laser which can pump simultaneously every atom regardless of its velocity. Furthermore the saturation intensity for optical pumping is reduced compared to saturation of the free transition by the factor 21"/T, where T is the optical pumping relaxation time [9]. Consequently, the absorption line can be easily broadened, allowing a shorter laser or a larger light beam. In summary, very long multimode lasers are relatively simple to operate and have important potential benefits for atom cooling and pumping. The author thanks the M.I.T. Regional Laser Facility for help in carrying out preliminary experimental work, and R.S. Dasari, M.M, Kash and R.G. Hulet for assistance. He also thanks J.V. Prodan, H. Metcalf and W.D. Phillips for offering their assistance in testing the application of a long cavity laser to the cooling of a sodium beam. The author wishes to thank T.I). Hansch for pointing out the possible ad. vantage of using a mode locked laser, D. Kleppner, S. Haroche and C. Cohen-Tannoudji for helpful discussions and for assistance in preparing the manuscript. This work was partially supported by the Office of Naval Research, Grant NR393-039, and the National Science Foundation, Grant 8210486-A01.PHY.
351
Volume 50, number 6
OPTICS COMMUNICATIONS
References [ 1] Laser cooled and trapped atoms, Proc. Workshop on Spectroscopic application of slow atomic beams, NBS, Gaithersburg, MD, April 1983, ed. W.D. Phillips, NBS Special Publication 653. [2] J.V. Prodan, W.D. Phillips and H. Metcalf, Phys. Rev. Lett. 49 (1982) 1149. [3] S. Letokhov, V.G. Minogin and B.D. Pavlik, Optics Comm. 19 (1976) 72. [4] J.V. Prodan and W.D. Phillips, Cooled and trapped atoms, Proc. Workshop on Spectroscopic applications of slow atomic beams, NBS, Gaithersburg, MD, April 1983, ed., W.D. Phillips, NBS Special Publication 653, p. 137.
352
15 July 1984
[5] K. Shhnoda, High resolution laser spectroscopy, ed. K. Shimoda (Springer-Verlag 1976) p. 16-19. [6] I.V. Hertel, W. Muller and W. Stoll, IEEE J. Quantum Electron. QE13 (1977) 6. [7] C.T. Pike, Optics Comm. 10 (1974) 14. [8] J.T. Cusma and L.W. Anderson, Phys. Rev. Lett. 28 (1983) 1195. [9] M.S. Feld, M.M. Bums, T.U. Kuhl, P.G. Pappas and D.E. Murnick, Optics Lett. 5 (1980) 79.