Abstract

We report on a simple anisotropic magneto-optical trap for neutral atoms that produces a large sample of cold atoms confined in a cylindrically-shaped volume with a high aspect ratio (100:1). Due to the large number of trapped atoms, the laser beams that propagate along the optically thick axis of the trap to cool the atoms are substantially attenuated. We demonstrate that the resulting intensity imbalance produces a net force that spatially localizes the atoms. This limits both the trap length and the total number of trapped atoms. Rotating the cooling beams by a small angle relative to the trap axis avoids the problem of attenuation, and atoms can be trapped throughout the entire available trapping volume. Numerical and experimental results are reported that demonstrate the effects of absorption in an anisotropic trap, and a steady-state, line-center optical path length of 55 is measured for a probe beam propagating along the length of the trap.

© 2007 Optical Society of America

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    [CrossRef]
  2. G. Labeyrie, G.L. Gattobigio, T. Chaneli’ere, G.L. Lippi, T. Ackemann, R. Kaiser, "Nonlinear Lensing Mechanisms in a Cloud of Cold Atoms," Euro. Phys. Jn. D. 41, 337 (2007).
    [CrossRef]
  3. Y. Wang, M. Saffman, "Experimental Study of Nonlinear Focusing in a Magneto-optical Trap Using a Z-scan Technique," Phys. Rev. A 70, 013801 (2004).
    [CrossRef]
  4. M. Vengalatorre, M. Prentiss, "Radial Confinement of Light in an Ultracold Anisotropic Medium," Phys. Rev. Lett. 95, 243601 (2005).
    [CrossRef]
  5. G.L. Gattobigio, F. Michaud, J. Javaloyes, J.W.R. Tabosa, R. Kaiser, "Bunching-induced Asymmetry in Degenerate Four-wave Mixing with Cold Atoms," Phys. Rev. A 74, 043407 (2006).
    [CrossRef]
  6. K.R. Hansen, K. Mølmer, "Trapping of Light Pulses in Ensembles of Stationary ? Atoms," Phys. Rev. A 75, 053802 (2007).
    [CrossRef]
  7. H.W. Chan, A.T. Black, V. Vuleti’c, "Observation of Collective-Emission-Induced Cooling of Atoms in an Optical Cavity," Phys. Rev. Lett. 90, 063003 (2003).
    [CrossRef] [PubMed]
  8. A.T. Black, H.W. Chan, V. Vuleti’c, "Observation of Collective Friction Forces due to Spatial Self-Organization of Atoms: From Rayleigh to Bragg Scattering," Phys. Rev. Lett. 91, 203001 (2003).
    [CrossRef] [PubMed]
  9. R. Bonificio, L. De Salvo, "Collective Atomic Recoil Laser (CARL) Optical Gain Without Inversion by Collective Atomic Recoil and Self-bunching of Two-level Atoms," Nucl. Instrum. Methods Phys. Res. Sec. A 341, 360 (1994).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  14. M. Vengalatorre, W. Rooijakkers, M. Prentiss, "Ferromagnetic Atom Guide with In Situ Loading," Phys. Rev. A 66, 053403 (2002).
    [CrossRef]
  15. M. Vengalatorre, W. Rooijakkers, R. Conroy, M. Prentiss, "Suppression of Photon Rescattering due to Spatial Anisotropy in a Cold Atomic Gas," Phys. Rev. A 67, 063412 (2003).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  22. J. Dalibard, "Laser Cooling of an Optically Thick Gas: The Simplest Radiation Pressure Trap?," Opt. Commun. 68, 203 (1988).
    [CrossRef]
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    [CrossRef]
  26. M. Brzozowska, T. Brzozowski, J. Zachorowski, W. Gawlik, "Nondestructive Study of Nonequilibrium States of Cold Trapped Atoms," Phys. Rev. A 72, 061401 (2005).
    [CrossRef]

2007

G. Labeyrie, G.L. Gattobigio, T. Chaneli’ere, G.L. Lippi, T. Ackemann, R. Kaiser, "Nonlinear Lensing Mechanisms in a Cloud of Cold Atoms," Euro. Phys. Jn. D. 41, 337 (2007).
[CrossRef]

K.R. Hansen, K. Mølmer, "Trapping of Light Pulses in Ensembles of Stationary ? Atoms," Phys. Rev. A 75, 053802 (2007).
[CrossRef]

2006

G.L. Gattobigio, F. Michaud, J. Javaloyes, J.W.R. Tabosa, R. Kaiser, "Bunching-induced Asymmetry in Degenerate Four-wave Mixing with Cold Atoms," Phys. Rev. A 74, 043407 (2006).
[CrossRef]

2005

A.M.C. Dawes, L. Illing, S. M. Clark, D. J. Gauthier, "All Optical Switching in Rubidium Vapor," Science 308, 672 (2005).
[CrossRef] [PubMed]

S. Wu, E. Su, M. Prentiss, "Time Domain de Broglie Wave Interferometry Along a Magnetic Guide," Eur. Phys. J. D. 35, 111 (2005).
[CrossRef]

M. Vengalatorre, M. Prentiss, "Radial Confinement of Light in an Ultracold Anisotropic Medium," Phys. Rev. Lett. 95, 243601 (2005).
[CrossRef]

E.A. Donley, T.P. Heavner, F. Levi, M.O. Tataw, S.R. Jefferts, "Double-pass Acousto-optic Modulator System," Rev. Sci. Inst. 76, 063112 (2005).
[CrossRef]

M. Brzozowska, T. Brzozowski, J. Zachorowski, W. Gawlik, "Nondestructive Study of Nonequilibrium States of Cold Trapped Atoms," Phys. Rev. A 72, 061401 (2005).
[CrossRef]

2004

Y. Wang, M. Saffman, "Experimental Study of Nonlinear Focusing in a Magneto-optical Trap Using a Z-scan Technique," Phys. Rev. A 70, 013801 (2004).
[CrossRef]

2003

H.W. Chan, A.T. Black, V. Vuleti’c, "Observation of Collective-Emission-Induced Cooling of Atoms in an Optical Cavity," Phys. Rev. Lett. 90, 063003 (2003).
[CrossRef] [PubMed]

A.T. Black, H.W. Chan, V. Vuleti’c, "Observation of Collective Friction Forces due to Spatial Self-Organization of Atoms: From Rayleigh to Bragg Scattering," Phys. Rev. Lett. 91, 203001 (2003).
[CrossRef] [PubMed]

M. Vengalatorre, W. Rooijakkers, R. Conroy, M. Prentiss, "Suppression of Photon Rescattering due to Spatial Anisotropy in a Cold Atomic Gas," Phys. Rev. A 67, 063412 (2003).
[CrossRef]

2002

M. Vengalatorre, W. Rooijakkers, M. Prentiss, "Ferromagnetic Atom Guide with In Situ Loading," Phys. Rev. A 66, 053403 (2002).
[CrossRef]

2001

T. Ackemann, W. Lange, "Optical Pattern Formation in Alkali Metal Vapors: Mechanisms, Phenomena and Use." Appl. Phys. B 72, 21 (2001).
[CrossRef]

G. Grynberg, C. Robbiliard, "Cold Atoms in Dissipative Optical Lattices," Phys. Rep. 3, 355 (2001).

1998

1996

A. Lambrecht, T. Coudreau, A.M. Steinberg, E. Giacobino, "Squeezing with Cold Atoms," Europhys. Lett. 36, 93 (1996).
[CrossRef]

1994

R. Bonificio, L. De Salvo, "Collective Atomic Recoil Laser (CARL) Optical Gain Without Inversion by Collective Atomic Recoil and Self-bunching of Two-level Atoms," Nucl. Instrum. Methods Phys. Res. Sec. A 341, 360 (1994).
[CrossRef]

1993

W. Ketterle, K. Davis, M. Joffe, A. Martin, D. Pritchard, "High Densities of Cold Atoms in a Dark Spontaneous-Force Optical Trap," Phys. Rev. Lett. 70, 2253 (1993).
[CrossRef] [PubMed]

J. Guo, P.R. Berman, B. Dubetsky, "Recoil-induced Resonances in Nonlinear Spectroscopy," Phys. Rev. A 46, 1426 (1993).
[CrossRef]

1992

1988

J. Dalibard, "Laser Cooling of an Optically Thick Gas: The Simplest Radiation Pressure Trap?," Opt. Commun. 68, 203 (1988).
[CrossRef]

Ackemann, T.

G. Labeyrie, G.L. Gattobigio, T. Chaneli’ere, G.L. Lippi, T. Ackemann, R. Kaiser, "Nonlinear Lensing Mechanisms in a Cloud of Cold Atoms," Euro. Phys. Jn. D. 41, 337 (2007).
[CrossRef]

T. Ackemann, W. Lange, "Optical Pattern Formation in Alkali Metal Vapors: Mechanisms, Phenomena and Use." Appl. Phys. B 72, 21 (2001).
[CrossRef]

Berman, P.R.

J. Guo, P.R. Berman, B. Dubetsky, "Recoil-induced Resonances in Nonlinear Spectroscopy," Phys. Rev. A 46, 1426 (1993).
[CrossRef]

Black, A.T.

H.W. Chan, A.T. Black, V. Vuleti’c, "Observation of Collective-Emission-Induced Cooling of Atoms in an Optical Cavity," Phys. Rev. Lett. 90, 063003 (2003).
[CrossRef] [PubMed]

A.T. Black, H.W. Chan, V. Vuleti’c, "Observation of Collective Friction Forces due to Spatial Self-Organization of Atoms: From Rayleigh to Bragg Scattering," Phys. Rev. Lett. 91, 203001 (2003).
[CrossRef] [PubMed]

Bonificio, R.

R. Bonificio, L. De Salvo, "Collective Atomic Recoil Laser (CARL) Optical Gain Without Inversion by Collective Atomic Recoil and Self-bunching of Two-level Atoms," Nucl. Instrum. Methods Phys. Res. Sec. A 341, 360 (1994).
[CrossRef]

Brzozowska, M.

M. Brzozowska, T. Brzozowski, J. Zachorowski, W. Gawlik, "Nondestructive Study of Nonequilibrium States of Cold Trapped Atoms," Phys. Rev. A 72, 061401 (2005).
[CrossRef]

Brzozowski, T.

M. Brzozowska, T. Brzozowski, J. Zachorowski, W. Gawlik, "Nondestructive Study of Nonequilibrium States of Cold Trapped Atoms," Phys. Rev. A 72, 061401 (2005).
[CrossRef]

Castin, Y.

Y. Castin, J.I. Cirac, M. Lewenstein, "Reabsorption of Light by Trapped Atoms," Phys. Rev. Lett. 80, 5305 (1998).
[CrossRef]

Chan, H.W.

A.T. Black, H.W. Chan, V. Vuleti’c, "Observation of Collective Friction Forces due to Spatial Self-Organization of Atoms: From Rayleigh to Bragg Scattering," Phys. Rev. Lett. 91, 203001 (2003).
[CrossRef] [PubMed]

H.W. Chan, A.T. Black, V. Vuleti’c, "Observation of Collective-Emission-Induced Cooling of Atoms in an Optical Cavity," Phys. Rev. Lett. 90, 063003 (2003).
[CrossRef] [PubMed]

Chaneli’ere, T.

G. Labeyrie, G.L. Gattobigio, T. Chaneli’ere, G.L. Lippi, T. Ackemann, R. Kaiser, "Nonlinear Lensing Mechanisms in a Cloud of Cold Atoms," Euro. Phys. Jn. D. 41, 337 (2007).
[CrossRef]

Chu, S.

Cirac, J.I.

Y. Castin, J.I. Cirac, M. Lewenstein, "Reabsorption of Light by Trapped Atoms," Phys. Rev. Lett. 80, 5305 (1998).
[CrossRef]

Clark, S. M.

A.M.C. Dawes, L. Illing, S. M. Clark, D. J. Gauthier, "All Optical Switching in Rubidium Vapor," Science 308, 672 (2005).
[CrossRef] [PubMed]

Conroy, R.

M. Vengalatorre, W. Rooijakkers, R. Conroy, M. Prentiss, "Suppression of Photon Rescattering due to Spatial Anisotropy in a Cold Atomic Gas," Phys. Rev. A 67, 063412 (2003).
[CrossRef]

Corwin, K. L.

Coudreau, T.

A. Lambrecht, T. Coudreau, A.M. Steinberg, E. Giacobino, "Squeezing with Cold Atoms," Europhys. Lett. 36, 93 (1996).
[CrossRef]

Dalibard, J.

J. Dalibard, "Laser Cooling of an Optically Thick Gas: The Simplest Radiation Pressure Trap?," Opt. Commun. 68, 203 (1988).
[CrossRef]

Davis, K.

W. Ketterle, K. Davis, M. Joffe, A. Martin, D. Pritchard, "High Densities of Cold Atoms in a Dark Spontaneous-Force Optical Trap," Phys. Rev. Lett. 70, 2253 (1993).
[CrossRef] [PubMed]

Dawes, A.M.C.

A.M.C. Dawes, L. Illing, S. M. Clark, D. J. Gauthier, "All Optical Switching in Rubidium Vapor," Science 308, 672 (2005).
[CrossRef] [PubMed]

De Salvo, L.

R. Bonificio, L. De Salvo, "Collective Atomic Recoil Laser (CARL) Optical Gain Without Inversion by Collective Atomic Recoil and Self-bunching of Two-level Atoms," Nucl. Instrum. Methods Phys. Res. Sec. A 341, 360 (1994).
[CrossRef]

Donley, E.A.

E.A. Donley, T.P. Heavner, F. Levi, M.O. Tataw, S.R. Jefferts, "Double-pass Acousto-optic Modulator System," Rev. Sci. Inst. 76, 063112 (2005).
[CrossRef]

Dubetsky, B.

J. Guo, P.R. Berman, B. Dubetsky, "Recoil-induced Resonances in Nonlinear Spectroscopy," Phys. Rev. A 46, 1426 (1993).
[CrossRef]

Epstein, R. J.

Gattobigio, G.L.

G. Labeyrie, G.L. Gattobigio, T. Chaneli’ere, G.L. Lippi, T. Ackemann, R. Kaiser, "Nonlinear Lensing Mechanisms in a Cloud of Cold Atoms," Euro. Phys. Jn. D. 41, 337 (2007).
[CrossRef]

G.L. Gattobigio, F. Michaud, J. Javaloyes, J.W.R. Tabosa, R. Kaiser, "Bunching-induced Asymmetry in Degenerate Four-wave Mixing with Cold Atoms," Phys. Rev. A 74, 043407 (2006).
[CrossRef]

Gauthier, D. J.

A.M.C. Dawes, L. Illing, S. M. Clark, D. J. Gauthier, "All Optical Switching in Rubidium Vapor," Science 308, 672 (2005).
[CrossRef] [PubMed]

Gawlik, W.

M. Brzozowska, T. Brzozowski, J. Zachorowski, W. Gawlik, "Nondestructive Study of Nonequilibrium States of Cold Trapped Atoms," Phys. Rev. A 72, 061401 (2005).
[CrossRef]

Giacobino, E.

A. Lambrecht, T. Coudreau, A.M. Steinberg, E. Giacobino, "Squeezing with Cold Atoms," Europhys. Lett. 36, 93 (1996).
[CrossRef]

Gibble, K.E.

Grynberg, G.

G. Grynberg, C. Robbiliard, "Cold Atoms in Dissipative Optical Lattices," Phys. Rep. 3, 355 (2001).

Guo, J.

J. Guo, P.R. Berman, B. Dubetsky, "Recoil-induced Resonances in Nonlinear Spectroscopy," Phys. Rev. A 46, 1426 (1993).
[CrossRef]

Hand, C. F.

Hansen, K.R.

K.R. Hansen, K. Mølmer, "Trapping of Light Pulses in Ensembles of Stationary ? Atoms," Phys. Rev. A 75, 053802 (2007).
[CrossRef]

Heavner, T.P.

E.A. Donley, T.P. Heavner, F. Levi, M.O. Tataw, S.R. Jefferts, "Double-pass Acousto-optic Modulator System," Rev. Sci. Inst. 76, 063112 (2005).
[CrossRef]

Illing, L.

A.M.C. Dawes, L. Illing, S. M. Clark, D. J. Gauthier, "All Optical Switching in Rubidium Vapor," Science 308, 672 (2005).
[CrossRef] [PubMed]

Javaloyes, J.

G.L. Gattobigio, F. Michaud, J. Javaloyes, J.W.R. Tabosa, R. Kaiser, "Bunching-induced Asymmetry in Degenerate Four-wave Mixing with Cold Atoms," Phys. Rev. A 74, 043407 (2006).
[CrossRef]

Jefferts, S.R.

E.A. Donley, T.P. Heavner, F. Levi, M.O. Tataw, S.R. Jefferts, "Double-pass Acousto-optic Modulator System," Rev. Sci. Inst. 76, 063112 (2005).
[CrossRef]

Joffe, M.

W. Ketterle, K. Davis, M. Joffe, A. Martin, D. Pritchard, "High Densities of Cold Atoms in a Dark Spontaneous-Force Optical Trap," Phys. Rev. Lett. 70, 2253 (1993).
[CrossRef] [PubMed]

Kaiser, R.

G. Labeyrie, G.L. Gattobigio, T. Chaneli’ere, G.L. Lippi, T. Ackemann, R. Kaiser, "Nonlinear Lensing Mechanisms in a Cloud of Cold Atoms," Euro. Phys. Jn. D. 41, 337 (2007).
[CrossRef]

G.L. Gattobigio, F. Michaud, J. Javaloyes, J.W.R. Tabosa, R. Kaiser, "Bunching-induced Asymmetry in Degenerate Four-wave Mixing with Cold Atoms," Phys. Rev. A 74, 043407 (2006).
[CrossRef]

Kasapi, S.

Ketterle, W.

W. Ketterle, K. Davis, M. Joffe, A. Martin, D. Pritchard, "High Densities of Cold Atoms in a Dark Spontaneous-Force Optical Trap," Phys. Rev. Lett. 70, 2253 (1993).
[CrossRef] [PubMed]

Labeyrie, G.

G. Labeyrie, G.L. Gattobigio, T. Chaneli’ere, G.L. Lippi, T. Ackemann, R. Kaiser, "Nonlinear Lensing Mechanisms in a Cloud of Cold Atoms," Euro. Phys. Jn. D. 41, 337 (2007).
[CrossRef]

Lambrecht, A.

A. Lambrecht, T. Coudreau, A.M. Steinberg, E. Giacobino, "Squeezing with Cold Atoms," Europhys. Lett. 36, 93 (1996).
[CrossRef]

Lange, W.

T. Ackemann, W. Lange, "Optical Pattern Formation in Alkali Metal Vapors: Mechanisms, Phenomena and Use." Appl. Phys. B 72, 21 (2001).
[CrossRef]

Levi, F.

E.A. Donley, T.P. Heavner, F. Levi, M.O. Tataw, S.R. Jefferts, "Double-pass Acousto-optic Modulator System," Rev. Sci. Inst. 76, 063112 (2005).
[CrossRef]

Lewenstein, M.

Y. Castin, J.I. Cirac, M. Lewenstein, "Reabsorption of Light by Trapped Atoms," Phys. Rev. Lett. 80, 5305 (1998).
[CrossRef]

Lippi, G.L.

G. Labeyrie, G.L. Gattobigio, T. Chaneli’ere, G.L. Lippi, T. Ackemann, R. Kaiser, "Nonlinear Lensing Mechanisms in a Cloud of Cold Atoms," Euro. Phys. Jn. D. 41, 337 (2007).
[CrossRef]

Lu, Z.

Martin, A.

W. Ketterle, K. Davis, M. Joffe, A. Martin, D. Pritchard, "High Densities of Cold Atoms in a Dark Spontaneous-Force Optical Trap," Phys. Rev. Lett. 70, 2253 (1993).
[CrossRef] [PubMed]

Michaud, F.

G.L. Gattobigio, F. Michaud, J. Javaloyes, J.W.R. Tabosa, R. Kaiser, "Bunching-induced Asymmetry in Degenerate Four-wave Mixing with Cold Atoms," Phys. Rev. A 74, 043407 (2006).
[CrossRef]

Mølmer, K.

K.R. Hansen, K. Mølmer, "Trapping of Light Pulses in Ensembles of Stationary ? Atoms," Phys. Rev. A 75, 053802 (2007).
[CrossRef]

Prentiss, M.

M. Vengalatorre, M. Prentiss, "Radial Confinement of Light in an Ultracold Anisotropic Medium," Phys. Rev. Lett. 95, 243601 (2005).
[CrossRef]

S. Wu, E. Su, M. Prentiss, "Time Domain de Broglie Wave Interferometry Along a Magnetic Guide," Eur. Phys. J. D. 35, 111 (2005).
[CrossRef]

M. Vengalatorre, W. Rooijakkers, R. Conroy, M. Prentiss, "Suppression of Photon Rescattering due to Spatial Anisotropy in a Cold Atomic Gas," Phys. Rev. A 67, 063412 (2003).
[CrossRef]

M. Vengalatorre, W. Rooijakkers, M. Prentiss, "Ferromagnetic Atom Guide with In Situ Loading," Phys. Rev. A 66, 053403 (2002).
[CrossRef]

Pritchard, D.

W. Ketterle, K. Davis, M. Joffe, A. Martin, D. Pritchard, "High Densities of Cold Atoms in a Dark Spontaneous-Force Optical Trap," Phys. Rev. Lett. 70, 2253 (1993).
[CrossRef] [PubMed]

Robbiliard, C.

G. Grynberg, C. Robbiliard, "Cold Atoms in Dissipative Optical Lattices," Phys. Rep. 3, 355 (2001).

Rooijakkers, W.

M. Vengalatorre, W. Rooijakkers, R. Conroy, M. Prentiss, "Suppression of Photon Rescattering due to Spatial Anisotropy in a Cold Atomic Gas," Phys. Rev. A 67, 063412 (2003).
[CrossRef]

M. Vengalatorre, W. Rooijakkers, M. Prentiss, "Ferromagnetic Atom Guide with In Situ Loading," Phys. Rev. A 66, 053403 (2002).
[CrossRef]

Saffman, M.

Y. Wang, M. Saffman, "Experimental Study of Nonlinear Focusing in a Magneto-optical Trap Using a Z-scan Technique," Phys. Rev. A 70, 013801 (2004).
[CrossRef]

Steinberg, A.M.

A. Lambrecht, T. Coudreau, A.M. Steinberg, E. Giacobino, "Squeezing with Cold Atoms," Europhys. Lett. 36, 93 (1996).
[CrossRef]

Su, E.

S. Wu, E. Su, M. Prentiss, "Time Domain de Broglie Wave Interferometry Along a Magnetic Guide," Eur. Phys. J. D. 35, 111 (2005).
[CrossRef]

Tabosa, J.W.R.

G.L. Gattobigio, F. Michaud, J. Javaloyes, J.W.R. Tabosa, R. Kaiser, "Bunching-induced Asymmetry in Degenerate Four-wave Mixing with Cold Atoms," Phys. Rev. A 74, 043407 (2006).
[CrossRef]

Tataw, M.O.

E.A. Donley, T.P. Heavner, F. Levi, M.O. Tataw, S.R. Jefferts, "Double-pass Acousto-optic Modulator System," Rev. Sci. Inst. 76, 063112 (2005).
[CrossRef]

Vengalatorre, M.

M. Vengalatorre, M. Prentiss, "Radial Confinement of Light in an Ultracold Anisotropic Medium," Phys. Rev. Lett. 95, 243601 (2005).
[CrossRef]

M. Vengalatorre, W. Rooijakkers, R. Conroy, M. Prentiss, "Suppression of Photon Rescattering due to Spatial Anisotropy in a Cold Atomic Gas," Phys. Rev. A 67, 063412 (2003).
[CrossRef]

M. Vengalatorre, W. Rooijakkers, M. Prentiss, "Ferromagnetic Atom Guide with In Situ Loading," Phys. Rev. A 66, 053403 (2002).
[CrossRef]

Wang, Y.

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Figures (5)

Fig. 1.
Fig. 1.

a) The atom trap setup. b) Magnetic field contours (0.6 G/line) resulting from the magnetic cores (only a portion of the cores is shown). The orientation and polarization of the trapping beams (red arrows) are also shown, along with the orientation of the quadrupolar field lines.

Fig. 2.
Fig. 2.

a) The experimental beam geometry. The trapping beams are in the x-y-plane oriented at 45° to the y-axis and the cooling beams are in the x-z-plane. b) The model beam geometry with effective cooling and trapping beams shown. Also, the relative direction and magnitude of the magnetic field are shown.

Fig. 3.
Fig. 3.

The effect of the cooling beam intensity imbalance on trap formation. a1)-a4) Experimental longitudinal atomic density profiles that result when θ=0, OD=10, δ=-1.5Γ, I + c :I - c =25:4, 5:3, 3:5, 4:25. b1)-b4) The result of numerical simulations modeling the effects of intensity imbalance when θ=0, OD=10, δ=-Γ, I +:I-=3:2, 5:4, 4:5, 2:3 (note that OD here is defined for unsaturated absorption).

Fig. 4.
Fig. 4.

a) Experimental longitudinal atomic density profiles of traps obtained for equal intensity cooling beams at θ=0° and 10°. b) Numerically modeled atomic density profiles for equal intensity cooling beams at θ=0° and 10°.

Fig. 5.
Fig. 5.

Measured trap absorption. The absorption is fit using linear absorption theory for a two level atom. The best fit (obtained via a χ 2 fit) corresponds to OD=55±5.

Equations (5)

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P t ± ( r , z ) = 1 4 ( Ω t ± ) 2 ( Γ 2 ) 2 + 1 2 ( Ω t ± ) 2 + ( δ k t · v μ B B h ¯ ) 2 ,
P c ± ( r , z ) = 1 4 ( Ω c ± ) 2 ( Γ 2 ) 2 + 1 2 ( Ω c ± ) 2 + ( δ k c · v ) 2 ,
( Ω t ± ) 2 = 2 I t ± d 2 c ε 0 h ¯ 2 exp ( z 2 w t 2 ) ,
( Ω c ± ) 2 = 2 I c ± d 2 c ε 0 h ¯ 2 exp ( r 2 w c 2 ) exp ( n [ z ] σ ) ,
P ¯ i j = P i j ( P t + + P t + P c + + P c ) ,

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