Abstract

We demonstrate quantitative phase imaging of a neutral atomic beam by using a noninterferometric technique. A collimated thermal atomic beam is phase shifted by an off-resonant traveling laser beam with both a Gaussian and a TEM01 profile and with both red and blue detuning of as much as 50 GHz. Phase variations of more than 1000 rad were recovered from velocity-selective measurements of the propagation of the atomic beam and were found to be in quantitative agreement with theoretical predictions based on independently measured phase object intensity profiles and detunings.

© 2002 Optical Society of America

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References

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  1. P. R. Berman, ed., Atom Interferometry (Academic, San Diego, Calif., 1997).
  2. T. L. Gustavson, A. Landragin, and M. A. Kasevich, “Rotation sensing with a dual atom-interferometer Sagnac gyroscope,” Class. Quantum Grav. 17, 2385–2398 (2000).
    [CrossRef]
  3. A. Peters, K. Y. Chung, and S. Chu, “Measurement of gravitational acceleration by dropping atoms,” Nature 400, 849–852 (1999).
    [CrossRef]
  4. K. A. Nugent and D. Paganin, “Matter–wave phase measurement: a noninterferometric approach,” Phys. Rev. A 61, 063614 (2000).
    [CrossRef]
  5. D. Paganin and K. A. Nugent, “Noninterferometric phase imaging with partially coherent light,” Phys. Rev. Lett. 80, 2586–2589 (1998).
    [CrossRef]
  6. K. A. Nugent, D. Paganin, and T. E. Gureyev, “A phase odyssey,” Phys. Today 54(8), 27–32 (2001).
    [CrossRef]
  7. A. Messiah, Quantum Mechanics (North-Holland, Amsterdam, 1961), Vol. 1, p. 222.
  8. M. R. Teague, “Deterministic phase retrieval: a Green’s function solution,” J. Opt. Soc. Am. A 73, 1434–1441 (1983).
    [CrossRef]
  9. T. E. Gureyev, A. Roberts, and K. A. Nugent, “Partially coherent fields, the transport-of-intensity equation, and phase uniqueness,” J. Opt. Soc. Am. A 12, 1942–1946 (1995).
    [CrossRef]
  10. M. R. Walkiewicz, P. J. Fox, and R. E. Scholten, “Candlestick rubidium beam source,” Rev. Sci. Instrum. 71, 3342–3344 (2000).
    [CrossRef]
  11. R. E. Scholten, R. Gupta, J. J. McClelland, R. J. Celotta, M. S. Levenson, and M. G. Vangel, “Laser collimation of a chromium beam,” Phys. Rev. A 55, 1331–1338 (1997).
    [CrossRef]
  12. J. P. Gordon and A. Ashkin, “Motion of atoms in a radiation trap,” Phys. Rev. A 21, 1606–1617 (1980).
    [CrossRef]
  13. E. C. Harvey, J. P. Hayes, B. C. Dempster, T. R. Mackin, and R. E. Scholten, “Excimer laser ablation used for the fabrication of micro-optic phase and diffraction elements,” in Micro-Opto-Electro-Mechanical Systems, R. R. Syms, ed., Proc. SPIE 4075, 152–158 (2000).
    [CrossRef]

2001 (1)

K. A. Nugent, D. Paganin, and T. E. Gureyev, “A phase odyssey,” Phys. Today 54(8), 27–32 (2001).
[CrossRef]

2000 (4)

M. R. Walkiewicz, P. J. Fox, and R. E. Scholten, “Candlestick rubidium beam source,” Rev. Sci. Instrum. 71, 3342–3344 (2000).
[CrossRef]

T. L. Gustavson, A. Landragin, and M. A. Kasevich, “Rotation sensing with a dual atom-interferometer Sagnac gyroscope,” Class. Quantum Grav. 17, 2385–2398 (2000).
[CrossRef]

K. A. Nugent and D. Paganin, “Matter–wave phase measurement: a noninterferometric approach,” Phys. Rev. A 61, 063614 (2000).
[CrossRef]

E. C. Harvey, J. P. Hayes, B. C. Dempster, T. R. Mackin, and R. E. Scholten, “Excimer laser ablation used for the fabrication of micro-optic phase and diffraction elements,” in Micro-Opto-Electro-Mechanical Systems, R. R. Syms, ed., Proc. SPIE 4075, 152–158 (2000).
[CrossRef]

1999 (1)

A. Peters, K. Y. Chung, and S. Chu, “Measurement of gravitational acceleration by dropping atoms,” Nature 400, 849–852 (1999).
[CrossRef]

1998 (1)

D. Paganin and K. A. Nugent, “Noninterferometric phase imaging with partially coherent light,” Phys. Rev. Lett. 80, 2586–2589 (1998).
[CrossRef]

1997 (1)

R. E. Scholten, R. Gupta, J. J. McClelland, R. J. Celotta, M. S. Levenson, and M. G. Vangel, “Laser collimation of a chromium beam,” Phys. Rev. A 55, 1331–1338 (1997).
[CrossRef]

1995 (1)

1983 (1)

M. R. Teague, “Deterministic phase retrieval: a Green’s function solution,” J. Opt. Soc. Am. A 73, 1434–1441 (1983).
[CrossRef]

1980 (1)

J. P. Gordon and A. Ashkin, “Motion of atoms in a radiation trap,” Phys. Rev. A 21, 1606–1617 (1980).
[CrossRef]

Ashkin, A.

J. P. Gordon and A. Ashkin, “Motion of atoms in a radiation trap,” Phys. Rev. A 21, 1606–1617 (1980).
[CrossRef]

Celotta, R. J.

R. E. Scholten, R. Gupta, J. J. McClelland, R. J. Celotta, M. S. Levenson, and M. G. Vangel, “Laser collimation of a chromium beam,” Phys. Rev. A 55, 1331–1338 (1997).
[CrossRef]

Chu, S.

A. Peters, K. Y. Chung, and S. Chu, “Measurement of gravitational acceleration by dropping atoms,” Nature 400, 849–852 (1999).
[CrossRef]

Chung, K. Y.

A. Peters, K. Y. Chung, and S. Chu, “Measurement of gravitational acceleration by dropping atoms,” Nature 400, 849–852 (1999).
[CrossRef]

Dempster, B. C.

E. C. Harvey, J. P. Hayes, B. C. Dempster, T. R. Mackin, and R. E. Scholten, “Excimer laser ablation used for the fabrication of micro-optic phase and diffraction elements,” in Micro-Opto-Electro-Mechanical Systems, R. R. Syms, ed., Proc. SPIE 4075, 152–158 (2000).
[CrossRef]

Fox, P. J.

M. R. Walkiewicz, P. J. Fox, and R. E. Scholten, “Candlestick rubidium beam source,” Rev. Sci. Instrum. 71, 3342–3344 (2000).
[CrossRef]

Gordon, J. P.

J. P. Gordon and A. Ashkin, “Motion of atoms in a radiation trap,” Phys. Rev. A 21, 1606–1617 (1980).
[CrossRef]

Gupta, R.

R. E. Scholten, R. Gupta, J. J. McClelland, R. J. Celotta, M. S. Levenson, and M. G. Vangel, “Laser collimation of a chromium beam,” Phys. Rev. A 55, 1331–1338 (1997).
[CrossRef]

Gureyev, T. E.

Gustavson, T. L.

T. L. Gustavson, A. Landragin, and M. A. Kasevich, “Rotation sensing with a dual atom-interferometer Sagnac gyroscope,” Class. Quantum Grav. 17, 2385–2398 (2000).
[CrossRef]

Harvey, E. C.

E. C. Harvey, J. P. Hayes, B. C. Dempster, T. R. Mackin, and R. E. Scholten, “Excimer laser ablation used for the fabrication of micro-optic phase and diffraction elements,” in Micro-Opto-Electro-Mechanical Systems, R. R. Syms, ed., Proc. SPIE 4075, 152–158 (2000).
[CrossRef]

Hayes, J. P.

E. C. Harvey, J. P. Hayes, B. C. Dempster, T. R. Mackin, and R. E. Scholten, “Excimer laser ablation used for the fabrication of micro-optic phase and diffraction elements,” in Micro-Opto-Electro-Mechanical Systems, R. R. Syms, ed., Proc. SPIE 4075, 152–158 (2000).
[CrossRef]

Kasevich, M. A.

T. L. Gustavson, A. Landragin, and M. A. Kasevich, “Rotation sensing with a dual atom-interferometer Sagnac gyroscope,” Class. Quantum Grav. 17, 2385–2398 (2000).
[CrossRef]

Landragin, A.

T. L. Gustavson, A. Landragin, and M. A. Kasevich, “Rotation sensing with a dual atom-interferometer Sagnac gyroscope,” Class. Quantum Grav. 17, 2385–2398 (2000).
[CrossRef]

Levenson, M. S.

R. E. Scholten, R. Gupta, J. J. McClelland, R. J. Celotta, M. S. Levenson, and M. G. Vangel, “Laser collimation of a chromium beam,” Phys. Rev. A 55, 1331–1338 (1997).
[CrossRef]

Mackin, T. R.

E. C. Harvey, J. P. Hayes, B. C. Dempster, T. R. Mackin, and R. E. Scholten, “Excimer laser ablation used for the fabrication of micro-optic phase and diffraction elements,” in Micro-Opto-Electro-Mechanical Systems, R. R. Syms, ed., Proc. SPIE 4075, 152–158 (2000).
[CrossRef]

McClelland, J. J.

R. E. Scholten, R. Gupta, J. J. McClelland, R. J. Celotta, M. S. Levenson, and M. G. Vangel, “Laser collimation of a chromium beam,” Phys. Rev. A 55, 1331–1338 (1997).
[CrossRef]

Nugent, K. A.

K. A. Nugent, D. Paganin, and T. E. Gureyev, “A phase odyssey,” Phys. Today 54(8), 27–32 (2001).
[CrossRef]

K. A. Nugent and D. Paganin, “Matter–wave phase measurement: a noninterferometric approach,” Phys. Rev. A 61, 063614 (2000).
[CrossRef]

D. Paganin and K. A. Nugent, “Noninterferometric phase imaging with partially coherent light,” Phys. Rev. Lett. 80, 2586–2589 (1998).
[CrossRef]

T. E. Gureyev, A. Roberts, and K. A. Nugent, “Partially coherent fields, the transport-of-intensity equation, and phase uniqueness,” J. Opt. Soc. Am. A 12, 1942–1946 (1995).
[CrossRef]

Paganin, D.

K. A. Nugent, D. Paganin, and T. E. Gureyev, “A phase odyssey,” Phys. Today 54(8), 27–32 (2001).
[CrossRef]

K. A. Nugent and D. Paganin, “Matter–wave phase measurement: a noninterferometric approach,” Phys. Rev. A 61, 063614 (2000).
[CrossRef]

D. Paganin and K. A. Nugent, “Noninterferometric phase imaging with partially coherent light,” Phys. Rev. Lett. 80, 2586–2589 (1998).
[CrossRef]

Peters, A.

A. Peters, K. Y. Chung, and S. Chu, “Measurement of gravitational acceleration by dropping atoms,” Nature 400, 849–852 (1999).
[CrossRef]

Roberts, A.

Scholten, R. E.

M. R. Walkiewicz, P. J. Fox, and R. E. Scholten, “Candlestick rubidium beam source,” Rev. Sci. Instrum. 71, 3342–3344 (2000).
[CrossRef]

E. C. Harvey, J. P. Hayes, B. C. Dempster, T. R. Mackin, and R. E. Scholten, “Excimer laser ablation used for the fabrication of micro-optic phase and diffraction elements,” in Micro-Opto-Electro-Mechanical Systems, R. R. Syms, ed., Proc. SPIE 4075, 152–158 (2000).
[CrossRef]

R. E. Scholten, R. Gupta, J. J. McClelland, R. J. Celotta, M. S. Levenson, and M. G. Vangel, “Laser collimation of a chromium beam,” Phys. Rev. A 55, 1331–1338 (1997).
[CrossRef]

Teague, M. R.

M. R. Teague, “Deterministic phase retrieval: a Green’s function solution,” J. Opt. Soc. Am. A 73, 1434–1441 (1983).
[CrossRef]

Vangel, M. G.

R. E. Scholten, R. Gupta, J. J. McClelland, R. J. Celotta, M. S. Levenson, and M. G. Vangel, “Laser collimation of a chromium beam,” Phys. Rev. A 55, 1331–1338 (1997).
[CrossRef]

Walkiewicz, M. R.

M. R. Walkiewicz, P. J. Fox, and R. E. Scholten, “Candlestick rubidium beam source,” Rev. Sci. Instrum. 71, 3342–3344 (2000).
[CrossRef]

Class. Quantum Grav. (1)

T. L. Gustavson, A. Landragin, and M. A. Kasevich, “Rotation sensing with a dual atom-interferometer Sagnac gyroscope,” Class. Quantum Grav. 17, 2385–2398 (2000).
[CrossRef]

J. Opt. Soc. Am. A (2)

Nature (1)

A. Peters, K. Y. Chung, and S. Chu, “Measurement of gravitational acceleration by dropping atoms,” Nature 400, 849–852 (1999).
[CrossRef]

Phys. Rev. A (3)

K. A. Nugent and D. Paganin, “Matter–wave phase measurement: a noninterferometric approach,” Phys. Rev. A 61, 063614 (2000).
[CrossRef]

R. E. Scholten, R. Gupta, J. J. McClelland, R. J. Celotta, M. S. Levenson, and M. G. Vangel, “Laser collimation of a chromium beam,” Phys. Rev. A 55, 1331–1338 (1997).
[CrossRef]

J. P. Gordon and A. Ashkin, “Motion of atoms in a radiation trap,” Phys. Rev. A 21, 1606–1617 (1980).
[CrossRef]

Phys. Rev. Lett. (1)

D. Paganin and K. A. Nugent, “Noninterferometric phase imaging with partially coherent light,” Phys. Rev. Lett. 80, 2586–2589 (1998).
[CrossRef]

Phys. Today (1)

K. A. Nugent, D. Paganin, and T. E. Gureyev, “A phase odyssey,” Phys. Today 54(8), 27–32 (2001).
[CrossRef]

Proc. SPIE (1)

E. C. Harvey, J. P. Hayes, B. C. Dempster, T. R. Mackin, and R. E. Scholten, “Excimer laser ablation used for the fabrication of micro-optic phase and diffraction elements,” in Micro-Opto-Electro-Mechanical Systems, R. R. Syms, ed., Proc. SPIE 4075, 152–158 (2000).
[CrossRef]

Rev. Sci. Instrum. (1)

M. R. Walkiewicz, P. J. Fox, and R. E. Scholten, “Candlestick rubidium beam source,” Rev. Sci. Instrum. 71, 3342–3344 (2000).
[CrossRef]

Other (2)

A. Messiah, Quantum Mechanics (North-Holland, Amsterdam, 1961), Vol. 1, p. 222.

P. R. Berman, ed., Atom Interferometry (Academic, San Diego, Calif., 1997).

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Figures (4)

Fig. 1
Fig. 1

Experimental setup. The probability density of the atomic beam is modified by interaction with an off-resonant laser beam. Measurement of the fluorescence profile with the phase object on and off determines the evolution of the atomic beam. Images were taken with a CCD camera oriented along yˆ. ECDL, external-cavity diode laser.

Fig. 2
Fig. 2

Scanning-electron micrograph of the diffraction mask used to generate the TEM01 mode pattern, fabricated from a microscope coverslip by excimer-laser ablation, and the measured (dotted curve) and calculated (solid curve) profiles along x. Grating spacing, 20 µm.

Fig. 3
Fig. 3

Retrieved phase at λdB=0.016 nm for TEM01 phase objects. Results at small detunings show low-spatial-frequency artifacts induced by noise in regions of small phase gradients. The statistical uncertainty in the original fluorescence images is 0.3%.

Fig. 4
Fig. 4

Retrieved phase at λdB=0.016 nm for Gaussian phase objects. The discrepancy at small positive detunings is due to optical pumping losses into the undetected hyperfine ground state.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

j(r)=1m  pW(r, p)dp,
j(r)=1mρ(r)Φ(r),
ρ(r)z=-p·[ρ(r)Φ(r)],
U(x, z)=δ2 ln1+I0Is Γ2(Γ2+4δ2)G(x, z),
G00(x, z)=exp-2x2σx2+z2σz2

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