Abstract

We present a general strategy of quantum state engineering. We describe how an arbitarily prescribed superposition of internal Zeeman levels of an atom can be prepared by Raman pulses.

© 1998 Optical Society of America

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References

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  1. C.K. Law and J.H. Eberly, Phys. Rev. Lett. 76, 1055 (1996).
  2. A.S. Parkins, P. Marte, P. Zoller, and H.J. Kimble, Phys. Rev. Lett. 71, 3095 (1993).
  3. A.S. Parkins, P. Marte, P. Zoller, O. Carnal, and H.J. Kimble, Phys. Rev. A 51, 1578 (1995).
  4. K. Vogel, V.M. Akulin, and W.P. Schleich, Phys. Rev. Lett. 71, 1816 (1993).
  5. B.M. Garraway, B. Sherman, H. Moya-Cessa, P.L. Knight, and G. Kurizki, Phys. Rev. A 49, 535 (1994).
  6. A. Kozhekin, G. Kurizki, and B. Sherman, Phys. Rev. A 54, 3535 (1996).
  7. D.M. Meekhof, C. Monroe, B.E. King, W.M. Itano, and D.J. Wineland, Phys. Rev. Lett. 76, 1796 (1996).
  8. S.A. Gardiner, J.I. Cirac, and P. Zoller, Phys. Rev. A 55, 1683 (1997).
  9. K. Moler, D.S. Weiss, M. Kasevich, and S. Chu, Phys. Rev. A 45, 342 (1992).
  10. H.J. Kimble and W. Lange (private communication).
  11. C.K. Law and H.J. Kimble, J. Mod. Optics 44, 2067 (1997).
  12. See for example J. Martin, B.W. Shore, and K. Bergmann, Phys. Rev. A 54, 1556 (1996) and references therein.
  13. Measurement of atomic angular momentum states can be made by Stern-Gerlach measurements proposed by R.G. Newton and B. Young, Ann. Phys. (N.Y)  49, 393 (1968).

1997 (2)

S.A. Gardiner, J.I. Cirac, and P. Zoller, Phys. Rev. A 55, 1683 (1997).

C.K. Law and H.J. Kimble, J. Mod. Optics 44, 2067 (1997).

1996 (4)

See for example J. Martin, B.W. Shore, and K. Bergmann, Phys. Rev. A 54, 1556 (1996) and references therein.

A. Kozhekin, G. Kurizki, and B. Sherman, Phys. Rev. A 54, 3535 (1996).

D.M. Meekhof, C. Monroe, B.E. King, W.M. Itano, and D.J. Wineland, Phys. Rev. Lett. 76, 1796 (1996).

C.K. Law and J.H. Eberly, Phys. Rev. Lett. 76, 1055 (1996).

1995 (1)

A.S. Parkins, P. Marte, P. Zoller, O. Carnal, and H.J. Kimble, Phys. Rev. A 51, 1578 (1995).

1994 (1)

B.M. Garraway, B. Sherman, H. Moya-Cessa, P.L. Knight, and G. Kurizki, Phys. Rev. A 49, 535 (1994).

1993 (2)

K. Vogel, V.M. Akulin, and W.P. Schleich, Phys. Rev. Lett. 71, 1816 (1993).

A.S. Parkins, P. Marte, P. Zoller, and H.J. Kimble, Phys. Rev. Lett. 71, 3095 (1993).

1992 (1)

K. Moler, D.S. Weiss, M. Kasevich, and S. Chu, Phys. Rev. A 45, 342 (1992).

1968 (1)

Measurement of atomic angular momentum states can be made by Stern-Gerlach measurements proposed by R.G. Newton and B. Young, Ann. Phys. (N.Y)  49, 393 (1968).

Akulin, V.M.

K. Vogel, V.M. Akulin, and W.P. Schleich, Phys. Rev. Lett. 71, 1816 (1993).

Bergmann, K.

See for example J. Martin, B.W. Shore, and K. Bergmann, Phys. Rev. A 54, 1556 (1996) and references therein.

Carnal, O.

A.S. Parkins, P. Marte, P. Zoller, O. Carnal, and H.J. Kimble, Phys. Rev. A 51, 1578 (1995).

Chu, S.

K. Moler, D.S. Weiss, M. Kasevich, and S. Chu, Phys. Rev. A 45, 342 (1992).

Cirac, J.I.

S.A. Gardiner, J.I. Cirac, and P. Zoller, Phys. Rev. A 55, 1683 (1997).

Eberly, J.H.

C.K. Law and J.H. Eberly, Phys. Rev. Lett. 76, 1055 (1996).

Gardiner, S.A.

S.A. Gardiner, J.I. Cirac, and P. Zoller, Phys. Rev. A 55, 1683 (1997).

Garraway, B.M.

B.M. Garraway, B. Sherman, H. Moya-Cessa, P.L. Knight, and G. Kurizki, Phys. Rev. A 49, 535 (1994).

Itano, W.M.

D.M. Meekhof, C. Monroe, B.E. King, W.M. Itano, and D.J. Wineland, Phys. Rev. Lett. 76, 1796 (1996).

Kasevich, M.

K. Moler, D.S. Weiss, M. Kasevich, and S. Chu, Phys. Rev. A 45, 342 (1992).

Kimble, H.J.

C.K. Law and H.J. Kimble, J. Mod. Optics 44, 2067 (1997).

A.S. Parkins, P. Marte, P. Zoller, O. Carnal, and H.J. Kimble, Phys. Rev. A 51, 1578 (1995).

A.S. Parkins, P. Marte, P. Zoller, and H.J. Kimble, Phys. Rev. Lett. 71, 3095 (1993).

H.J. Kimble and W. Lange (private communication).

King, B.E.

D.M. Meekhof, C. Monroe, B.E. King, W.M. Itano, and D.J. Wineland, Phys. Rev. Lett. 76, 1796 (1996).

Knight, P.L.

B.M. Garraway, B. Sherman, H. Moya-Cessa, P.L. Knight, and G. Kurizki, Phys. Rev. A 49, 535 (1994).

Kozhekin, A.

A. Kozhekin, G. Kurizki, and B. Sherman, Phys. Rev. A 54, 3535 (1996).

Kurizki, G.

A. Kozhekin, G. Kurizki, and B. Sherman, Phys. Rev. A 54, 3535 (1996).

B.M. Garraway, B. Sherman, H. Moya-Cessa, P.L. Knight, and G. Kurizki, Phys. Rev. A 49, 535 (1994).

Lange, W.

H.J. Kimble and W. Lange (private communication).

Law, C.K.

C.K. Law and H.J. Kimble, J. Mod. Optics 44, 2067 (1997).

C.K. Law and J.H. Eberly, Phys. Rev. Lett. 76, 1055 (1996).

Marte, P.

A.S. Parkins, P. Marte, P. Zoller, O. Carnal, and H.J. Kimble, Phys. Rev. A 51, 1578 (1995).

A.S. Parkins, P. Marte, P. Zoller, and H.J. Kimble, Phys. Rev. Lett. 71, 3095 (1993).

Martin, J.

See for example J. Martin, B.W. Shore, and K. Bergmann, Phys. Rev. A 54, 1556 (1996) and references therein.

Meekhof, D.M.

D.M. Meekhof, C. Monroe, B.E. King, W.M. Itano, and D.J. Wineland, Phys. Rev. Lett. 76, 1796 (1996).

Moler, K.

K. Moler, D.S. Weiss, M. Kasevich, and S. Chu, Phys. Rev. A 45, 342 (1992).

Monroe, C.

D.M. Meekhof, C. Monroe, B.E. King, W.M. Itano, and D.J. Wineland, Phys. Rev. Lett. 76, 1796 (1996).

Moya-Cessa, H.

B.M. Garraway, B. Sherman, H. Moya-Cessa, P.L. Knight, and G. Kurizki, Phys. Rev. A 49, 535 (1994).

Newton, R.G.

Measurement of atomic angular momentum states can be made by Stern-Gerlach measurements proposed by R.G. Newton and B. Young, Ann. Phys. (N.Y)  49, 393 (1968).

Parkins, A.S.

A.S. Parkins, P. Marte, P. Zoller, O. Carnal, and H.J. Kimble, Phys. Rev. A 51, 1578 (1995).

A.S. Parkins, P. Marte, P. Zoller, and H.J. Kimble, Phys. Rev. Lett. 71, 3095 (1993).

Schleich, W.P.

K. Vogel, V.M. Akulin, and W.P. Schleich, Phys. Rev. Lett. 71, 1816 (1993).

Sherman, B.

A. Kozhekin, G. Kurizki, and B. Sherman, Phys. Rev. A 54, 3535 (1996).

B.M. Garraway, B. Sherman, H. Moya-Cessa, P.L. Knight, and G. Kurizki, Phys. Rev. A 49, 535 (1994).

Shore, B.W.

See for example J. Martin, B.W. Shore, and K. Bergmann, Phys. Rev. A 54, 1556 (1996) and references therein.

Vogel, K.

K. Vogel, V.M. Akulin, and W.P. Schleich, Phys. Rev. Lett. 71, 1816 (1993).

Weiss, D.S.

K. Moler, D.S. Weiss, M. Kasevich, and S. Chu, Phys. Rev. A 45, 342 (1992).

Wineland, D.J.

D.M. Meekhof, C. Monroe, B.E. King, W.M. Itano, and D.J. Wineland, Phys. Rev. Lett. 76, 1796 (1996).

Young, B.

Measurement of atomic angular momentum states can be made by Stern-Gerlach measurements proposed by R.G. Newton and B. Young, Ann. Phys. (N.Y)  49, 393 (1968).

Zoller, P.

S.A. Gardiner, J.I. Cirac, and P. Zoller, Phys. Rev. A 55, 1683 (1997).

A.S. Parkins, P. Marte, P. Zoller, O. Carnal, and H.J. Kimble, Phys. Rev. A 51, 1578 (1995).

A.S. Parkins, P. Marte, P. Zoller, and H.J. Kimble, Phys. Rev. Lett. 71, 3095 (1993).

Other (13)

C.K. Law and J.H. Eberly, Phys. Rev. Lett. 76, 1055 (1996).

A.S. Parkins, P. Marte, P. Zoller, and H.J. Kimble, Phys. Rev. Lett. 71, 3095 (1993).

A.S. Parkins, P. Marte, P. Zoller, O. Carnal, and H.J. Kimble, Phys. Rev. A 51, 1578 (1995).

K. Vogel, V.M. Akulin, and W.P. Schleich, Phys. Rev. Lett. 71, 1816 (1993).

B.M. Garraway, B. Sherman, H. Moya-Cessa, P.L. Knight, and G. Kurizki, Phys. Rev. A 49, 535 (1994).

A. Kozhekin, G. Kurizki, and B. Sherman, Phys. Rev. A 54, 3535 (1996).

D.M. Meekhof, C. Monroe, B.E. King, W.M. Itano, and D.J. Wineland, Phys. Rev. Lett. 76, 1796 (1996).

S.A. Gardiner, J.I. Cirac, and P. Zoller, Phys. Rev. A 55, 1683 (1997).

K. Moler, D.S. Weiss, M. Kasevich, and S. Chu, Phys. Rev. A 45, 342 (1992).

H.J. Kimble and W. Lange (private communication).

C.K. Law and H.J. Kimble, J. Mod. Optics 44, 2067 (1997).

See for example J. Martin, B.W. Shore, and K. Bergmann, Phys. Rev. A 54, 1556 (1996) and references therein.

Measurement of atomic angular momentum states can be made by Stern-Gerlach measurements proposed by R.G. Newton and B. Young, Ann. Phys. (N.Y)  49, 393 (1968).

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Figures (2)

Fig. 1.
Fig. 1.

Two types of interactions connecting different states. (a) Vertical (b) Diagonal

Fig. 2.
Fig. 2.

An 8-pulse sequence that force any given state (upper left) in the hyperfine manifold of 32 S 1/2 of sodium to evolve into |F = 2, mF = -2〉 (bottom right). The solid and empty circles represent occupied and unoccupied states respectively

Equations (3)

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| Ψ = n = 1 N c n | n
| 1 = U V ( λ 1 ) U D ( λ 2 ) U V ( λ 3 ) U D ( λ N 2 ) U V ( λ N 1 ) | Ψ
| Ψ = 1 2 ( | F = 2 , m = 2 + | F = 2 , m = 2 )

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