Preparation of arbitrary entangled quantum states of a trapped ion

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 57, Issue 3, 1998, Pages 2096-2104

  Kneer, B ^a,b   Law, C K ^b  

^a UNIVERSITY OF ULM   (Germany)

^b UNIVERSITY OF ROCHESTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000368080     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.57.2096     Document Type: Article

References (36)

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27. The validity of this approximation for the arbitrary state preparation method was discussed in Ref. 17.
28. Our scheme is applicable for every Hamiltonian of this form. Therefore arbitrary state preparation is even possible in the time-dependent Paul trap potential beyond the secular approximation, as can be seen with the derivation in Ref. 11, where the micromotion is taken into account.
29. U. W. Hochstrasser, in Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun (Dover, New York, 1965), Chap. 22.
30. In the nonentanglement case (Formula presented), we have (Formula presented).
31. Recognize that we always obtain solutions (Formula presented) and (Formula presented). Thus there is also the possibility to have constant electric fields (Formula presented) for each pulse, and to adjust the time (Formula presented) Therefore the time of preparation can be optimized; see Ref. 19.
32. It is obvious that Eqs. (21) and (22) always have a solution, since the right-hand side can be chosen to be real by adjusting the phases (Formula presented) and (Formula presented), respectively. In fact there is always more than one solution because the inverse function of (Formula presented) has an infinite amount of branches.
33. A (Formula presented) pulse is actually a (Formula presented) pulse in our notation, as we defined the Rabi frequency to be periodical with (Formula presented), and not with (Formula presented).
34. In the Lamb-Dicke regime, where the Rabi frequencies (Formula presented) associated with the carrier frequency channel become automatically independent of (Formula presented), one can even use always the same field amplitude (Formula presented) and time (Formula presented) for that laser.
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