Three-dimensional theory for interaction between atomic ensembles and free-space light

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 66, Issue 2, 2002, Pages 1-13

  Duan, L M ^a,b   Cirac, J I ^c   Zoller, P ^d  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^b University of Science and Technology of China   (China)

^c MAX PLANCK INSTITUT FÜR QUANTENOPTIK   (Germany)

^d UNIVERSITY OF INNSBRUCK   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

ATOMIC PHYSICS; ATOMS; LIGHT PROPAGATION; MATHEMATICAL MODELS; NUMERICAL METHODS; PUMPING (LASER);

ATOMIC ENSEMBLES; FREE SPACE LIGHT; QUANTUM INFORMATION PROCESSING SCHEMES; THREE DIMENSIONAL THEORY;

QUANTUM THEORY;

EID: 84983698493     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevA.66.023818     Document Type: Article

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18. Note that for rapidly moving atoms, we also have the effect of Doppler shifts which are not included in the Hamiltonian “6”. However, the Doppler shifts are not important for the off-resonant coupling considered here “they are still significantly smaller than the detuning”. In addition, the Doppler shifts will cancel for the spontaneous emission modes that are nearly collinear with the pumping laser “including the important signal light mode”.
19. 0 and zero outside.
20. Note that this is a valid picture for room-temperature atomic cells. However, for ultracold atoms, each atom will be localized in a small space, and the density fluctuation basically will not depend on the size and geometry of the ensemble. Thus, for cold atoms, one may have a different interaction picture and a smaller noise ratio.