TY - JOUR

T1 - Pythagorean coupling

T2 - Complete population transfer in a four-state system

AU - Suchowski, Haim

AU - Silberberg, Yaron

AU - Uskov, Dmitry B.

PY - 2011/7/18

Y1 - 2011/7/18

N2 - Complete population transfer in a four-coupled-modes system is analyzed from a geometrical point of view. An analytical solution of the dynamics is written by the use of two distinct frequencies, the generalization of the single Rabi frequency of the two-state dynamics. We also present its visualization on two separate Bloch spheres with two independent torque equations. With this scheme we analytically derive the requirements for complete population transfer in a four-state quantum system. Interestingly, the solutions are found to be linked to fundamental number theory, whereas complete population transfer occurs only if the ratios between coupling coefficients exactly match a set of Pythagorean triples.

AB - Complete population transfer in a four-coupled-modes system is analyzed from a geometrical point of view. An analytical solution of the dynamics is written by the use of two distinct frequencies, the generalization of the single Rabi frequency of the two-state dynamics. We also present its visualization on two separate Bloch spheres with two independent torque equations. With this scheme we analytically derive the requirements for complete population transfer in a four-state quantum system. Interestingly, the solutions are found to be linked to fundamental number theory, whereas complete population transfer occurs only if the ratios between coupling coefficients exactly match a set of Pythagorean triples.

UR - http://www.scopus.com/inward/record.url?scp=79961096407&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.84.013414

DO - 10.1103/PhysRevA.84.013414

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AN - SCOPUS:79961096407

SN - 1050-2947

VL - 84

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

IS - 1

M1 - 013414

ER -