|
Article information
2014 , Volume 19, ¹ 4, p.32-41
Zhukov V.P., Beterov I.I., Fedoruk M.P., Ryabtsev I.I.
Semi-analytical method for ensemble of Rydberg atoms
The problem for determination of wave function for an ensemble of Rydberg atoms requires solution of a set of ordinaries differential equations. The number of equations increases exponentially with the number of atoms. The solution of this problem is of oscillatory type character. Calculation of the oscillation's phase and normalization of the wave function with a high degree of accuracy is very difficult for times which are much greater than the oscillations period. In the article, we suggest a very effective semi-analytic splitting method for finding of the wave function for the ensemble of Rydberg atoms. It is based on analytical (exact) solution of the problem for two states (two connected oscillators). The method gives very high accuracy for determination of the wave function (including the phases of the function) and exactly conserves particles number. It takes several hours for PC to calculate the ensemble of ten atoms with 3 levels. Earlier ensemble of only 7 atoms was calculated using Adam's type methods. The suggested semi-analytical method can be implemented to other similar problems. Aknowlegements: This research is supported by the Grant of President of Russian Federation for government support of leading scientific school RF (Ac. Yu. Shokin school, project NSh- 5006.2014.9) and the integration project 62. Received 14 February 2014.
[full text]
Keywords: Symplectic algorithm, solution of the ordinary differential equations, Rydberg atoms
Author(s):
Zhukov Vladimir Petrovich
Dr.
Position: Senior Research Scientist
Office: Federal Research Center for Information and Computational Technologies
Address: 630090, Russia, Novosibirsk, Ac. Lavrentiev ave., 6
Phone Office: (383) 330 97 72
E-mail: zuk@ict.nsc.ru
Beterov Ilya Igorevich
PhD.
Position: Senior Research Scientist
Office: Rzhanov Institute of Semiconductor Physics SBRAS
Address: 630090, Russia, Novosibirsk, Ac. Lavrentiev Ave. 13
Phone Office: (383) 333-24-08
E-mail: beterov@isp.nsc.ru
Fedoruk Mikhail Petrovich
Dr. , Academician RAS, Professor
Position: Chancellor
Office: Novosibirsk State University, Federal Research Center for Information and Computational Technologies
Address: 630090, Russia, Novosibirsk, str. Pirogova, 2
Phone Office: (3832) 349105
E-mail: mife@net.ict.nsc.ru
SPIN-code: 4929-8753Ryabtsev Igor Ilyich
Dr.
Position: Head of Laboratory
Office: Rzhanov Institute of Semiconductor Physics SBRAS
Address: 630090, Russia, Novosibirsk, Ac. Lavrentiev Ave. 13
Phone Office: (383) 333-24-08
E-mail: ryabtsev@isp.nsc.ru
References:
[1] Lukin M.D., Fleischhauer M., Cote R. Dipole blockade and quantum information processing in mesoscopic atomic ensembles. Phys. Rev. Lett. 2001; 87: Paper 037901 (4).
[2] Robicheaux F., Hernandez J.V. Many-body wave function in a dipole blockade configuration.Phys. Rev. A. 2005; 72: Paper 063403 (4 ).
[3] Stanojevic J., Cote R. Many-body Rabi oscillations of Rydberg excitation in small mesoscopic samples. Ibid. 2009; 80: Paper 033418 (9 ).
[4] Beterov I.I., Tretyakov D.B., Entin V.M. et al. Deterministic single-atom excitation via adiabatic passage and Rydberg blockade. Ibid. 2011; 84: Paper 023413 (6 ).
[5] Chegodaeva E.A. Metod parallel’nogo simplekticheskogo integrirovanija uravnenij dvizhenija malyh tel Solnechnoj sistemy [The parallel simplectic method of integrating of equations of small solar system bodies motion]. Vestnik JuUrGU. Matematika, fizika, himija. 2006; 7: 150-151. (In Russ.)
[6] Chegodaeva E.A. Metod simplekticheskogo integrirovanija uravnenij dvizhenija malyh tel solnechnoj sistemy [The simplectic method of integrating of equations of small solar system bodies motion].Vestnik YuUrGU. Mathematics, physics, chemistry.2005; 5: 49-55. (In Russ.)
[7] Emel’yanenko V. An explicit symplectic integrator for cometary orbits. Celestial Mech. and Dynam. Astronomy. 2001; 74: 287-295.
[8] Wisdom J., Holman M. Symplectic maps for the N-body problem. The Astronomical J. 1991; 1528-1538.
[9] Kuvshinov B.N., Schep T.J. Double-periodic arrays of vortices. Phys. Fluids. 2000; 12: 3283-3284.
[10] Kuvshinov B.N., Schep T.J. Holtsmark distributions in point-vortex systems. Phys. Rev. Lett. 2000; 84(4): 650-653.
[11] Beterov I.I., Saffman M., Yakshina E.A. et al. Quantum gates in mesoscopic atomic ensembles based on adiabatic passage and Rydberg blockade. Phys. Rev. A. 2013; 88(1): 010303(R) (5 p.).
[12] Muslu G.M., Erbay H.A. High-order split-step Fourier schemes for generalized nonlinear Schrodinger equation. Math. and Appl. Mathematics. 1977; 57(1): 1-12.
Bibliography link:
Zhukov V.P., Beterov I.I., Fedoruk M.P., Ryabtsev I.I. Semi-analytical method for ensemble of Rydberg atoms // Computational technologies. 2014. V. 19. ¹ 4. P. 32-41
|
