[en] Kicked atoms under a constant Stark or gravity field are investigated for experimental setups with cold and ultracold atoms. The parametric stability of the quantum dynamics is studied using the fidelity. In the case of a quantum resonance, it is shown that the behavior of the fidelity depends on arithmetic properties of the gravity parameter. Close to a quantum resonance, the long-time asymptotics of the fidelity is studied by means of a pseudoclassical approximation introduced by Fishman et al. [J. Stat. Phys. 110, 911 (2003)]. The long-time decay of fidelity arises from the tunneling out of pseudoclassical stable islands, and a simple ansatz is proposed
which satisfactorily reproduces the main features observed in numerical simulations.
Disciplines :
Physics
Author, co-author :
Dubertrand, Rémy ; Université de Liège - ULiège > Département de physique > Optique quantique
Guarneri, I
Wimberger, S
Language :
English
Title :
Fidelity for kicked atoms with gravity near a quantum resonance
Publication date :
March 2012
Journal title :
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
ISSN :
1539-3755
eISSN :
1550-2376
Publisher :
American Physical Society, College Park, United States - Maryland
A. Peres, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.30.1610 30, 1610 (1984).
R. A. Jalabert and H. M. Pastawski, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.2490 86, 2490 (2001). (Pubitemid 32286687)
T. Gorin, T. Prosen, T. H. Seligman, and M. Znidaric, Phys. Rep. PRPLCM 0370-1573 10.1016/j.physrep.2006.09.003 435, 33 (2006); (Pubitemid 44696158)
P. Jacquod and C. Petitjean, Adv. Phys. ADPHAH 0001-8732 10.1080/00018730902831009 58, 67 (2009).
G. Casati, in Stochastic Behavior in Classical and Quantum Hamiltonian Systems, edited by, G. Casati, and, J. Ford, (Springer, Berlin, 1979), p. 334.
B. V. Chirikov, Phys. Rep. PRPLCM 0370-1573 10.1016/0370-1573(79)90023-1 52, 263 (1979).
F. L. Moore, J. C. Robinson, C. F. Bharucha, B. Sundaram, and M. G. Raizen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.75.4598 75, 4598 (1995);
C. F. Bharucha, J. C. Robinson, F. L. Moore, B. Sundaram, Q. Niu, and M. G. Raizen, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.60.3881 60, 3881 (1999).
F. M. Izrailev and D. L. Shepelyanskii, Sov. Phys. Dokl. TMPHAH 0040-5779 10.1007/BF01029131 24, 996 (1979)
F. M. Izrailev and D. L. Shepelyanskii [Theor. Math. Phys. 0040-5779 10.1007/BF01029131 43, 553 (1980)].
S. Fishman, I. Guarneri, and L. Rebuzzini, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.084101 89, 084101 (2002);
S. Fishman, I. Guarneri, and L. Rebuzzini, J. Stat. Phys. JSTPBS 0022-4715 10.1023/A:1022176306198 110, 911 (2003).
S. Wimberger, I. Guarneri, and S. Fishman, Nonlinearity NONLE5 0951-7715 10.1088/0951-7715/16/4/312 16, 1381 (2003);
S. Wimberger, I. Guarneri, and S. Fishman, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.084102 92, 084102 (2004).
M. Abb, I. Guarneri, and S. Wimberger, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.80.035206 80, 035206 (R) (2009).
M. Sadgrove and S. Wimberger, Adv. At. Mol. Opt. Phys. 1049-250X 10.1016/B978-0-12-385508-4.00007-3 60, 315 (2011).
S. Wimberger and A. Buchleitner, J. Phys. B JPAPEH 0953-4075 10.1088/0953-4075/39/7/L01 39, L145 (2006).
I. Dana and D. L. Dorofeev, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.73.026206 73, 026206 (2006); (Pubitemid 43287698)
I. Guarneri, Ann. Henri Poincaré 1424-0637 10.1007/s00023-009- 0008-9 10, 1097 (2009).
I. Guarneri, L. Rebuzzini, and S. Fishman, Nonlinearity NONLE5 0951-7715 10.1088/0951-7715/19/5/006 19, 1141 (2006). (Pubitemid 43593336)
I. Guarneri and L. Rebuzzini, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.234103 100, 234103 (2008).
M. Sheinman, S. Fishman, I. Guarneri, and L. Rebuzzini, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.052110 73, 052110 (2006). (Pubitemid 43788067)
M. K. Oberthaler, R. M. Godun, M. B. d'Arcy, G. S. Summy, and K. Burnett, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.83.4447 83, 4447 (1999);
M. B. d'Arcy, R. M. Godun, M. K. Oberthaler, G. S. Summy, K. Burnett, and S. A. Gardiner, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.64.056233 64, 056233 (2001).
M. Sadgrove, S. Wimberger, S. Parkins, and R. Leonhardt, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.174103 94, 174103 (2005); (Pubitemid 41492261)
S. Wimberger, M. Sadgrove, S. Parkins, and R. Leonhardt, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.053404 71, 053404 (2005); (Pubitemid 41481325)
M. Sadgrove, S. Wimberger, S. Parkins, and R. Leonhardt, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.78.025206 78, 025206 (R) (2008).
M. Sadgrove, M. Horikoshi, T. Sekimura, and K. Nakagawa, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.043002 99, 043002 (2007); (Pubitemid 47173192)
M. Sadgrove and S. Wimberger, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/11/8/083027 11, 083027 (2009).
G. Behinaein, V. Ramareddy, P. Ahmadi, and G. S. Summy, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.244101 97, 244101 (2006). (Pubitemid 44927280)
I. Talukdar, R. Shrestha, and G. S. Summy, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.105.054103 105, 054103 (2010).
C. Ryu, M. F. Andersen, A. Vaziri, M. B. d'Arcy, J. M. Grossman, K. Helmerson, and W. D. Phillips, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.160403 96, 160403 (2006). (Pubitemid 43667832)
S. Wu, A. Tonyushkin, and M. G. Prentiss, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.103.034101 103, 034101 (2009);
A. Tonyushkin, S. Wu, and M. G. Prentiss, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.79.051402 79, 051402 (R) (2009).
S. Schlunk, M. B. d'Arcy, S. A. Gardiner, D. Cassettari, R. M. Godun, and G. S. Summy, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.054101 90, 054101 (2003).
A. Ullah and M. D. Hoogerland, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.83.046218 83, 046218 (2011).
R. A. Horne, R. H. Leonard, and C. A. Sackett, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.83.063613 83, 063613 (2011).
S.-J. Chang and K.-J. Shi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.34.7 34, 7 (1986).
I. Dana and V. Roitberg, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.76.015201 76, 015201 (R) (2007). (Pubitemid 47115671)
A. Erdelyi, Higher Transcendental Functions, Vol. 2 (McGraw-Hill, New York, 1955).
G. H. Hardy and J. E. Littlewood, Acta Math. ACMAA8 0001-5962 10.1007/BF02401834 37, 193 (1914);
J. H. Hannay and M. V. Berry, Physica D PDNPDT 0167-2789 10.1016/0167-2789(80)90026-3 1, 267 (1980);
M. V. Berry and J. Goldberg, Nonlinearity NONLE5 0951-7715 10.1088/0951-7715/1/1/001 1, 1 (1988);
J. Marklof, Duke Math. J. DUMJAO 0012-7094 10.1215/S0012-7094-99-09706-5 97, 127 (1999).
Y. Krivolapov, S. Fishman, E. Ott, and T. M. Antonsen, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.83.016204 83, 016204 (2011).
A. Buchleitner, D. Delande, and J. Zakrzewski, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(02)00270-3 368, 409 (2002);
S. Wimberger, P. Schlagheck, Ch. Eltschka, and A. Buchleitner, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.043001 97, 043001 (2006). (Pubitemid 44118069)
