Abstract
We reconsider the one-axis twisting Hamiltonian, which is commonly used for generating spin squeezing, and treat its dynamics within the Heisenberg operator approach. To this end we solve the underlying Heisenberg equations of motion perturbatively and evaluate the expectation values of the resulting time-dependent Heisenberg operators in order to determine approximately the dynamics of spin squeezing. Comparing our results with those originating from exact numerics reveals that they are more accurate than the commonly used frozen spin approximation.
Graphical abstract
Article PDF
Similar content being viewed by others
References
C. Gross, J. Phys. B: At. Mol. Opt. Phys. 45, 103001 (2012)
J. Ma, X. Wang, C.P. Sun, F. Nori, Phys. Rep. 509, 89 (2011)
D.J. Wineland, J.J. Bollinger, W.M. Itano, F.L. Moore, D.J. Heinzen, Phys. Rev. A 46, R6797 (1992)
D.J. Wineland, J.J. Bollinger, W.M. Itano, D.J. Heinzen, Phys. Rev. A 50, 67 (1994)
E.S. Polzik, Nature 453, 45 (2008)
A.D. Cronin, J. Schmiedmayer, D.E. Pritchard, Rev. Mod. Phys. 81, 1051 (2009)
A. Sorensen, L.M. Duan, J.I. Cirac, P. Zoller, Nature 409, 63 (2001)
N. Bigelow, Nature 409, 27 (2001)
O. Guehne, G. Toth, Phys. Rep. 474, 1 (2009)
M. Kitagawa, M. Ueda, Phys. Rev. A 47, 5138 (1993)
Q.A. Turchette, C.S. Wood, B.E. King, C.J. Myatt, D. Leibfried, W.M. Itano, C. Monroe, D.J. Wineland, Phys. Rev. Lett. 81, 3631 (1998)
V. Meyer, M.A. Rowe, D. Kielpinski, C.A. Sackett, W.M. Itano, C. Monroe, D.J. Wineland, Phys. Rev. Lett. 86, 5870 (2001)
D. Leibfried, M.D. Barrett, T. Schaetz, J. Britton, J. Chiaverini, W.M. Itano, J.D. Jost, C. Langer, D.J. Wineland, Science 304, 1476 (2004)
X. Wang, B.C. Sanders, Phys. Rev. A 68, 012101 (2003)
J.K. Korbicz, J.I. Cirac, M. Lewenstein, Phys. Rev. Lett. 95, 120502 (2005)
S. Yi, H. Pu, Phys. Rev. A 73, 023602 (2006)
C. Orzel, A.K. Tuchman, M.L. Fenselau, M. Yasuda, M.A. Kasevich, Science 291, 2386 (2001)
M.F. Riedel, Nature 464, 1170 (2010)
J. Esteve, C. Gross, A. Weller, S. Giovanazzi, M.K. Oberthaler, Nature 455, 1216 (2008)
W. Muessel, H. Strobel, D. Linnemann, T. Zibold, B. Juliá-Diaz, M.K. Oberthaler, Phys. Rev. A 92, 023603 (2015)
M. Jaaskelainen, P. Meystre, Phys. Rev. A 73, 013602 (2006)
C.K. Law, H.T. Ng, P.T. Leung, Phys. Rev. A 63, 055601 (2001)
G.R. Jin, S.W. Kim, Phys. Rev. A 76, 043621 (2007)
G.R. Jin, C.K. Law, Phys. Rev. A 78, 063620 (2008)
G.R. Jin, X.W. Wang, Y.W. Lu, J. Phys. B: At. Mol. Opt. Phys. 43, 045301 (2010)
A.B. Bhattacherjee, V. Ranjan, M. Mohan, Int. J. Mod. Phys. B 17, 2579 (2003)
Z.W. Bian, X.B. Lai, Int. J. Theor. Phys. 52, 3922 (2013)
G.J. Hu, X.X. Hu, Int. J. Theor. Phys. 53, 533 (2014)
S.S. Li, H.G. Yi, R.H. Chen, Int. J. Theor. Phys. 52, 1175 (2013)
J. Vidal, G. Palacios, C. Aslangul, Phys. Rev. A 70, 062304 (2004)
Y.H. Jiang, S.S. Li, Int. J. Theor. Phys. 52, 2826 (2013)
D. Kajtoch, E. Witkowska, Phys. Rev. A 93, 023627 (2016)
A. Vardi, J.R. Anglin, Phys. Rev. Lett. 86, 568 (2001)
G. Chen, X. Wang, J.Q. Liang, Z.D. Wang, Phys. Rev. A 78, 023634 (2008)
N.N. Bogoliubov, Y.A. Mitropolsky, Asymptotic methods in the theory of non-linear oscillations (Gordonand Breach, New York, 1961)
N. Minorsky, Nonlinear oscillation (Van Nostrand, Princeton, 1962)
R. Mickens, Introduction to nonlinear oscillations (Cambridge University Press, Cambridge, 1981)
A. Pelster, H. Kleinert, M. Schanz, Phys. Rev. E 67, 016604 (2003)
I. Vidanovic, A. Balaž, H. Al-Jibbouri, A. Pelster, Phys. Rev. A 84, 013618 (2011)
H. Al-Jibbouri, I. Vidanovic, A. Balaž, A. Pelster, J. Phys. B 46, 065303 (2013)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bhattacherjee, A.B., Sharma, D. & Pelster, A. Heisenberg operator approach for spin squeezing dynamics. Eur. Phys. J. D 71, 337 (2017). https://doi.org/10.1140/epjd/e2017-80534-6
Received:
Published:
DOI: https://doi.org/10.1140/epjd/e2017-80534-6