Abstract
A stationary physical system satisfies peculiar balance conditions involving mean values of appropriate observables. In this paper, we show how to deduce such quantitative links, named balance equations, demonstrating as well their usefulness in bringing to light physical properties of the system without solving the Schrödinger equation. The knowledge of such properties in the case of the Rabi Hamiltonian is exploited to provide arguments to make easier the variational engineering of the ground state of this model.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V. V. Dodonov and V. I. Man’ko, Invariants and the Evolution of Nonstationary Quantum Systems, Proceedings of the P. N. Lebedev Physical Institute, Nauka, Moscow (1987), Vol. 183 [translated by Nova Science, New York (1989)].
G. Benivegna and A. Messina, Phys. Rev A, 35, 3313 (1987).
G. Benivegna and A. Messina, Phys. Rev A, 37, 4747 (1988).
G. Benivegna and A. Messina, J. Phys. A: Math. Gen., 27, L453 (1994).
G. Benivegna, A. Messina, and E. Paladino, J. Phys. A: Math. Gen., 29, 2485 (1996).
G. Benivegna, A. Messina, and E. Paladino, Nuovo Cim. B, 112, 905 (1997).
I. I. Rabi, Phys. Rev., 49, 324 (1936).
D. Braak, Phys. Rev. Lett., 107, 100401 (2011).
L. Yu, S. Zhu, Q. Liang, et al., Phys. Rev. A, 86, 015803 (2012).
H. -P. Breuer and F. Petruccione, The Theory of Open Quantum Systems, Oxford University Press, Oxford, UK (2002)
S. Haroche and J. M. Raimond, Exploring the Quantum: Atoms, Cavities and Photons, Oxford University Press, Oxford, UK (2006)
T. Niemczyk, F. Deppe, H. Huebl, et al., Nature Phys., 6, 772 (2010).
P. Forn-Diaz, J. Lisenfeld, D. Marcos, et al., Phys. Rev. Lett., 105, 237001 (2010).
X. Cao, J. Q. You, H. Zheng, et al., Phys. Rev. A, 82, 022119 (2010).
O. Q. You and F. Nori, Nature, 474, 589 (2011).
J. M. Raimond, M. Brune, and S. Haroche, Rev. Mod. Phys., 73, 565 (2001).
A. Moroz, Los Alamos ArXiv:1302.2565v3 (2013).
G. Gunter, A. A. Anappara, J. Hees, et al., Nature, 458, 178 (2009).
Y. Todorov, A. M. Andrews, R. Colombelli, et al., Phys. Rev. Lett., 105, 196402 (2010).
E. Wigner, Phys. Rev., 40, 749 (1932).
F. J. Narcowich and R. F. O’Connel, Phys. Rev. A, 34, 1 (1986).
W. P. Schleich, Quantum Optics in Phase Space, Wiley, Weinheim, Germany (2005).
O. V. Man’ko, V. I. Man’ko, and G. Marmo, J. Phys. A: Math. Gen., 35, 699 (2002).
M. A. Man’ko, V. I. Man’ko, G. Marmo, et al., Nuovo Cim. C, 36, Ser. 3, 163 (2013).
G. G. Amosov, Ya. A. Korennoy, and V. I. Man’ko, Phys. Rev. A, 85, 052119 (2012).
Author information
Authors and Affiliations
Corresponding author
Additional information
Dedicated to the memory of our friend and colleague Allan Solomon, Emeritus Professor at Sorbonne Unversity, Paris and Emeritus Professor of Mathematical Physics at the Open University, Milton Keynes, UK.
Rights and permissions
About this article
Cite this article
Messina, A., Napoli, A., Man’ko, M.A. et al. Balance Equations-Based Properties of the Rabi Hamiltonian. J Russ Laser Res 35, 101–109 (2014). https://doi.org/10.1007/s10946-014-9405-8
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10946-014-9405-8