Abstract
We study the method of generation of states that approximate superpositions of large-amplitude coherent states (SCSs) with high fidelity in free-traveling fields. Our approach is based on the representation of an arbitrary single-mode pure state, and SCSs in particular, in terms of displaced number states with an arbitrary displacement amplitude. The proposed optical scheme is based on alternation of photon additions and displacement operators (in the general case, N photon additions and N − 1 displacements are required) with a seed coherent state to generate both even and odd displaced squeezed SCSs regardless of the parity of the used photon additions. It is shown that the optical scheme studied is sensitive to the seed coherent state if the other parameters are unchanged. Output states can approximate either even squeezed SCS or odd SCS shifted relative to each other by some value. This allows constructing a local rotation operator, in particular, the Hadamard gate, which is a mainframe element for quantum computation with coherent states. We also show that three-photon additions with two intermediate displacement operators are sufficient to generate even displaced squeezed SCS with the amplitude 1.7 and fidelity more than 0.99. The effects deteriorating the quality of output states are considered.
Similar content being viewed by others
References
B. Yurke, Phys. Rev. Lett. 56, 1515 (1986); B. Yurke, S. L. McCall, and J. R. Klauder, Phys. Rev. A: At., Mol., Opt. Phys. 33, 4033 (1986); M. Hillery and L. Mlodinow, Phys. Rev. A: At., Mol., Opt. Phys. 48, 1548 (1993); J. P. Dowling, Phys. Rev. A: At., Mol., Opt. Phys. 57, 4736 (1998).
A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733 (2000); G. Björk, L. L. Sanchez-Soto, and J. Söderholm, Phys. Rev. Lett. 86, 4516 (2001).
D. Bouwmeester, A. Ekert, and A. Zeilinger, The Physics of Quantum Information (Springer, Berlin, 2000).
E. Schrödinger, Naturwissenschaften 23, 807, 823, 844 (1935).
V. V. Dodonov, I. A. Malkin, and V. I. Manko, Physica (Amsterdam) 72, 597 (1974); I. A. Malkin and V. I. Manko, Dynamical Symmetries and Coherent States of Quantum Systems (Nauka, Moscow, 1979) [in Russian].
M. D. Reid, arXiv:quant-ph/0101052.
W. Schleich, M. Pernigo, and F. L. Kien, Phys. Rev. A: At., Mol., Opt. Phys. 44, 2172 (1991).
B. Yurke and D. Stoler, Phys. Rev. Lett. 57, 13 (1986); C. C. Gerry, Phys. Rev. A: At., Mol., Opt. Phys. 59, 4095 (1999).
M. Dakna, T. Anhut, T. Opatrn, L. Knöll, and D.-G. Welsch, Phys. Rev. A: At., Mol., Opt. Phys. 55, 3184 (1997).
A. P. Lund, H. Jeong, T. C. Ralph, and M. S. Kim, Phys. Rev. A: At., Mol., Opt. Phys. 70, 020101(R) (2004).
A. M. Lance, H. Jeong, N. B. Grosse, T. Symul, T. C. Ralph, and P. K. Lam, Phys. Rev. A: At., Mol., Opt. Phys. 73, 041801(R) (2006).
H. Jeong, A. M. Lance, N. B. Grosse, T. Symul, P. K. Lam, and T. C. Ralph, Phys. Rev. A: At., Mol., Opt. Phys. 74, 033813 (2006).
H. Jeong, A. P. Lund, and T. C. Ralph, Phys. Rev. A: At., Mol., Opt. Phys. 72, 013801 (2005).
S. Kim, E. Park, P. L. Knight, and H. Jeong, Phys. Rev. A: At., Mol., Opt. Phys. 71, 043805 (2005); S. Olivares and M. G. A. Paris, J. Opt. B: Quantum Semiclassical Opt. 7, S616 (2005); Laser Phys. 16, 1533 (2006); S. Suzukia, K. Tsujinoa, F. Kannarib, and M. Sasaki, Opt. Commun. 259, 758 (2006).
J. Wenger, R. Tualle-Brouri, and P. Grangier, Phys. Rev. Lett. 92, 153601 (2004); A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and Ph. Grangier, Nature (London) 312, 83 (2006); J. S. Neergaard-Nielsen, B. M. Nielsen, C. Hettich, K. Mølmer, and E. S. Polzik, Phys. Rev. Lett. 97, 083604 (2006); K. Wakui, H. Takahashi, A. Furusawa, and M. Sasaki, Opt. Express 15, 3568 (2007).
A. Ourjoumtsev, H. Jeong, R. Tualle-Brouri, and Ph. Grangier, Nature (London) 448, 784 (2007).
P. Marek and M. S. Kim, Phys. Rev. A: At., Mol., Opt. Phys. 78, 022309 (2008).
P. Marek, H. Jeong, and M. S. Kim, Phys. Rev. A: At., Mol., Opt. Phys. 78, 063811 (2008).
M. Sasaki, M. Takeoka, and H. Takahashi, Phys. Rev. A: At., Mol., Opt. Phys. 77, 063840 (2008); M. Takeoka, H. Takahashi, and M. Sasaki, Phys. Rev. A: At., Mol., Opt. Phys. 77, 062315 (2008).
H. Takahashi, K. Wakui, S. Suzuki, M. Takeoka, K. Hayasaka, A. Furusawa, and M. Sasaki, arXiv:0806.2965.
T. Gerris, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdall, S. W. Nam, R. P. Mirin, and E. Knill, arXiv:1004.2727(quant-ph).
M. Dakna, J. Clausen, L. Knöll, and D.-G. Welsch, Phys. Rev. A: At., Mol., Opt. Phys. 59, 1658 (1999).
S. A. Podoshvedov, JETP 112(4), 551 (2011).
S. A. Podoshvedov and J. Kim, Phys. Rev. A: At., Mol., Opt. Phys. 77, 032319 (2008); S. A. Podoshvedov, Phys. Rev. A: At., Mol., Opt. Phys. 79, 012319 (2009).
S. A. Podoshvedov, JETP 110(4), 576 (2010).
A. L. Lvovsky, H. Hausen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, Phys. Rev. Lett. 87, 050402 (2001); A. I. Lvovsky and S. A. Babischev, Phys. Rev. A: At., Mol., Opt. Phys. 66, 011801(R) (2002).
D. F. Walls and G. J. Milburn, Quantum Optics (Springer, Berlin, 1994).
A. Zavatta, S. Viciani, and M. Bellini, Science (Washington) 306, 660 (2004); A. Zavatta, S. Viciani, and M. Bellini, Phys. Rev. A: At., Mol., Opt. Phys. 70, 053821 (2004).
Author information
Authors and Affiliations
Corresponding author
Additional information
The article is published in the original.
Rights and permissions
About this article
Cite this article
Podoshvedov, S.A. Generation of displaced squeezed superpositions of coherent states. J. Exp. Theor. Phys. 114, 451–464 (2012). https://doi.org/10.1134/S1063776112020288
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063776112020288