Entangled State Creation by a Nonlinear Coupler Pumped in Two Modes
Le Duc V. 1, Cao Long V. 2*
1 Faculty of Natural Sciences, Hong Duc University
Quang Trung 665, 450000 Thanh Hoa, Vietnam2 Quantum Optics and Engineering Division, Institute of Physics, University of Zielona Góra
A. Szafrana 4a, 65-516 Zielona Góra, Poland*E-mail: V.CaoLong@if.uz.zgora.pl
Received:
Received: 07 December 2016; revised: 19 December 2016; accepted: 20 December 2016; published online: 31 December 2016
DOI: 10.12921/cmst.2016.0000062
Abstract:
In this paper we consider a system with two nonlinear oscillators which are coupled via a nonlinear interaction. In order to excite the system, we use two external coherent fields. Two oscillators have different frequencies. It follows from numerical simulation that evolution of the system is similar to that of a combination of n-photon states. Therefore, the considered system behaves as so-called nonlinear quantum scissor. Nevertheless, evolution of the system generates Bell-like states in several times with very high probability. Because of the nonlinear properties of oscillators and their interaction, the system creates a truncation of optical states, which leads to obtain two-qubit states. It will also be shown that these states appear several times in the qutrit-qutrit system.
Key words:
Bell-like states, entanglement, Kerr-like systems, quantum scissor
References:
[1] M. A. Nielsen and I. L. Chuang, Quantum Computation
and Quantum Information, Cambridge University Press, 71-
90 (2000).
[2] M. Le Bellac, A Short Introdution To Quantum Information
and Quantum Computation, Cambridge University Press, 49-54
(2006).
[3] S. Babichev, J. Ries and A. Lvovsky, Quantum scissors: Tele-
portation of single-mode optical state by means of nonlocal
single photon, Europhys. Lett. 64, 1-7. (2003).
[4] E. Bimbard, N. Jain, A. MacRae and A.I. Lvovsky, Quantum-
optical state engineering up to the two-photon levels. Nature
Photonic, 10, 243-247 (2010).
[5] A. Miranowicz and W. Leonski, Two-mode optical state trun-
cation and generation of maximally entangled states in pumped
nonlinear couplers, Phys. B: At. Mol. Opt. Phys. 39, 1683-1700
(2006).
[6] W. Leonski, Kicked nonlinear quantum scissors and entangle-
ment generation, Phys. Rev. A 55, 4250-4265 (1997).
[7] A. Kowalewska-Kudlaszyk and W. Leonski, Finite-
dimensional states and entanglement generation for a
nonlinear coupler, Phy. Rev. A 73, 042318-042334 (2006).
[8] N. T. Dung, W. Leonski, V. Cao Long , Computer Simulation
of Two – mode Nonlinear Scissors, Comp. Meth. Sci. Technol.
Vol 19 (3), 175-181 (2013).
[9] A. Kowalewska-Kudlaszyk, W. Leonski, V. Cao Long, N.T
Dung, Kicked nonlinear quantum scissors and entanglement
generation, Phys.Scr. 160, 014023-014032 (2014).
[10] A. Kowalewka – Kudlaszyk and W. Leonski, Exciting field
phase effect on the entanglement death and birth phenomena for
nonlinearcoupler system, Journal of Computational Methods in
Sciences and Engineering, vol.10, no. 3-6, 425-431 (2010)
[11] A. Kowalewska-Kudlaszyk and W. Leonski, Sudden death
and birth of entanglement effects for Kerr-nonlinear coupler, J.
Opt. Soc. Am. B Vol 26. 7, 1289-1294 (2009)
[12] A. Kowalewska-Kudlaszyk and W. Leonski, Sudden death
of entanglement and its rebirth in a system of two nonlinear
oscillators, Phys. Scr. T140, 014051-10456 (2010).
[13] D. T. Pegg, L.S. Phillips and S. M. Barnett, Quantum scis-
sors: teleportation of single-mode optical states by means of a
nonlocal single photon, Phys. Rev. Lett. 81, 1604-1608 (1998).
[14] W. Leonski, S. Dyrting and R. Tanas, Fock states generation
in a kicked cavity with a nonlinear medium, J. Mod. Opt. 44,
2105-2123 (1997).
[15] W. Leonski and A. Miranowicz, Kerr nonlinear coupler and
entanglement, J. Opt. B: Quantum Semiclassical Opt. 6, S37-
S42 (2004).
[16] A. Kowalewka-Kudlaszyk and W. Leonski, A Quantum scis-
sors finite-dimensional states engineering, , Progress in Optics,
vol 56, 131–185 (2011).
[17] W. K. Wootters, Entanglement of formation of an arbitrary
state of two qubits, Phys. Rev. Lett, 80, 2245 – 2251 (1998).
[18] G. Jaeger, Entanglement information and interpretation of
quantum mechanics, Springer Press, 12-24 (2009)
[19] A. Kent, Entangled Mixed States and Local Purification Phys.
Rev. Lett. 81, 2839-2844 (1998).
[20] R. Horodecki, M. Horodecki and P. Horodecki, General tele-
portation channel, singlet fraction, and quasidistillation, Phys.
Rev. A. 60, 4144-4150 (1999).
In this paper we consider a system with two nonlinear oscillators which are coupled via a nonlinear interaction. In order to excite the system, we use two external coherent fields. Two oscillators have different frequencies. It follows from numerical simulation that evolution of the system is similar to that of a combination of n-photon states. Therefore, the considered system behaves as so-called nonlinear quantum scissor. Nevertheless, evolution of the system generates Bell-like states in several times with very high probability. Because of the nonlinear properties of oscillators and their interaction, the system creates a truncation of optical states, which leads to obtain two-qubit states. It will also be shown that these states appear several times in the qutrit-qutrit system.
Key words:
Bell-like states, entanglement, Kerr-like systems, quantum scissor
References:
[1] M. A. Nielsen and I. L. Chuang, Quantum Computation
and Quantum Information, Cambridge University Press, 71-
90 (2000).
[2] M. Le Bellac, A Short Introdution To Quantum Information
and Quantum Computation, Cambridge University Press, 49-54
(2006).
[3] S. Babichev, J. Ries and A. Lvovsky, Quantum scissors: Tele-
portation of single-mode optical state by means of nonlocal
single photon, Europhys. Lett. 64, 1-7. (2003).
[4] E. Bimbard, N. Jain, A. MacRae and A.I. Lvovsky, Quantum-
optical state engineering up to the two-photon levels. Nature
Photonic, 10, 243-247 (2010).
[5] A. Miranowicz and W. Leonski, Two-mode optical state trun-
cation and generation of maximally entangled states in pumped
nonlinear couplers, Phys. B: At. Mol. Opt. Phys. 39, 1683-1700
(2006).
[6] W. Leonski, Kicked nonlinear quantum scissors and entangle-
ment generation, Phys. Rev. A 55, 4250-4265 (1997).
[7] A. Kowalewska-Kudlaszyk and W. Leonski, Finite-
dimensional states and entanglement generation for a
nonlinear coupler, Phy. Rev. A 73, 042318-042334 (2006).
[8] N. T. Dung, W. Leonski, V. Cao Long , Computer Simulation
of Two – mode Nonlinear Scissors, Comp. Meth. Sci. Technol.
Vol 19 (3), 175-181 (2013).
[9] A. Kowalewska-Kudlaszyk, W. Leonski, V. Cao Long, N.T
Dung, Kicked nonlinear quantum scissors and entanglement
generation, Phys.Scr. 160, 014023-014032 (2014).
[10] A. Kowalewka – Kudlaszyk and W. Leonski, Exciting field
phase effect on the entanglement death and birth phenomena for
nonlinearcoupler system, Journal of Computational Methods in
Sciences and Engineering, vol.10, no. 3-6, 425-431 (2010)
[11] A. Kowalewska-Kudlaszyk and W. Leonski, Sudden death
and birth of entanglement effects for Kerr-nonlinear coupler, J.
Opt. Soc. Am. B Vol 26. 7, 1289-1294 (2009)
[12] A. Kowalewska-Kudlaszyk and W. Leonski, Sudden death
of entanglement and its rebirth in a system of two nonlinear
oscillators, Phys. Scr. T140, 014051-10456 (2010).
[13] D. T. Pegg, L.S. Phillips and S. M. Barnett, Quantum scis-
sors: teleportation of single-mode optical states by means of a
nonlocal single photon, Phys. Rev. Lett. 81, 1604-1608 (1998).
[14] W. Leonski, S. Dyrting and R. Tanas, Fock states generation
in a kicked cavity with a nonlinear medium, J. Mod. Opt. 44,
2105-2123 (1997).
[15] W. Leonski and A. Miranowicz, Kerr nonlinear coupler and
entanglement, J. Opt. B: Quantum Semiclassical Opt. 6, S37-
S42 (2004).
[16] A. Kowalewka-Kudlaszyk and W. Leonski, A Quantum scis-
sors finite-dimensional states engineering, , Progress in Optics,
vol 56, 131–185 (2011).
[17] W. K. Wootters, Entanglement of formation of an arbitrary
state of two qubits, Phys. Rev. Lett, 80, 2245 – 2251 (1998).
[18] G. Jaeger, Entanglement information and interpretation of
quantum mechanics, Springer Press, 12-24 (2009)
[19] A. Kent, Entangled Mixed States and Local Purification Phys.
Rev. Lett. 81, 2839-2844 (1998).
[20] R. Horodecki, M. Horodecki and P. Horodecki, General tele-
portation channel, singlet fraction, and quasidistillation, Phys.
Rev. A. 60, 4144-4150 (1999).
