Computer Simulation of Two-Mode Nonlinear Quantum Scissors
Dung Nguyen T., Leoński W., Cao Long V. *
Quantum Optics and Engineering Division, Institute of Physics
University of Zielona Góra, A. Szafrana 4a, 65-516 Zielona Góra, Poland
∗E-mail: caolongvanuz@gmail.com
Received:
Received: 4 August 2013; accepted: 21 August 2013; published online: 6 September 2013
DOI: 10.12921/cmst.2013.19.03.175-181
OAI: oai:lib.psnc.pl:453
Abstract:
We present a simulation method allowing for modeling of quantum dynamics of nonlinear quantum scissors’ (NQS) systems. We concentrate on the two-mode model involving two mutually interacting nonlinear quantum oscillators (Kerr nonlinear coupler) excited by a series of ultra-short external coherent pulses. We show that despite the simplicity of the method one can obtain non-trivial results. In particular, we discuss and compare two cases of kicked nonlinear coupler, showing that the quantum evolution of the system remains closed within a two-qubit Hilbert space and can lead to maximally entangled states generation.
Key words:
Kerr coupler, nonlinear quantum scissors, quantum state engineering, qubit
References:
[1] W. Leoński, A. Kowalewska-Kudłaszyk, Quantum Scissors-
Finite-Dimensional States Engineering. Prog. Opt. 56, 131-
185 (2011).
[2] N. Korolkova, J. Perina, Quantum statistics and dynamics of
Kerr nonlinear couplers. Opt. Commun. 136, 135-149 (1997).
[3] A. Miranowicz, W. Leoński, Two-mode optical state trunca-
tion and generation of maximally entangled states in pumped
nonlinear couplers. J. Phys. B: At. Mol. Opt. Phys. 39, 1683-
1700 (2006).
[4] W. Leoński, A. Kowalewska-Kudłaszyk, A. Miranowicz, Com-
puter Simulations of Entanglement Dynamics for Nonlinear
Systems. CMST 16, 169-172 (2010).
[5] Matlab documentation, available at:
http://www.mathworks.com/help/matlab/index.html
[6] For Octave language documentation see: http://www.gnu.org/
software/octave/doc/interpreter/
[7] R. J. Glauber, Photon Correlations. Phys. Rev. Lett. 10, 84-86
(1963); coherent and Incoherent States of Radition Field. Phys.
Rev. 131, 2766-2788
[8] W. Leoński, R. Tanaś, Possibility of producing the one-photon
state in a kicked cavity with a nonlinear Kerr medium. Phys.
Rev. A 49, R20-R23 (1994).
[9] T.V. Gevorgyan, A. R. Shahinyan, G.Yu. Kryuchkyan, Quan-
tum interference and sub-Poissonian statistics for time-
modulated driven dissipative nonlinear oscillators. Phys. Rev.
A 79, 053828 (2009).
[10] D. A. Antonosyan,T.V. Gevorgyan,G.Yu. Kryuchkyan, Three-
photon states in nonlinear crystal superlattices. Phys. Rev. A
83, 043807 (2011).
[11] T.V. Gevorgyan, A. R. Shahinyan, G.Yu. Kryuchkyan, Genera-
tion of Fock states and qubits in periodically pulsed nonlinear
oscillators. Phys. Rev. A 85, 053802 (2012).
We present a simulation method allowing for modeling of quantum dynamics of nonlinear quantum scissors’ (NQS) systems. We concentrate on the two-mode model involving two mutually interacting nonlinear quantum oscillators (Kerr nonlinear coupler) excited by a series of ultra-short external coherent pulses. We show that despite the simplicity of the method one can obtain non-trivial results. In particular, we discuss and compare two cases of kicked nonlinear coupler, showing that the quantum evolution of the system remains closed within a two-qubit Hilbert space and can lead to maximally entangled states generation.
Key words:
Kerr coupler, nonlinear quantum scissors, quantum state engineering, qubit
References:
[1] W. Leoński, A. Kowalewska-Kudłaszyk, Quantum Scissors-
Finite-Dimensional States Engineering. Prog. Opt. 56, 131-
185 (2011).
[2] N. Korolkova, J. Perina, Quantum statistics and dynamics of
Kerr nonlinear couplers. Opt. Commun. 136, 135-149 (1997).
[3] A. Miranowicz, W. Leoński, Two-mode optical state trunca-
tion and generation of maximally entangled states in pumped
nonlinear couplers. J. Phys. B: At. Mol. Opt. Phys. 39, 1683-
1700 (2006).
[4] W. Leoński, A. Kowalewska-Kudłaszyk, A. Miranowicz, Com-
puter Simulations of Entanglement Dynamics for Nonlinear
Systems. CMST 16, 169-172 (2010).
[5] Matlab documentation, available at:
http://www.mathworks.com/help/matlab/index.html
[6] For Octave language documentation see: http://www.gnu.org/
software/octave/doc/interpreter/
[7] R. J. Glauber, Photon Correlations. Phys. Rev. Lett. 10, 84-86
(1963); coherent and Incoherent States of Radition Field. Phys.
Rev. 131, 2766-2788
[8] W. Leoński, R. Tanaś, Possibility of producing the one-photon
state in a kicked cavity with a nonlinear Kerr medium. Phys.
Rev. A 49, R20-R23 (1994).
[9] T.V. Gevorgyan, A. R. Shahinyan, G.Yu. Kryuchkyan, Quan-
tum interference and sub-Poissonian statistics for time-
modulated driven dissipative nonlinear oscillators. Phys. Rev.
A 79, 053828 (2009).
[10] D. A. Antonosyan,T.V. Gevorgyan,G.Yu. Kryuchkyan, Three-
photon states in nonlinear crystal superlattices. Phys. Rev. A
83, 043807 (2011).
[11] T.V. Gevorgyan, A. R. Shahinyan, G.Yu. Kryuchkyan, Genera-
tion of Fock states and qubits in periodically pulsed nonlinear
oscillators. Phys. Rev. A 85, 053802 (2012).