Nonlinear quantum scissors and quantum states engineering: numerical simulations

We discuss the simulation method allowing modeling of quantum unitary dynamics for quantum nonlinear scissors systems. In particular, we consider the model of two nonlinear oscillators (Ker-like coupler) excited by an external field. We show that the time-evolution of the system is closed within a finite set of n-photo states and the Bell-like states are generated. Thus, we prove that the numerical method applied can be used as tools of quantum-mechanical simulations leading to the interesting results.

[1]  Maira Amezcua,et al.  Quantum Optics , 2012 .

[2]  W. Leoński Quantum and classical dynamics for a pulsed nonlinear oscillator , 1996 .

[3]  Entropic uncertainty in two two-level atoms interacting with a cavity field in presence of degenerate parametric amplifier , 2010 .

[4]  Jan Perina,et al.  Direct measurement and reconstruction of nonclassical features of twin beams generated in spontaneous parametric down-conversion , 2005 .

[5]  Dissipation in systems of linear and nonlinear quantum scissors , 2004, quant-ph/0402024.

[6]  J. Peřina,et al.  Squeezing properties of the Kerr-down conversion system , 2007, 1107.3640.

[7]  J. Pevrina,et al.  Photon-number entangled states generated in Kerr media with optical parametric pumping , 2011, 1104.4889.

[8]  R. Glauber Coherent and incoherent states of the radiation field , 1963 .

[9]  Tanaś,et al.  Squeezing and its graphical representations in the anharmonic oscillator model. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[10]  Leonski Fock states in a Kerr medium with parametric pumping. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[11]  Photon-pair generation in random nonlinear layered structures , 2009, 0908.3583.

[12]  A. Miranowicz,et al.  Two-mode optical state truncation and generation of maximally entangled states in pumped nonlinear couplers , 2006, quant-ph/0603149.

[13]  T. V. Gevorgyan,et al.  Generation of Fock states and qubits in periodically pulsed nonlinear oscillators , 2012, 1201.3877.

[14]  M. S. Abdalla,et al.  Single-mode quantum properties of the codirectional Kerr nonlinear coupler: frequency mismatch and exact solution , 2004, 0908.0381.

[15]  W. Leoński,et al.  Quantum scissors - finite-dimensional states engineering , 2013, 1312.0118.

[16]  G. Kryuchkyan,et al.  Time-modulated type-II optical parametric oscillator: Quantum dynamics and strong Einstein-Podolsky-Rosen entanglement , 2006 .

[17]  W. Press,et al.  Numerical Recipes: The Art of Scientific Computing , 1987 .

[18]  V. Degiorgio,et al.  About photon correlations , 2013 .

[19]  G. Kryuchkyan,et al.  Three-photon states in nonlinear crystal superlattices , 2010, 1011.1577.

[20]  W. Leon-acuteski Finite-dimensional coherent-state generation and quantum-optical nonlinear oscillator models , 1997 .

[21]  Entanglement in optical parametric down-conversion with losses and noise , 2009 .

[22]  R. Tanas,et al.  Possibility of producing the one-photon state in a kicked cavity with a nonlinear Kerr medium. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[23]  Knight,et al.  Comparison of quantum-state diffusion and quantum-jump simulations of two-photon processes in a dissipative environment. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[24]  J. Peřina,et al.  Higher-order squeezing for the codirectional Kerr nonlinear coupler , 2004, 0907.5085.

[25]  C. P. Sun,et al.  Qubit-induced phonon blockade as a signature of quantum behavior in nanomechanical resonators , 2009, 0910.3066.

[26]  Kerr nonlinear coupler and entanglement , 2004, quant-ph/0408024.

[27]  M. Koashi,et al.  Generation of maximum spin entanglement induced by a cavity field in quantum-dot systems , 2002, quant-ph/0205030.

[28]  J. Peřina Spatial properties of entangled photon pairs generated in nonlinear layered structures , 2011, 1111.1616.

[29]  W. Leoński,et al.  Squeezed vacuum reservoir effect for entanglement decay in the nonlinear quantum scissor system , 2010, 1009.1068.

[30]  S. Kielich,et al.  Generation of discrete superpositions of coherent states in the anharmonic oscillator model , 1990, 1111.0866.

[31]  J. Peřina,et al.  Intense ultra-broadband down-conversion from randomly poled nonlinear crystals. , 2010, Optics express.

[32]  J. Peřina,et al.  Antisymmetric entangled two-photon states generated in nonlinear GaN/AlN photonic-band-gap structures , 2007, 0708.2242.

[33]  B A Umarov,et al.  Generation of three-qubit entangled W state by nonlinear optical state truncation , 2006 .

[34]  A. Kowalewska-Kudlaszyk,et al.  Finite-dimensional states and entanglement generation for a nonlinear coupler , 2006, quant-ph/0603090.