Quantum steering in an asymmetric chain of nonlinear oscillators

Abstract

We discuss here a possibility of generation of steerable states in asymmetric chains comprising three Kerr-like nonlinear oscillators. We show that steering between modes can be generated in the system and it strongly depends on the asymmetry of internal couplings in our model. We can lead to the appearance of new steering effects, which were not present in symmetric models already studied in the literature. Full Text: PDF ReferencesE. Schrödinger, "Discussion of Probability Relations between Separated Systems", Math. Proc. Camb. Phil. Soc. 31, 555 (1935). CrossRef M.D. Reid, "Demonstration of the Einstein-Podolsky-Rosen paradox using nondegenerate parametric amplification", Phys. Rev. A 40, 913 (1989). CrossRef E.G. Cavalcanti, M.D. Reid, "Uncertainty relations for the realization of macroscopic quantum superpositions and EPR paradoxes", Journal of Modern Optics 54, 2373 (2007). CrossRef S.P. Walborn, A. Salles, R.M. Gomes, F. Toscano, P.H. Souto Ribeiro, "Revealing Hidden Einstein-Podolsky-Rosen Nonlocality", Phys. Rev. Lett. 106, 130402 (2011). CrossRef H.M. Wiseman, S.J. Jones, A.C. Doherty, "Steering, Entanglement, Nonlocality, and the Einstein-Podolsky-Rosen Paradox", Phys. Rev. Lett. 98, 140402 (2007). CrossRef S.J. Jones, H.M. Wiseman, A.C. Doherty, "Entanglement, Einstein-Podolsky-Rosen correlations, Bell nonlocality, and steering", Phys. Rev. A 76, 052116 (2007). CrossRef J.K. Kalaga, W. Leoński, "Quantum steering borders in three-qubit systems", Quantum Inf Process 16, 175 (2017). CrossRef Q. He, Z. Ficek, "Einstein-Podolsky-Rosen paradox and quantum steering in a three-mode optomechanical system", Phys. Rev. A 89, 022332 (2014). CrossRef S. Kiesewetter, Q.Y. He, P.D. Drummond, M.D. Reid, "Scalable quantum simulation of pulsed entanglement and Einstein-Podolsky-Rosen steering in optomechanics", Phys. Rev. A 90, 043805 (2014). CrossRef K. Bartkiewicz, A. Cernoch, K. Lemr, A. Miranowicz, F. Nori, "Experimental temporal quantum steering", Scientific Reports 6, 38076 (2016). CrossRef A. Barasiński, B. Brzostowski, R. Matysiak, P. Sobczak, D. Woźniak, In: R. Wyrzykowski, J. Dongarra, K. Karczewski, J. Wasniewski editor, Parallel Processing and Applied Mathematics (PPAM 2013), Lecture Notes in Computer Science, vol 8385. Springer, Berlin, Heidelberg (2014). CrossRef A. Drzewiński, J. Sznajd, "On the real-space renormalization-group study of some 2D quantum spin systems", Physica A 170, 415 (1991). CrossRef G.J. Milburn, C.A. Holmes, "Quantum coherence and classical chaos in a pulsed parametric oscillator with a Kerr nonlinearity", Phys. Rev. A 44, 4704 (1991). CrossRef W. Leoński, "Quantum and classical dynamics for a pulsed nonlinear oscillator", Physica A 233, 365 (1996). CrossRef A. Kowalewska-Kudłaszyk, J.K. Kalaga, W. Leoński, "Long-time fidelity and chaos for a kicked nonlinear oscillator system", Physics Letters A 373, 1334 (2009). CrossRef J.K. Kalaga, W. Leoński, "Two proposals of quantum chaos indicators related to the mean number of photons: pulsed Kerr-like oscillator case", Proc. SPIE 10142, 101421L (2016). CrossRef A. Barasiński, W. Leoński, T. Sowiński, "Ground-state entanglement of spin-1 bosons undergoing superexchange interactions in optical superlattices", J. Opt. Soc. Am. B 31, 1845 (2014). CrossRef A. Barasiński, W. Leoński, "Symmetry restoring and ancilla-driven entanglement for ultra-cold spin-1 atoms in a three-site ring", Quantum Inf Process 16, 6 (2017). CrossRef D. Woźniak, A. Drzewiński, G. Kamieniarz, "Relaxation Dynamics in the Spin-1 Heisenberg Antiferromagnetic Chain after a Quantum Quench of the Uniaxial Anisotropy", Acta Physica Polonica A 130, 1395 (2016). CrossRef R. Szczęśniak, D. Szczęśniak, E.A. Drzazga, "Superconducting state in the atomic metallic hydrogen just above the pressure of the molecular dissociation", Solid State Communications 152, 2023 (2012). CrossRef A. P. Durajski, R. Szczęśniak, M.W. Jarosik, "Properties of the superconducting state in compressed sulphur", Phase Transitions 85, 727 (2012). CrossRef R. Szczęśniak, A. P. Durajski, "The thermodynamic properties of the high-pressure superconducting state in the hydrogen-rich compounds", Solid State Sciences 25, 45 (2013). CrossRef X. Wang, A. Miranowicz, H.R. Li, F. Nori, "Multiple-output microwave single-photon source using superconducting circuits with longitudinal and transverse couplings", Phys. Rev. A 94, 053858, (2016). CrossRef Y.X. Liu, X.W. Xu, A. Miranowicz, F. Nori, "From blockade to transparency: Controllable photon transmission through a circuit-QED system", Phys. Rev. A 89, 043818 (2014). CrossRef M.K. Olsen, "Spreading of entanglement and steering along small Bose-Hubbard chains", Phys. Rev. A 92, 033627 (2015). CrossRef E.G. Cavalcanti, Q.Y. He, M.D. Reid, H.M. Wiseman, "Unified criteria for multipartite quantum nonlocality", Phys. Rev. A 84, 032115 (2011). CrossRef

Creation of bipartite steering correlations by a fast damped auxiliary mode

“…However, for quantum steering to be observed the correlations between modes must be stronger than those for entanglement. Specifically, for the case determined by the steady-state (17), the criterion (24) for quantum steering between the cavity and mirror modes yields the inequality…”

“…According to (17), there are nonzero X a P b and X b P a correlations between the modes. Therefore, in the definition of the steering parameter (24), we choose O b ≡ P b for the quadrature of the mode b. In addition, since ∆ 2 P a = ∆ 2 X a , ∆ 2 P b = ∆ 2 X b and X a P b = X b P a , we see that the steering parameter E a|b is of the form…”

“…Various systems have been theoretically studied for the creation of quantum steering [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. The experimental realization of quantum steering has been accomplished in several systems [27][28][29][30][31][32][33][34][35][36].…”

Enhancement of the entanglement generation via randomly perturbed series of external pulses in a nonlinear Bose–Hubbard dimer

“…Moreover, depending on the time of the free system's evolution (time between two subsequent external pulses), a superposition of only two Fock states or superposition of a much larger number of Fock states can be achieved [65,66]. Such models were also considered in other contexts, such as the ergodicity of systems [67,68], quantum-classical correspondence [69,70] or quantum chaotic behavior [71][72][73][74][75][76][77][78].…”