Three-color entanglement generated by single-pass cascaded sum-frequency processes

Abstract

Three-color continuous-variable (CV) entangled beams can be produced by single-pass cascaded sum-frequency processes of third-harmonic generation by quasi-phase-matching technique in only one optical superlattice. Firstly, second-harmonic field is generated by the first double-frequency process of the fundamental field. Then, the third-harmonic field can be generated by the second cascaded sum-frequency process between the second-harmonic and the fundamental fields by quasi-phase-matching technique in the same optical superlattice. By using the quantum stochastic method, we investigated the conversion dynamics of the cascaded sum-frequency processes and the quantum correlation nature among the fundamental, second-harmonic, and third-harmonic fields. The results show that the higher conversion efficiency of third-harmonic generation can be achieved with the larger nonlinear coupling parameter of the second cascaded sum-frequency process. We also show that the fundamental, second-, and third-harmonic beams are CV entangled with each other according to the necessary and sufficient CV entanglement criterion. This scheme of three-color entanglement generation without involving optical cavity is easy to realize in experiment. Moreover, the three-color entangled beams are separated by an octave in frequency which has potential applications in quantum communication and computation networks.

Third-harmonic entanglement and Einstein-Podolsky-Rosen steering over a frequency range of more than an octave

“…1, for κ 1 = 10 −2 , κ 2 = 1.5κ 1 , and N 0 (0) = 10 4 . We note here that these solutions are not consistent with those given by Yu et al [28], which reach a steady state at ξ ≈ 6, after which the modes at ω 0 and ω 2 are totally depleted, leaving only the second harmonic. As we know that the term κ 1â1â † 2 0 in the Hamiltonian will act to down convert the second harmonic with no other modes present, and this is in fact what is responsible for the revivals of the fundamental seen in traveling-wave SHG [39], we have confidence in our solutions.…”

“…Also, is the coherent pump amplitude, γ j is the cavity loss rate for mode j , and the η j are Gaussian random variables with the correlations η j (t) = 0 and η j (t)η k (t ) = δ jk δ(t − t ). Note that our noise terms are not exactly the same as those in Yu et al [27][28][29] and that this is due to the freedom available in the factorization of the diffusion matrix of the Fokker-Planck equation for the positive-P function of the system. We have chosen to use real rather than complex noise terms, which is a matter of taste since exactly the same physical system can be represented by either.…”

“…This process involves two parametric processes generated by a quasi-phase-matched optical superlattice [27][28][29]. In the first, the fundamental mode at frequency ω 0 acts via the nonlinearity represented by κ 1 to produce a harmonic mode at ω 1 , where ω 1 = 2ω 0 .…”

“…The cascaded method has the advantage that it is amenable to a theoretical treatment using the positive-P method, as there are no terms in the Hamiltonian of higher than third order in creation and annihilation operators. The scheme has been analyzed theoretically using this powerful method in both the traveling-wave [27,28] and intracavity [29] configurations. These works analyzed the scheme in terms of both its mean-field and entanglement properties, using the method of symplectic eigenvalues [38] to demonstrate that entanglement exists among the possible bipartitions of a multimode system.…”

Compact 6 dB Two-Color Continuous Variable Entangled Source Based on a Single Ring Optical Resonator

“…Various entangled states, including two-color [19][20][21][22][23][24][25] and three-color [26][27][28] CV quantum-entangled states, have been generated. We have utilized a single ring resonator, which combines both the NOPA and non-degenerate optical parametric oscillator (NOPO), and prepared quantum-entangled states with a large wavelength difference.…”