Analysis of a continuous-variable quadripartite cluster state from a single optical parametric oscillator

Abstract

We examine the feasibility of generating continuous-variable multipartite entanglement in an intracavity concurrent downconversion scheme that has been proposed for the generation of cluster states by Menicucci et al. [Phys. Rev. Lett. 101, 130501 (2008)]. By calculating optimized versions of the van Loock-Furusawa correlations we demonstrate genuine quadripartite entanglement and investigate the degree of entanglement present. Above the oscillation threshold the basic cluster state geometry under consideration suffers from phase diffusion. We alleviate this problem by incorporating a small injected signal into our analysis. Finally, we investigate squeezed joint operators. While the squeezed joint operators approach zero in the undepleted regime, we find that this is not the case when we consider the full interaction Hamiltonian and the presence of a cavity. In fact, we find that the decay of these operators is minimal in a cavity, and even depletion alone inhibits cluster state formation.

Multipartite entanglement in the optical frequency comb of a depleted-pump optical parametric oscillator

“…The search for optimal entanglement witnesses for this system is a promising approach to illuminate this question. Note that previous work has shown that multipartite cluster-state generation, which was experimentally demonstrated in a single OPO below threshold [12], should actually fail above threshold [13]. However, the multipartite entanglement that we discovered in the simple OPO above threshold would certainly be useful for quantum communication applications, such as quantum secret sharing.…”

“…In Section 3, we solve the equations of motion for the system by employing a linearization procedure. We are certainly aware that more sophisticated treatments exist [13,[16][17][18][19] and may indeed be interesting to use in order to explore this system further. In particular, it is worth mentioning the new physics of noncritical squeezing generation-that is, squeezing independent of the system parameters such as pump amplitudein the transverse spatial modes of an OPO, which was recently predicted via the phenomena of spontaneous symmetry breaking [20,21] and pump clamping [22], the latter having already been observed in the laboratory [23].…”

Spectral analysis of a four mode cluster state

“…As shown in Ref. [7], the system has an oscillation threshold and for the parameters used here the critical pump amplitude is c = 61.8. The parameters used in the following calculations are γ = 1, χ = 0.01 and = 0.94 c , giving a pump rate approximately 12% below threshold in intensity.…”

“…The system considered here is a pumped optical cavity containing a χ (2) non-linear crystal, as investigated theoretically in Ref. [7]. We extend our analysis to incorporate the results of a full spectral analysis in the frequency domain.…”

“…with the χ i representing the effective nonlinearities and a i andâ † i denoting the bosonic annihilation and creation operators for the intra-cavity modes at frequencies ω i . We note here that we are using the full interaction Hamiltonian rather than making a classical undepleted pump approximation leading to linear Heisenberg equations as used by Pysher et al [1] (see also the Supplemental Material), which has the advantage that our formalism may also be used above the oscillation threshhold [6,7]. In a rotating frame, the pumping Hamiltonian,Ĥ pump is given byĤ…”