Parallel Generation of Quadripartite Cluster Entanglement in the Optical Frequency Comb

Scalability and coherence are two essential requirements for the experimental implementation of quantum information and quantum computing. Here, we report a breakthrough toward scalability: the simultaneous generation of a record 15 quadripartite entangled cluster states over 60 consecutive cavity modes ($Q$ modes), in the optical frequency comb of a single optical parametric oscillator. The amount of observed entanglement was constant over the 60 $Q$ modes, thereby proving the intrinsic scalability of this system. The number of observable $Q$ modes was restricted by technical limitations, and we conservatively estimate the actual number of similar clusters to be at least 3 times larger. This result paves the way to the realization of large entangled states for scalable quantum information and quantum computing.

Figure 1

Principle of the experiment. The OFC of a single OPO is made polarization-degenerate by using a cavity with 2 identical crystals rotated 90° from each other in the polarization plane. One crystal simultaneously phase-matches the $zzz$, $yzy$, and $yyz$ nonlinear interactions (bottom). This creates square weighted cluster states (top, in blue) [18].

Figure 2

Experimental setup. HWP, half wave plate; QWP, quarter wave plate; FI, Faraday isolator; PZT, piezoelectric transducer; PLL, phase-lock loop; AOM, acousto-optic modulator; EOM, waveguide electro-optic modulator; KTP, ${\mathrm{KTiOPO}}_4$; RTA, ${\mathrm{RbTiAsO}}_4$ EOM; PBS, polarizing beam splitter; ATT, rf attenuator; SA, spectrum analyzer.

Figure 3

Scaling quadripartite entanglement in the optical frequency comb of a single OPO: nullifier variance $\Delta A_{\pm }[\theta ({\theta }_{\mathrm{LO}}){]}^2$, relative to the vacuum noise, versus the LO phase ${\theta }_{\mathrm{LO}}$. Note that the squeezing depends on ${\theta }_{\mathrm{LO}}$ but not on $\theta$ [17]. Single-sweep measurements were taken at 1.25 MHz frequency; RBW: 30 kHz; VBW: 30 Hz. The $Q$ modes (black lines) measured are marked by the LO sidebands (purple arrows). The green line references half the pump frequency.

Figure 4

Detection and entanglement checks. As in Fig. 3, the plots display nullifier variance measurement relative to the vacuum noise versus the LO phase ${\theta }_{\mathrm{LO}}$. Top row, left and center: Single-sideband detection displays no single-mode squeezing in the OPO comb, in any quadrature. Top row, right, and bottom row, left and center: LO sidebands coincide with uncorrelated comb lines, which yields no multimode squeezing whatsoever, again no matter the LO phase used. Bottom row, right: OPO pump detuned from the comb ($2{\omega }_0\ne {\omega }_{-n}+{\omega }_n$), which makes the nonlinear interaction singly (instead of doubly) resonant and yields negligible squeezing. Notations and legends are as in Fig. 3. The dashed purple line references the phase-locked laser’s frequency.

Figure 5

Squeezing spectra for $A_{+}$ (left) and $A_{-}$ (right). The squeezed trace on the left was recorded simultaneously with the antisqueezed trace on the right, for ${\theta }_{\mathrm{LO}}=\pi /2$, and vice versa, for ${\theta }_{\mathrm{LO}}=0$, as with measurements in Figs. 3, 4.

Figure 6

Variances $(\Delta A_{+}{)}^2$ (blue) and $(\Delta A_{-}{)}^2$ (red) with measurement gains set to 0.3 in lieu of $1/\Phi =0.618$. (The van Loock–Furusawa criterion allows us to deviate from nullifier measurements to find the optimum gain values for maximum violation.) The dashed lines indicate the sub-vacuum-noise violation levels required to prove inseparability.