Abstract: Multi-mode continuous-variable entanglement has become increasingly important for practical quantum information processing. We generate 2-mode vacuum-squeezed optical states through a 4-wave mixing (4WM) process in Rb atomic vapor and conduct a detailed study using homodyne measurements. By dividing the squeezing bandwidth into smaller frequency bins, we show that different sideband frequencies represent independent sources of two-mode squeezing. We then mix the different sideband frequencies (frequency qumodes) using an electro-optical modulator (EOM), thereby producing a pattern of entanglement correlations that constitute a continuous-variable graph state that is transformable into a cluster state by Gaussian local unitary operations. Using a single-frequency EOM drive we correlate neighboring frequency bands within the 4WM squeezing bandwidth, to create a dual-rail 1-D optical cluster state. By driving the EOM with additional frequencies, we create 2-, 3-, and 4-D optical cluster states with hundreds of qumodes and demonstrate the entanglement structure of these as well by verifying that the state nullifier variances return values close to the original squeezing levels.
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