Ultra-Large-Scale Deterministic Entanglement Containing $2\times 20400$ Optical Modes Based on Time-Delayed Quantum Interferometer

Quantum entanglement is an indispensable resource for implementing quantum information processing. The scale of quantum entanglement directly determines its quantum information processing capability. Therefore, it is of great importance to generate ultra-large-scale (ULS) quantum entanglement for the development of quantum information science and technology. Many efforts have been made to increase the scale of quantum entanglement. Recently, time-domain multiplexing has been introduced into continuous-variable (CV) quantum systems to greatly enlarge the scale of quantum entanglement. In this Letter, based on a time-delayed quantum interferometer, we theoretically propose and experimentally demonstrate a scheme for generating an ULS CV deterministic entanglement containing $2\times 20400$ optical modes. In addition, such ULS entanglement contains 81 596 squeezed modes. Our results provide a new platform for implementing ULS CV quantum information processing.

Figure 1

Generating ULS CV quantum entanglement based on a time-delayed SU(1,1) quantum interferometer. (a) Experimental schematic. The yellow and blue spheres represent the time wave packets of probe beam and conjugate beam with time duration $T$, respectively. The whole process can be divided into four steps. The time delay caused by optical fiber is equal to $T$. The magenta links represent the interaction of optical wave packets. $\dots ,k-1,k,k+1,\dots$ stand for the time wave packet index. LO, local oscillator; BHD, balanced homodyne detection; OS, oscilloscope. (b) The double-$\mathrm{\Lambda }$ energy level configuration of the $D1$ line of ${}^{85}\mathrm{Rb}$. $\mathrm{\Delta }$, one-photon detuning; $\delta$, two-photon detuning; ${\mathrm{\Delta }}_{-}$, the ${}^{85}\mathrm{Rb}$ ground-state hyperfine splitting.

Figure 2

Witnessing the ULS CV quantum entanglement. (a) Measured smallest symplectic eigenvalues of 20 399 wave packet units when $G_1=1.3$ and $G_2=1.2$. Seven dfferent colors represent the smallest symplectic eigenvalues $v$ of the seven bipartitions. All the eigenvalues $v$ are less than 1, indicating that each wave packet unit is entangled or inseparable. $N$ represents the wave packet unit index. (b) The corresponding results of the first wave packet unit ($N=1$).

Figure 3

Eigenmodes and the corresponding squeezing levels of the first output wave packet unit retrieved from CM when $G_1=1.3$ and $G_2=1.2$. Eigenmode I and eigenmode III are amplitude quadrature squeezed while eigenmode II and eigenmode IV are phase quadrature squeezed. The height of bars represents the relative weight of modes ${\widehat{a}}_{\mathrm{pr},1}^{(4)}$, ${\widehat{a}}_{\mathrm{conj},1}^{(4)}$, ${\widehat{a}}_{\mathrm{pr},2}^{(4)}$, and ${\widehat{a}}_{\mathrm{conj},2}^{(4)}$ for each eigenmode.

Figure 4

Eigenvalues of 20 399 consecutive output wave packet units when $G_1=1.3$ and $G_2=1.2$. The amplitude (phase) quadrature eigenvalues of all output wave packet units are plotted in regions I and III (II and IV). There are 20 399 different colors in regions I–IV, respectively. The eigenvalues are measured in decibels.