High-dimensional entanglement between distant atomic-ensemble memories

Abstract

Entangled quantum states in high-dimensional space show many advantages compared with entangled states in two-dimensional space. The former enable quantum communication with higher channel capacity, enable more efficient quantum-information processing and are more feasible for closing the detection loophole in Bell test experiments. Establishing high-dimensional entangled memories is essential for long-distance communication, but its experimental realization is lacking. We experimentally established high-dimensional entanglement in orbital angular momentum space between two atomic ensembles separated by 1 m. We reconstructed the density matrix for a three-dimensional entanglement and obtained an entanglement fidelity of (83.9±2.9)%. More importantly, we confirmed the successful preparation of a state entangled in more than three-dimensional space (up to seven-dimensional) using entanglement witnesses. Achieving high-dimensional entanglement represents a significant step toward a high-capacity quantum network.

Keywords: high-dimensional entanglement; orbital angular momentum; quantum memory.

Figure 1

Experimental details. (a) Energy level diagrams and the time sequence for creating and storing entanglement. (b) Experimental setup. Lenses L1 and L2 are used to focus signal 1 onto the center of MOT 2. L3, L4 and L5 are used to focus the phase structure of signal 2 onto the surface of SLM 2. L6 and L7 are used to couple the OAM mode of signal 2 to C2. There is an asymmetric optical path for coupling signal 1 with C1 in the right half of the figure. C, fiber coupler; L, lens; M, mirror; P1/2, pump 1/2; S1/2, signal 1/2.

Figure 2

Correlation between signal 1 and signal 2, with m=−7→7 before and after storage. (a) Coincidence rate before storage, measured over an interval of 100 s. (b) Coincidence rate after storage, measured over an interval of 600 s. (c) Distributions of the correlated OAM modes generated from SRS, where red dots and black squares represent data sets of input and output OAM correlations, respectively. Both correlations are fitted using the fitting function , with (y₀=0, x_c=0, w=7.7, A=2030) and (y₀=12.7, x_c=0, w=4.57, A=1463), respectively. (d) The efficiency of storing different OAM modes. The black curve is calculated using the same fitting function, with fitted values (y₀=0.132, x_c=0, w=2.274, A=0.354); w specifies the half-width at half-maximum of y. We identify w with the effective quantum spiral bandwidth. For panels c and d, the correlation refers to the coincidences of signal 1 and 2 photons, while the efficiency corresponds to the ratio of the coincidences before and after storage. Error bars represent ±s.d.

Figure 3

Constructed density matrix of three-dimensional entanglement. (a and b) Real and imaginary parts before storage; (c and d) those after storage. The dotted bars added in each density matrix correspond to the expected value of the ideal density matrix.

Figure 4

Bases and measured visibilities. (a) The diagonal/anti-diagonal, left/right and horizontal/vertical bases in the phase and intensity spaces, with OAM modes m=5 and m=−1. The superposition is calculated by adding equal amounts of the two modes and the phase is calculated from the argument of the resultant complex, with the function Arg(LG₅+e^iϑLG_-1), where LG₅ and LG_-1 are the amplitudes of OAM states, with azimuthal indexes of 5 and −1, respectively, and θ represents the relative phase. (b and c) are the visibilities before and after storage. A sum of the visibilities in three arbitrary OAM modes larger than six indicates the existence of two-dimensional entanglement.