Two-photon interference of 16 hyperentangled Bell states for the first time at Nanjing University

The research group of Huitian Wang-Hi-Lin Wang at the School of Physics, Nanjing University, has made important progress in quantum interference research. The group has achieved the first two-photon interference between 16 fully hyperentangled Bell states with polarization and orbital angular momentum, and in this process, by introducing new degrees of freedom, the overall phase of the particle exchange in a single degree of freedom is converted into the internal phase of the two-degree-of-freedom quantum state, which enables the direct measurement of the symmetric and antisymmetric phases of the particle exchange, and this achievement lays a solid foundation for the wider application of quantum interference.

The work was published as "Hong-Ou-Mandel Interference between Two Hyperentangled Photons Enables Observation of Symmetric and Antisymmetric Particle Exchange Phases" published in the Journal of the American Physical Society, Physical Review Letter [Phys. Rev. Lett. 129, 263602 (2022)].

Zhifeng Liu, a PhD student in the School of Physics, Nanjing University, is the first author of the paper, and Huitian Wang and Xilin Wang are the co-corresponding authors. This work was supported by the State Key Laboratory of Solid State Microstructure Physics, Nanjing Collaborative Innovation Center of Microstructure, and Hefei National Laboratory, and was supported by the National Key Research and Development Program of China, National Natural Science Foundation of China, Jiangsu Province "Double Innovation Talents", and Guangdong Province Key Area Research and Development Program.

Two-photon Hong-Ou-Mandel (HOM) interference is a quantum effect without classical counterpart. Since a single HOM interference experiment can reveal both wave-particle duality and particle homogeneity, HOM has aroused widespread interest in basic research and has been extended to other particles or quasi-particle systems besides photons, including atoms, surface isotropic excitons, phonons, etc. The clustering effect appears in HOM interference for all-homogeneous bosons, and conversely, HOM interference for all-homogeneous fermions produces an anti-clustering effect. In the field of applied research, HOM interference has become the core of modern quantum technology, which is not only widely used to inscribe the full homogeneity of photons, but also an important way to construct photon controlled non-gates and various multi-particle entangled states. Meanwhile, HOM interferometry is also the basis of Bell state measurement, which plays a key role in many important quantum protocols such as quantum invisible transfer, entangled exchange and quantum networks. Therefore, HOM interferometry has become an important topic in quantum optics and quantum information research. However, the existing HOM interference is mainly limited to a single degree of freedom, and it is still a challenge to realize HOM interference in multiple degrees of freedom.

Based on the already prepared hyperentangled Bell states and their quantum phantom game studies [Phys. Rev. Lett. 129, 050402 (2022)], the research group further developed an efficient orbital angular momentum modulation technique to flexibly prepare fully 16 hyperentangled Bell states with polarization and orbital angular momentum, and systematically carried out multi-degree-of-freedom two-photon HOM interference studies. As shown in Figure 1, among the four Bell states with a single degree of freedom in polarization or orbital angular momentum, three are symmetric states with exchange symmetry, i.e., Bosonic states, which produce the converging beam effect in two-photon interference leading to the appearance of valleys on the interference curve; the other quantum state is an antisymmetric state with exchange antisymmetry, i.e., Fermi state, which produces the inverse converging beam effect in two-photon interference leading to the appearance of peaks on the interference curve. For the polarization and orbital angular momentum double degrees of freedom, there are 16 super entangled Bell states, including 10 symmetric states, including 9 Bose-Boson states and 1 Fermi-Fermi state; and 6 antisymmetric states, including 3 Bose-Fermi states and 3 Fermi-Boson states. Experimentally, as shown in Figure 2, one peak and three valleys were measured in the interference curves for the four Bell states in a single degree of freedom, and 10 valleys and six peaks were observed in the interference curves for the 16 superentangled Bell states in two degrees of freedom, exactly as expected from the theory.

Figure1. Two-photon interferometric clustering and anticluster phenomena. (a) 3 symmetric and 1 antisymmetric Astates among 4 single-degree-of-freedom Bell states; (b) 10 symmetric and 6 antisymmetric states among 16 polarization and orbital angular momentum superentanglement Bell states.

Figure 2. Results of two-photon quantum interference experiments. (a) 4 polarization Bell states; (b) 4 orbital angular momentum Bell states; (c) 16 polarization and orbital angular momentum hyperentanglement Bell states.

Further, it was found that this multi-degree-of-freedom two-photon interference can be used to measure the particle exchange phase. For the two-particle single degree of freedom, the exchange phase is 0 when the quantum state has exchange symmetry, if the two-particle is in three symmetric Bell states or their superposition, and π when the quantum state has antisymmetry, if the two-particle is in the antisymmetric Bell state, and cannot be measured directly because the exchange phase of the two-particle is the overall phase of the single-degree-of-freedom quantum state. By introducing new degrees of freedom to extend the Hilbert space of the two-particle, the overall phase of the single-degree-of-freedom quantum state is transformed into the internal phase of the two-degree-of-freedom quantum state, which is not measurable but can be read out directly.

The basic principle is shown in Fig. 3. In order to extract the particle exchange phase of the orbital angular momentum degree of freedom, the polarization degree of freedom is introduced; the two particles are put in the superposition of the orthogonal polarization HH and VV, where the HH component is used as the reference component and no particle exchange occurs, while the VV component performs the particle exchange through the polarization beam splitter; after the interferometric conjunction, the particle exchange phase of the orbital angular momentum degree of freedom is converted into the internal relative phase between the polarization degree of freedom HH and the internal relative phase between VV, which can be read out. Experimentally, the measured symmetric exchange phases are 0.012 ± 0.002, 0.025 ± 0.002 and 0.027 ± 0.002 radians for the three bosonic states in the orbital angular momentum degrees of freedom, and 0.991π ± 0.002 radians for the antisymmetric exchange phase of the Fermi state, as expected from the theory.

Figure 3. Schematic diagram of the direct measurement of the orbital angular momentum particle exchange potential phase. The orbital angular momentum two-photon exchange potential phase is converted to the internal potential phase of polarization by introducing polarization as an auxiliary degree of freedom with the help of hyperentangled Bell-state two-photon interference.