# Entangled Photons

### Quantum Langevin theory

Phys. Rev. A 107, 053703 (2023)

In an open quantum system involving loss or gain, the Langevin noises have been intensively studied to preserve the fundamental of quantum physics -- the commutation relations, as well as to obtain the quantum correlations correctly. However, the common approach to deriving quantum Langevin equations requires knowing microscopic details of such system, making it extremely difficult to calculate and impossible to extend to other systems. In this work, we obtain self-consistent quantum Langevin equations for any two coupled phase-conjugated electromagnetic fields from their general expression of the coupling matrix, and for the first time, investigate Langevin noises induced by a complex nonlinear coupling coefficient. Our macroscopic phenomenological method to solve quantum Langevin coupled equations is more readable and accessible, and can be easily applied to study two-mode squeezing, parametric oscillation, and other quantum light state generation.

### Energy-time entangled photons

Phys. Rev. Lett. 124, 010509 (2020)

We produce energy-time entangled narrow-band biphotons from spontaneous four-wave mixing in a cloud of 85Rb atoms prepared in a dark-line two-dimensional magnetooptical trap. With the continuous-wave pump and coupling laser fields, the spontaneously generated phase-matched Stokes and anti-Stokes photon pairs are frequency-time entangled because of the energy originating from time translation symmetry. We first determine the joint temporal uncertainty by measuring the two-photon temporal correlation using two single-photon counters and confirm its nonclassical property and quantum nature by correlation function measurement. The two-photon joint spectrum is then determined by an ultra-narrowband transmission optical cavity, showing the Stokes and anti-Stokes photon frequencies are anticorrelated and hence indicating the energy-time entanglement. Moreover, the joint frequency-time uncertainty product also satisfies the steering inequality, which is sufficient for raising the EPR paradox.

### Frequency-bin entangled photons

Optica 4, 388 (2017)

Based on these entangled photon pairs, we create discrete frequency-bin entanglement and confirm the genuine entanglement through Bell’s inequality test. By assigning frequency shifts in different paths, we prepare frequency-bin entangled narrowband biphotons. Making use of polarization optics, we have full controllability of the entangled state, i.e. the amplitude ratio and relative phase. we also construct the Bell-CHSH inequality test experimentally by extending the conventional treatment of polarization entanglement to our case. With the time-resolved detection technique, we confirm the genuine entanglement from violation of Bell inequality. Moreover, the nonlocal phase correlation and nonclassical biphoton beating also reveal entanglement consistently.

### Atomic beam splitter of single photons

Phys. Rev. A 97, 063805 (2018)

Biphotons can serve as a probabilistic single-photon source or a single-photon qubit. This heralded pure single photon can be utilized in various quantum experiments. Here, we demonstrate one single photon experiment with an atomic beam splitter based on electromagnetically induced transparency (EIT) storage. We observe high-visibility interference result together with a significant antibunching phenomenon, concluding that the single-photon wave-particle duality is well-preserved in this atomic beam splitter. The splitting ratio and relative phase can be dynamically controlled with the control beams and the atomic parameters. Furthermore, the system can be viewed as a quantum device integrating quantum memory with a configurable beam splitter, which may have applications in programmable quantum information science.

### Loading atomic ensemble into optical cavity

Rev. Sci. Instrum. 90, 013105 (2019)

Since the quantum storage efficiency is limited by the atom-light interaction strength, i.e. the optical depth (OD). We design and build up a new apparatus by loading our two-dimension cold atomic ensemble into an optical cavity to enhance the photon-atom interaction. Photons in cavity mode can be bounced back and forth by cavity mirrors, so that they pass through the atomic ensemble many times before leaking out. In this apparatus, we get the cavity-enhanced atomic optical depth up to 7600 by measuring vacuum Rabi splitting, with peak splitting up to 627 MHz. The cavity-enhanced OD is 190 times higher than that without enhancement. This apparatus is an ideal platform for future photon-atom interaction studies, such as high-efficiency quantum memory or high-fidelity photon gate generation.