Bright narrowband biphoton generation from a hot rubidium atomic vapor cell

We demonstrate the generation of high-quality narrowband biphotons from a Doppler-broadened hot rubidium atomic vapor cell. Choosing a double-K atomic energy level scheme for optimizing both spontaneous four-wave mixing nonlinear parametric interaction and electromagnetically induced trans-parency (EIT), we achieve a biphoton spectral brightness as high as 14 000 s (cid:2) 1 MHz (cid:2) 1 . Meanwhile, we apply a spatially tailored optical pumping beam for reduction of the Raman noise and obtain a violation of the Cauchy-Schwarz inequality by a factor of 1023. Published by AIP Publishing.

We demonstrate the generation of high-quality narrowband biphotons from a Doppler-broadened hot rubidium atomic vapor cell. Choosing a double-K atomic energy level scheme for optimizing both spontaneous four-wave mixing nonlinear parametric interaction and electromagnetically induced transparency (EIT), we achieve a biphoton spectral brightness as high as 14 000 s À1 MHz À1 . Meanwhile, we apply a spatially tailored optical pumping beam for reduction of the Raman noise and obtain a violation of the Cauchy-Schwarz inequality by a factor of 1023. Published by AIP Publishing. Quantum-network protocols based on efficient atomphoton interactions require entangled photons with a bandwidth narrower than the atomic natural linewidth (about 10 MHz). 1 Using the conventional method of spontaneous parametric down conversion with nonlinear crystals, biphoton generation with such a bandwidth requires implementing a single-mode cavity with special care. [2][3][4] In free space, spontaneous four-wave mixing (SFWM) in laser-cooled atoms has been demonstrated as an effective method in producing subnatural-linewidth biphotons, 5-7 but cold atom apparatuses are large, expensive, and require a complicated operation.
Recently, we demonstrated the generation of subnaturallinewidth (2 MHz) biphotons from a Doppler-broadened hot 87 Rb vapor cell, 8 which provides a possibility of miniaturized narrowband biphoton source based on free-space atomic vapor cell. The paraffin coating in increasing the groundstate coherence time and the spatially separated optical pumping were the two keys in suppressing on-resonance Raman scattering noise photons. However, the scheme demonstrated in Ref. 8 can still be further optimized. First, the double-K atomic energy levels can be carefully chosen to maximize the third-order nonlinearity for enhancing the photon pair generation efficiency and the brightness. Second, the spatial profile of the optical pumping beam can be optimized to improve the optical pumping efficiency and minimize the Raman scattering noise.
In this letter, we demonstrate an optimized scheme for hot 87 Rb atomic-vapor-cell-based narrowband biphoton source. Compared to our previous work in Ref. 8, we carefully choose new energy levels with a higher third-order nonlinear susceptibility to increase the photon pair generation rate by a factor of 2.5. Meanwhile, we design a spatially hollow beam for the optical pumping laser to effectively shield the atoms in the SFWM volume for reducing the uncorrelated noise photons from the on-resonance Raman scattering. By operating the system at a temperature of 66 C with the upgraded optical pumping, we achieve a biphoton rate as high as 40 000 s À1 . Figure 1 illustrates schematics of our experimental setup. Driven by two vertically (V) polarized counterpropagating pump laser (780 nm, x p ) and coupling laser (795 nm, x c ) beams, phase-matched and backward Stokes (x s ) and anti-Stokes (x as ) photon pairs are spontaneously generated from a paraffin-coated hot 87 Rb vapor cell. The generated photon pairs are sent to two polarization beam splitters (PBS) as polarization filters and coupled into two opposing single mode fibers (SMF). After going through two optical frequency filters (F s and F as ), the photon pairs are detected by two single-photon counting modules (SPCM s and SPCM as , Excelitas SPCM-AQRH-16-FC). We use a time-to-digit converter (Fast Comtec P7888) with 1 ns bin width to record the coincidence counts. The fiber coupling efficiency and SPCM detection efficiency are 70% and 50%, respectively. We also consider the polarizer efficiency, which is 80%. The etalon filters have free spectrum range FSR ¼ 13.6 GHz. The bandwidth, transmission efficiency, and extinction ratio of the frequency filters are 350 MHz, 60%, and 60 dB for F s ; and 80 MHz, 40%, and 40 dB for F as . To spatially separate the generated biphotons, the pump and coupling laser beams are aligned with an angle of 0.2 to the biphoton collection directions. Figure 2 shows the effect of the SFWM energy-level scheme on the biphoton generation rate. The pump laser is red detuned by 2.7 GHz from the transition j5S 1=2 ; F ¼ 1i ! j5P 3=2 ; F ¼ 2i. To depopulate the upper ground state, j5S 1=2 ; F ¼ 2i, we apply a strong hollow-shaped optical pumping beam at the frequency of x op , which is tuned to the transition j5S 1=2 ; F ¼ 2i ! j5P 3=2 ; F ¼ 1i. In the first case, the same as the previous experiment, 8  Published by AIP Publishing. 110, 161101-1 Fig. 2(b), we tune the coupling laser to the transition j5S 1=2 ; F ¼ 2i ! j5P 1=2 ; F ¼ 2i, and thus, the anti-Stokes photons are generated in the transition j5P 1=2 ; F ¼ 2i ! j5S 1=2 ; F ¼ 1i. We note that the on-resonance two-level absorption cross section changes from k 2 as =ð12pÞ in the previous energy-level scheme to 5k 2 as =ð12pÞ in the optimal scheme. That is, the electric dipole matrix element of the anti-Stokes transition in the optimal scheme increases by a factor of ffiffi ffi 5 p as compared to the previous energy-level scheme. 11 The electric dipole matrix element of the coupling transition remains the same in both schemes. Consequently, the SFWM third-order nonlinear susceptibility increases by a factor of ffiffi ffi 5 p . As confirmed by the measurement of coincidence counts in Figs. 2(a) and 2(b), the photon pair counts increase by a factor of about 3. The solid curves in Figs. 2(a) and 2(b) are obtained following the theoretical treatment in Refs. 8 and 10, showing the perfect agreement with the experimental data.
Next, we engineer the spatial profile of the optical pumping beam to suppress the noise from on-resonance Raman scattering of the coupling laser beam because of residual atoms in the upper ground state, j5S 1=2 ; F ¼ 2i. In the previous experiment, the cross-sectional beam profile was Gaussian shape, 8 which was located aside from the SFWM volume. To increase the interaction area of optical pumping, we use a hollow-shaped beam in this work, as shown in the inset of Fig. 1. Compared to the previously used Gaussian beam, the hollow beam depopulates the upper ground state more efficiently, since we optically pump all the atoms colliding on the paraffin-coated wall and then moving toward SFWM region. Figure 3 shows a comparison of the hollowbeam optical pumping method to the Gaussian beam. In order not to interfere with the EIT-assisted SFWM process, we block the center of the enlarged Gaussian beam (1 cm diameter) with a 4 mm dark spot and make the light intensity zero at the center. Thus, the hollow-shaped optical pumping beam covers most of the area for depopulating the upper ground state (j5S 1=2 ; F ¼ 2i) and suppresses uncorrelated photons from the on-resonance Raman scattering of the coupling laser arising from the same central frequency and polarization as the anti-Stokes photons following the transition: The results indicate a significant improvement in the biphoton signal contrast ratio (½g ð2Þ s;as m , the peak value of the normalized cross correlation function ½g ð2Þ s;as ðsÞ) for the case of the hollow optical pumping beam. The value increases rapidly at low optical pumping power until it reaches 10 mW and slowly increases up to the optimum value at 60 mW, then saturates for higher powers.
With the above two optimizations, we now characterize the biphoton source. For biphotons generated from SFWM process, the photon pair rate depends on the pump power and optical depth. Thus, we scan the pump power by setting the vapor cell at two temperatures 59 C and 66 C. Figure 4 shows that the biphoton rate increases linearly with pump power, while ½g ð2Þ s;as m decreases monotonically both in log-log scale. Specifically, at T ¼ 66 C and the maximum pump power of 60 mW, we obtain a biphoton rate of about 40 000 s À1 with correction of signal collection efficiency. With the biphoton bandwidth of 2.9 MHz, the spectral brightness is about 14 000 s À1 MHz À1 with a signal contrast ratio of about 6. At T ¼ 59 C and the minimum pump power of 0.75 mW, the rate and the signal contrast ratio are 345 s À1 and 56, respectively. The high biphoton signal contrast ratio in our system indicates a strong violation of the Cauchy-Schwarz inequality ½g s;as m , 56, is about five times higher than 12, the value that appeared in the previous research. 8 Besides, the overall photon pair rate ($40 000 s À1 ) is also about more than 20 times higher than that obtained in Ref. 8.
The biphoton coherence time, and thus the bandwidth, can be tuned with EIT by varying the coupling laser power. Fig. 5(a) shows biphoton waveforms as functions of relative time delay s at coupling laser powers of 20 and 3 mW, respectively. As expected, the 1=e correlation time increases from 40 to 85 ns as we reduce the coupling laser power. The insets of Figs. 5(a1) and 5(a2) are the measured conditional auto-correlation g  Figure 5(b) also shows that we obtain the optimum value of ½g ð2Þ s;as m at 10 mW coupling power. To conclude, we have optimized the generation of narrowband ($2 MHz) biphotons from a hot Rb atomic vapor cell with a high contrast ratio of 56, and a bright photon pair rate of 40 000 s À1 . The biphoton spectral brightness reaches as high as 14 000 s À1 MHz À1 in our hot atomic vapor cell system. This bright signal is due to two key improvements: one is to increase the biphoton generation rate by more than two times with a new energy-level configuration and the other is to further reduce the noise by a half, utilizing the spatially tailored hollow beam for optical pumping. Our hotatomic biphoton generator might be useful in quantum information applications, such as a quantum repeater 13 or in quantum key distribution. 14,15 FIG. 2. Biphoton waveforms with two different SFWM energy-level schemes: (a) the scheme used in the previous work, 8 and (b) the optimal scheme in this work. The two-photon coincidence counts are collected over 300 s with 1 ns bin width, as a function of the relative time delay s between the paired Stokes and anti-Stokes photons. The insets denote the relevant 87 Rb atomic energy-level diagram. The incident pump and coupling laser powers are 6 mW and 10 mW, respectively. The hollow-shape optical pumping power is 80 mW, and the temperature of the cell is 59 C. The blue circles denote the experimental data while the solid red theoretical curves.