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ABSTRACT Entangled photon pairs, termed as biphotons, have been the benchmark tool for experimental quantum optics. The quantum-network protocols based on photon–atom interfaces have

stimulated a great demand for single photons with bandwidth comparable to or narrower than the atomic natural linewidth. In the past decade, laser-cooled atoms have often been used for

producing such biphotons, but the apparatus is too large and complicated for engineering. Here we report the generation of subnatural-linewidth (<6 MHz) biphotons from a Doppler-broadened

(530 MHz) hot atomic vapour cell. We use on-resonance spontaneous four-wave mixing in a hot paraffin-coated 87Rb vapour cell at 63 °C to produce biphotons with controllable bandwidth

(1.9–3.2 MHz) and coherence time (47–94 ns). Our backward phase-matching scheme with spatially separated optical pumping is the key to suppress uncorrelated photons from resonance

fluorescence. The result may lead towards miniature narrowband biphoton sources. SIMILAR CONTENT BEING VIEWED BY OTHERS BEATING ABSORPTION IN SOLID-STATE HIGH HARMONICS Article Open access

30 October 2020 SPECTRAL–TEMPORAL BIPHOTON WAVEFORM OF PHOTON PAIRS FROM CASCADE-TYPE WARM ATOMS Article Open access 02 October 2020 BRIGHT CONTINUOUSLY TUNABLE VACUUM ULTRAVIOLET SOURCE FOR

ULTRAFAST SPECTROSCOPY Article Open access 11 January 2024 INTRODUCTION Biphotons (entangled photon pairs) are the benchmark tools in the field of quantum optics for probing fundamental

quantum properties of light quanta such as the wave-particle duality and non-locality1. They have also played an important role in developing advanced technologies in quantum information

processing2. The quantum-network protocols based on efficient photon–atom interaction require photons have bandwidth sufficiently narrower than the atomic natural linewidth3,4. Here we are

interested in generating frequency-anticorrelated biphotons whose sum frequency is fixed and the biphoton bandwidth refers to the spectrum of individual photons. With a fast time-resolved

detector, narrowband biphotons can be used to generate pure heralded single photons with the bandwidth equal to the biphoton bandwidth5. In earlier days, spontaneous parametric down

conversion using nonlinear crystals6,7 and four-wave mixing in optical fibres8 were standard methods for producing biphotons. However, these biphotons have typically very wide bandwidth

(>THz) and short coherence time (<ps), which make them extremely difficult for implementing photonic quantum information processing in an atomic-memory-based quantum network9,10. To

solve this problem, many researches have focused on narrowing down the paired photon bandwidth by putting the nonlinear crystal inside an optical cavity11,12,13,14. Subnatural-linewidth

biphotons with controllable waveforms have been produced from spontaneous four-wave mixing (SFWM) in cold atoms (10–100 μK) assisted with electromagnetically induced transparency

(EIT)15,16,17,18,19 or cavity20. However, cold-atom systems require expert knowledge in laser cooling and trapping. A cold-atom apparatus is not only expensive, but also large and

complicated in its vacuum–optical–electronic–mechanical configuration. Moreover, operating cold atoms for producing paired photons requires a complex timing control with a low duty cycle21.

If a hot atomic vapour cell can be used as an alternative source to produce narrowband biphotons, the system size and operation can be markedly simplified and the cost will be significantly

reduced. However, the use of hot atomic vapour cell for producing narrowband biphotons has not been as successful as those with cold atoms. In an early demonstration in 2005, Lukin _et

al_.22 generated nonclassical correlated light pulses from a room temperature 87Rb atomic vapour cell with writing–reading pulse operation, but these photons are not time-frequency entangled

and the photon number in each pulse is barely below the two-photon threshold. In this work, we focus on paired photon generation with time-frequency entanglement in continuous-wave

operation mode. There have been some attempts in generating biphotons from hot atomic vapour cells, but with coherence time not exceeding 20 ns, corresponding to a bandwidth of >50 MHz

that is much wider than the typical atomic natural linewidths23,24,25. Here we demonstrate generating subnatural-linewidth biphotons using on-resonance SFWM in a hot 87Rb vapour cell

assisted with EIT. Different from the off-resonance double-Raman scheme26 and diamond energy-level scheme24,25, where the photon bandwidth (∼500 MHz) is determined by the Doppler-broadening

decoherence time (∼2 ns) of the excited atomic states, the EIT effect can significantly prolong the photon coherence time and narrow down the bandwidth27. However, when directly applying the

EIT-assisted SFWM scheme to a hot vapour cell, there is a serious noise problem: uncorrelated photons generated from resonance Raman scattering of the strong coupling laser field overwhelm

the entangled photon pairs. To overcome this problem, we coat the inner wall of the cell with paraffin to increase the atomic ground-state coherence time and apply an additional strong

optical-pumping beam to suppress the on-resonance scattering of the coupling field. The optical-pumping beam is spatially separated from the SFWM volume and does not interfere with the

biphoton generation. This noise reduction together with other optical filtering allows us observing biphotons with a high contrast ratio. RESULTS BIPHOTON GENERATION WITH OPTICAL PUMPING We

produce subnatural-linewidth biphotons from a paraffin-coated 87Rb vapour cell at 63 °C, as illustrated in Fig. 1. The details of the experimental set-up are described in the Methods

section. In presence of two counter-propagating pump (_ω_p) and coupling (_ω_c) laser beams, backward and phase-matched Stokes (_ω_s) and anti-Stokes (_ω_as) photon pairs are spontaneously

generated. After spatial and frequency filtering, these photons are detected by two single-photon counting modules (SPCMs and SPCMas). We find the major noise source of uncorrelated photons

is the on-resonance Raman scattering of the coupling field following the transition |5_S_1/2, _F_=2〉→|5_P_1/2, _F_=1〉→|5_S_1/2, _F_=1〉. These photons have the same central frequency and

polarization as the anti-Stokes photons, and cannot be filtered away by the polarization and frequency filters. To clean up the residual atoms in the level |5_S_1/2, _F_=2〉, we apply a

strong optical-pumping beam (_ω_op) on the transition |5_S_1/2, _F_=2〉→|5_P_3/2, _F_=1〉. In order not to interfere with the SFWM transitions, the optical-pumping beam is aligned parallel to

the Stokes–anti-Stokes mode without spatial overlap. The atoms in the level |5_S_1/2, _F_=2〉 are optically pumped to the ground level |5_S_1/2, _F_=1〉, and thus the Raman scattering on the

anti-Stokes channel is suppressed, owing to the long ground-state coherence time because of the paraffin coating. To confirm that the spatially separated optical-pumping beam reduces the

on-resonance Raman scattering of the coupling laser beam, we perform a control experiment of biphoton generation with and without optical pumping. The powers of the pump and coupling laser

beams are 6 and 27 mW, respectively. We observe that, after switching on the optical-pumping beam (32 mW), the photon detection rate on the anti-Stokes channel drops from 12,000 s−1 to 3,600

 s−1, while the photon-pair rate is nearly unaffected. The contrast ratio between the biphoton coincidence (signal) and the accidental coincidence (noise) can be characterized by the

normalized two-photon correlation functions , which are plotted in Fig. 2. It clearly shows that the peak value of the normalized two-photon correlation or the biphoton–noise contrast ratio

increases by a factor of ∼3 when we switch on the optical-pumping beam due to the reduction of the accidental coincidence counts. SUBNATURAL-LINEWIDTH BIPHOTONS Figure 3 shows the biphoton

waveforms. We fix the pump laser power at 6 mW and vary the coupling laser power, which is 27, 9 and 1 mW for Fig. 3a–c, respectively. As expected, the two-photon correlation time becomes

longer as we reduce the coupling laser power for narrower EIT window. Shown in Fig. 3a–c, the biphoton waveforms are exponential decay. The 1/_e_ correlation times are 47, 60 and 94 ns, for

Fig. 3a–c, respectively, all exceeding the natural lifetime 26.5 ns of Rb 5_P_ excited states. The blue theoretical curves are obtained numerically by taking into account the Doppler effect

(Supplementary Note 1) and agree well with the experiment. This agreement allows us to extract the biphoton temporal wave function and joint spectrum. The bandwidths of these biphotons are

3.2, 2.6 and 1.9 MHz, for Fig. 3a–c, respectively (Supplementary Fig. 1). They are substantially narrower than the natural linewidth of 6 MHz of Rb D1/D2 lines. To characterize the

nonclassical property of the photon-pair source, we confirm its violation of the Cauchy–Schwarz inequality28. Normalizing the coincidence counts to the accidental background floor in Fig.

3a–c, we get the normalized cross-correlation function with maximum values =11±1, 11±2 and 6±1. With the measured autocorrelations and , we obtain violation of the Cauchy–Schwarz inequality

by factors of 38±8, 38±11 and 11±3, for Fig. 3a–c, respectively. We further verify the quantum nature of heralded anti-Stokes photons by measuring their conditional autocorrelation function

(ref. 29). An ideal single-photon source gives =0. A two-photon Fock state gives =0.5, and a coherent state gives =1. The measured as a function of coincidence window width are plotted as

Fig. 3d–f, which are below the two-photon threshold within their coherence time. As we reduce the coupling laser power, the EIT bandwidth becomes narrower and the dispersion induced phase

mismatching further constrains the biphoton joint spectrum27. Therefore, the biphoton bandwidth and coherence time are not determined by the lifetime of the excited states even though the

photon pairs are indeed generated spontaneously. Figure 4a shows the measured decay time constant (square) and 1/_e_ correlation time (circle) of the biphoton waveform as functions of

coupling laser power. The longest correlation time at 1 mW coupling power approaches ∼100 ns. On the other side, , the maximum value of the normalized cross-correlation function, decreases

as we reduce the coupling power. Figure 4b shows the and photon-pair generation rate as functions of the pump power. While the photon-pair rate is proportional to the pump laser power, the

drops at a high pump power. Limited by our available pump laser power of 7 mW, we produced ∼2,000 pairs per second. As the threshold of the is 2.0 for violating the Cauchy–Schwarz

inequality, the nonclassical property of the photon source is still preserved at 170 mW pump power, which corresponds to a generation rate of∼47,000 pairs per second. DISCUSSION In summary,

we demonstrate generation of subnatural-linewidth biphotons from a hot paraffin-coated 87Rb vapour cell using EIT-assisted SFWM. The biphoton coherence time, controlled by the coupling laser

power, can be as long as 94 ns. The corresponding bandwidth of 1.9 MHz is substantially narrower than the natural linewidth 6 MHz of Rb D1/D2 transitions. It can be used to generate nearly

pure heralded single photons5. The exponential waveform with tunable time constant is perfect for interacting with atoms30 and coupling to an optical cavity31. In this work, the heralding

efficiency of the photon pairs is 3.1%. This is determined by the small optical depth of ∼1 of the atomic vapour cell, which is limited by the maximally allowed temperature (<70 °C) of

the paraffin coating. If we can further increase the cell temperature while maintaining a low spin relaxation rate, we expect to improve the heralding efficiency and generate biphotons with

richer waveforms by engineering the spatial profile of the pump beam, as those demonstrated in cold atoms19. The two key elements to make the SFWM narrowband biphoton generation feasible are

the paraffin coating and the spatially separated optical pumping. The long ground-state coherence time preserved by the paraffin coating enables the efficient optical pumping, which is

spatially separated from the biphoton generation volume, for the flying atoms without interfering the SFWM transitions. As a general state preparation method, the technology demonstrated

here can be immediately applied to reduce incoherent photon noise thus improve the fidelity of the Raman-based quantum memory32. Future improvements could include improving the quality of

optical frequency filtering (etalon Fabry–Perot cavity, polarization filter, spatial-mode filter) and optimizing the power and spatial profile of the optical pump beam. As compared with the

cold-atom experiments33,34, the hot atomic vapour cell configuration is much simpler for operation and maintenance, and it is a continuous biphoton source. Our demonstration may lead to

miniature narrowband biphoton sources based on atomic vapour cells for practical quantum applications and engineering. METHODS EXPERIMENTAL SET-UP The experimental set-up and associated

atomic energy-level diagram are illustrated in Fig. 1. A paraffin-coated 87Rb (99% enrichment purity, Precision Glassblowing Inc) vapour cell is placed in a temperature-stabilized hot-air

heating oven, which is not shown in Fig. 1a, and is set at 63 °C with fluctuation <0.2 °C. The length of the vapour cell is _L_=0.5 inch and its inner diameter is _d_=10 mm. The

longitudinal orientation of the cell is from east to west and there is no magnetic shielding in this experiment. The SFWM process is driven by two laser fields: the pump laser (D2 line: 780 

nm, _ω_p) is locked to the 85Rb transition |5_S_1/2, _F_=2〉→|5_P_3/2, _F_=3〉, which is red detuned by 2.7 GHz from the 87Rb transition |5_S_1/2, _F_=1〉→|5_P_3/2, _F_=2〉, and the coupling

laser (D1 line: 795 nm, _ω_c) is on resonance to the transition |5_S_1/2, _F_=2〉→|5_P_1/2, _F_=1〉. The vertically polarized pump and coupling laser beams are counter propagating with the

same 1/_e_2 beam diameter of 1.4 mm. Backward, horizontally polarized, Stokes (780 nm, _ω_s) and anti-Stokes (795 nm, _ω_as) photon pairs are spontaneously generated, coupled into two

opposing single-mode fibres, passing through optical frequency filters (_F_s and _F_as), and detected by two single-photon counting modules (SPCMs and SPCMas, Excelitas/PerkinElmer

SPCM-AQRH-16-FC). The two-photon coincidence counts are recorded by a time-to-digit converter (Fast Comtec P7888) with a temporal bin width of 1 ns. Two polarization beam splitters are used

as polarization filters to distinguish the paired photons from the two driving laser beams. The spatially separated optical pumping is implemented by applying a strong vertically polarized

optical-pumping beam (_ω_op) that is on resonance to the transition |5_S_1/2, _F_=2〉→|5_P_3/2, _F_=1〉. The optical-pumping beam is aligned parallel to the pump-coupling beams without

overlap. The laser beam profiles on the cross-section of the cell are shown in the inset of Fig. 1a. The optical-pumping beam, with a power of 32 mW, has a 1/_e_2 beam diameter of 2 mm. The

Stokes and anti-Stokes single-mode diameter on the cell centre is 250 μm. To further separate the generated photon pairs from the two driving laser beams, the pump and coupling laser beams

are aligned with an angle of ∼0.5° to the Stokes and anti-Stokes directions. NORMALIZED CROSS- AND AUTOCORRELATION FUNCTIONS The normalized two-photon cross-correlation function is defined

as , where and are the creation and annihilation operators of the Stokes and anti-Stokes fields, respectively. The experimental is obtained by normalizing the two-photon coincidence counts

to the flat background floor of accidental coincidence counts. The normalized autocorrelation functions are defined as and . The autocorrelation functions are measured using a fibre beam

splitter. THEORETICAL CALCULATION OF BIPHOTON WAVEFORMS The theoretical curves in Fig. 3 are obtained numerically following the Schrodinger picture approach27 by integrating over the

Doppler-broadening profile (Supplementary Note 1). The solid theoretical curve in Fig. 4b is obtained by taking into account the uncorrelated noise photons (Supplementary Note 2). DATA

AVAILABILITY The data that support the findings of this study are available from the corresponding author on request. ADDITIONAL INFORMATION HOW TO CITE THIS ARTICLE: Shu, C. _et al._

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emissions in an atomic ensemble via four-wave mixing. _Ann. Phys._ 360, 556 (2015). Article  CAS  MathSciNet  Google Scholar  Download references ACKNOWLEDGEMENTS We thank K. Zhao at Fudan

University and L. Zhao at the Hong Kong University of Science and Technology for helpful discussions. T.K.A.C. and L.Z. acknowledge support from the Undergraduate Research Opportunities

Program at the Hong Kong University of Science and Technology. The work was supported by Hong Kong Research Grants Council (project no. 16301214). AUTHOR INFORMATION AUTHORS AND AFFILIATIONS

* Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China Chi Shu, Peng Chen, Tsz Kiu Aaron Chow, Lingbang Zhu, M.M.T. Loy 

& Shengwang Du * Department of Physics, State Key Laboratory of Surface Physics, Key Laboratory of Micro and Nano Photonic Structures, Fudan University, Shanghai, 200433, China Yanhong

Xiao Authors * Chi Shu View author publications You can also search for this author inPubMed Google Scholar * Peng Chen View author publications You can also search for this author inPubMed 

Google Scholar * Tsz Kiu Aaron Chow View author publications You can also search for this author inPubMed Google Scholar * Lingbang Zhu View author publications You can also search for this

author inPubMed Google Scholar * Yanhong Xiao View author publications You can also search for this author inPubMed Google Scholar * M.M.T. Loy View author publications You can also search

for this author inPubMed Google Scholar * Shengwang Du View author publications You can also search for this author inPubMed Google Scholar CONTRIBUTIONS S.D. conceived the idea. C.S. and

S.D. designed the experiment. C.S., P.C., T.K.A.C. and L.Z. performed the experiment. C.S. did the theory calculation and analysed the data. S.D., C.S. and Y.X. discussed the feasibility of

the experiment. S.D. and M.M.T.L. directed the project. All authors contributed to the final manuscript. CORRESPONDING AUTHOR Correspondence to Shengwang Du. ETHICS DECLARATIONS COMPETING

INTERESTS The authors declare no competing financial interests. SUPPLEMENTARY INFORMATION SUPPLEMENTARY INFORMATION Supplementary Figure 1, Supplementary Notes 1-2 and Supplementary

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ARTICLE CITE THIS ARTICLE Shu, C., Chen, P., Chow, T. _et al._ Subnatural-linewidth biphotons from a Doppler-broadened hot atomic vapour cell. _Nat Commun_ 7, 12783 (2016).

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