⇦Chinese Physics Letters, 2019, Vol. 36, No. 7, Article code 074203 Nanosecond Pulses Generation with Samarium Oxide Film Saturable Absorber * N. F. Zulkipli1, M. Batumalay2, F. S. M. Samsamnun1, M. B. H. Mahyuddin1, E. Hanafi1, T. F. T. M. N. Izam1, M. I. M. A. Khudus3, S. W. Harun1,4** Affiliations 1Photonics Engineering Laboratory, Department of Electrical Engineering, University of Malaya, Kuala Lumpur 50603, Malaysia 2Faculty of Information Technology & Sciences, Inti International University, Perdana BBN, Putra Nilai, Nilai 71800, Negeri Sembilan 3Department of Physics, University of Malaya, Kuala Lumpur 50603, Malaysia 4Department of Physics, Faculty of Science and Technology, Airlangga University, Surabaya, Indonesia Received 10 April 2019, online 20 June 2019 *Supported by the INTI Research Grant Scheme 2018 under Grant No INTI-FITS-01-06-2018.
**Corresponding author. Email: swharun@um.edu.my Citation Text: Zulkipli N F, Batumalay M, Samsamnun F S M, Mahyuddin M B H and Hanafi E et al 2019 Chin. Phys. Lett. 36 074203    Abstract Nanosecond pulse generation is demonstrated in a mode-locked erbium-doped fiber laser (EDFL) utilizing a samarium oxide (Sm$_{2}$O$_{3}$) film. The Sm$_{2}$O$_{3}$ film exhibits a modulation depth of 33%, which is suitable for mode-locking operation. The passively pulsed EDFL operates stably at 1569.8 nm within a pumping power from 109 to 146 mW. The train of generated output pulses has a pulse width of 356 nm repeated at a fundamental frequency of 0.97 MHz. The average output power of 3.91 mW is obtained at a pump power of 146 mW, corresponding to 4.0 nJ pulse energy. The experimental result indicates that the proposed Sm$_{2}$O$_{3}$ saturable absorber is viable for the construction of a flexible and reliably stable mode-locked pulsed fiber laser operating in the 1.5 μm region. DOI:10.1088/0256-307X/36/7/074203 PACS:42.55.Wd, 42.60.Gd, 42.70.Nq © 2019 Chinese Physics Society Article Text Nanosecond-duration pulses produced by mode-locked fiber lasers have attracted tremendous interest for applications in various fields including optical communication, mechanical processing and scientific research.[1–3] The lasers have typical repetition rates of few MHz and thus their pulse energies can be simply amplified to microjoule levels using an external optical amplifier. Previously, nanosecond pulses were actively generated using electro-optic and acousto-optic modulators. However, this active modulation approach requires a bulky component and is costly as well. The nanosecond pulses can also be achieved by various passive approaches using either Q-switching or mode-locking schemes. In passive Q-switching, a crystal based saturable absorber (SA) such as Cr:YAG was normally used as a Q-switcher. It is difficult to produce a stable pulse train using this approach. However, stable nanosecond pulses can be achieved in an extended cavity fiber laser, which is mode-locked based on a nonlinear polarization rotation (NPR) technique[4] or by employment of semiconductor saturable absorber mirrors (SESAMs).[5] However, NPR based lasers require the adjustment of the polarization state of the oscillating light in the cavity to achieve mode-locking. Thus, this approach is relatively disadvantageous in terms of reliability and environmental stability. SESAMs provide a much more stable pulses train and thus they are widely used. However, they are still quite costly for purposes of commercial production. Therefore, the passive mode-locking was also largely explored using various types of nano-materials such as graphene[6] and single-walled carbon nanotubes (SWCNTs).[7] SWCNTs are advantageous due to the easier material preparation, but its absorption efficiency, which determines the operation bandwidth, is dependent on its tube sizes. Graphene has the advantage of a wider absorption range and thus, it was widely demonstrated for pulsed laser generation. However, optoelectronics applications of the material have been limited due to its zero-bandgap structure. Recently, other 2D nanomaterials such as transition metal dichalcogenides,[8,9] black phosphorus[10,11] and topological insulators[12,13] have also attracted great interest for SA applications. However, there are still many efforts exploring other new SA materials as well as to design new schemes for generating Q-switched pulses train especially in erbium-doped fiber laser (EDFL) cavities. Despite many new SA materials being proposed and demonstrated, transition metal oxide (TMO) based materials are rarely investigated for Q-switching applications. Previously, titanium dioxide (TiO$_{2})$ and nickel oxide (NiO), which belong to the TMO family, were successfully used as functional SA in promoting pulsed lasers.[14,15] In another work, Das et al. demonstrated a passively Q-switched ytterbium-doped fiber laser using samarium-doped fiber as an SA.[16] In this Letter, we report the utilization of samarium oxide (Sm$_{2}$O$_{3})$ film-based SA in generating stable mode-locking pulses from an EDFL. To obtain the SA, commercial Sm$_{2}$O$_{3}$ powder particles are embedded into a polyvinyl alcohol (PVA) film. This is performed so that the SA can be easily integrated into an EDFL cavity. The results show that a mode-locking output pulse train has a pulse width of 356 ns with repetition at fundamental frequency of 0.97 MHz. The average output power of 3.91 mW was obtained at a pump power of 146 mW, corresponding to 4.0 nJ pulse energy which was successfully realized, and the proposed Q-switched laser operates at 1569.8 nm. This is a desirable wavelength especially for optical communications and sensing applications. We fabricated the Sm$_{2}$O$_{3}$ polymer film by mixing the Sm$_{2}$O$_{3}$ powder and polyvinyl alcohol (PVA) solution. In this work, 1 g of PVA powder was dissolved into 120 ml of distilled water to produce the PVA solution. A magnetic stirrer was used to stir the mixture for about 24 h, at room temperature. Then, 50 mg of Sm$_{2}$O$_{3}$ powder was mixed into 50 ml of the prepared PVA solution. Sm$_{2}$O$_{3}$ PVA solution was further stirred for at least 1 h with a magnetic stirrer. The mixed solution was then sonicated for at least 1 h in an ultra-sonic bath. This process completely dispersed the powder by breaking the bond between the molecules that were bound by the van der Waals force. Finally, the homogenous solution obtained was dispensed onto a small glass Petri dish. It was allowed to dry for approximately 48 h at room temperature to form a thin film.
cpl-36-7-074203-fig1.png
Fig. 1. Sm$_{2}$O$_{3}$ PVA film: (a) physical image, (b) FESEM image, (c) linear absorption profile, and (d) nonlinear optical curve of the SA film.
The image of the fabricated Sm$_{2}$O$_{3}$ PVA film, which has a thickness of about 50 µm, is given in Fig. 1(a). It can be observed that the white film is partially transparent and the Sm$_{2}$O$_{3}$ seems to be evenly distributed across the film. The existence of Sm$_{2}$O$_{3}$ particles in the PVA film was confirmed by the high-resolution image in Fig. 1(b), which was provided by the field-emission scanning electron microscope (FESEM) measurement. It shows a homogeneous distribution of Sm$_{2}$O$_{3}$ particles in the film. The linear optical absorption profile of the Sm$_{2}$O$_{3}$ PVA film is shown in Fig. 1(c), which indicates that the absorption loss of around 3.9 dB at 1569 nm. For comparison, the absorption profile of the pristine PVA was also measured, as shown in Fig. 1(c). The pristine PVA has a significantly lower absorption of 0.5 dB at 1569 nm, which indicates that the mode-locking operation is mainly attributed to the Sm$_{2}$O$_{3}$. It is worth noting that the absorption rate is too low to show the peak profile of PVA film absorption. On the other hand, nonlinear optical response is also an important parameter for SA. To confirm the saturable absorption ability of the fabricated Sm$_{2}$O$_{3}$ PVA film, we employed the amplified mode-locked fiber laser to measure nonlinear optical response based on a balanced twin-detector measurement technique. In the proposed technique, a 1560 nm mode-locked laser source operating at 1.0 MHz repetition rate with 3 ps pulse width was used to perform the measurement. As the absorption power is recorded as a function of launched photon intensity on the Sm$_{2}$O$_{3}$ film by varying the input laser power as shown in Fig. 1(d), it is observed that the absorption decreases with optical intensity, which verifies the saturable absorption property of the Sm$_{2}$O$_{3}$ film. The SA film has a modulation depth of 33%, saturable intensity 25 MW/cm$^{2}$ and nonsaturable absorption of 65%. The modulation depth of the film is relatively high, thus the mode-locked laser operating in picosecond regime is difficult to be realized. A smaller modulation depth may lead to strong pulse shaping by the SA, which can lead to a shorter pulse duration and reliable self-starting, but also to Q-switching instabilities.
cpl-36-7-074203-fig2.png
Fig. 2. Configuration of the Sm$_{2}$O$_{3}$ based nanosecond mode-locked EDFL. Inset: a tiny piece of the Sm$_{2}$O$_{3}$ PVA film, which was placed onto the ferrule tip with the aid of index matching gel.
Figure 2 depicts the configuration of the proposed nanosecond mode-locked EDFL using the prepared Sm$_{2}$O$_{3}$ PVA film as a saturable absorber (SA). The EDFL cavity comprises of a 2.8-m-long gain medium, a 90/10 output coupler, an isolator, a wavelength division multiplexer (WDM), a 200-m-long standard single mode fiber (SMF) and the newly developed Sm$_{2}$O$_{3}$ PVA film based SA. A 980-nm pump was used to pump the erbium-doped fiber (EDF) via the WDM based on the forward pumping scheme. At 980 nm, the pump absorption rate was about 14.5 dB/m. The isolator was deployed inside the cavity to prevent any detrimental effects inside the laser ring resonator by ensuring the unidirectional propagation of light. A fiber-compatible SA device was produced by inserting a small segment of the prepared Sm$_{2}$O$_{3}$ PVA film between two fiber ferrules via a fiber adapter. At the connection, the parasitic reflection is minimized by applying index matching gel. The output coupler was used to tap out the 10% of output for observation and retain 90% to oscillate in the ring cavity. An optical spectrum analyzer (OSA) with 0.05 nm spectral resolution was used to observe the optical spectrum of the laser. The output pulse train was analyzed with 500-MHz digital oscilloscope via a photodetector. The optical power meter was then used to replace the OSA to measure the average output power of the laser. The Q-switching repetition rate and the stability of the laser were analyzed by measuring the electrical radio frequency (rf) spectrum signal using a 7.8 GHz rf spectrum analyzer. The laser cavity overall length was about 211 m.
cpl-36-7-074203-fig3.png
Fig. 3. The characteristics of the output pulses train: (a) output spectrum, (b) typical pulses train, (c) enlarged pulse train, and (d) rf spectrum.
Firstly, we investigate the performance of the proposed Sm$_{2}$O$_{3}$ based mode-locked laser by varying the 980 nm pump power launched into the gain medium. Stable and self-starting mode-locked operation is obtained just by adjusting the pump power over a threshold of 109 mW. The optical spectrum obtained at pump power of 109 mW is plotted in Fig. 3(a). It indicates a laser output with a peak power intensity of $-$21.8 dBm and central wavelength of 1569.8 nm. The 3 dB bandwidth of the spectrum is measured to be around 1.1 nm, indicating a slight spectral broadening effect due to self-phase modulation (SPM) effect in the cavity. A weak Kelly sideband-like structure is also observed on the optical spectrum. Since the pulse duration is in the range of nanoseconds, the mode-locked laser is not operating in soliton regime. In this work, PVA film functions to hold the Sm$_{2}$O$_{3}$ so that it can be easily incorporated into a laser setup and it is not involved in the mode-locking operation. However, the saturable absorption effect can also be induced by PVA due to O–H bond absorption in a wide absorption band in the range of 1.5 µm–2.0 µm.[17,18] To verify that the Sm$_{2}$O$_{3}$ material was responsible for the laser's mode-locking pulse generation, the Sm$_{2}$O$_{3}$ PVA film was replaced with the pristine PVA film in the setup. In this case, no mode-locking pulses were visible on the oscilloscope at any pump powers. This confirms that the mode-locking operation was attributed to the Sm$_{2}$O$_{3}$ SA. The mode-locking operation is limited to the maximum pump power of 146 mW. No pulses were observed beyond this pump power. Figure 3(b) shows the oscilloscope trace of the mode-locked pulse train indicating very stable mode-locking without any Q-switching instabilities. An enlarged view of the pulses is shown in Fig. 3(c). The pulse period was found to be 1.03 µs that corresponds to a repetition rate of 0.97 MHz. The fundamental frequency corresponds well to the cavity length of 211 m. The pulse width was measured to be approximately 356 ns at full wave half maximum (FWHM). Based on the rf spectrum obtained at 109 mW pump power as provided in Fig. 3(d), the stability of the pulsed laser was further investigated. The fundamental frequency was found to be 0.97 MHz with at least 9 harmonics. This result is in good agreement with the pulse period obtained via the oscilloscope trace. The harmonic trend indicates that the mode-locking pulses are operating in nanosecond regime. From the rf spectrum, it can also be seen that the SNR is high at 56 dB, which indicates a stable mode-locking operation. To substantiate that the laser's mode-locking pulse generation was due to the Sm$_{2}$O$_{3}$, the Sm$_{2}$O$_{3}$ PVA film was replaced with a pristine PVA film. Using this configuration, no pulses were visible on the oscilloscope at any pump power. This affirms that the prepared Sm$_{2}$O$_{3}$ SA is responsible for the mode-locking operation.
cpl-36-7-074203-fig4.png
Fig. 4. Output power and pulse energy responses at various pump powers for the mode-locked laser.
The output power and single pulse energy performances at varying input pump powers are shown in Fig. 4. The plot shows that the output power escalated linearly from 3.03 mW to 3.91 mW with the increase of the input pump power from 109 mW to 146 mW. This can be translated to a slope efficiency of about 2.41%. This relatively low efficiency was the result of high insertion loss from the SA. Cavity optimization can be used to further improve the efficiency which depends on the intra-cavity loss. It is also observed from the graph that the pulse energy increases linearly when the pump power is increased. At 146 mW pump power, the maximum pulse energy of 4.0 nJ was obtained. These results verify that the Sm$_{2}$O$_{3}$ material could be used as mode-locker in EDFL cavity for C band operation. The pulse performance in the proposed Sm$_{2}$O$_{3}$ based laser was also compared to similar approaches based on other SAs as listed in Table 1. Compared to graphene, SWCNT and GaN materials, the Sm$_{2}$O$_{3}$ provides a higher attainable pulse energy. However, the silver nanoparticle (SNP) based SA provides a higher pulse energy compared to the proposed Sm$_{2}$O$_{3}$ SA. This is attributed to the silver based laser, which was operated at a higher pump power. Furthermore, the modulation depth of the silver SA (19%) is more suitable for mode-locking operation. Nevertheless, the proposed Sm$_{2}$O$_{3}$ has a lower insertion loss of 0.53 dB at 1569 nm and thus the laser operated at a lower threshold power compared to the SNP based laser. The performance of mode-locked pulses including the threshold pump power is expected to be further improved by optimization of both SA parameter and the laser cavity design. The Sm$_{2}$O$_{3}$ SA loss can be improved by reducing the PVA film thickness. The reduction of Sm$_{2}$O$_{3}$ concentration inside the film is also expected to reduce the modulation depth and to enhance the mode-locking performance of the laser. These results verify the mode-locking ability and show that the Sm$_{2}$O$_{3}$ material could be used in optoelectronics and communication devices in the C band region. These nanoseconds pulsed fibre laser based on the Sm$_{2}$O$_{3}$ PVA SA would offer simplicity, compactness and reliability towards the development of portable laser source system. Future work should focus on realizing mode-locking using PVA films. It is expected that the mode-locked EDFL could be achieved using a thicker PVA film because the modulation depth should be increased for mode locking.
Table 1. Performance comparison of the proposed Sm$_{2}$O$_{3}$ SA with other SAs.
SA Materials $\lambda$ (nm) Threshold (mW) Pulsewidth (ns) Repetition rate (kHz) Maximum pulse energy (nJ)
Graphene 1560 27 6 388 1 Ref.  [19]
SWCNT 1570.4 41.3 332 909 0.34 Ref.  [7]
GaN 1562 149.51 485 967 3.1 Ref.  [20]
SNP 1561.5 198 202 1000 52.3 Ref.  [21]
Sm$_{2}$O$_{3}$ 1569.8 109 356 969 4 This work
In conclusion, generation of nanosecond pulses has been successfully demonstrated in an EDFL through a mode-locking process using a homemade Sm$_{2}$O$_{3}$ PVA film as an SA. The fabricated SA film has a modulation depth and saturable optical intensity of 33% and 25 MW/cm$^{2}$, respectively. The EDFL can produce stable mode-locked nanosecond pulses operating at 1569.8 nm with spectral bandwidth of 1.1 nm, fundamental repetition rate of 0.97 MHz and pulse duration of 356 ns. The average output power of 3.91 mW is obtained, which corresponds to a single pulse energy of 4.0 nJ when the pump power is fixed at 146 mW. These results suggest that the proposed Sm$_{2}$O$_{3}$ has a promising application for ultrafast light generation operating in the C-band region. References Recent Advances in Mechanical MicromachiningNext Generation Light Sources for Biomedical Applications1-GHz optical communication system using chaos in erbium-doped fiber lasersGeneration and amplification of high-energy nanosecond pulses in a compact all-fiber laserUltra-low repetition rate linear-cavity erbium-doped fibre laser modelocked with semiconductor saturable absorber mirrorIonization in alkali-halogen atom collisions: Comparison of the Landau-Zener-Stueckelberg approximation with JWKB calculationsNanosecond soliton pulse generation by mode-locked erbium-doped fiber laser using single-walled carbon-nanotube-based saturable absorberS-band Q-switched fiber laser using molybdenum disulfide (MoS 2 ) saturable absorberPassively Q-switched erbium-doped fiber laser at C-band region based on WS_2 saturable absorberBlack phosphorus crystal as a saturable absorber for both a Q-switched and mode-locked erbium-doped fiber laserGeneration of Mode-Locked Ytterbium Doped Fiber Ring Laser Using Few-Layer Black Phosphorus as a Saturable AbsorberMode-locked erbium-doped fiber laser based on evanescent field interaction with Sb2Te3 topological insulatorPassively Q-switched Erbium-doped and Ytterbium-doped fibre lasers with topological insulator bismuth selenide (Bi 2 Se 3 ) as saturable absorberA generation of 2 μm Q-switched thulium-doped fibre laser based on anatase titanium(IV) oxide film saturable absorberNickel oxide nanoparticles as a saturable absorber for an all-fiber passively Q-switched erbium-doped fiber laserPassively Q-switched Yb- and Sm-doped fiber laser at 1064nmPassively Q-switched fiber lasers based on pure water as the saturable absorberSelf-starting ultrafast fiber lasers mode-locked with alcoholNanosecond-pulsed erbium-doped fiber lasers with graphene saturable absorberNanosecond pulse generation with a gallium nitride saturable absorberNanosecond Pulse Generation with Silver Nanoparticle Saturable Absorber
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⇦Chinese Physics Letters, 2019, Vol. 36, No. 7, Article code 074202 Generation of Gaussian-Shape Single Photons for High Efficiency Quantum Storage * Jian-Feng Li (李建锋)1, Yun-Fei Wang (王云飞)1, Ke-Yu Su (苏柯宇)1, Kai-Yu Liao (廖开宇)1, Shan-Chao Zhang (张善超)1, Hui Yan (颜辉)1**, Shi-Liang Zhu (朱诗亮)2,1** Affiliations 1Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, GPETR Center for Quantum Precision Measurement and SPTE, South China Normal University, Guangzhou 510006 2National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093 Received 11 March 2019, online 20 June 2019 *Supported by the National Key Research and Development Program of China under Grant Nos 2016YFA0301800 and 2016YFA0302800, the National Natural Science Foundation of China under Grant Nos 11822403, 91636218, U1801661, 11704131, 11804105 and 11804104, the Natural Science Foundation of Guangdong Province under Grant Nos 2015TQ01X715 and 2018A0303130066, and the KPST of Guangzhou under Grant No 201804020055.
**Corresponding author. Email: yanhui@scnu.edu.cn; slzhu@nju.edu.cn Citation Text: Li J F, Wang Y F, Su K Y, Liao K Y and Zhang S C et al 2019 Chin. Phys. Lett. 36 074202    Abstract We report the generation of heralded single photons with Gaussian-shape temporal waveforms through the spatial light modulation technique in an atomic ensemble. Both the full width at half maximum and the peak position of the Gaussian waveform can be controlled while the single photon nature holds well. We also analyze the bandwidth of the generated single photons in frequency domain and show how the sidebands of the frequency spectrum are modified by the shape of the temporal waveform. The generated single photons are especially suited for the realization of high efficiency quantum storage based on electromagnetically induced transparency. DOI:10.1088/0256-307X/36/7/074202 PACS:42.50.-p, 32.80.-t, 03.67.-a © 2019 Chinese Physics Society Article Text A highly controllable paired photon source is of great interest, not only for its application in the fundamental research,[1–3] but also for its essential role in quantum information processing.[4–7] In the past several decades, photon pairs are usually produced from spontaneous parametric down-conversion process, which have a wide bandwidth ($>$THz).[8–10] Heralded single photons with such a wide bandwidth are hard to realize strong enough interaction with atoms, which is required for memory-based quantum networks.[11–17] Later, a new type of single photon source based on the electromagnetically induced transparency (EIT)-assisted spontaneous four-wave mixing (SFWM), which generates pair photons in an atomic ensemble, was reported.[18–30] With the help of the EIT slow light effect, heralded photons with long coherent times were generated and a subnatural line width was achieved. However, to store and couple the single photons with atoms or cavity efficiently, having only a narrow bandwidth in the frequency domain is not enough. The optimization of the temporal waveform is also required.[31–33] Although an arbitrary temporal waveform can be realized using an electro-optic modulator (EOM),[34] an unavoidable loss will be introduced. Another method that shapes the heralded single photon's waveform with modulated classical fields has also been realized,[35] which also limits its application because of its low generating rate. Recently, a more practical idea has been demonstrated to shape the temporal waveform by the spatial-light-modulation technique.[36,37] This method greatly simplifies the process and simultaneously reduces the loss. As for the realization of high efficiency quantum storage through EIT, single photons with Gaussian-shape temporal waveform are preferred.[15,16] The spatial-light-modulation technique is a good choice for generating such a waveform. This method can still be improved in practical applications. In this Letter, we report the generation of Gaussian-shape heralded single photons with a simpler spatial-light-modulation method. Instead of using a spatial-light modulator (SLM), we use an aspheric lens to shape the pump beam and then control the single photon's waveform. Compared with the SLM setup which potentially has active electronic noise, this lens-based method is more reliable. The energy level configuration of the SFWM is shown in Fig. 1(c). The frequency of the pump beam ($\omega_{\rm p}$) is off resonance and the frequency of the coupling beam ($\omega_{\rm c}$) is on resonance. In the presence of these two beams, a pair of a Stokes photon ($\omega_{\rm s}$) and anti-Stokes photon ($\omega_{\rm as}$) are generated from the atomic ensemble through the SFWM process. The pump beam is far detuning and its Rabi frequency is extremely small to suppress the multi-photon generation probability to guarantee the single photon nature of the source. The experimental setup is shown in Fig. 1(a), and a cigar-shaped two-dimensional (2D) magneto-optical trap (MOT) is used to generate the heralded single photons. The longitudinal length of the atomic ensemble is $L=1.7$ cm and the optical depth (OD) of the MOT is optimized to about 120 by applying the dark-line MOT technique.[38–40] In the presence of the counter-propagating pump beam (780 nm, $\sigma^{-}$, $\omega_{\rm p}$) and coupling beam (795 nm, $\sigma^{+}$, $\omega_{\rm c}$), a pair of phase-matched counter-propagating Stokes (780 nm, $\sigma^{-}$, $\omega_{\rm s}$) and anti-Stokes (795 nm, $\sigma^{+}$, $\omega_{\rm as}$) photons will be produced along the longitudinal direction of the atomic ensemble. Here the angle between the Stokes/anti-Stokes axis ($z$ axis) and the pump/coupling ($z'$ axis) is chosen to be $\theta=3.14^{\circ}$ to provide spatial separation of the weak Stokes and anti-Stokes fields from the strong pump and coupling fields, while also helping to generate the profile of the pump beam on the $z$ axis simultaneously as shown in Fig. 1(b). Both the coupling beam and the pump beam are Gaussian beams. The coupling beam is collimated and the beam diameter ($1/e^2$) is about 1.8 mm. The pump beam has a frequency blue detune of 80 MHz from the transition $|1\rangle\leftrightarrow|4\rangle$ and is focused onto the MOT by an aspheric lens (THORLABS, A375TM-B) of 7.5 mm focal length and the waist radius is 450 µm. The distance from the lens to the atomic ensemble is about 133 cm. Between the lens and the atomic ensemble, a high-reflectivity mirror mounted on a linear translation stage (LTS) is used and the pump beam is incident on the mirror with an angle of 45$^{\circ}$. By moving the LTS, one can translate the pump beam to shift the spatial profile of the pump beam along the $z$ direction. The generated paired photons are collected by two fiber couplers (FCs). Each fiber coupler contains an aspheric lens (THORLABS, C220TMD-B) and links to a polarization maintaining single mode fiber with numerical aperture of 0.11. The quarter wave plates and the polarizing beam splitters before the FCs are used to convert the circular polarization to the linear polarization for the coupling of the single mode fibers, and also to provide a polarization filtering at the same time. After two narrowband Fabry–Pérot (FP) filters (F$_{1}$ and F$_{2}$) with isolation ratio of 41 dB, the Stokes and anti-Stokes photons are detected by the single-photon counter modules (SPCMs, Perkin Elmer, SPCM-AQRH-16FC) with dark count rate of 25 counts per second. The detected signals are sent to a fast commercially multiple-event time digitizer (FAST ComTec, P7888) for coincidence measurement.
cpl-36-7-074202-fig1.png
Fig. 1. (a) The experimental setup of the heralded single photon source. MOT: magneto-optical trap; $\omega_{\rm c}$: coupling beam; $\omega_{\rm p}$: pump beam; $\omega_{\rm as}$: anti-Stokes photon; $\omega_{\rm s}$: Stokes photon; QWP: quarter wave plate; PBS: polarizing beam splitter; FC: fiber coupler; F1 and F2: multi-level Fabry–Pérot filter; SMF: single mode fiber; SPCM1 and SPCM2: single-photon counter module; HR: high-reflectivity mirror; LTS: linear translation stage. (b) A simplified model of the pump beam profile along the $z$ direction. O: center of the MOT; O$'$: waist position of the pump beam; $z'$: optical axis of the pump beam; A: intersection point of the $z$ and $z'$ axis; $w_0$: waist radius of the pump beam; $\theta$: the angle between $z$ and $z'$ axes. (c) The energy levels for the spontaneous-four-wave-mixing (SFWM) configuration: $|1\rangle=|5S_{1/2}, F=2\rangle$, $|2\rangle=|5S_{1/2},F=3\rangle$, $|3\rangle=|5P_{1/2},F=3\rangle$, and $|4\rangle=|5P_{3/2},F=3\rangle$.
When the coupling beam is uniform along the $z$ axis and the pump beam has a profile $f_{\rm p}(z)$ (here $z=0$ indicates the center of the MOT), the temporal wave function of the heralded single photons can be expressed as[36,37] $$\begin{align} \psi(\tau)\approx{\kappa_{0}V_{\rm g}f_{\rm p}(L/2-V_{\rm g}\tau)},~~ \tag {1} \end{align} $$ where $\kappa_{0}$ is the nonlinear coupling strength of the SFWM process, and $V_{\rm g}={\it \Omega}_{\rm c}^{2} L/(2 {\rm OD} \gamma_{13})$ is the group velocity of the heralded single photons (here ${\it \Omega}_{\rm c}$ is the Rabi frequency of the coupling beam, and $\gamma_{13}$ is the decay rate between $|1\rangle$ and $|3\rangle$). For a simplified model sketched in Fig. 1(b), the profile of the pump beam along the $z$ axis can be described as $$\begin{align} f_{\rm p}(z)=\frac{w_0}{w[z'_0-(z-z_0)\cdot{\cos\theta}]}\cdot e^{-\frac{(z-z_0)^2\cdot{\sin^2\theta}}{w[z'_0-(z-z_0)\cdot{\cos\theta}]^2}},~~ \tag {2} \end{align} $$ where $w_0$ is the waist radius of the pump beam, $w(z')=w_0\sqrt{1+(z'/f)^2}$ is the radius at which the field intensity falls to $1/e^2$ of their axial values at the plane $z'$ along the pump beam, and $f=\pi{w^2_0}/\lambda$ is the Rayleigh length of the pump beam ($\lambda$ is the wavelength of the pump beam). As shown in Fig. 1(a), when the LTS has a translation along the $z'$ axis, it will lead to a translation of the pump beam in both $z'$ direction and $z$ direction. If the LTS translates for a length of $\Delta z'$ in $z'$ direction, $z'_0$ will gain a variation of $-\Delta z'$ while $z_0$ will gain a variation of $-\Delta{z'}/\sin{\theta}$. In our experiment, as the waist radius of the pump beam is 450 µm, which corresponds to a Rayleigh length of about 80 cm. This is much larger than the scale of the MOT ($z'\ll f$), we could have the approximation of ${w[z'_0-(z-z_0)\cdot{\cos\theta}]}\approx{w_0}$ and obtain $$\begin{align} \!\!\!\!f_{\rm p}(L/2\!-\!V_{\rm g}{\tau})=\exp\Big[-\frac{({\tau}\!-\!\frac{L/2-z_0}{V_{\rm g}})^2\cdot{(V_{\rm g}\sin\theta)}^2}{w_0^2}\Big].~~ \tag {3} \end{align} $$ Equation (3) shows that the FWHM of the heralded single photon's wave function can be controlled by the group velocity of the heralded single photon, which can be modified by changing the Rabi frequency of the coupling beam. The peak position of the heralded single photon's wave function can be controlled by shifting $z_0$ with the LTS. First of all, we demonstrate a method to shift the peak position of the heralded single photon's waveform. The Rabi frequency of the coupling beam is set to ${\it \Omega}_{\rm c}=2\pi{\times}13.0$ MHz. The Rabi frequency of the pump beam at the beam waist is set to ${\it \Omega}_{\rm p}=2\pi{\times}1.6$ MHz. Then we adjust the LTS to obtain different profiles of the pump beam on the $z$ axis, as shown in Figs. 2(a1)–2(a3). The main results are shown in Figs. 2(a2), 2(b2) and 2(c2). Here the theoretical curve is calculated from the theory in Ref.  [37]. The measurement time for each curve is $T=3000$ s and the time bin of the SPCM is set to $\Delta{t_{\rm bin}}=1$ ns. The repetition rate of the measurement is 100 Hz. The joint-detection efficiency of our system is $\eta=\eta_{\rm c}\eta_{\rm F1}\eta_{\rm F2}\eta_{\rm D}^{2}\approx 4\%$, where $\eta_{\rm c}$ is the Stokes to anti-Stokes coupling efficiency, $\eta_{\rm F1}$ and $\eta_{\rm F2}$ are the transmission efficiency of the narrow band filters, and $\eta_{\rm D}$ is the detection efficiency of the SPCM. With a duty cycle $\xi=5\%$, the coincidence counts can be calculated from the formula ${\rm CCount}(\tau)=\eta{\xi}|\psi(\tau)|^2\Delta{t_{\rm bin}}T$. We first set $z_0=-0.5$ mm and $\Delta{z'}=0$, which correspond to a pump-beam profile shown in Fig. 2(a1), and obtain a Gaussian-shape single photon waveform shown in Fig. 2(a2). After that, we adjust the LTS to set $\Delta{z'}=-0.3$ mm and $\Delta{z'}=0.3$ mm and obtain the waveforms shown in Figs. 2(b2) and 2(c2), which correspond to the profiles in Figs. 2(b1) and 2(c1), respectively. These results demonstrate that by adjusting the LTS to shift the profile of the pump beam along the 2D MOT, the peak position of the Gaussian-shape waveforms of the heralded single photons can be well controlled. The pairing rates of the Stokes and anti-Stokes photons from the atomic ensemble are calculated to be about 14000, 11000 and 8000 pair/s for Figs. 2(a2), 2(b2) and 2(c2), respectively, while the corresponding heralded efficiencies are about 0.36, 0.36 and 0.31.
cpl-36-7-074202-fig2.png
Fig. 2. The Gaussian-shape waveforms of the heralded single photons. Here (a1), (b1) and (c1) are the profiles of the pump beam along the $z$ axis ($z=0$ is the center of the MOT); (a2), (b2) and (c2) are the corresponding coincidence counts of the measured heralded single photons in 3000 s; (a3), (b3) and (c3) are the corresponding $g_{\rm c}^{(2)}$ of the measured heralded single photons.
In addition to the waveform, we also investigate the non-classical nature of the single anti-Stokes photons with a Hanbury–Brown–Twiss (HBT) interferometer,[41] which shows the non-separability of a single photon. By sending the anti-Stokes photon to a 50/50 fiber beam splitter (FBS), we obtain its conditional zero delay 2nd order auto-correlation function ${g_{\rm c}}^{(2)}={N_{\rm G}}{N_{\rm GTR}}/({N_{\rm GT}}{N_{\rm GR}})$, where $N_{\rm G}$ is the Stokes photon counts, $N_{\rm GR}$ ($N_{\rm GT}$) is the twofold coincidence counts between the Stokes photon and the anti-Stokes photon coming out of the reflection (transmission) port of FBS, and $N_{\rm GTR}$ is the threefold coincidence counts between the Stokes photon and the anti-Stokes photon coming out of both ports of FBS. Here a pure single photon state promises $g_{\rm c}^{(2)}=0$, while a two-photon state gives $g_{\rm c}^{(2)}=0.5$. The measured 2nd order auto-correlation function of the heralded single photon is shown in Figs. 2(a3), 2(b3) and 2(c3). It shows that in all the three cases, $g_{\rm c}^{(2)} < 0.5$ holds well within the entire temporal waveform and indicates a good single-photon nature.
cpl-36-7-074202-fig3.png
Fig. 3. The normalized spectrum of the heralded single photon's temporal waveform. The black squares, red circles and blue triangles correspond to $\Delta{z'}=-0.3$ mm, $\Delta{z'}=0$ and $\Delta{z'}=+0.3$ mm, respectively.
cpl-36-7-074202-fig4.png
Fig. 4. The full width at half maximum (FWHM) of the Gaussian-shape heralded single photon versus different Rabi frequencies of the coupling beam (${\it \Omega}_{\rm c}$). The red solid curve is the theoretical curve and the black squares are the experimental data. Here $\gamma_{13}$ is the decay rate between $|1\rangle$ and $|3\rangle$.
Furthermore, we analyze the spectrum of the heralded single photon's temporal waveform in Fig. 3. The spectra contain different sidebands while have the same centreband. For the EIT-based quantum memory, which is a promising way in achieving the high efficiency single photon storage, the storage bandwidth is usually several MHz.[15–17,42] Thus the sidebands in the heralded single photon's spectrum will lead to the decrease of both the storage efficiency and the fidelity. The sidebands are mainly caused by the sharp spike in front of the main Gaussian-shape waveform, which is called the optical precursor.[43] We also find in Fig. 3 that as $\Delta z'$ increases, the sidebands are suppressed. As shown in Figs. 2(a2), 2(b2) and 2(c2), as the main Gaussian-shape waveform moves away from the precursor, the coincidence counts of the optical precursor decrease faster than the coincidence counts of the main Gaussian-shape waveform. However, if the main Gaussian-shape waveform keeps moving away from the precursor, the signal-to-noise ratio will get worse and worse as the total signal decreases and finally leads to the destruction of the single-photon nature. Hence, in the practical application for the quantum storage, both the sideband and the single-photon nature should be considered simultaneously to obtain an optimal waveform. In the following we show how to control the FWHM of the heralded single photon's temporal waveform by adjusting the Rabi frequency of the coupling beam. The OD here is about 126. The pump-beam Rabi frequency is kept to be stable and $\Delta{z'}=0$ is also maintained during the experiment. The FWHM is proportional to $|\psi(\tau)|^2$. Considering Eqs. (1) and (3), we could obtain ${\rm FWHM}=\frac{\sqrt{2{\rm ln}2}w_0}{{V_{\rm g}\sin\theta}}=\frac{(2\sqrt{2{\rm ln}2}){\rm OD}w_0{\gamma_{13}}}{{{\it \Omega}_{\rm c}}^2L\sin\theta}$. As shown in Fig. 4, the experimental data fit the theoretical curve very well. By controlling the FWHM of the temporal waveform, the bandwidth of the Gaussian-shape single photons can be modified to meet the requirement of the EIT-based quantum memory.[15,16] In conclusion, we have generated Gaussian-shape narrowband heralded single photons with a simple and self-stabilizing spatial light modulation technique. By adjusting the Rabi frequency of the coupling beam and the LTS, both the FWHM and the peak position of the Gaussian-shape waveform can be controlled. The HBT measurement shows that the condition $g_{\rm c}^{(2)} < 0.5$ holds well within the entire temporal waveform, which indicates a very good single-photon nature. Furthermore, we have also found that the sidebands of the heralded single photons in frequency domain can be suppressed by adjusting the peak position of the waveform. With this source, we have achieved a $>90\%$ efficiency quantum storage and the result is shown in Ref.  [44]. We believe that this source will have a potential application in quantum information processing. 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