Abstract This review article focuses on biphoton sources based on the double‐ spontaneous four‐wave mixing (SFWM) process in laser‐cooled as well as room‐temperature or hot atomic ensembles. These biphoton sources have the advantage of providing stable frequencies, ultranarrow linewidths, and a tunability of the temporal biphoton width of more than one order of magnitude for high‐bandwidth applications. Therefore, the generated photons can be efficiently interfaced to, e.g., atomic quantum memories. In contrast, solid‐state biphoton sources typically require assistance by an optical cavity to operate at narrow linewidth that limits the tunability of the temporal width of the biphotons. Present state‐of‐the‐art double‐ SFWM biphoton sources can achieve one of the following results: a spectral linewidth of 50 kHz (290 kHz) or a temporal width of 13 (580 ns) with cold (hot) atoms, a detection rate of about 7 cps, and a generation rate of cps at a duty cycle of 0.4% or of cps in the steady state. The theoretical background of these biphoton sources, experimental implementations with cold and hot atoms, and progress over the years, will be illustrated.
Review of Biphoton Sources Based on the Double‐ΛΛ Spontaneous Four‐Wave Mixing Process
Abstract This review article focuses on biphoton sources based on the double‐ spontaneous four‐wave mixing (SFWM) process in laser‐cooled as well as room‐temperature or hot atomic ensembles. These biphoton sources have the advantage of providing stable frequencies, ultranarrow linewidths, and a tunability of the temporal biphoton width of more than one order of magnitude for high‐bandwidth applications. Therefore, the generated photons can be efficiently interfaced to, e.g., atomic quantum memories. In contrast, solid‐state biphoton sources typically require assistance by an optical cavity to operate at narrow linewidth that limits the tunability of the temporal width of the biphotons. Present state‐of‐the‐art double‐ SFWM biphoton sources can achieve one of the following results: a spectral linewidth of 50 kHz (290 kHz) or a temporal width of 13 (580 ns) with cold (hot) atoms, a detection rate of about 7 cps, and a generation rate of cps at a duty cycle of 0.4% or of cps in the steady state. The theoretical background of these biphoton sources, experimental implementations with cold and hot atoms, and progress over the years, will be illustrated.
Biphotons, generated from a hot atomic vapor via the process of spontaneous four-wave mixing (SFWM), have the following merits: Stable and tunable frequencies as well as linewidth. Such merits are very useful in the application of long-distance quantum communication. However, the hot-atom SFWM biphoton sources previously had far lower values of generation rate per linewidth, i.e., spectral brightness, as compared with the sources of biphotons generated by the spontaneous parametric down-conversion process. Here we report a hot-atom SFWM source of biphotons with a linewidth of 960 kHz and a generation rate of $3.7\ifmmode\times\else\texttimes\fi{}{10}^{5}$ pairs/s. The high generation rate, together with the narrow linewidth, results in a spectral brightness of $3.8\ifmmode\times\else\texttimes\fi{}{10}^{5}$ pairs/s/MHz, which is 17 times the previous best result with atomic vapors and also better than all known results with all kinds of media. The all-co-propagating scheme together with a large optical depth (OD) of the atomic vapor is the key improvement, enabling the achieved spectral brightness to be about one quarter of the ultimate limit. Furthermore, this biphoton source had a signal-to-background ratio (SBR) of 2.7, which violated the Cauchy-Schwartz inequality for classical light by about 3.6-fold. Although an increasing spectral brightness usually leads to a decreasing SBR, our systematic study indicates that both of the present spectral brightness and SBR can be enhanced by further increasing the OD. This work demonstrates a significant advancement and provides useful knowledge in quantum technology using photons.
Abstract Utilizing the double-Λ spontaneous four-wave mixing (SFWM) process, the biphoton source generates narrow-linewidth pairs of signal and probe photons. In a medium, the signal photon propagates at nearly the speed of light in a vacuum, while the probe photon propagates as slow light. Typically, signal photons arrive at the detector first and are used as the heralding photons in conventional biphoton sources. In this work, we propose using probe photons as the heralding photons to enhance the heralding probability, an approach that has been overlooked previously. We also investigate a time-reversed double-Λ SFWM biphoton source using heated atomic vapor. Compared with the conventional biphoton source under the same experimental conditions, the time-reversed one exhibits a time-reversed temporal profile with a similar full-width-at-half-maximum linewidth of 3.4 MHz, increased the heralding efficiency by a factor of 5.3, and enhanced the detection rate by 1.3 times. With the time-reversed source, we achieved a heralding probability of 82±6% and a generation rate of (1.8 ± 0.2)× 10 6 pairs/s, referring to biphotons collected within polarization-maintained single-mode optical fibers. Furthermore, the time-reversed temporal profile is more suitable for quantum memory. Simulation results show that, at an optical depth of 150 (or 50), the storage efficiency of a quantum memory using the time-reversed source can reach 91% (or 81%), compared with 81% (or 67%) using the conventional source. This study demonstrates the significance of using the slow-light photon in biphoton pairs as the heralding photon for quantum operations. We have achieved a biphoton source with high heralding probability, high generation rate, and narrow linewidth in a room-temperature or hot medium.
The biphotons, or pairs of time-energy entangled photons, generated from a hot atomic vapor via the process of spontaneous four-wave mixing (SFWM) have the following merits: stable and tunable frequencies as well as linewidth. Such merits are very useful in the applications of long-distance quantum communication. However, the hot-atom SFWM biphoton sources previously had far lower values of generation rate per linewidth, i.e., spectral brightness, as compared with the sources of biphotons generated by the spontaneous parametric down conversion (SPDC) process. Here, we report a hot-atom SFWM source of 960-kHz biphotons with a generation rate of 3.7×105 pairs/s. The high generation rate, together with the narrow linewidth, results in a spectral brightness of 3.8×105 pairs/s/MHz, which is 17 times of the previous best SFWM result and also better than all known SPDC results. The all-copropagating scheme employed in our biphoton source is the key improvement, enabling the achieved spectral brightness to be about one quarter of the ultimate limit. Furthermore, this biphoton source had a signal-to-background ratio (SBR) of 2.7, which violated the Cauchy-Schwartz inequality for classical light by about two-fold. Although an increasing spectral brightness usually leads to a decreasing SBR, our systematic study indicates that both of the present spectral brightness and SBR can be further enhanced. This work demonstrates a significant advancement and provides useful knowledge in the quantum technology using photons.
We report the generation of biphotons, with a temporal full width at the half maximum (FWHM) of 13.4 ± 0.3 µs and a spectral FWHM of 50 ± 1 kHz, via the process of spontaneous four-wave mixing with laser-cooled atoms. The temporal width is the longest, and the spectral linewidth is the narrowest to date. This is also the first biphoton result that obtains a linewidth below 100 kHz, reaching a new milestone. The very long biphoton wave packet has a signal-to-background ratio of 3.4, which violates the Cauchy–Schwarz inequality for classical light by 4.8 folds. Furthermore, we demonstrated a highly tunable-linewidth biphoton source and showed that while the biphoton source’s temporal and spectral width were controllably varied by about 24 folds, its generation rate only changed by less than 15%. A spectral brightness or generation rate per pump power per linewidth of 1.2× 106 pairs/(s mW MHz) was achieved at the temporal width of 13.4 µs. The above results were made possible by the low decoherence rate and high optical depth of the experimental system, as well as a novel scheme of classical fields’ and biphotons’ propagation directions in the experiment. This work has demonstrated a high-efficiency ultranarrow-linewidth biphoton source and has made substantial advancements in quantum technology utilizing heralded single photons.
We utilized the all-copropagating scheme, which maintains the phase-match condition, in the spontaneous four-wave mixing (SFWM) process to generate biphotons from a hot atomic vapor. The linewidth and spectral brightness of our biphotons surpass those of the biphotons produced with the hot-atom SFWM in the previous works. Moreover, the generation rate of the sub-MHz biphoton source in this work can also compete with those of the sub-MHz biphoton sources of the cold-atom SFWM or cavity-assisted spontaneous parametric down conversion. Here, the biphoton linewidth is tunable for an order of magnitude. As we tuned the linewidth to 610 kHz, the generation rate per linewidth is 1,500 pairs/(s·MHz) and the maximum two-photon correlation function, g s , a s ( 2 ) , of the biphotons is 42. This g s , a s ( 2 ) violates the Cauchy-Schwarz inequality for classical light by 440 folds, and demonstrates that the biphotons have a high purity. By increasing the pump power by 16 folds, we further enhanced the generation rate per linewidth to 2.3×10 4 pairs/(s·MHz), while the maximum g s , a s ( 2 ) became 6.7. In addition, we are able to tune the linewidth down to 290±20 kHz. This is the narrowest linewidth to date among all single-mode biphoton sources of room-temperature and hot media.
C-band photons are recognized for having the lowest loss coefficient in optical fibers, making them highly favorable for optical fiber-based communication. In this study, we systematically investigated the temporal width of C-band heralded single photons and developed a theoretical model for biphoton generation via the spontaneous four-wave mixing (SFWM) process using a diamond-type transition scheme, which has not been previously reported. Our experimental data on temporal width closely aligns with the predictions of this model. In addition, we introduced a new concept: the atomic velocity group relating to the two-photon resonance condition and the one-photon detuning in this atomic frame. These two parameters are crucial for understanding the behavior of the biphoton source. The concept indicates that the hot-atom source behaves similarly to the cold-atom source. Guided by our theoretical model, we observed 1529 nm (C-band) heralded single photons with a temporal width of 28.3 ± 0.6 ns, corresponding to a linewidth of 11.0 ± 0.2 MHz. For comparison, the ultimate linewidth limit is 6.1 MHz, determined by the natural linewidth of the atoms. Among all atom-based sources of 1300–1550 nm heralded single photons utilizing either cold or hot atoms, the temporal width achieved in this work represents the first instance of a width exceeding 10 ns, making it (or its linewidth) the longest (or narrowest) record to date. This work significantly enhances our understanding of diamond-type or cascade-type SFWM biphoton generation and marks an important milestone in achieving greater temporal width in atom-based sources of C-band heralded single photons.