Sub-megahertz linewidth single photon source

Quantum technologies are primed to revolutionise information processing, with large companies already investing in basic quantum computing devices. While these potentially offer local computational enhancement, distributing quantum information will also require dedicated quantum networks designed to faithfully transmit quantum bits (qubit).¹ Photons are the natural choice for information carriers due to their high mobility and low interaction with the environment. Overcoming the inevitable transmission losses in such networks demands repeater nodes with entanglement swapping operations.^2–5 The absence of high fidelity entangling gates in linear optical quantum computing (LOQC) and true on-demand sources means that the repeater node will also require noiseless amplification as well as a memory to hold the photonic qubit. As photons are notoriously difficult to store locally, the transfer of the qubit from the photonic state to a locally storable qubit, such as atoms,^6,7 ions,⁸ nitrogen-vacancy centres in diamonds,⁹ or rare-earth doped solids,^10,11 is essential. For this kind of hybridisation, the spectral properties of the photons and the chosen transition of the storage qubit need to be matched. As the spectral properties of the memories are limited in their tunability, the single photon source needs to be engineered to match the wavelength and the bandwidth of the atomic transition.

Suitable photons can be generated through four-wave mixing in a magneto-optical trap;^12,13 however, this requires substantial experimental effort, and the duty cycles are low. Alternatively, spontaneous parametric downconversion (SPDC)¹⁴ produces high-purity heralded single photons at flexible wavelengths. SPDC-based sources have demonstrated near ideal heralded second-order autocorrelation function $g s , s ( 2 ) ( 0 ) ≤ 0.01$⁠, far below the classical limit^15–18 of 1. However, the spontaneous nature of the downconversion process combined with energy conservation and phase matching conditions results in a frequency spectrum typically on the order of 100s of GHz up to THz, several orders-of-magnitude larger than the bandwidths of atomic transitions. This can be compensated either by spectral filtering,^19–21 which severely reduces the available brightness, or by using an optical cavity to enhance the probability of creating the photons in the spectral and spatial resonator mode.^22–29 

One of the most promising candidates for quantum memories to date is the gradient echo memory (GEM),^30–34 with recall fidelities⁷ of up to 98% and coherence times of up to $195 μ$s in rubidium³³ and even longer storage times in rare earth ion crystals.³⁵ To achieve these high fidelities and storage times in GEM, the spectral bandwidth of the photons needs to be well below the natural linewidth, e.g., sub-MHz for a GEM using rubidium as the natural linewidth is 5.8 MHz. Previous cavity-based SPDC sources have achieved bandwidths comparable to atomic linewidths, but divide their operation time into stabilisation and photon production phases, resulting in typical duty cycles $< 50$%. Fekete et al. reported the so far narrowest photons from SPDC—around 2 MHz,²⁸ still unsuitable for efficient GEM in rubidium—and only one source has demonstrated 100% duty cycle,²⁵ referring to the capability of the source to probabilistically produce single photon pairs at any given time.

Here we report on a triply resonant sub-megahertz source of orthogonally polarised single photon pairs with a 100% duty cycle. The photons are created via cavity-enhanced SPDC at the 795 nm Rb wavelength, with bandwidths for signal and idler of $666 ± 16$ and $667 ± 15$ kHz, both matching the D₁ line in Rb used in GEM. The obtained $g s , s ( 2 ) ( 0 ) = 0.016 ± 0.002$ at 5 kHz heralding rate is 500 standard deviations below the classical limit, strongly indicating the quantum character of the source.

Generating photons resonant to atomic transitions requires the length of the SPDC cavity to be locked to an absolute frequency reference. Previous sources commonly achieved this during the feedback part of a cycle by stabilising the cavity to a laser beam on resonance with the atomic ensemble. As the reference beam is at the target frequency, no single photons can be observed during this phase. For the remainder of the cycle, the cavity is not actively stabilised and only the pump light is present, generating resonant single photon pairs. This procedure reduces the duty cycle to well below 100%. Our system overcomes this issue by stabilising the SPDC cavity to the pump light, which itself is referenced back to the targeted Rb transition, as explained in detail below.

The schematic experimental setup is shown in Fig. 1. The starting point is a continuous-wave amplified diode laser (Toptica TA Pro) emitting laser light at 795 nm (subscript r for red) through two output ports. The light from the master port is modulated by a 1.25 MHz RF signal with small modulation depth in an electro-optic modulator (EOM₁) and enters a rubidium cell (TEM CoSy), where Doppler-free spectroscopy is performed. The optimal signal to noise ratio for modulation was empirically found at 1.25 MHz, limited by the detection bandwidth of the CoSy cell. The modulation is used to derive an error signal via the Pound-Drever-Hall (PDH) technique.^36,37 This is a standard technique for stabilising laser systems and is utilised for all frequency locks in the experiment. The output of the amplified slave port is modulated at 12.5 MHz (EOM₂), which is clearly higher than the cavity bandwidth, but not too high as the sideband modulation gets less efficient and the lock becomes less precise, and then coupled into the cavity for second-harmonic generation (SHG). The cavity enhances the efficiency of the frequency doubling inside a 20 mm long periodically poled potassium titanyl phosphate (ppKTP) crystal to 38%, and the created laser light at 397.5 nm (subscript b for blue) is subsequently pumping the downconversion. The free spectral range (FSR) of the cavity is $F S R r , S H G ≈ 278$ MHz with a finesse of $F r , S H G ≈ 100$ (for detailed numbers including uncertainties see the supplementary material). The laser system is stabilised to the error signal, derived from the SHG cavity reflection on PD₁ (home-made fast photodiode), using the PDH technique. The feedback loop simultaneously adjusts the current driving the laser diode and the position of a grating reflecting some laser light back into the diode, cancelling out high frequency noise. To compensate for long-term drifts, the length of the SHG cavity is stabilised to the rubidium D₁ transition at 795 nm via a mirror mounted on a piezo-electric transducer. After leaving the SHG cavity, the remaining red light is separated from the blue pump light by a dichroic mirror (DM), with the cavity resonance being monitored at PD₂. The pump light is modulated at 12.175 MHz (EOM₃) to prevent beating with the formerly applied 12.5 MHz and coupled into the downconversion cavity.

The SPDC process takes place in a dual anti-reflective coated 25 mm long ppKTP crystal (coating Layertec, crystal Raicol) with a poling period of $8.8 μ m$⁠, cut for type-II quasi-phase-matching. The crystal is placed in a copper mount that is temperature controlled with a stability of $Δ$T $< ± 1.5$ mK. The bow-tie cavity surrounding the crystal is designed following Refs. 38 and 39 and mounted on a monolith of Invar to increase stability. The cavity consists of three high-reflecting mirrors plus one partially reflecting outcoupling/incoupling mirror at 795 nm/397.5 nm (all Layertec, see the supplementary material). The half-wave plate (HWP) inside the cavity rotates the polarisation of the single photons by 90° every physical round-trip but leaves the pump light unaffected. This “flip-trick” effectively doubles the cavity length for the single photons, reducing their free spectral range to $F S R r ≈ 121$ MHz compared with $F S R b ≈ 241$ MHz. It also cancels out any birefringence between the orthogonally polarised single photons, as on average the number of round-trips travelled in each polarization is the same. Thereby the flip-trick alleviates the need for a compensation crystal,^23,25,29 reducing the overall loss and achieving finesses of $F r ≈ 181$ and $F b ≈ 8.5$⁠.

In order to achieve enhanced emission into the desired mode while simultaneously maintaining a 100% duty cycle of the source, the cavity needs to be kept triply resonant. To ensure this, a complex active stabilisation circuit for signal, idler, and pump photons has been implemented. The first step uses a signal derived from PD₃ to stabilise the length of the cavity to the pump frequency via a mirror mounted on a piezo-electric transducer. Second, the flip-trick always ensures double resonance of signal and idler, as it eliminates birefringence of the single photons. Temperature tuning the ppKTP crystal allows to fulfil the phase-matching condition for SPDC while simultaneously achieving triple resonance at temperatures of around T $≈ 41.3 °$ C with a $F W H M ≈ 10$ mK. Conventionally, the FSR of a cavity is independent of the frequency of the light field, resulting in twice the number of resonances for every second harmonic frequency (pump) compared with its fundamental (single photons). Locking to an unmatched resonance would yield no useful single photons. The flip-trick compensates for this as well by effectively doubling the cavity length only for the fundamental frequency, ensuring every resonance of the pump is matched with one for the single photons.

After leaving the cavity, a dichroic mirror and an ultra-narrow bandpass filter at 795 nm (FWHM 1.0 nm) separate the down-converted photons from the leaking pump light. A polarising beamsplitter (PBS) deterministically splits the paired photons, which are then separately coupled into single mode fibres, detected on single photon detectors (Perkin Elmer SPCM-AQR-14-FC)—SPD₁ for idler, SPD₂ for signal—and recorded with a time-tagging module (Roithner Lasertechnik, 100.1 ps time resolution). In the $g s , s ( 2 ) ( 0 )$ measurement (Fig. 1, case B), the signal fibre is sent through an additional 50/50 fibre beamsplitter before both outputs are detected on SPD₂ and SPD₃. The self-relocking optical stabilisation loops for the laser frequency, the SHG, and the PDC cavity lengths commonly allow continuous data acquisition for 90 min and regularly reach up to half a day.

Fig. 2 shows measurements of $G s , i ( 2 ) ( τ )$ for four different angular configurations of the HWP without background correction. The comb-like structure arises from the increased probability of detecting signal and idler photons at integer multiples of their effective round-trip time, $t r t = 1 / F S R r , k = 8.28$ ns, equaling two physical round-trips. At perfect alignment (Fig. 2(a)), the HWP rotates horizontal to vertical polarisation and vice versa at each pass. Therefore, the photon mode inside the cavity does not overlap with itself one physical round-trip earlier. It has to traverse the cavity a second time to complete an effective round-trip and get detected with its partner as a coincidence on the SPDs. This halves the FSR and thus reduces the photon bandwidth. Additionally, it ensures double resonance of signal and idler photons by cancelling the birefringence of the ppKTP crystal. Slight misalignment of the HWP angle results in a non-zero probability for the photons to be detected as coincidences after an odd number of physical round-trip differences. This can be seen in the cross correlation functions (Fig. 2) as peaks with half the temporal spacing, which reach their maximum when the round-trip difference between the signal and idler photons is an integer multiple of $45 ° Δ α$⁠. Thus changing $Δ α$ from 0° to 45° (optical axis of HWP) allows one to set $F S R r , 0 ≈ 121$ MHz and $F S R r , 45 ≈ 242$ MHz.

In case of perfect alignment of the HWP, fitting a double exponential decay $exp ( − 2 π Δ ν τ )$ can be used to extract the bandwidth $Δ ν$ of the single photons, as shown in Fig. 3(a). The FWHM correlation time of 331 ns and the corresponding bandwidths of $Δ ν S = 666 ± 16$ kHz and $Δ ν I = 667 ± 15$ kHz are, to our knowledge, the narrowest values observed from SPDC to date. The source therefore meets the spectral requirements for efficient coupling with the D₁ transition in rubidium in GEM, making the photons suitable carries for quantum information between memories. The slight difference between signal and idler bandwidth is within error of the fit. Fig. 3(b) shows a zoom into delay times of $± 200 μ s$ around zero delay with a finer resolution of 200.2 ps/time bin. The fit of Eq. (1) is in excellent agreement with the data. The finesse of $F r ≈ 181$ corresponds to internal losses of 3.4% per effective round-trip, leading to an escape efficiency⁴¹ of ∼0.29.

Experimentally, this is realised by opening a coincidence window of width $τ c = 250$ ns (∼FWHM of the decay in Fig. 3(a)) symmetrically around the detection of an idler photon and measuring events on either signal detector to determine N_12,13, while events on both signal detectors are added up to N₁₂₃. The latter case are unwanted events indicating the creation of more than one photon pair and should be suppressed for an ideal source. As the arrival time differences of the photon pairs are very well known (Fig. 3(b)), we post-selected the measured data to 1 ns (∼FWHM of each peak) around the peak maxima for each t_rt, leading to an effective $τ c = 33$ ns. Fig. 4 shows the dependence of $g s , s ( 2 ) ( 0 )$ on the idler (heralding) rate R₁$= N 1 / T$⁠, where T is the overall measurement time. Each data point contains 200 million idler events and is not corrected for dark counts which would reduce $g s , s ( 2 ) ( 0 )$ even further. Antibunching below 0.5⁴² is achieved up to R₁ = 250 kHz, with a minimum measured value of $g s , s ( 2 ) ( 0 ) = 0.016 ± 0.002$ for a idler rate of 5 kHz, giving clear proof of the quantum character of the single photon source.

In conclusion, we report on the first sub-MHz cavity-enhanced single photon source, resonant with the D₁ transition in rubidium. The linewidth of 666 kHz is the narrowest from SPDC to date, matching the spectral requirements of GEM—currently the most efficient quantum memory. The ultra-narrow bandwidth is achieved by introducing a new method, the flip-trick, which also cancels out birefringence between orthogonally polarised single photons. Antibunching as low as $g s , s ( 2 ) ( 0 )$ = 0.016 confirms the single photon nature of our source. Average locking times of several hours are achieved and stabilising the cavity to the pump light enables a 100% duty cycle. The next step will be to filter a single cavity mode by using either active spectral filtering by an external cavity or, internally, the clustering effect^27,28 or an etalon. Additionally, the whole setup fits on two small breadboards, which are easy to transport, and we are planning on combining our source with the GEM developed at the Australian National University to gain further insight into the memory’s performance at a single photon level.

See the supplementary material for further details and specifications on both cavities and a full characterisation of the HWP.

This work was partially supported by the Centre for Quantum Computation and Communication Technology (Grant No. CE110001027) and by the Centre for Engineered Quantum Systems (Grant No. CE110001013). A.G.W. acknowledges support from a UQ Vice-Chancellor’s Research and Teaching Fellowship. The authors thank the team from the Austrian Institute of Technology and Roithner Lasertechnik for kindly providing time-tagging modules.