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Observation of intensity squeezing in resonance fluorescence from a solid-state device

Intensity squeezing, i.e., photon number fluctuations below the shot noise limit, is a fundamental aspect of quantum optics and has wide applications in quantum metrology. It was predicted in 1979 that the intensity squeezing could be observed in resonance fluorescence from a two-level quantum system. Yet, its experimental observation in solid states was hindered by inefficiencies in generating, collecting and detecting resonance fluorescence. Here, we report the intensity squeezing in a single-mode fibre-coupled resonance fluorescence single-photon source based on a quantum dot-micropillar system. We detect pulsed single-photon streams with 22.6% system efficiency, which show subshot-noise intensity fluctuation with an intensity squeezing of 0.59 dB. We estimate a corrected squeezing of 3.29 dB at the first lens. The observed intensity squeezing provides the last piece of the fundamental picture of resonance fluorescence; which can be used as a new standard for optical radiation and in scalable quantum metrology with indistinguishable single photons.

A fundamental tool in optical quantum information science is the single-photon source [6][7] , which ideally should emit one, and only one, indistinguishable light quanta on demand. The absence of two-or more-photon components gives rise to antibunching-a highly nonclassical behaviour-which is relevant for quantum cryptography applications 8 . The indistinguishability between independent single photons, which can be measured by two-photon Hong-Ou-Mandel quantum interference 9 , lies at the heart of quantum teleportation 10 , quantum networks 11 , and linear optical quantum computing 12,13 .
In principle, an ideal single-photon device is also useful for quantum metrology.
For example, there is a growing interest in redefining the international standard base unit of luminous intensity, candela, by counting the number of fundamental light quanta, photons 14 . Compared to conventional light sources, such as lasers or lightemitting diodes, an ideal single-photon source has the unique quantum advantage that its intensity uncertainty can be greatly suppressed, thus offer a way to beat the fundamental shot noise limit. Such a feature would find applications in various fields, such as imaging or measurement in the ultralow power regime of light-sensitive biological samples 15,16 .
While the high single-photon purity, indistinguishability, and extraction efficiency has been demonstrated [17][18][19] , the simultaneous observation of intensity squeezing in a single-photon source remains challenging. This is due to the inevitable photon loss from the generation, transmission, collection, and detection in experiments; such that, in each time slot, there was much more often vacuum rather than one photon detected.
While the low overall efficiency only affected the data accumulation time in the measurements of the single-photon purity and indistinguishability, the intensity squeezing, which heavily relies on the overall efficiency; can be diminished by the low efficiency and washed out in the presence of fluctuation of the experimental parameters. Therefore, there were rarely observations of intensity squeezing in singlephoton sources. The first observation, with a very small squeezing of ~0.00183±0.00038 dB, dated back to 1983 from a single atom 1 . Recently, a single molecule embedded inside a metallodielectric antenna was designed for a strong enhancement of photon collection efficiency and showed a squeezing of 2.2 dB 20 .
However, these single photons were not in a single mode, and due to the incoherent excitation, they were distinguishable. A related work reported intensity squeezing with confined polaritons in semiconductor micropillars 21 .
Recently, semiconductor quantum dots embedded in microcavities emerged as a scalable solid-state platform for quantum information technologies [22][23] . Pulsed and resonant excitation of the single quantum dots was used to efficiently generate single photons with near-unity purity and indistinguishability 24 . Polarized microcavities were deterministically coupled to the emitter and efficiently funnelled the single photons into a single spatial mode 25 . In all physical systems, the long sought-after goal of observing intensity squeezing in pulsed resonance fluorescence remained a challenge. Here, we report the first single-mode fibre-coupled semiconductor source of indistinguishable single photons with subshot-noise intensity fluctuation.
The reduction of the intensity fluctuation in a single-photon source compared to the shot noise can be expressed as 20 : , where  is the internal efficiency of the quantum emitter (including its quantum efficiency and excited-state preparation efficiency), andT denotes the total external efficiency (including extraction efficiency and the overall transmission efficiency in the experiment setup).
Due to the quantum uncertainty principle, when the uncertainty of the intensity is smaller than the shot noise, the uncertainty of its conjugate variable-phase-is accordingly increased.
In our experiment, we use a self-assembled semiconductor InAs/GaAs quantum dot coupled in a 2-μm diameter micropillar cavity. The sample is cooled at 4 K where the emitter is resonant with the cavity, so that both the efficiency and indistinguishability are improved due to the Purcell effect. A confocal microscope is utilized to excite the emitter and collect resonance fluorescence single photons. A cross-polarization set-up suppresses the laser leakage with an extinction ratio of ~10 7 :1.
First, we study the resonance fluorescence single photons under continuous-wave (CW) laser excitation. Due to the high photon flux and the limited recovery time (~5 ns) of the superconducting nanowire single-photon detectors used, we attenuate the single-photon stream by 1000 times. The corrected single-photon count rate as a function of laser power is shown in Fig. 1(a), from which we extract a saturation power of 4.9 sat P  nW and a saturated photon flux of 9 (1.87 This is so far the brightest single-photon source reported in any physical system.
A CW laser can prepare the emitter in its excited state with a maximal probability of 50% in the limit of high laser power 26 . The theoretically predicted single-photon flux is T is the excited state lifetime. Fig. 1(b)    In Fig. 2(b), the occurrences at different single-photon counts are plotted (deep blue) and fitted by a binominal function (see Supplementary Information), which is reduced by 12.68% compared to the shot noise limit (green). Considering the optical transmission loss, cross-polarization filtering loss, coupling loss into the single-mode fiber, and the detection efficiency at the detector, the intensity squeezing out of the first lens should be 3.29 dB (light blue). Fig. 2(c) shows the amount of intensity squeezing as a function of the excitation laser amplitude. As expected, by tuning the laser power gradually to π pulse, the excited-state population-proportional to the single-photon generation efficiency-grows, which increases the amount of intensity squeezing.
It is clear that the intensity squeezing critically relies on the overall efficiency. We analyse the photon loss budget in detail. First, we estimate the external efficiency, which accounts for all photon loss from the first lens to the single-photon detector: collection efficiency by the first objective, polarization filtering, single-mode fibre coupling, and detection. To estimate the single-mode fibre coupling efficiency, we performed a separate experiment using multimode fibres (with diameters of 100 μm, 200 μm, which gives the same counts, indicating the efficiency is saturated and equal to unity). The ratio of single-photon count using a single-mode fibre is measured to be 74% of that using multimode fibres, which determines the single-mode coupling efficiency. The overall transmission efficiency of the optical path (including the first lens, optical window, polarized beam splitter, and two wave plates) is measured to be 83%. The first lens collection efficiency is estimated to be 78%. The superconducting nanowire single-photon detection efficiency is 86%. The micropillar cavity shows a small mode splitting due to a slight ellipticity of its cross section. In this case, the intensity of one eigenmode will be higher than that of another one 32 . By measuring the single photon counts in two modes respectively, the determined polarization filtering efficiency is 55%.  19 . We note that such an intensity squeezed single-photon source with subshot noise fluctuations has natural application to benchmarking singlephoton detector efficiency 42 , redefining the standard base unit of luminous intensity at ultralow power level 43 , and optical spectroscopy of light-sensitive biological samples 15,16 .