1. Introduction

Efficient control of light-matter interaction at a single-particle level is a key factor enabling several quantum applications. One of the main goals in quantum technology is to deliver a quantum network platform for secure quantum communication. Atom or trapped ion implementations of quantum memories and quantum repeaters together with photonic information carriers are one of the proposed scenarios [1–3]. Moreover, quantum imaging and sensing benefit from single-photons interaction with matter. In particular, this is apparent when discussing quantum illumination, sub-shot-noise imaging, ghost imaging, and absolute detector calibration [4]. Further, absorption microscopy exhibts higher signal to noise ratio when quantum light is applied [5]. Entangled two-photon absorption is another microscopy technique which has a great potential to outperform its classical counterpart in terms of applicability [6]. It may also serve as a tool for virtual-state spectroscopy [7–9]. However, all the above-mentioned applications require an efficient single-photon and single atomic system interaction, which still remains a challenge. The narrow atom absorption spectrum together with spectrally broad single-photon sources demand cavities to enhance the interaction efficiency [10–12].

Here, for the first time, a different solution is proposed and the mismatch problem is solved by using a spectrally broad absorber, such as a color center in diamond, where a nonresonant excitation is possible due to phononic sidebands [13]. This eliminates the need for excitation with a narrow bandwidth light. A plethora of such systems, like SiV, GeV, SiC or dyes used in biological imaging, is already known and investigated [14–16]. A simple, room-temperature, cavity- and vacuum-free interface for photon-matter interaction is reported. The heralded single-photon source (HSPS) is based on the spontaneous parametric down conversion (SPDC) process, where the detection of an infrared photon is used as a herald for the visible one. In the experiment, a heralded single photon is absorbed by a single atom-like system, specifically a nitrogen vacancy center (NV) in diamond. The NV center then emits another photon, whose arrival time is measured by means of a time-resolved single-photon detection technique. As opposed to Ref. [17] we do not use a stimulated absorption-emission process and our method is single atom oriented.

2. Experimental setup

The experimental setup is depicted in Fig. 1(a). A red laser photon beam incident on the BiBO crystal is frequency doubled. Then a blue pump photon is converted through the SPDC process into a pair of photons – one in visible and one in infrared spectral range. When the superconducting single photon detector (SSPD) measures the latter, the existence of the former is heralded and the time reference is defined. Subsequently, the heralded visible photon is delivered to the custom-made confocal microscope (CM), where it is reflected off a dichroic mirror (DM) and focused with a microscope objective (MO) onto an ensemble of color centres. The sample used in the experiment is a high-pressure high-temperature (HPHT) diamond with a dense concentration of negatively charged nitrogen-vacancy (NV$^-$) centres, approximately $18$ ppm. Full sample characterization and preparation description, including spectrum and ODMR measurement, is given in Refs. [18,19]. Next, the photon excites a color centre, which results in a fluorescence photon emission in the range of $600-800$ nm [20], see Fig. 1(d). The resulting photon is collected by the same MO and propagates through the DM and a longpass filter. This allows observation of fluorescence only in the spectral range above $700$ nm, which corresponds to the emission of the negatively charged NV centers mainly [20]. Finally, its arrival time is measured by a single-photon avalanche diode (SPAD) supported by a digital oscilloscope. The statistics of arrival times collected by the measurement system are used to build a histogram exhibiting the characteristic fluorescence decay shape.

 

Fig. 1. Interaction between photons and NV centers. (a) The experimental setup. (b) Magnification of the diamond surface: One of the NV centers from the illuminated ensemble absorbs a heralded green photon and then emits a fluorescence photon. (c) Simplified energy level structure of an NV centre: a green photon excites an electron from the ${}^3A_2$ (ground) state to a ${}^3E$ (excited) state. The electron then decays non-radiatively to a lower energy excited state, transferring some of its energy to the diamond lattice. Finally, the electron decays radiatively back to the ${}^3A_2$ (ground) state via the emission of a lower energy red photon. (d) Blue: NV$^-$ fluorescence spectrum with zero phonon line (ZPL) at $637$ nm and vibronic sideband up to $800$ nm. Red: the transmission range of the spectral filtering setup (DM3 and F3).

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The HSPS used in the experiment is tunable in the range of $452$-$575$ nm [21]. The FWHM of the HSPS in the visible spectrum is around $4$ nm, which corresponds to $3.2$ THz at $575$ nm and $5.9$ THz at $450$ nm. The scenario with a $532$ nm single-photon was chosen but other pumping scenarions were tested as well giving similiar results. Two pumping power settings, 1 and 5 mW, were used for the source, which are referred to as lower and higher, respectively. The high quality of heralded single photon state was verified by measuring the correlation function $g^{(2)}(0)$ [22,23], describing the goodness of the single-photon source. In the perfect case it is $0$ for a single photon Fock state and $1$ for attenuated laser described by a coherent state. Here, for lower power pump it took the value of $g^{(2)}_{l}(0)=0.0011(2)$, whereas for higher pump power $g^{(2)}_{h}(0)=0.0111(5)$. The corresponding heralded photon count rates were $4.5$ kcps (lower power) and $40$ kcps (higher power). The HSPS characterization was done for $532$ nm.

3. Fluorescence decay measurement

In Fig. 2 the obtained NV fluorescence decay pumped with heralded single photons is shown for the two pumping power settings. The probability of the fluorescence emission in time, $p(t)$, can be described by a simple exponential model including a non-radiative decay path. The model assumes a fast non-radiative decay followed by a radiative decay, with characteristic times $\tau _N$ and $\tau _R$, respectively. The explicit formula can be obtained by taking a convolution of the two single exponential decays

 

Fig. 2. NV$^-$ fluorescence decay measurement pumped with single photons. Single photons with wavelength of $532$ nm are generated in the SPDC process in (a) higher and (b) lower pumping power setting. Red dots show experimental data and red curve represents fitted model. Black curve shows a histogram of visible and infrared (IR) photon coincidences measured from HSPS source. Large and small peaks correspond to proper and accidental coincidences, respectively. The accidental coincidences almost disappear in the lower power setting. More detailed information can be found in Supplement 1.

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The radiative, $\tau _R$, and non-radiative, $\tau _N$, decay times along with the ratio $r$ can be estimated by fitting the model to the experimental data. Their values for higher (lower) pumping setting were determined to be $7.68(23)$ ns and $107(14)$ ps ($7.17(14)$ ns and $112(13)$ ps), respectively. The obtained radiative decay times are shorter with respect to what is reported in the literature [24]. Two possible explanations for this discrepancy are proposed. Firstly, the sample is illuminated with single photons resulting in the NV center not being spin-polarized, as opposed to the case of the excitation with a high power laser [24,25]. Secondly, the experiment is performed on a very dense sample, where the shorter decay time can be attributed to the Förster resonance energy transfer (FRET). It makes the fluorescence emission faster when the emitters are close to each other [26]. Next, the fitted ratio, $r$, takes the value of $0.233(9)$ ($0.0225(81)$) in the higher (lower) pumping power setting. The difference reflects the fact that for the higher pump power setting of the HSPS the ratio of accidental to proper coincidences is higher. It can be clearly seen when comparing black histograms in Fig. 2.

As a reference measurement, an experiment was performed with the heralded single photons replaced with an highly attenuated, pulsed laser. The histogram of the measured photon detection times with respect to the optical laser pules is given in Fig. 3. A fluorescence lifetime model, which takes into account repetitive excitation, was used for fitting. The obtained radiative and non-radiative dacay times equalled $\tau _R = 6.6 (2)$ ns and $\tau _N = 127 (8)$ ns, respectively.

 

Fig. 3. NV$^-$ fluorescence decay measurement pumped with puled attenuated laser. The pumping wavelength was $532$ nm, pulse duration approximately $200$ fs and repetition rate $80$ MHz.

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4. Discussion

The detector monitoring the fluorescence has an active area of $50$ $\mu$m diameter, photon detection efficiency of the order of $15-28$ % for the spectral range of interest, which is $700-800$ nm, and exhibits $65(8)$ dark counts per second. When taking into account the number of fluorescence photons, the signal to noise ratio (SNR) for the higher (lower) power setting was $0.65(46)$ ($0.154(16)$). However, the heralding scheme applied in the experiment, taking into account only the heralded fluorescence photons and dark counts, improves SNR because it benefits from the ability to reject a substantial part of the dark counts. It stems from the fact that the detection window for the fluorescence monitoring detector is being opened only when a heralding photon was already detected. Hence, the effective detection probability of a fluorescence photon is higher than of a dark count within a given detection window. For experimental conditions in the higher (lower) power setting this results in $2.96(27)$% ($1.42(16)$%) of the real fluorescence and $0.446(12)$% ($0.172(22)$%) of the dark counts being heralded. This leads to the increase of SNR for the higher (lower) power setting to $4.3(8)$ ($1.3(6)$). In principle, the SNR can be improved even further by replacing the fluorescence monitoring by one with active area of $30$ $\mu$m diameter giving and reduced dark count rate $1$ per second [27]. The expected SNR would increase by a factor of $65$. Details on SNR calculation can be found Supplement 1.

Now the problem of converting a heralded photon generated by HSPS to the fluorescence photon emitted by an NV center is adressed. This quantity can be estimated based on the observed count rates to be $1.46(32) \cdot 10^{-4}$ ($2.1(8) \cdot 10^{-4}$) for higher (lower) power setting. This is the efficiency of the sample, meaning the experimental setup imperfections are excluded. The setup sets additional limits resulting in the observed conversion efficiency, $\eta _{conv.}$, of $7.0(7)\cdot 10^{-6}$ ($1.01(25)\cdot 10^{-5}$) for higher (lower) pumping setting. This is due to experimental factors including: efficiency of extracting fluorescence photons from the diamond, losses in optical elements, fiber coupling efficiencies and quantum efficiencies of the detectors.

The low conversion efficiency results in long time of data acquisition. The typical time of the reported experiments was of the order of 24 hours. The heralded fluorescence photon count rate (signal), $n_{sh}$, depends on the SPDC generation rate, $N_{SPDC}$, visible photon fiber coupling, $\eta _{VIS}$, infrared photon fiber coupling, $\eta _{IR}$, infrared photon detection efficiency, $\eta _{IR det.}$, and the conversion efficiency, $\eta _{conv.}$. The exact formula is a product of those factors, $n_{sh} = N_{SPDC} \cdot \eta _{VIS} \cdot \eta _{IR} \cdot \eta _{IR det.} \cdot \eta _{conv.}$. Hence it is clear, that improvement of the SPDC photon pair coupling efficiency, increasing the SPDC source pomp power, and detectors with higher quantum efficiency can speed up the measurement. It is estimated, that when switching from pulsed to continuous-wave laser pumping of the SPDC source, the power can be safely increased up to single Watts with preserved single photon characteristics of the source. This would result in 3 orders of magnitude faster measurement when leaving all other settings unchanged. It is also worth mentioning that while the experiment was performed with the aid of an oil-immersion MO, it is possible to conduct it with a dry air MO. Such configuration would result in longer data aquisition time but would enable cryogenic experiments.

5. Summary

In conclusion, a simple, room-temperature, cavity- and vacuum-free single-photon single atom-like system interaction was demonstrated. The experiment was performed on a high NV$^-$-concentration diamond sample with a tunable, SPDC-based heralded single-photon source. Interaction efficiency, usually limited by the very small spectrum overlap between the broadband quantum light and narrow atomic transitions, was significantly enhanced thanks to phonon-broadened absorption in nitrogen-vacancy centers in diamond.

The result can also be considered as a useful technique paving the way for development of new applications like quantum microscopy [5,6] or virtual-state spectroscopy [7–9]. In particular, the ability of interaction of NVs with statistics-controlled quantum light enables two-photon processes, such as ionization of negatively-charged NV centers, to be eliminated. Moreover, it can be extended to the scenario of a low NV$^-$ concentration sample, which would enable addressing of a single color centers. It would facilitate testing of the fundamental properties of quantum light interacting with atomic systems. As a further step, several applications, such as quantum microscopy, can be enhanced when non-classical properties of quantum light are exploited.