Abstract
Quantum Entanglement is widely regarded as one of the most prominent features of quantum mechanics and quantum information science. Although, photonic entanglement is routinely studied in many experiments nowadays, its signature has been out of the grasp for realtime imaging. Here we show that modern technology, namely triggered intensified charge coupled device (ICCD) cameras are fast and sensitive enough to image in realtime the effect of the measurement of one photon on its entangled partner. To quantitatively verify the nonclassicality of the measurements we determine the detected photon number and error margin from the registered intensity image within a certain region. Additionally, the use of the ICCD camera allows us to demonstrate the high flexibility of the setup in creating any desired spatialmode entanglement, which suggests as well that visual imaging in quantum optics not only provides a better intuitive understanding of entanglement but will improve applications of quantum science.
Introduction
Entanglement in quantum mechanics describes correlations between at least two systems that are stronger than classically explainable^{1,2,3}. A prominent system to create and analyse quantum entanglement is the photonic system. Single photons have the experimental advantage to offer different degrees of freedom which are rather simple to address and investigate. A fairly young but vibrant field that studies the spatial structure of the optical modes of photons (e.g. LaguerreGauss^{4}, InceGauss^{5}, BesselGauss^{6}) continues to attract wide interest. Each spatial mode offers many interesting features, like orbital angular momentum^{7} or continuous vortex splitting^{8}, which already lead to novel insights in quantum optics like higher dimensional entanglement^{9,10,11,12}, novel uncertainty relations for the angular and OAM degreeoffreedom^{13,14}, remote object identification^{15} or angular sensitivity enhancement with very high OAM^{16}.
The rapid progress in imaging technologies over the last few years has made CCD cameras an interesting option for single photon detection in quantum optics experiments, since the spatial information is directly accessible. Due to high detection efficiencies, electron multiplied CCD cameras have attracted attention recently and have been used to show nonclassical correlations from photons produced via spontaneous parametric down conversion (SPDC)^{17,18,19,20}. The downside of such cameras is that they only allow relatively long exposure times (μs) which makes it necessary to sum over many images with a sparse number of photons and makes it unfeasible to use them for coincidence imaging of entanglement. In contrast, ICCD cameras have lower quantum efficiencies due to the intensifier and fluorescence screen in front of the CCD chip but show a very good signal to noise ratio and therefore good single photon sensitivity. They have been used to illustrate nonclassical effects of the photons from the SPDC process^{21,22,23,24,25}. However, the biggest advantage of ICCD cameras is the very fast (~2 ns) and precise (~10 ps) optical gating of the intensifier which makes it possible to use them in a coincidence scheme for realtime imaging of quantum entanglement.
Results
In our experiment, we use a combination of the polarization and spatial degreeoffreedom (DOF) to be able to directly image entanglement. We start with a highfidelity polarizationentangled twophoton state (Figure 1). One photon is unchanged; the other photon is brought to a second setup, which transfers the polarization DOF to a wide range of specifically chosen spatial mode. In this interferometric setup^{16}, the photons get transferred by a liquidcrystal spatial light modulator, dependent on their polarization (methods), to a hybridentangled twophoton state
where α, β and φ are real and α^{2} + β^{2} = 1, H and V denote the horizontal and vertical polarization, spM_{1} and spM_{2} correspond to arbitrary spatial modes and the positions of the ketvectors label the different photons. In order to image the created spatial mode and demonstrate entanglement between the two photons, the polarization encoded photon is projected onto a certain polarization and detected by a single photon detector. The signal from the detector is used as a trigger for the ICCD camera, which in turn registers the transferred photon.
In our measurements, we use an ICCD (Andor iStar ADH334T18F03) with a quantum efficiency of 3% for 810 nm wavelength, a gating of 5 ns and a spatial resolution of 1024 × 1024 pixels (effective pixel size: 13 × 13 μm). With this camera we observe clear singlephoton images even for very complex mode structures (Figure 2 c and Figure 4), where the whole spatial information is directly available with a very high precision. Compared to scanning or masking of singlepixel detectors, direct imaging with an ICCD also shortens the measurement time significantly. Thus, the advantage of realtime imaging with an ICCD is an improvement  both spatially and temporally  of many orders of magnitude, opening up possible novel applications in quantum information and quantum metrology. Note that similar ICCD cameras with 20% efficiency and 2 ns gating, which are readily available, promise a 20fold increase in the signal to noise ratio. Since the adjustable insertion delay time for triggering the ICCD is at least 35 ns, we delay the second photon with a fibre before sending it through the transfer setup. If a wrong delay is chosen nearly no accidental photon events can be seen at the camera (see Figure 2 b) and hence no background correction has to be applied. This suggests the possibility for precise measurements in the temporal domain. A few residual events appear due to the high triggering rate (MHz) and the resulting thermal noise from the intensifier and from the afterglowing of the fluorescing phosphorous screen. We find the ratio between the number of detected photon events in a picture (right delay) to the residual events (wrong delay) to be on the order of 75 : 1. Those undesirable residual events may be suppressed substantially, with more efficient ICCD cameras and/or smaller gating times.
To image the effect of entanglement, we scan the Poincaré sphere of the polarization encoded trigger photon and register the appearing mode pattern from the transferred photons at the ICCD camera. In this way, we are able to visualize directly the probability distribution of complex spatial modes of the whole Bloch sphere (Figure 2 a). Because the measurement time to image each spatial mode is very short, the influence of the polarization measurement of the first photon is visible in realtime at the ICCD camera (Supplementary Movie 1). In the movie the frames were recorded with a rate of 0.3 Hz, which could be speed up to the maximal frame rate of 4 Hz of the ICCD camera. Entanglement is already visible in this video, since the highcontrast minima and maxima shift in very good correspondence to the polarization angle measured on the partner photon.
While visual observation already intuitively confirms the presence of entanglement, we also verify it quantitatively: Since the registered signal of the camera depends linearly on the detected photon number, we determine the average signal per detected photon and its error margin from many single photon events (see Methods for more information). With this relation between registered signal and corresponding photon number it is possible to spatially analyse any recorded intensity image without the need for individual counting of single photons over a time consuming data acquisition of many sparse images.
To confirm entanglement we make use of a specific feature of the LaguerreGauss (LG) mode family. The spatial structure of two superimposed LG modes with opposite helicities shows a radially symmetric distribution where a change of the phase ϕ between the two modes directly translates to a spatial rotation of . To discriminate between different orientations of the structure and therefore different superpositions, we evaluate the photon number per angular region from the measured intensity image for different trigger polarizations (Figure 3 a and b). From the maximal and minimal detected photon numbers the visibilities in two mutually unbiased bases and therefore the expectation value of an entanglement witness operator can be calculated^{26} (Supplementary Information). For all separable states the inequality
holds and surpassing this bound verifies entanglement. Capital letters stand for the polarization of the trigger photon (D = diagonal, A = antidiagonal, R = right circular, L = left circular). For first order LG modes with l = ±1 we obtained a value of 1.68 ± 0.03 which violates the inequality (2) by more than 20 standard deviations, therefore proving entanglement. For LG_{±2}, LG_{±3}, LG_{±5} and LG_{±10} the measured witnesses are 1.53 ± 0.05, 1.50 ± 0.05, 1.50 ± 0.04 and 1.46 ± 0.05 respectively and thus violate the bound for separable states by around 10 standard deviations. We note that no background subtraction was applied, but the measured photon numbers from the registered signal of the ICCD might be a bit smaller than they were in the actual measurement, due to saturation effects where a lot of photons are registered in the same region of the camera, namely the maxima. However, a bigger actual photon number in the maximum would correspond to a higher value of the visibility and therefore a stronger violation than the one presented here.
Recently, it was shown that hybridentangled twophoton states of higherorder LG modes can be used to improve sensitivity in the remote sensing of an angular rotation^{16}. By using an ICCD camera to image the mode patterns it is possible to visualize this gearlike behaviour between the rotation of the polarization and the petal structure of the spatial mode without any masking and its inherent significant reduction in count rates. In contrast to the experiment in Ref. 16, this significantly shortens the acquisition time. A scan of the polarization around the equator of the trigger photons' Poincare sphere leads to a rotation of the structure by 180° for LG_{±1}, 90° for LG_{±2} and 36° for LG_{±5} (Supplementary Movie 2).
Furthermore, the capability of the ICCD camera of resolving complex spatial pattern with a very high precision enables the first demonstration of the high flexibility of the presented setup. If transferring one of the photons to the HermiteGauss (HG) mode family or the general family of InceGauss (IG) modes, all registered singlephoton images show a very good agreement with the theoretical prediction (Figure 4 a and b). Additionally, it is possible to create entanglement between polarization and an artificial mixture of two different mode families at the same time, here a superposition of a higher order LG and higher order HG mode (Figure 4c). Since no mask is required the imaging with an ICCD camera is a very general way to measure entanglement of any spatial mode or complex pattern of single photons which might advance quantum optics experiments where information is encoded in the spatial domain.
Discussion
Our results represent the first imaging of entanglement in realtime, where the influence of the measurement of one system on its entangled, distant partner system is directly visible. The use of an ICCD camera to evaluate the number of photons from a registered intensity within a given region opens up new experimental possibilities to determine more efficiently the structure and properties of spatial modes from only single intensity images. The presented results suggest that triggered ICCD cameras will advance quantum optics and quantum information experiments where complex structures of single photons need to be investigated with high spatiotemporal resolution.
Methods
Source and spatial light modulator (SLM)
The polarizationentangled photon pairs were created in a SPDC process using a 15 mmlong typeII nonlinear crystal (periodically poled potassium titanyl phosphate (ppKTP)) in a Sagnactype configuration^{27,28}. A blue 405 nm continuouswave diode laser with up to 35 mW of power pumps the crystal and thereby creates photon pairs of 810 nm wavelength. Two 3 nm bandpass filters were used before the photons were coupled into singlemode fibers. With this approximately 1.3 million pairs per second can be detected at full pump power. Any polarization change between the source and the transfer setup is undone by fiber polarization controllers. The SLM (resolution: 1920 × 1080, pixel size: 8 μm, Holoeye Photonics AG) in the transfer setup, which modulates only the phase of the light, was used to create the desired spatial modes.
Evaluation of the photon number
The registered intensity at the ICCD camera is read out as a signal in counts per pixel, which does linearly depend on a specific photon number. In order to evaluate the photon number corresponding to a registered intensity, we need to know the average signal caused by a single photon. For this purpose we analyse around 5800 detected single photon events to get a statistically significant mean value. In each shot we subtracted at first the camerainduced readout noise (mean background) of each pixel. In a second step, we summed up all signal counts of a contiguous pixel array as one photon where at least one pixel value is more than 5 standard deviations above the background fluctuations. This has to be done since the photons are spread over a few pixels due to different resolutions of the intensifier and the CCD pixel size (see insets in Figure 5a). With the mean value it is now possible to determine the number of photons which correspond to detected signal counts within a certain region of the intensity image. To evaluate the error margin for each photon number, we performed a Monte Carlo simulation based on the obtained probability distribution from the single photon measurements (Figure 5a). A very good fit to the resulting histogram of the distribution was found to be a lognormal probability function. With this distribution 50000 possible signal counts were simulated for each photon number. The resulting average signal for every photon number corresponds to the one obtained with the mean value from the single photon events. The thereby found standard deviation can now be used as a lookup table to determine the error margin of each photon number. The linear dependence of registered signal on the photon number as well as the standard deviation is shown in Figure 5 and was used to demonstrate the nonclassical behaviour (Figure 3 a and b in the main text) and demonstrate entanglement quantitatively by violating the bound of an entanglement witness (equation (2)).
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Acknowledgements
The authors thank T. Pieper and LOTQuantumDesign for providing the camera. This work was supported by the European Research Council (advanced grant QIT4QAD, 227844) and the Austrian Science Fund (FWF) through the Special Research Program (SFB) Foundations and Applications of Quantum Science (FoQuS; Project No. F4006N16) and W12102 (Vienna Doctoral Program on Complex Quantum Systems; CoQuS).
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R.F. designed and built the experiment, collected and analysed the data and wrote the manuscript. R.L. and S.R. participated in designing and building of the experiment. M.K. and S.R. assisted on the theoretical side and the simulation analysis. The project was supervised by A.Z. All authors contributed to conceiving the experiment, discussing the results and contributing to the final text of the manuscript.
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Fickler, R., Krenn, M., Lapkiewicz, R. et al. RealTime Imaging of Quantum Entanglement. Sci Rep 3, 1914 (2013). https://doi.org/10.1038/srep01914
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