We use two perpendicular crystals of periodically-poled KTP to directly generate polarization-entangled photon pairs, the majority of which are emitted into a single Gaussian spatial mode. The signal and idler photons have wavelengths of 810 nm and 1550 nm, respectively, and the photon-pair generation rate is 1.2×107 sec-1 for a pump power of 62 mW. The apparatus is compact, flexible, and easily to use.
©2004 Optical Society of America
Polarization-entangled photon pairs have been central to recent experiments in quantum information, including investigations of quantum cryptography, quantum teleportation, and preliminary results in linear-optical quantum computation. Perhaps the best-known scheme for generating such photon pairs involves spontaneous parametric downconversion with type-II birefringent phase matching, in which a pair of orthogonally-polarized photons are emitted into two intersecting cones . However, in this case, only a small fraction of the generated photon pairs are entangled. On the other hand, all of the frequency-degenerate pairs are entangled in a scheme involving type-I phasematching in two separate crystals, allowing for significant improvement in the generation efficiency . In this case, the optic axis of the first crystal is oriented horizontally, the optic axis of the second crystal is oriented vertically, and the pump is polarized at 45° with respect to each of the axes. There is thus an equal probability that two vertically polarized (V) photons will be generated in the first crystal or that two horizontally polarized (H) photons will be generated in the second crystal. These two possibilities are made indistinguishable by using thin crystals, so that the generated photons emerge in two overlapping cones. The conical emission is inconvenient, though, for coupling the emitted photons into optical fibers, while the need to use thin crystals limits the pair generation rate.
We have therefore developed a two-crystal source of entangled photons which uses quasi-phasematched (QPM) materials. QPM materials have previously been used for efficient generation of photon pairs without polarization entanglement [3, 4], and for probabilistic generation of polarization-entangled photon pairs by postselection . In our scheme, by contrast, polarization-entangled photons are generated directly. Compared to schemes that involve pumping a single QPM crystal from opposite sides , the two-crystal scheme has the advantage of not requiring a stabilized interferometer.
The poling period of our crystals is chosen to allow for co-polarized (ZZZ), colinear down-conversion. The colinear configuration means that the output modes of the photons created in the first and second crystals have nearly complete spatial overlap, regardless of crystal length. In other words, it is possible to use long crystals, thereby increasing the pair generation rate, without reducing the degree of entanglement. As well, the signal and idler beams have a large overlap with a simple Gaussian (TEM00) mode, allowing for efficient coupling of the generated photons into single-mode optical fibers. Finally, since the entanglement is generated directly in the downconversion process, it is not necessary that the signal and idler be frequency degenerate. We have thus chosen the idler to have a wavelength of 1550 nm, corresponding to the transmission-loss minimum in optical fibers, while choosing the signal to have a wavelength of 810 nm, allowing for efficient, low-noise photon counting using Si-based detectors . Very nearly the same wavelength pair is also of interest for quantum teleportation systems in which the signal photon is used to load a Rb-based quantum memory .
Our nonlinear crystals are flux-grown, periodically poled potassium titanyl phosphate (PP-KTP) [9, 10]. Each crystal is 5 mm long (in the X direction) and 0.5 mm high (in the Z direction). A photoresist grating with a 9.6 µm period is patterned on the top side of the unpoled crystal, and poling is achieved by applying voltage pulses across the crystal using liquid electrodes. The poling is monitored via the electro-optic effect, by observing polarization changes of a He-Ne laser beam passing through the sample in the X direction .
Since downconversion occurs with high efficiency in the PPKTP crystals, only a moderate pump power is needed. This is provided by a compact, diode-pumped, frequency-doubled Nd:YAG laser, which has a continuous-wave output at a wavelength of 532 nm. This source is small compared to the large-frame lasers generally used for downconversion (only 120×50×36 mm), allowing the entire pair-generation system to be compact and inexpensive. Stray light is reduced by sending the pump beam through a bandpass (BP) filter. The two PPKTP crystals are mounted orthogonally on a temperature-controlled brass block.
Figure 1(a) shows the measured signal wavelength as a function of sample temperature. Also shown are the predicted wavelengths, calculated using published Sellmeier coefficients [12, 13]. Good agreement between theory and experiment is seen. The results show that a temperature of 109.3°C will give a signal wavelength of 810 nm, corresponding to an idler wavelength of 1550 nm. Figure 1(b) shows the signal spectrum at this temperature; it can be seen that the signal has a bandwidth of only 5 nm.
The idler beam was sent through a lens, and its profile was measured at various distances from the crystal using an InGaAs detector array. A sample profile is shown in Fig. 2(a); it can be seen that the profile has the symmetric, circular shape characteristic of a fundamental TEM00 mode. In order to make a more quantitative analysis, the measured profiles were integrated in the horizontal and vertical directions, and the integrated profiles were fitted to Gaussians in order to obtain beam diameters, shown in Fig. 2(b). The results were fitted to the standard formula for nearly Gaussian beam propagation , giving M 2 parameters of 2.4±0.3 and 2.0±0.2 in the horizontal and vertical directions, respectively. This indicates that the majority of the beam is contained within a single Gaussian spatial mode. The slight difference between the two different directions may be due to ellipticity of the pump beam, or imperfect alignment of the lenses or the crystal axes relative to the pump beam.
Figure 3 shows theoretically estimated M 2 values for different pump beam waists . These values were obtained by numerically integrating the nonlinear interaction Hamiltonian over the length of the crystal, thereby calculating the angular distribution of the photon-pair probability amplitude. This probability amplitude was used to calculate the idler density matrices. For each eigenvector of these density matrices, the spatial distribution of the electric field was determined; these spatial profiles were summed incoherently to give the total intensity distribution. These calculated profiles were then fitted in the same way as the experimental profiles in order to obtain M 2 values. Our experimental focussing condition corresponds to a beam waist of approximately 8 µm, giving a theoretical M 2 value of approximately 2.7. Considering the imprecisions involved in using Gaussians to fit more complex beam profiles, we have reasonable agreement between the theoretical prediction and our experimental results. Optimization of the pump focussing conditions should allow a lower M 2 value to be achieved, corresponding to an even larger overlap with the fundamental Gaussian mode.
Figure 4 shows a schematic of the apparatus used to generate and characterize the polarization-entangled photons. After the BP filter, the pump beam is sent through a polarizing beamsplitter (PBS) and a half-wave plate (HWP), which is rotated until the detection rates for horizontally- and vertically-polarized signal photons are the same. Following the crystals, the signal and idler beams are collimated, and are then separated using a dichroic beamsplitter.
At this point, the generated photon pairs are not yet highly entangled. Since the signal and idler have very different wavelengths, they will experience significantly different group velocities in the PPKTP. Two V photons generated in the first crystal will pass through a greater length of PPKTP than two H photons generated in the second crystal, and will thus be separated further from one another by the time they leave the material. This means that photons with different polarizations are distinguishable, destroying the entanglement. In order to recover the entanglement, it is necessary to delay the V photons relative to the H photons in only one of the beams (signal or idler), thereby eliminating the temporal separation between photons with different polarizations and erasing the distinguishing information. This delay is provided by two calcite crystals, each 1 mm thick, which we place in the idler arm. Following the calcite crystals is a quarter-wave plate, which adjusts the phase between the two polarizations.
In order to evaluate the entanglement between the photons, we place a HWP followed by a PBS in each of the signal and idler arms. Pump laser light is removed by sending the signal and idler beams through BP filters with bandwidths of 10 nm. The beams are then coupled into single-mode optical fibers using aspheric lenses. Additional rejection of pump laser light is provided by chromatic aberrations in the focussing lenses, which ensure that only the desired wavelengths are focussed exactly onto the fiber tips. The fiber used for the idler photons is designed for single-mode operation at the telecommunications wavelength of 1550 nm, while the fiber used for the signal is designed for single-mode operation at 820 nm. The fiber for the idler photons leads to a home-built detector module incorporating an InGaAs/InP avalanche photodiode (APD) , while the fiber for the signal photons leads to a low-noise Si-based APD module. The output pulses from this detector are sent to a delay/pulse generator, which, in turn, sends gate pulses (4.0 V amplitude, 5 ns duration) to the InGaAs APD module. The delay is adjusted so that the gate pulses arrive at the InGaAs detector at the same time as the idler photons. This means that the InGaAs APD module detects coincidences (i.e., signal and idler photons generated simultaneously by the source). We note that the delay/pulse generator cannot relay a second pulse if it arrives less than 1 µs after a first pulse, so that some of the output pulses from the Si APD module are lost; this effectively means a slight reduction in our overall detection efficiency.
To measure the polarization correlations between signal and idler photons, we set the HWP in the signal path to a particular angle and rotate the HWP in the idler path; for each setting, we measure a coincidence rate. This rate includes both “true” coincidences, corresponding to photons generated simultaneously in the PPKTP, and “accidental” coincidences, corresponding to photons generated at different times that happen to both arrive at the detector within the 5 ns detection time window. The accidental coincidence rate was measured, for each polarizer setting, by increasing the gate pulse delay by more than 5 ns, and was then subtracted from the total measured coincidence rate to obtain the rate of true coincidences.
Results are shown in Fig. 5; for these measurements, the incident pump power was 62 mW. There is a strong correlation between signal and idler polarizations, regardless of the measurement basis; this is the signature of entanglement. The fitted visibilities in the H, V, and 45° bases are 95.2±0.4%, 95.4±1.0%, and 79.7±0.6%, respectively. The visibilities in the H and V bases are probably limited by the fact that the crystals are not exactly perpendicular to one another. In future work, this will be corrected by mounting one of the samples on a rotation stage, so that its orientation can be optimized with respect to the other . The reduced visibility in the 45° basis, on the other hand, is largely due to the fact that the calcite crystal thicknesses have not been optimized. The birefingence of these crystals is used to compensate for group-velocity differences between the signal and idler in the PPKTP crystals, as described above. The degree of compensation is determined by the amount of calcite material the idler photons pass through, which must be carefully adjusted in order to exactly cancel the differences in group delay and restore a high degree of entanglement . The reduced visibility is also partially due to small differences between the two PPKTP crystals, possibly caused by inhomogeneities in poling period, refractive indices, and nonlinear coefficient. More uniform crystals can be obtained (albeit at a greater expense) using the hydrothermal growth technique. However, a more practical solution may be to test a number of imperfect crystals until two are found which have nearly identical nonlinear-optical properties; using these two crystals together will cancel out the effects of their imperfections.
The quantum efficiency of the InGaAs detector module was calibrated by measuring the count rates when sending in light from a fiber-coupled laser, attenuated by various degrees. After correcting the measured count rates for the Poissonian statistics of the input light, we calculated a quantum efficiency of 8%, including any losses in the optical fiber, as well as coupling losses between the fiber and detector. The quantum efficiency of the Si detector was similarly determined to be 57%. Using these detector efficiencies, we deduced the photon pair number in the single-mode optical fibers, shown on the right-hand axis of Fig. 5. We obtain approximately 3200 pairs/s in the fibers for every mW of pump power, better than any fiber-coupled source of polarization-entangled photons that we are aware of, regardless of wavelength [17, 18].
We also calculated the overall photon detection efficiencies by comparing singles rates to coincidence rates. Photons are generated in pairs at a rate R. The number of signal and idler photons detected are Ss=ηsR and Si=ηiR, respectively, where ηs and ηi are the overall signal- and idler-photon detection efficiencies. The number of coincidences detected, on the other hand, is C=ηsηiR, so the overall detection efficiencies can be simply determined by calculating the ratios ηs=C/Ss and ηi=C/Si. These total efficiencies are the products of the detector quantum efficiencies, described above, and the coupling efficiencies into the single-mode fibers; the coupling efficiencies can thus be determined by dividing the measured overall efficiencies by the calibrated detector efficiencies. Following this procedure, we determined coupling efficiencies of 21% and 7.5% for the signal and idler, respectively. This means that we have a total entangled-pair generation rate in a single spatial mode of approximately 1.2×107 sec-1, comparable to the best reported rates for polarization-entangled photon pairs . In this first experiment, we have not attempted to optimize coupling into the single-mode fibers. The relatively low coupling efficiencies we obtain are due to imperfect matching between the incoming signal and idler beams and the modes of the optical fibers; this matching is likely poorer for the idler beam, resulting in a lower coupling efficiency. By optimizing the focussing optics, it should be possible to obtain better mode matching and, therefore, significantly better fiber coupling .
In summary, we have demonstrated a new, efficient source of highly frequency-nondegenerate, polarization-entangled photon pairs using two crystals of periodically poled KTP, with the majority of the photons emitted into single spatial modes. The idler photons have a wavelength of 1550 nm, suitable for long-distance fiber transmission, while the signal photons have a wavelength of 810 nm, suitable for detection with high-quality Si-based photon counters. The downconversion efficiency is high, so that a relatively low-power pump laser can be used, thereby reducing the cost and size of the system. The design is highly flexible; for example, straightforward modifications would make it possible to generate any two-photon polarization state , while different pairs of signal and idler wavelengths could be generated simply by changing the crystal poling period (or temperature) and the pump wavelength. In this sense, our system should be able to serve as an all-purpose source of polarization-entangled photon pairs.
We would like to thank G. Björk for his helpful comments, and J. Waldebäck for his indispensable assistance with electronics. This work was supported by the Swedish Foundation for Strategic Research (SSF) and the European Commission through the IST 199-100 33 QuComm project.
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