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Abstract
Silicon ring resonators are used as photon pair sources by taking advantage of silicon’s large third order nonlinearity with a process known as spontaneous four wave mixing. These sources are capable of producing pairs of indistinguishable photons but typically suffer from an effective 50% loss. By slightly decoupling the input waveguide from the ring, the desired photons generated in the ring can preferentially be directed to the drop port. Thus, the ratio between the coincidences from the drop port and the total number of coincidences from all ports (coincidence efficiency) can be significantly increased, with the trade-off being that the pump is less efficiently coupled into the ring. In this paper, ring resonators with this design have been demonstrated having coincidence efficiency of ∼ 96% but requiring a factor of ∼ 10 increase in the pump power. Through the modification of the coupling design that relies on additional spectral dependence, it is possible to achieve similar coincidence efficiencies without the increased pumping requirement. This can be achieved by coupling the input waveguide to the ring multiple times, thus creating a Mach-Zehnder interferometer. This coupler design can be used on both sides of the ring resonator so that resonances supported by one of the couplers are suppressed by the other. This is the ideal configuration for a photon-pair source as it can only support the pump photons at the input side while only allowing the generated photons to leave through the output side. This work realizes a device with preliminary results exhibiting the desired spectral dependence and with a coincidence efficiency as high as ∼ 97% while allowing the pump to be nearly critically coupled to the ring. The coincidence efficiency is measured to be near unity and reflects a significant reduction in the intrinsic losses typically associated with double bus resonators This device has the potential to greatly improve the scalability and performance of quantum computing and communication systems.
© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Silicon photonics is proving to be a very promising platform for quantum information processing. Microring resonators are becoming a key component of such systems as they have been shown to be effective as photon-pair sources by means of spontaneous four wave mixing (SFWM) [1–10]. Often, it is desirable to have precisely one photon. While SFWM sources generate pairs of photons, single photons can be achieved through heralding. Heralding is a technique in which the detection of a single photon from a pair is used to determine the existence of the other. One of the fundamental issues with ring resonators is their inherent 50% loss when critically coupled, regardless of operation in a single bus or double bus configuration [11–13]. For single bus resonators, half of the generated photons are lost to scattering within the cavity. Double bus resonators are slightly different as the photons are free to leave the ring through either port - resulting in an effective loss of 50%. All of this assumes that the ring resonator is critically coupled to straight waveguides. By straying from this standard coupling scheme, it is possible to dramatically decrease the effective loss of the source. Presented here, are experimental results for two different coupling schemes that achieve greatly reduced photon-pair loss when compared to the critically coupled ring resonator.
2. Asymmetric Gap Microring Resonator
2.1. Dual Bus Microring Resonator Theory
One method for increasing the heralding efficiency of a microring resonator is to slightly decouple the input waveguide from the ring. A diagram of an asymmetrically coupled double bus ring resonator is shown in Fig. 1. Assuming the ring itself to be lossless, the probability of a photon generated inside the ring to couple out the drop port is the ratio between the input and output couplers given as
where κ and t represent the complex coupling coefficients for the evanescent couplers.
Fig. 1 Diagram of an asymmetrically coupled double bus ring resonator with an enlarged schematic of the evanescent couplers.
Therefore, photons generated within a symmetric double bus ring resonator (i.e. t1 = t2) will exit both ports with equal probability. The effects of loss through undesired ports of the ring can be quantified through the coincidence efficiency [a ratio between coincidences from the desired port (drop port in this case) and the total number of coincidences from all ports]
The heralding efficiency will be proportional to the coincidence efficiency but requires the absolute losses from the system to be known in order to be calculated [14]. Due to uncertainties in detection efficiencies coupled with detector saturation effects and the spectral dependence in filtering, the results from this work will be reported in terms of coincidence efficiency instead of heralding efficiency. As is evident in Eq. (2), an increase in the gap between the input waveguide and the ring (an increase in |t1|2) raises the percentage of drop port coincidences from 25% (symmetric coupling) to near unity. The drawback of decreasing through port coupling is that the pump will under couple into the ring, resulting in an increase in required pump power to achieve the same level of ring excitation. The choice of either high coincidence efficiency or lower pump powers is application specific. Increasing the pump power can have some negative effects such as an increased filtering requirement, increased broadband SFWM in the bus waveguide, and larger nonlinear effects. An inherent advantage of the dual bus microring resonator is the filtering of the non-resonance matched broadband photon-pairs generated in the input bus, which increases as the input bus is further decoupled from the ring. Vernon et. al worked through the complete theory for a single bus ring, reaching a similar conclusion [13].
2.2. Asymmetric Gap Microring Experimental Procedure
In this experiment, illustrated in Fig. 2, a tunable continuous wave pump laser was set to the resonant wavelength (of the microring cavity) closest to 1.55 μm. The linearly polarized pump passed through a series of bandpass filters (passband insertion loss ∼ 3 dB, blocking region extinction ∼ 140 dB) to minimize the excess laser noise injected into the system. Coupling efficiency was increased by utilizing an inverse taper on the silicon waveguide and fusion splicing a short section of high index fiber (Nufern UHNA-7) to the optical fiber (SMF-28) which was buttcoupled to the chip [coupling losses (including device loss) were determined to be ∼ 2 dB per facet] [6, 10]. Once on the chip, the pump coupled into the ring resonator (R = 18.75 μm, W = 500 nm, H = 220 nm, free spectral range ∼ 5 nm, and quality factor ∼ 28k at λ = 1.55 µm) where non-degenerate photon pairs were produced at resonances spaced symmetrically about the pumped resonance. The generated photons then left the resonator through either port before coupling back into fiber. A series of notch filters (pump rejection) were used (for both outputs of the chip) to remove any remaining pump photons (passband insertion loss ∼ 2 dB, blocking region extinction ∼ 128 dB). A subsequent set of arrayed waveguide gratings (AWGs) spectrally separated the non-degenerate photon pairs (insertion loss ∼ 5 dB) into different fibers that each led to a free running single photon detector (ID Quantique ID230) with a detection efficiency of ∼ 15%. Time correlation measurements were then collected with a time to digital converter (ID Quantique ID800) receiving signals from each of the four detectors.
Fig. 2 (a) Transmission spectrum of the ring resonator source from the drop port of the device with a 150 nm input gap. The arrows indicate the locations of the pump, signal, and idler photons. (b) Energy conservation schematic for the non-degenerate SFWM configuration that was used. (c) Schematic of the experimental setup along with plots of the filter transmission spectra.
Coincidence measurements were made for multiple devices with varying gaps (input gaps ranging from 150 to 350 nm with a constant drop port gap of 150 nm). For each of these, coincidences were integrated for 900 s with a timing resolution of 81 ps for pump powers ranging from −5 to +5 dBm. The variation in pump power enabled determination of the difference in the required pump power between devices to achieve the same level of ring excitation.
2.3. Asymmetric Gap Microring Coincidence Efficiency Measurements
As the waveguide-resonator gap on the input side of the ring was incrementally increased, the measured cross coincidences (through-drop) rapidly decreased, matching the expectation that the photons would only exit out the drop port [Figs. 3(a) and 3(b)]. However, the coincidences from the through port remained high. The cause of this was determined to be the generation of photons in the input waveguide leading up to the ring resonator, which is a broadband four wave mixing process. To prove this, the pump laser was tuned to be off-resonance (eliminating the possibility of photon generation within the ring) and coincidences were collected [Fig. 3(c)]. It was immediately obvious that the through port coincidence counts between the two cases (on-resonance and off-resonance) were very comparable to each other while the drop and split coincidences were approximately equal to zero in the off-resonance case. Therefore, to remove the effect of photon generation from the input waveguide, it was necessary to determine the coincidence efficiency of the source using the drop port coincidences (Cdrop,drop) and the split coincidences (Cthru,drop and Cdrop,thru) only using the following equation:
Fig. 3 (a) On-resonance coincidence peaks for a device with a 150 nm input gap. (b) On-resonance and (c) off-resonance coincidence peaks for a device with a 350 nm input gap. The peak in the off-resonance case is a result of broadband SFWM in the input bus waveguide. In all cases, coincidences were counted for a period of 900 s and with a pump power of 5 dBm.
In order to get accurate values for the coincidence efficiency, corrections needed to be made to the raw data from each device. First, the variation in fiber-chip coupling efficiency between the two outputs of the silicon chip was addressed by analyzing the spectrum of the ring resonator from both the through and drop ports. The other source of error to correct for was the variation in the loss between the four different optical paths leading from the chip to the detectors. This was addressed by collecting additional sets of data for each device after swapping the paths that the through and drop port photons took after they exited the chip.
The resulting coincidence plots [Fig. 3] clearly show that the drop port coincidences remain significant (the large drop in total coincidences is due to the decreased coupling of the pump into the ring) while the split coincidences (thru-drop and drop-thru) decreased to approximately zero between a device with symmetric 150 nm gaps and one with a 350 nm input gap. Comparing the ring spectra of the various devices allowed the determination of how efficiently the pump was coupling into the ring relative to the critically coupled device. This allowed proper comparison of all of the devices [Fig. 4]. The symmetric device was found to have a coincidence efficiency [Eq. (2)] of ηcoinc = 0.370. While this is significantly higher than the theoretical value of 0.25, a very small imperfection in the device fabrication can easily result in that ring-gap variation as it is at the most sensitive point on the theory curve. Increasing the input gap to 225 nm resulted in a device with a largely improved coincidence efficiency of 0.809 (2.19 x improvement) and requiring a factor of 2.56 increased pump power. Further improvements were made with input gaps of 300 nm and 350 nm having coincidence efficiencies of 0.911 (2.46 x improvement) and 0.967 (2.61 x improvement) respectively while requiring increased pumping by factors of 8.60 and 10.1 respectively. As can be seen in Fig. 4, these results are in agreement with the theory. This trade-off between coincidence efficiency and the additional pumping requirement can be removed by taking a different approach to the problem.
Fig. 4 Comparison between the experimental results and the theory. The size of the gap between the input waveguide and the ring is labeled for each data point.
3. Dual Mach-Zehnder Microring Resonator
3.1. Dual Mach-Zehnder Microring Theory
In 1995, Barbarossa et al. found that resonant wavelengths of a microring cavity could theoretically be suppressed by coupling the input waveguide to the ring at two points [15]. This design essentially makes a Mach-Zehnder interferometer (MZI) out of the input waveguide and the ring [16] and has since been demonstrated experimentally [17–19]. To understand how such a device will operate, it is useful to first think of the individual components.
Being a cavity, the ring will only support specific wavelengths of light (where the resonance condition is satisfied) separated by the free spectral range (FSR). The spectrum of an unbalanced MZI is sinusoidal with the difference in optical path length between the two paths determining where in the spectrum the constructive and destructive interference will occur. For both the ring and the MZI, this is known as phase-matching. For the case of the ring this is phase-matching between consecutive round-trips while in the MZI it is phase-matching between the two different paths. The points of constructive interference in the spectra of these devices can be tuned by adjusting the relative phase between the different paths. In a fabricated device this can be accomplished by heaters or electro-optic phase shifters. The combination of these two elements results in a phase-matching condition that relies on both the resonance condition of the ring and the interference pattern of the MZI. If the spectral width between two wavelengths of constructive interference in the MZI is twice the FSR of the ring, it is possible to suppress every second resonance of the ring. A schematic of such a device is shown in Fig. 5(a).
Fig. 5 (a) Schematic and (b) optical microscope image of the fabricated microring source with Mach-Zehnder interferometer couplers. The green lines are the silicon waveguides and the brown are the thermal tuners.
For the case of a photon-pair source, one side of the ring can be used as the input for the pump photons and the drop side as the output for the generated photon-pairs. The MZI (MZI1) on the input side can be tuned to suppress every other resonance, while MZI2 on the output of the ring can be tuned to suppress the resonances allowed by MZI1 (i.e. they are perfectly out of phase with each other). This configuration will ensure the pump laser is critically coupled into the ring while not allowing it to exit out the drop port, and ensures that any photons that are generated at the resonances allowed by the drop port will only exit the over-coupled drop port (because MZI1 is tuned to not be phased matched with those photons). This makes the device function as though it is two independent single bus ring resonators, one for the input side and one for the output side. The input side ring is characterized by the transmission from the input port to the through port while the output side ring is characterized by the transmission from the add port to the drop port. The theoretical spectral response for both the input and output sides are shown in Fig. 6. There is a trade-off between efficiency and purity that must be considered with this design. While the goal of this work is to develop a bright source of photon-pairs even if that means that there are spectral correlations, a modified device design for the generation of pure states is currently being explored [16]. Another consideration is the impact of photon-pair generation within the long arms of the interferometric couplers. Operating in the low pumping rate regime, the low reflectivity of the couplers along with the resonant enhancement of the ring suggest that the generation rate within the long arms of the couplers would be at least an order of magnitude less than the generation rate within the ring. A complete model of this effect is currently being explored.
Fig. 6 Theoretical spectra of a microring resonator (dotted), Mach-Zehnder interferometer (dot-dashed), and a combination of the two (solid) for both (a) input and (b) output sides. The green, blue, and red shaded regions indicate the location of the pump, signal, and idler resonances respectively.
3.2. Dual Mach-Zehnder Microring Experimental Results
An image of a fabricated device and design dimensions are shown in Fig. 5(b) and Table 1 respectively. Coupling losses of ∼ 3 dB per facet (including device loss) were consistently achievable across multiple devices resulting largely from field boundary stitching during fabrication. The free spectral range of the device was found to be ∼ 6 nm at a wavelength of 1.55 µm and quality factors ranged from 15k to 35k depending on the voltage applied to the thermal tuners. Without the use of the thermal tuners, all resonances of interest are supported by both couplers [Figs. 7(a) and 7(b)]. Upon performing a full 3-D sweep of voltages ranging from 0 to 10 V across the three heaters, an optimum heater configuration (Ring Heater = 1 V, MZI1 Heater = 9 V, MZI2 Heater = 7 V) was found that exhibited the desired spectral dependence [Figs. 7(c) and 7(d)].
Table 1. Device Design Dimensions
Fig. 7 Transmission spectra for the (a) input side and (b) output side of the DMZR without any thermal tuning. Transmission spectra for the (c) input side and (d) output side of the DMZR after optimization of the heaters. The green, blue, and red shaded regions indicate the locations of the pump, signal, and idler resonances respectively. In all cases, the power of the pump laser was set to −10 dBm.
A test setup similar to that shown in Fig. 2(c) was used for time correlation measurements. Coincidences were collected for 60 s with a timing resolution of 81 ps. The coincidence plots for the case where the heaters were not tuned are shown in Fig. 8(a). Due to the difference in the coupling gaps between the input side and the output side, the device already had an enhanced coincidence efficiency of ηcoinc = 0.73 but the pump was not critically coupled to the ring [evident by the ∼ 4 dB extinction in Fig. 7(a)]. The coincidence efficiency was further improved in this configuration, resulting in a value of 0.97. Even more notable is the enhancement to the pumping efficiency when compared to the untuned configuration. This is evident from both the ∼ 11 dB extinction of the through port transmission and 3.7 x increase in the drop port coincidence counts [shown in Fig. 7(c) and Fig. 8(b) respectively].
Fig. 8 Measured results from the dual Mach-Zehnder device showing the increase in coincidence counts when the resonances are (a) out of tune and (b) tuned. In both cases, coincidences were counted for a period of 60 s with a pump power of 0 dBm.
4. Conclusion
In conclusion, this research shows that the coincidence efficiency of a silicon ring resonator photon-pair source can be dramatically increased by engineering the coupling of a ring resonator. Two approaches were taken, the first decreased the input coupling to the ring but the pump power had to be correspondingly increased. However, this trade-off can be completely overcome with the addition of Mach-Zehnder legs attached to the resonator allowing for critical coupling of the pump into the resonator, and over coupling of the signal/idler photons through the drop port. This design has three key advantages: (i) The pump is critically coupled, so the photon generation rate will be maximized; (ii) The pump is filtered from the photons that exit the drop port, minimizing noise and reducing the amount of required off-chip filtering; (iii) The generated photon pairs will, with high probability, couple out of the same port. These advantages are evident in the measured coincidence efficiency of 0.97 from a device with a nearly critically coupled pump. The heralding efficiency is a very important characteristic of a photon-pair source, especially when studying the quantum mechanical properties of the photons. This is an essential and necessary step toward high performance and scalable quantum computers and communication systems.
Funding
National Science Foundation (NSF) (ECCS-14052481);
Air Force Research Laboratory (AFRL) (FA8750-16-2-0140);
Air Force Ofice of Scientific Research (AFOSR) (FA9550-16-1-0419)
Acknowledgments
This work was performed in part at the Cornell NanoScale Facility, a member of the National Nanotechnology Coordinated Infrastructure (NNCI), which is supported by the National Science Foundation (Grant ECCS-1542081). We acknowledge support for this work from the Air Force Research Lab (AFRL) under Award No. FA8750-16-2-0140. This material is based upon work supported by the Air Force Office of Scientific Research under award number FA9550-16-1-0419. This material is based upon work partially supported by the National Science Foundation under Award No. ECCS-14052481. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the United States Air Force, AFRL, or the National Science Foundation.
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