This work was performed in part at the Cornell University NanoScale Science and Technology Facility, a member of the National Nanotechnology Infrastructure Network, which is supported by the National Science Foundation (Grant ECCS-1542081). We acknowledge support for this work from the Air Force Research Lab (AFRL). This material is based upon work partially supported by the National Science Foundation under Award No. ECCS14052481.

NOTE: This protocol assumes that the photonic chip has already been fabricated. The chip described here (shown in Figure 1A) was fabricated at the Cornell University NanoScale Science &#38; Technology Facility using standard processing techniques for silicon photonic devices11. These include the use of silicon-on-insulator wafers (composed of a 220 nm-thick silicon layer, a 3-&#181;m layer of silicon dioxide, and a 525 &#181;m-thick silicon substrate), electron-beam lithography to define the strip waveguides (500 nm-wide), and the plasma-enhanced chemical vapor deposition of the silicon dioxide cladding (~3 &#181;m-thick). The micro-ring resonators were designed with an inner radius of 18.5 &#181;m and a waveguide-to-ring gap of 150 nm. Figures of merit for this device include loss, quality factor, free spectral range, and dispersion.
1. Photonic Chip Preparation
<ol>
	<li>Place a small amount of wax on a cross-sectioning polishing mount and heat it to ~130 &#176;C. 
	NOTE: The amount of wax to be used depends upon the size of the sample being mounted. There must be enough wax to keep the chip immobile, while too much will result in wax on the chip facets.</li>
	<li>Place the photonic chip on the portion of the polishing mount with the wax. Ensure that the wax is melted completely so that the chip is flat against the mount. Use plastic tweezers when handling the chip to avoid damaging the facets.</li>
	<li>Allow the mount to cool in ambient air so that the wax solidifies. Cooling faster than this may result in damage to the chip.</li>
	<li>Polishing the chip facets. 
	NOTE: It is important to choose the correct lapping pad as starting with a pad that is too aggressive can result in polishing away more of the chip than desired.
	<ol>
		<li>Attach the polishing mount to the polisher and polish for only a few seconds. A pad with a 3-&#181;m roughness has shown to be a good starting point for silicon chips with facet lengths of ~1 cm.</li>
		<li>Remove the polishing mount and inspect the chip facet to determine how level the chip is mounted. 
		NOTE: A microscope is useful for measuring the distance between the ends of the waveguides and the facet of the chip. These measurements allow for the angle between the facet and the waveguide to be determined.</li>
		<li>Make the necessary adjustments to the micrometers on the polisher in order to improve the leveling of the chip.</li>
		<li>Repeat steps 1.4.1-1.4.3 until the facet of the chip and the waveguides are within 0.15&#176; of being orthogonal to each other.</li>
		<li>Polish the chip in steps of ~50 &#181;m, inspecting the chip between each step to monitor the distance remaining, until there is ~100 &#181;m left to polish. If at any point the cladding appears to be delaminating from the surface, ensure that the pad is rotating so as to polish from the top of the chip to the bottom. 
		NOTE: It may also help to use a polishing lubricant instead of water. This delamination is a result of stress in the cladding and is an indication that the fabrication process needs to be optimized.</li>
		<li>Change to a 1-&#181;m lapping pad and polish until there is ~20 &#181;m remaining.</li>
		<li>Change to a 0.5-&#181;m pad and continue polishing for another 15 &#181;m.</li>
		<li>Use a 0.1-&#181;m pad for the final 5 &#181;m to ensure a smooth facet. Microscope images of the facet of a silicon photonic chip before and after polishing are shown in Figure 2.</li>
	</ol>
	</li>
	<li>Heat the mount with the attached chip to ~130 &#176;C to allow the wax to melt.</li>
	<li>Once the wax is completely melted, remove the chip from the mount and allow it to cool slowly.</li>
	<li>Clean any of the remaining wax from the chip using acetone, isopropanol, and water.</li>
</ol>
2. Preparation of Fiber Pigtails
<ol>
	<li>Strip any buffer or coating from the end of a single mode fiber (SMF) pigtail and from one end of an ultra-high numerical aperture (UHNA) fiber.</li>
	<li>Clean the bare ends of the fibers with a mixture of acetone and methanol.</li>
	<li>Cleave the bare ends of both fibers with a commercial fiber cleaver.</li>
	<li>Fusion splice the cleaved end of the fibers. A recipe for splicing SMF to UHNA fiber is shown in Table 1.</li>
	<li>Slide a protective sleeve over the splice and place it in the sleeve oven to permanently attach it to the fiber.</li>
	<li>Repeat steps 2.1-2.5 to prepare a total of three fibers.</li>
</ol>
3. Configuration of the Testing Setup
NOTE: A diagram of the testing setup is shown in Figure 1B. The mount for the chip is a copper pedestal that is in contact with a thermo-electric cooler (TEC). There is a microscope fitted with both visible and infrared (IR) cameras for viewing the photonic chip.
<ol>
	<li>Place a small amount of wax on the chip mount and apply voltage to the TEC to melt the wax.</li>
	<li>Place the chip on the melted wax, ensuring that it is sitting flat on the mount.</li>
	<li>Remove the voltage from the TEC and allow the mount and chip to cool slowly.</li>
	<li>Attach each of the spliced fibers to a fiber v-groove with polyimide tape and mount a single v-groove to each of the 3-axis stages using the manufacturer-supplied mounting hardware.</li>
	<li>Fiber edge coupling.
	<ol>
		<li>Connect the three fibers to their respective components: one to the optical output of the laser and the other two to optical power meters.</li>
		<li>Adjust the microscope so that it is focused on the chip where the waveguides reach the edge.</li>
		<li>Position the fibers close to the chip edge so that they are in the view of the visible camera and adjust their heights so that the core of each fiber is in focus.</li>
		<li>Adjust the horizontal positioning of the fibers with the stage micrometers so that they are lined up with the waveguides.</li>
		<li>Turn on the optical output of the laser and tune the horizontal and vertical micrometer positions of the input fiber until the light is coupling into the waveguide. This will show up on the IR camera as scattering along the input waveguide.</li>
		<li>Tune the wavelength of the laser to a point where the micro-ring resonator is lit up on the camera. This indicates that the resonance condition is being satisfied and that the light is reaching the output waveguides.</li>
		<li>Adjust the horizontal and vertical micrometer positions of the output fibers until there is a measurable amount of light extending from the waveguides to the power meters.</li>
		<li>Maximize the power to both detectors by manipulating the horizontal and vertical micrometer positions of the three fibers.</li>
		<li>Further maximize the power to the detectors by making fine adjustments to the horizontal and vertical fiber positions using the piezo controllers.</li>
		<li>Use the piezo controllers to move the fibers slightly closer to the chip. Make sure not to use the micrometers to push the fibers onto the chip, as doing so will likely damage the cleaved ends of the fibers.</li>
		<li>Repeat steps 3.5.9 and 3.5.10 until the fibers are firmly pressed against the sides of the chip. 
		NOTE: Excessive scattered light from the waveguides, coupled with poor waveguide transmission, can be an indication of waveguide defects. These can include, but are not limited to, material defect sites, stitching boundaries, and excessive waveguide roughness.</li>
	</ol>
	</li>
	<li>Place a fiber-based polarization controller between the laser and the chip. This allows for control of the polarization state that makes it to the chip. The waveguides, being wider than they are tall, aid in minimizing any on-chip polarization rotation.</li>
	<li>Dispersion characterization.
	<ol>
		<li>Tune the polarization of the laser output to maximize the coupling to the chip. This device was designed for transverse-electric (TE) polarization and, as such, the transverse-magnetic (TM) polarization has a much higher loss.</li>
		<li>Scan a tunable laser over the wavelength range of interest (1,510 nm to 1,600 nm in this case) and monitor the power meters. Any artifacts in the transmission spectra are likely due to a combination of the TM component of the polarization and etalon effects from the fiber-chip interface.</li>
		<li>Locate the resonant wavelengths in the spectrum and also extract the bandwidth of each resonance. This particular chip had bandwidths as small as 65 pm, which translates to quality factors (Q) of up to 23,000.</li>
		<li>Determine the free spectral range (FSR), the separation between resonances, for each adjacent pair of resonances. This particular device had an FSR of ~5 nm.</li>
		<li>Calculate the group index (ng) of the guided mode for each value of the FSR using the following equation: 
		<img alt="Equation 5" src="/files/ftp_upload/55257/55257eq5.jpg" /> 
		where &#955; is the wavelength and r is the radius of the micro-ring resonator. The above equation is a first-order approximation of the group index.</li>
		<li>Use the bandwidth of each resonance to determine a width (&#916;ng) associated with each value of the group index.</li>
		<li>Choose the wavelengths for the two pump lasers such that they coincide with resonances in the spectrum and have an odd number of resonances between them (Figure 1C).</li>
		<li>Determine the wavelength of the degenerate bi-photons using the following equation: 
		<img alt="Equation 6" src="/files/ftp_upload/55257/55257eq6.jpg" /> 
		where &#955;Pump 1 and &#955;Pump 2 are the wavelengths of the pump photons.</li>
		<li>Add a horizontal line on the plot of group index versus wavelength that extends between the two pump wavelengths (Figure 3). If it is possible for the line to sit within ng &#177; &#916;ng at all three wavelengths of interest simultaneously, the phase-matching condition is satisfied and photons can be generated via SFWM. If it is not possible, try choosing pump wavelengths that are closer together and check again.</li>
	</ol>
	</li>
	<li>Add a second tunable laser source and polarization controller to the setup and combine the optical outputs from both lasers with a 1 x 2 fiber combiner.</li>
	<li>Add a series of fiber-based notch filters (enough of them achieve ~120 dB of attenuation) immediately before the chip. 
	NOTE: The filters allow both pump wavelengths to pass but reject the bi-photon wavelength. They help to remove excess noise (i.e., broadband Raman scattering in the optical fiber) before coupling to the chip. The filter spectrum is shown in Figure 1B.</li>
	<li>Add a series of fiber-based bandpass filters (enough of them to achieve ~150 dB of attenuation) immediately after the chip. 
	NOTE: The filters should be wide enough to allow the bi-photons to pass but narrow enough to reject the pump photons. Two sets of these are needed, one set for each output. The filter spectrum is shown in Figure 1B.</li>
	<li>Send the rejected photons from each set of filters to separate power meters. 
	NOTE: These power meters are used to monitor the optical coupling to the chip and can also be used to determine if the pump lasers are remaining on-resonance.</li>
	<li>Connect the individual optical output from each set of fiber-based filters to a single photon detector (SPD) and connect both electrical signal outputs from the SPDs to a coincidence correlator.</li>
	<li>Cross a pair of tungsten probes and set the tips down on one of the spiral legs (~1 mm in length) of the MZI.</li>
	<li>Connect a power supply to the two crossed probes such that they generate heat when voltage is applied. This will act as the phase-shifter for the MZI. 
	NOTE: See the discussion for a description of the more standardized method for the thermal tuning of photonic devices.</li>
</ol>
4. Measuring Two-photon Interference
<ol>
	<li>Tune both of the pump lasers to the chosen wavelengths. Use the power meters that are monitoring the rejected pump photons to ensure that both lasers are tuned to the resonances. When the lasers are properly tuned to the desired resonances, the rejected signal from the filters will be maximized.</li>
	<li>Set the optical power output from each laser to -3 dBm. 
	NOTE: This will result in &#60;100 &#181;W at the chip. It is important to keep the pump power this low in order to minimize loss (from multi-photon absorption and free-carrier absorption) and maintain stability (by minimizing light-induced thermal shifts). PN junctions can be used to remove carriers from the waveguide to better accommodate higher pump powers.</li>
	<li>Monitor the coincidence counts (synchronous singles across two ports) by integrating over ~220 ps about the peak of the data. A sufficient integration time has passed when a minimum of 100 coincidence counts have been collected. 
	Note: The integration window should be wide enough to account for the timing jitter of the SPDs.</li>
	<li>Set the power supply for the phase-shifter to the initial voltage (e.g., 0 V).</li>
	<li>Scan one of the tunable lasers over the entire wavelength range and use the power meters that are collecting the rejected pump photons to confirm the location of the resonances of interest. Set the pump lasers to the wavelengths corresponding to the desired resonances. 
	Note: It is important to complete this step every time the phase shifter voltage is changed as the thermal tuning can result in small shifts in the resonant wavelengths.</li>
	<li>Collect the resulting data (single-photon counts as well as the coincidence counts) from the coincidence correlator for the previously chosen integration time. Here, an integration time of 90 s was chosen with a timing resolution of 32 ps.</li>
	<li>Increase the voltage applied to the phase-shifter by 5 mV.</li>
	<li>Repeat steps 4.4-4.6 until data has been collected for the desired range of voltages. 
	NOTE: The maximum voltage was limited to 2.4 V due to rapid degradation of the probes above this voltage.</li>
	<li>Integrate the coincidence peaks for each power-supply voltage over ~220 ps to determine the total number of coincidences (Figure 4).</li>
	<li>Integrate over 320 ns away from the coincidence peak to obtain the accidental coincidences. Use this result to calculate the number of accidentals in the coincidence peak.</li>
	<li>Fit the singles counts from each detector with the following modified sine function: 
	<img alt="Equation 7" src="/files/ftp_upload/55257/55257eq7.jpg" /> 
	where A, B, C, D, E, and F are the fit parameters. This fit is necessary due to the nonlinear relationship between the voltage and the induced thermal shift (relative phase).</li>
	<li>Convert the independent variable to relative phase for all three sets of data (the singles counts from each detector and the coincidence counts) with the following equation: 
	<img alt="Equation 8" src="/files/ftp_upload/55257/55257eq8.jpg" /> 
	where B, C, D, and E are the fit parameters from step 4.11. This conversion is possible due to the well-known sinusoidal transfer function of an MZI12.</li>
	<li>Fit the coincidence data (with the relative phase as the independent variable) with the following sine function: 
	<img alt="Equation 9" src="/files/ftp_upload/55257/55257eq9.jpg" /> 
	where A and B are the fit parameters.</li>
	<li>Calculate the visibility of each interference pattern with the following equation: 
	<img alt="Equation 10" src="/files/ftp_upload/55257/55257eq10.jpg" /> 
	where &#402;(&#952;)max and &#402;(&#952;)min are the maximum and minimum values of &#402;(&#952;), respectively. A visibility of 1 corresponds to a perfect interference pattern.</li>
</ol>

<ol>
	<li>Silverstone, J. W., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=On-chip+quantum+interference+between+silicon+photon-pair+sources.">On-chip quantum interference between silicon photon-pair sources.</a> Nat. Photon. 8 (2), 104-108 (2014).</li><li>Harris, N. C., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Integrated+Source+of+Spectrally+Filtered+Correlated+Photons+for+Large-Scale+Quantum+Photonic+Systems.">Integrated Source of Spectrally Filtered Correlated Photons for Large-Scale Quantum Photonic Systems.</a> Phys. Rev. X. 041047, 1-10 (2014).</li><li>Grassani, D., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Micrometer-scale+integrated+silicon+source+of+time-energy+entangled+photons.">Micrometer-scale integrated silicon source of time-energy entangled photons.</a> Optica. 2 (2), 88 (2015).</li><li>Najafi, F., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Scalable+Integration+of+Single-Photon+Detectors.">Scalable Integration of Single-Photon Detectors.</a> Nat. Commun. 6, 1-8 (2015).</li><li>Dutt, A., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=On-Chip+Optical+Squeezing.">On-Chip Optical Squeezing.</a> Phys. Rev. Appl. 3 (4), 1-7 (2015).</li><li>Azzini, S., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Ultra-low+power+generation+of+twin+photons+in+a+compact+silicon+ring+resonator.">Ultra-low power generation of twin photons in a compact silicon ring resonator.</a> Opt. Express. 20 (21), 23100-23107 (2012).</li><li>Clemmen, S., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Continuous+wave+photon+pair+generation+in+silicon-on-insulator+waveguides+and+ring+resonators+erratum.">Continuous wave photon pair generation in silicon-on-insulator waveguides and ring resonators erratum.</a> Opt. Express. 17 (19), 16558 (2009).</li><li>Engin, E., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Photon+pair+generation+in+a+silicon+micro-ring+resonator+with+reverse+bias+enhancement.">Photon pair generation in a silicon micro-ring resonator with reverse bias enhancement.</a> Opt. Express. 21 (23), 27826-27834 (2013).</li><li>Steidle, J. a., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=High+spectral+purity+silicon+ring+resonator+photon-pair+source.">High spectral purity silicon ring resonator photon-pair source.</a> Proc. of SPIE. 9500, 950015 (2015).</li><li>Preble, S. F., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=On-Chip+Quantum+Interference+from+a+Single+Silicon+Ring-Resonator+Source.">On-Chip Quantum Interference from a Single Silicon Ring-Resonator Source.</a> Phys. Rev. Appl. 4, 021001 (2015).</li><li>Cao, L., Aboketaf, A. A., Preble, S. F. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=CMOS+compatible+micro-oven+heater+for+efficient+thermal+control+of+silicon+photonic+devices.">CMOS compatible micro-oven heater for efficient thermal control of silicon photonic devices.</a> Opt. Commun. 305, 66-70 (2013).</li><li>Chrostowski, L., Hochberg, M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> Silicon Photonics Design. , (2013).</li></ol>

We have nothing to disclose.

There are multiple challenges for the field of integrated photonics to overcome in order for complex and scalable systems of photonic devices to be feasible. These include, but are not limited to: tight fabrication tolerances, isolation from environmental instabilities, and minimization of all forms of loss. There are critical steps in the above protocol that help to minimize the loss of photonic devices.
One of the most crucial requirements in minimizing loss is closely matching the optical m...

Silicon is showing great promise as a photonics platform for quantum information processing1,2,3,4,5. One of the vital components of quantum photonic circuits is the photon source. Photon-pair sources have been developed from silicon in the form of micro-ring resonators made via a third-order nonlinear process, spontaneous four-wave mixing (SFWM)6,7,8. These sources are capable of producing pairs of indistinguishable photons, which are ideal for experiments involving photon entanglement9.
It is important to note that ring resonator sources can operate with both clockwise and counter-clockwise propagation, and the two different propagation directions are generally independent from one another. This allows a single ring to function as two sources. When optically pumped from both directions, these sources generate the following entangled state:
<img alt="Equation 1" src="/files/ftp_upload/55257/55257eq1.jpg" />
where <img alt="Equation 2" src="/files/ftp_upload/55257/55257eq2.jpg" /> and <img alt="Equation 3" src="/files/ftp_upload/55257/55257eq3.jpg" /> are the independent creation operators for clockwise- and counterclockwise-propagating bi-photons, respectively. This is a very desirable form of entangled state known as a N00N state (N=2)10.
Passing this state through an on-chip Mach-Zehnder interferometer (MZI) results in the state:
<img alt="Equation 4" src="/files/ftp_upload/55257/55257eq4.jpg" />
This state oscillates between maximum coincidence and zero coincidence at twice the frequency of classical interference in an MZI, effectively doubling the sensitivity of the interferometer10. Here, we present the procedure used to test such an integrated photon source and MZI device.

<table><tbody><tr><td>3-Axis NanoMax Flexure Stage</td><td>Thorlabs</td><td>MAX312D</td><td>Precision 3-axis stages</td></tr><tr><td>Three-Hole Fiber Stripping Tool</td><td>Thorlabs</td><td>FTS4</td><td>buffer stripping tool</td></tr><tr><td>Three Channel Piezo Controller</td><td>Thorlabs</td><td>MDT693B</td><td>Piezo controllers for NanoMax stages</td></tr><tr><td>Fiber Polarization Controller</td><td>Thorlabs</td><td>FPC562</td><td>3-Paddle fiber-based polarization controller</td></tr><tr><td>Fiber Cleaver</td><td>Thorlabs</td><td>XL411</td><td>Fiber cleaver</td></tr><tr><td>Standard V-Groove Fiber Holder</td><td>Thorlabs</td><td>HFV001</td><td>standard v-groove mount</td></tr><tr><td>Tapered V-Groove Fiber Holder</td><td>Thorlabs</td><td>HFV002</td><td>tapered v-groove mount</td></tr><tr><td>Right-Angle Top Plate for NanoMax Stage</td><td>Thorlabs</td><td>AMA011</td><td>right-angle bracket</td></tr><tr><td>50:50 Fiber Optic Coupler</td><td>Thorlabs</td><td>TW1550R5F1</td><td>50/50 combiner</td></tr><tr><td>Optical Fiber Fusion Splicer</td><td>Fujikura</td><td>FSM-40S</td><td>Fusion splicer</td></tr><tr><td>MultiPrep Polishing System - 8&quot;</td><td>Allied High Tech</td><td>15-2100</td><td>Chip polisher</td></tr><tr><td>GreenLube</td><td>Allied High Tech</td><td>90-209010</td><td>Polishing Lubricant</td></tr><tr><td>Cross-Sectioning Paddle with Reference Edge</td><td>Allied High Tech</td><td>15-1010-RE</td><td>Polishing mount</td></tr><tr><td>Lightwave Measurement System</td><td>Keysight</td><td>8164B</td><td>Mainframe for tunable laser</td></tr><tr><td>Tunable Laser Source</td><td>Keysight</td><td>81606A</td><td>Tunable laser</td></tr><tr><td>Optical Power Sensor</td><td>Keysight</td><td>81634B</td><td>Power meter</td></tr><tr><td>NIR Single Photon Detector</td><td>ID Quantique</td><td>ID210</td><td>Single photon detectors</td></tr><tr><td>NIR Single Photon Detector</td><td>ID Quantique</td><td>ID230</td><td>Low noise, free-running single photon detectors</td></tr><tr><td>PicoHarp</td><td>PicoQuant</td><td>PicoHarp 300</td><td>Time-correlated single photon counting</td></tr><tr><td>WiDy SWIR InGaAs Camera</td><td>NIT</td><td>640U-S</td><td>IR Camera</td></tr><tr><td>WDM Bandpass Filter</td><td>JDS Uniphase</td><td>30055053-368-2.2</td><td>pump cleanup filters</td></tr><tr><td>WDM Bandpass Filter</td><td>JDS Uniphase</td><td>1011787-012</td><td>pump rejection filters</td></tr><tr><td>Ultra-High Numerical Aperture Fiber</td><td>Nufern</td><td>UHNA-7</td><td>high index fiber</td></tr><tr><td>Ultra Optical Single Mode Fiber</td><td>Corning</td><td>SMF-28</td><td>standard single mode fiber</td></tr></tbody></table>

measurement of quantum interference in a silicon ring resonator photon source

Silicon photonic chips have the potential to realize complex integrated quantum information processing circuits, including photon sources, qubit manipulation, and integrated single-photon detectors. Here, we present the key aspects of preparing and testing a silicon photonic quantum chip with an integrated photon source and two-photon interferometer. The most important aspect of an integrated quantum circuit is minimizing loss so that all of the generated photons are detected with the highest possible fidelity. Here, we describe how to perform low-loss edge coupling by using an ultra-high numerical aperture fiber to closely match the mode of the silicon waveguides. By using an optimized fusion splicing recipe, the UHNA fiber is seamlessly interfaced with a standard single-mode fiber. This low-loss coupling allows the measurement of high-fidelity photon production in an integrated silicon ring resonator and the subsequent two-photon interference of the produced photons in a closely integrated Mach-Zehnder interferometer. This paper describes the essential procedures for the preparation and characterization of high-performance and scalable silicon quantum photonic circuits.

Individual photon counts from each detector, as well as the coincidence counts, were collected as the relative phase between the two paths was tuned. The individual counts (Figure 5A) show the classical interference pattern from an MZI with visibilities of 94.5 &#177; 1.6% and 94.9 &#177; 0.9%. The coincidence measurements (Figure 5B) show the quantum interference of the entangled state, as is evident by the oscillation at twice the frequency of the class...

Watch this Scientific Journal Video about Measurement of Quantum Interference in a Silicon Ring Resonator Photon Source at JoVE.com

Measurement of Quantum Interference in a Silicon Ring Resonator Photon Source

Silicon photonic chips have the potential to realize complex integrated quantum systems. Presented here is a method for preparing and testing a silicon photonic chip for quantum measurements.

Silicon photonic chips have the potential to realize complex integrated quantum information processing circuits, including photon sources, qubit ...

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8.3K Views.  Rochester Institute of Technology. Silicon photonic chips have the potential to realize complex integrated quantum systems. Presented here is a method for preparing and testing a silicon photonic chip for quantum measurements.

Video: Measurement of Quantum Interference in a Silicon Ring Resonator Photon Source

Fabrication of Silica Ultra High Quality Factor Microresonators

Whispering gallery resonant cavities confine light in circular orbits at their periphery.1-2 The photon storage lifetime in the cavity, quantified by the quality factor (Q) of the cavity, can be in excess of 500ns for cavities with Q factors above 100 million. As a result of their low material losses, silica microcavities have demonstrated some of the longest photon lifetimes to date1-2. Since a portion of the circulating light extends outside the resonator, these devices can also be used to probe the surroundings. This interaction has enabled numerous experiments in biology, such as single molecule biodetection and antibody-antigen kinetics, as well as discoveries in other fields, such as development of ultra-low-threshold microlasers, characterization of thin films, and cavity quantum electrodynamics studies.3-7
The two primary silica resonant cavity geometries are the microsphere and the microtoroid. Both devices rely on a carbon dioxide laser reflow step to achieve their ultra-high-Q factors (Q&gt;100 million).1-2,8-9 However, there are several notable differences between the two structures. Silica microspheres are free-standing, supported by a single optical fiber, whereas silica microtoroids can be fabricated on a silicon wafer in large arrays using a combination of lithography and etching steps. These differences influence which device is optimal for a given experiment.
Here, we present detailed fabrication protocols for both types of resonant cavities. While the fabrication of microsphere resonant cavities is fairly straightforward, the fabrication of microtoroid resonant cavities requires additional specialized equipment and facilities (cleanroom). Therefore, this additional requirement may also influence which device is selected for a given experiment.
Introduction
An optical resonator efficiently confines light at specific wavelengths, known as the resonant wavelengths of the device. 1-2 The common figure of merit for these optical resonators is the quality factor or Q. This term describes the photon lifetime (&tau;o) within the resonator, which is directly related to the resonator's optical losses. Therefore, an optical resonator with a high Q factor has low optical losses, long photon lifetimes, and very low photon decay rates (1/&tau;o). As a result of the long photon lifetimes, it is possible to build-up extremely large circulating optical field intensities in these devices. This very unique property has allowed these devices to be used as laser sources and integrated biosensors.10
A unique sub-class of resonators is the whispering gallery mode optical microcavity. In these devices, the light is confined in circular orbits at the periphery. Therefore, the field is not completely confined within the device, but evanesces into the environment. Whispering gallery mode optical cavities have demonstrated some of the highest quality factors of any optical resonant cavity to date.9,11 Therefore, these devices are used throughout science and engineering, including in fundamental physics studies and in telecommunications as well as in biodetection experiments. 3-7,12
Optical microcavities can be fabricated from a wide range of materials and in a wide variety of geometries. A few examples include silica and silicon microtoroids, silicon, silicon nitride, and silica microdisks, micropillars, and silica and polymer microrings.13-17 The range in quality factor (Q) varies as dramatically as the geometry. Although both geometry and high Q are important considerations in any field, in many applications, there is far greater leverage in boosting device performance through Q enhancement. Among the numerous options detailed previously, the silica microsphere and the silica microtoroid resonator have achieved some of the highest Q factors to date.1,9 Additionally, as a result of the extremely low optical loss of silica from the visible through the near-IR, both microspheres and microtoroids are able to maintain their Q factors over a wide range of testing wavelengths.18 Finally, because silica is inherently biocompatible, it is routinely used in biodetection experiments.
In addition to high material absorption, there are several other potential loss mechanisms, including surface roughness, radiation loss, and contamination loss.2 Through an optimization of the device size, it is possible to eliminate radiation losses, which arise from poor optical field confinement within the device. Similarly, by storing a device in an appropriately clean environment, contamination of the surface can be minimized. Therefore, in addition to material loss, surface scattering is the primary loss mechanism of concern.2,8
In silica devices, surface scattering is minimized by using a laser reflow technique, which melts the silica through surface tension induced reflow. While spherical optical resonators have been studied for many years, it is only with recent advances in fabrication technologies that researchers been able to fabricate high quality silica optical toroidal microresonators (Q&gt;100 million) on a silicon substrate, thus paving the way for integration with microfluidics.1
The present series of protocols details how to fabricate both silica microsphere and microtoroid resonant cavities. While silica microsphere resonant cavities are well-established, microtoroid resonant cavities were only recently invented.1 As many of the fundamental methods used to fabricate the microsphere are also used in the more complex microtoroid fabrication procedure, by including both in a single protocol it will enable researchers to more easily trouble-shoot their experiments.

We describe the use of a carbon dioxide laser reflow technique to fabricate silica resonant cavities, including free-standing microspheres and on-chip microtoroids. The reflow method removes surface imperfections, allowing long photon lifetimes within both devices. The resulting devices have ultra high quality factors, enabling applications ranging from telecommunications to biodetection.

Whispering gallery resonant cavities confine light in circular orbits at their periphery.1-2 The photon storage lifetime in the cavity, quantified by the ...

Fabrication And Characterization Of Photonic Crystal Slow Light Waveguides And Cavities

Slow light has been one of the hot topics in the photonics community in the past decade, generating great interest both from a fundamental point of view and for its considerable potential for practical applications. Slow light photonic crystal waveguides, in particular, have played a major part and have been successfully employed for delaying optical signals1-4 and the enhancement of both linear5-7 and nonlinear devices.8-11
Photonic crystal cavities achieve similar effects to that of slow light waveguides, but over a reduced band-width. These cavities offer high Q-factor/volume ratio, for the realization of optically12 and electrically13 pumped ultra-low threshold lasers and the enhancement of nonlinear effects.14-16 Furthermore, passive filters17 and modulators18-19 have been demonstrated, exhibiting ultra-narrow line-width, high free-spectral range and record values of low energy consumption.
To attain these exciting results, a robust repeatable fabrication protocol must be developed. In this paper we take an in-depth look at our fabrication protocol which employs electron-beam lithography for the definition of photonic crystal patterns and uses wet and dry etching techniques. Our optimised fabrication recipe results in photonic crystals that do not suffer from vertical asymmetry and exhibit very good edge-wall roughness. We discuss the results of varying the etching parameters and the detrimental effects that they can have on a device, leading to a diagnostic route that can be taken to identify and eliminate similar issues.
The key to evaluating slow light waveguides is the passive characterization of transmission and group index spectra. Various methods have been reported, most notably resolving the Fabry-Perot fringes of the transmission spectrum20-21 and interferometric techniques.22-25 Here, we describe a direct, broadband measurement technique combining spectral interferometry with Fourier transform analysis.26 Our method stands out for its simplicity and power, as we can characterise a bare photonic crystal with access waveguides, without need for on-chip interference components, and the setup only consists of a Mach-Zehnder interferometer, with no need for moving parts and delay scans.
When characterising photonic crystal cavities, techniques involving internal sources21 or external waveguides directly coupled to the cavity27 impact on the performance of the cavity itself, thereby distorting the measurement. Here, we describe a novel and non-intrusive technique that makes use of a cross-polarised probe beam and is known as resonant scattering (RS), where the probe is coupled out-of plane into the cavity through an objective. The technique was first demonstrated by McCutcheon et al.28 and further developed by Galli et al.29

Use of photonic crystal slow light waveguides and cavities has been widely adopted by the photonics community in many differing applications. Therefore fabrication and characterization of these devices are of great interest. This paper outlines our fabrication technique and two optical characterization methods, namely: interferometric (waveguides) and resonant scattering (cavities).

Slow light has been one of the hot topics in the photonics community in the past decade, generating great interest both from a fundamental point of view ...

Microwave Photonics Systems Based on Whispering-gallery-mode Resonators

Microwave photonics systems rely fundamentally on the interaction between microwave and optical signals. These systems are extremely promising for various areas of technology and applied science, such as aerospace and communication engineering, sensing, metrology, nonlinear photonics, and quantum optics. In this article, we present the principal techniques used in our lab to build microwave photonics systems based on ultra-high Q whispering gallery mode resonators. First detailed in this article is the protocol for resonator polishing, which is based on a grind-and-polish technique close to the ones used to polish optical components such as lenses or telescope mirrors. Then, a white light interferometric profilometer measures surface roughness, which is a key parameter to characterize the quality of the polishing. In order to launch light in the resonator, a tapered silica fiber with diameter in the micrometer range is used. To reach such small diameters, we adopt the "flame-brushing" technique, using simultaneously computer-controlled motors to pull the fiber apart, and a blowtorch to heat the fiber area to be tapered. The resonator and the tapered fiber are later approached to one another to visualize the resonance signal of the whispering gallery modes using a wavelength-scanning laser. By increasing the optical power in the resonator, nonlinear phenomena are triggered until the formation of a Kerr optical frequency comb is observed with a spectrum made of equidistant spectral lines. These Kerr comb spectra have exceptional characteristics that are suitable for several applications in science and technology. We consider the application related to ultra-stable microwave frequency synthesis and demonstrate the generation of a Kerr comb with GHz intermodal frequency.

The customized techniques developed in our lab to build microwave photonics systems based on ultra-high Q whispering gallery mode resonators are presented. The protocols to obtain and characterize these resonators are detailed, and an explanation of some of their applications in microwave photonics is given.

Microwave photonics systems rely fundamentally on the interaction between microwave and optical signals. These systems are extremely promising for various ...

Implementation of a Reference Interferometer for Nanodetection

A thermally and mechanically stabilized fiber interferometer suited for examining ultra-high quality factor microcavities is fashioned. After assessing its free spectral range (FSR), the module is put in parallel with a fiber taper-microcavity system and then calibrated through isolating and eliminating random shifts in the laser frequency (i.e. laser jitter noise). To realize the taper-microcavity junction and to maximize the optical power that is transferred to the resonator, a single-mode optical fiber waveguide is pulled. Solutions containing polystyrene nanobeads are then prepared and flown to the microcavity in order to demonstrate the system&#8217;s ability to sense binding to the surface of the microcavity. Data is post-processed via adaptive curve fitting, which allows for high-resolution measurements of the quality factor as well as the plotting of time-dependent parameters, such as resonant wavelength and split frequency shifts. By carefully inspecting steps in the time-domain response and shifting in the frequency-domain response, this instrument can quantify discrete binding events.

A reference interferometer technique, which is designed to remove undesirable laser jitter noise for nanodetection, is utilized for probing an ultra-high quality factor microcavity. Instructions for assembly, setup, and data acquisition are provided, alongside the measurement process for specifying the cavity quality factor.

A thermally and mechanically stabilized fiber interferometer suited for examining ultra-high quality factor microcavities is fashioned. After assessing ...

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Engineering non-classical states of the electromagnetic field is a central quest for quantum optics1,2. Beyond their fundamental significance, such states are indeed the resources for implementing various protocols, ranging from enhanced metrology to quantum communication and computing. A variety of devices can be used to generate non-classical states, such as single emitters, light-matter interfaces or non-linear systems3. We focus here on the use of a continuous-wave optical parametric oscillator3,4. This system is based on a non-linear &#967;2 crystal inserted inside an optical cavity and it is now well-known as a very efficient source of non-classical light, such as single-mode or two-mode squeezed vacuum depending on the crystal phase matching. 
Squeezed vacuum is a Gaussian state as its quadrature distributions follow a Gaussian statistics. However, it has been shown that number of protocols require non-Gaussian states5. Generating directly such states is a difficult task and would require strong &#967;3 non-linearities. Another procedure, probabilistic but heralded, consists in using a measurement-induced non-linearity via a conditional preparation technique operated on Gaussian states. Here, we detail this generation protocol for two non-Gaussian states, the single-photon state and a superposition of coherent states, using two differently phase-matched parametric oscillators as primary resources. This technique enables achievement of a high fidelity with the targeted state and generation of the state in a well-controlled spatiotemporal mode.

We describe the reliable generation of non-Gaussian states of traveling optical fields, including single-photon states and coherent state superpositions, using a conditional preparation method operated on the non-classical light emitted by optical parametric oscillators. Type-I and type-II phase-matched oscillators are considered and common procedures, such as the required frequency filtering or the high-efficiency quantum state characterization by homodyning, are detailed.

Engineering non-classical states of the electromagnetic field is a central quest for quantum optics1,2. Beyond their fundamental significance, such states ...

Fabrication and Testing of Microfluidic Optomechanical Oscillators

Cavity optomechanics experiments that parametrically couple the phonon modes and photon modes have been investigated in various optical systems including microresonators. However, because of the increased acoustic radiative losses during direct liquid immersion of optomechanical devices, almost all published optomechanical experiments have been performed in solid phase. This paper discusses a recently introduced hollow microfluidic optomechanical resonator. Detailed methodology is provided to fabricate these ultra-high-Q microfluidic resonators, perform optomechanical testing, and measure radiation pressure-driven breathing mode and SBS-driven whispering gallery mode parametric vibrations. By confining liquids inside the capillary resonator, high mechanical- and optical- quality factors are simultaneously maintained.

Parametric optomechanical excitations have recently been experimentally demonstrated in microfluidic optomechanical resonators by means of optical radiation pressure and stimulated Brillouin scattering. This paper describes the fabrication of these microfluidic resonators along with methodologies for generating and verifying optomechanical oscillations.

Cavity optomechanics experiments that parametrically couple the phonon modes and photon modes have been investigated in various optical systems including ...

Silicon Metal-oxide-semiconductor Quantum Dots for Single-electron Pumping

As mass-produced silicon transistors have reached the nano-scale, their behavior and performances are increasingly affected, and often deteriorated, by quantum mechanical effects such as tunneling through single dopants, scattering via interface defects, and discrete trap charge states. However, progress in silicon technology has shown that these phenomena can be harnessed and exploited for a new class of quantum-based electronics. Among others, multi-layer-gated silicon metal-oxide-semiconductor (MOS) technology can be used to control single charge or spin confined in electrostatically-defined quantum dots (QD). These QD-based devices are an excellent platform for quantum computing applications and, recently, it has been demonstrated that they can also be used as single-electron pumps, which are accurate sources of quantized current for metrological purposes. Here, we discuss in detail the fabrication protocol for silicon MOS QDs which is relevant to both quantum computing and quantum metrology applications. Moreover, we describe characterization methods to test the integrity of the devices after fabrication. Finally, we give a brief description of the measurement set-up used for charge pumping experiments and show representative results of electric current quantization.

The fabrication process and experimental characterization techniques relevant to single-electron pumps based on silicon metal-oxide-semiconductor quantum dots are discussed.

As mass-produced silicon transistors have reached the nano-scale, their behavior and performances are increasingly affected, and often deteriorated, by ...

High Resolution Phonon-assisted Quasi-resonance Fluorescence Spectroscopy

High resolution optical spectroscopy methods are demanding in terms of either technology, equipment, complexity, time or a combination of these. Here we demonstrate an optical spectroscopy method that is capable of resolving spectral features beyond that of the spin fine structure and homogeneous linewidth of single quantum dots (QDs) using a standard, easy-to-use spectrometer setup. This method incorporates both laser and photoluminescence spectroscopy, combining the advantage of laser line-width limited resolution with multi-channel photoluminescence detection. Such a scheme allows for considerable improvement of resolution over that of a common single-stage spectrometer. The method uses phonons to assist in the measurement of the photoluminescence of a single quantum dot after resonant excitation of its ground state transition. The phonon&#39;s energy difference allows one to separate and filter out the laser light exciting the quantum dot. An advantageous feature of this method is its straight forward integration into standard spectroscopy setups, which are accessible to most researchers.

The manuscript describes a method of phonon-assisted quasi-resonant fluorescence spectroscopy that incorporates both laser-limited resolution and photoluminescence (PL) spectroscopy. This method utilizes optical phonons to provide linewidth-limited resolution spectra of atom-like semiconductor structures in the energy domain. The method is also easily realized with a single spectrometer optical spectroscopy setup.

High resolution optical spectroscopy methods are demanding in terms of either technology, equipment, complexity, time or a combination of these. Here we ...

Fabrication and Characterization of Superconducting Resonators

Superconducting microwave resonators are of interest for a wide range of applications, including for their use as microwave kinetic inductance detectors (MKIDs) for the detection of faint astrophysical signatures, as well as for quantum computing applications and materials characterization. In this paper, procedures are presented for the fabrication and characterization of thin-film superconducting microwave resonators. The fabrication methodology allows for the realization of superconducting transmission-line resonators with features on both sides of an atomically smooth single-crystal silicon dielectric. This work describes the procedure for the installation of resonator devices into a cryogenic microwave testbed and for cool-down below the superconducting transition temperature. The set-up of the cryogenic microwave testbed allows one to do careful measurements of the complex microwave transmission of these resonator devices, enabling the extraction of the properties of the superconducting lines and dielectric substrate (e.g., internal quality factors, loss and kinetic inductance fractions), which are important for device design and performance.

Superconducting microwave resonators are of interest for detection of light, quantum computing applications and materials characterization. This work presents a detailed procedure for fabrication and characterization of superconducting microwave resonator scattering parameters.

Superconducting microwave resonators are of interest for a wide range of applications, including for their use as microwave kinetic inductance detectors ...

Generation and Coherent Control of Pulsed Quantum Frequency Combs

We present a method for the generation and coherent manipulation of pulsed quantum frequency combs. Until now, methods of preparing high-dimensional states on-chip in a practical way have remained elusive due to the increasing complexity of the quantum circuitry needed to prepare and process such states. Here, we outline how high-dimensional, frequency-bin entangled, two-photon states can be generated at a stable, high generation rate by using a nested-cavity, actively mode-locked excitation of a nonlinear micro-cavity. This technique is used to produce pulsed quantum frequency combs. Moreover, we present how the quantum states can be coherently manipulated using standard telecommunications components such as programmable filters and electro-optic modulators. In particular, we show in detail how to accomplish state characterization measurements such as density matrix reconstruction, coincidence detection, and single photon spectrum determination. The presented methods form an accessible, reconfigurable, and scalable foundation for complex high-dimensional state preparation and manipulation protocols in the frequency domain.

A protocol is presented for the practical generation and coherent manipulation of high-dimensional frequency-bin entangled photon states using integrated micro-cavities and standard telecommunications components, respectively.

We present a method for the generation and coherent manipulation of pulsed quantum frequency combs. Until now, methods of preparing high-dimensional ...