A fully packaged multi-channel cryogenic module for optical quantum memories

TL;DR

This paper presents a fully packaged, cryogenically stable multi-channel quantum emitter module based on color centers in diamond, advancing scalable quantum memory integration for quantum networks.

Contribution

It introduces a novel cryogenic packaging solution for multi-channel diamond-based quantum emitters, enabling scalable quantum memory modules for network applications.

Findings

The module operates reliably at cryogenic temperatures.

It demonstrates compatibility with quantum network architectures.

The design supports multi-channel integration for quantum memories.

Abstract

Realizing a quantum network will require long-lived quantum memories with optical interfaces incorporated into a scalable architecture. Color centers quantum emitters in diamond have emerged as a promising memory modality due to their optical properties and compatibility with scalable integration. However, developing a scalable color center emitter module requires significant advances in the areas of heterogeneous integration and cryogenically compatible packaging. Here we report on a cryogenically stable and network compatible quantum-emitter module for memory use. This quantum-emitter module is a significant development towards advanced quantum networking applications such as distributed sensing and processing.

Full text

I Introduction

Quantum memory systems are a crucial enabling technology for the continued development and realization of advanced quantum network capabilities and applications [1]. Indeed, memory systems scaled to tens or hundreds of memories with millisecond-class coherence times would enable quantum repeater functionality [2, 3] for improved network performance [4, 5, 6, 7] and quantum network applications such as improved sensing [8] and distributed quantum processing [9, 10].

There are multiple candidate qubit platforms for networked quantum memory use, including trapped ions [11, 12] and neutral atoms [13, 14], atomic ensembles in vapors [15, 16] and in solid-state materials [17, 18, 19], and individual color centers in solids [20, 21, 22]. Diamond color-center emitters have emerged as a particularly promising platform due to several beneficial characteristics [23]. Their coherent optical interface provides compatibility with optical fiber networks [24, 25]. They have the potential to scale to thousands of memory qubits through on-chip integration [26], and their electron spin degree of freedom can exhibit coherence times ranging from milliseconds [27] to seconds [28], providing utility as quantum repeaters and for quantum network applications. Furthermore, ancillary nuclear spins can be used as logical registers [29] for multi-qubit processing such as error detection [30] and correction [31]. However, the challenges of engineering a robust and scalable memory module has limited the use of these memories in network testbeds, delaying demonstration of advanced quantum network applications.

Here we report on our efforts to develop a robust, packaged quantum-emitter module. We build upon previous work [26, 32, 33] to demonstrate heterogeneous integration of optical fibers, photonic integrated circuits (PICs) and diamond color centers. Our results rely upon novel custom designed and fabricated silicon-nitride (Si3N4, SiN) PICs, matched diamond microchiplets with waveguides containing negatively charged silicon vacancy (SiV-) color centers, a custom diamond alignment and stamping process, as well as a novel precision fiber alignment and bonding procedure. We follow the previously reported general strategy of multi-waveguide-fiber architecture  [26, 32, 33] and incorporate our developments to realize a multi-emitter module that is fully packaged, cryogenically compatible, inherently scalable, and network-compatible. The resulting quantum-emitter module architecture enables scaling of large numbers of optical quantum memories to be readily integrated into emerging network testbeds [34, 35, 36] for the realization of applications in quantum networking.

II Design and Development

The conceptual goal of our work was to develop a cryo-compatible, fully-packaged module that interfaces optical fiber with a controllable quantum emitter, as shown in Fig. 1. To accomplish this task, our design uses a custom electronic interposer, an integrated photonic interposer (the PIC) and a diamond microchiplet—incorporated into a commercial dilution refrigerator. The electronic interposer was produced commercially, and the eight-channel diamond micro chiplet was fabricated using a similar process to the one shown in Refs. [37, 38, 26] (see Appendix A for details). In what follows, we will focus on the novel fabrication of the integrated photonic interposer and the packaging methodologies.

We designed and fabricated a custom PIC interposer to integrate a commercial optical fiber array with a diamond microchiplet. This process has been accomplished previously in Ref. [26] using unclad aluminum nitride waveguides on a sapphire wafer where the waveguides were exposed (unclad) to allow for heterogeneous integration. However, the small optical mode in the unclad aluminum nitride waveguide at the facet necessitated the use of lensed and/or high numerical aperture fiber to obtain efficient coupling. Additionally, it is possible to use a thin layer of cladding followed by a precision etch [39], but fabrication tolerances limit the depth of the window. Thick cladding, however, is critical to produce a large and symmetric mode well-coupled to cleaved optical fiber. Here, we demonstrate a silicon nitride (SiN) fabrication process that allows for both waveguides with thick oxide cladding at the facet and waveguides without oxide cladding for diamond integration. As shown in Fig. 2, we employed a titanium-aluminum etch-stop layer directly on top of the SiN waveguides used for diamond integration, allowing a standard oxide etch to open a precision window in the top SiO2 cladding without damaging the SiN layer (see Appendix B for details). The metal was then removed with a selective wet etch, and the resulting open window is shown in Fig. 3(a). The oxide-clad waveguides at the facet allows for a larger optical mode matched to cleaved optical fiber resulting in low-loss coupling to a 20-channel commercial fiber array with 630HP optical fiber.

The PIC was designed to support eight independent quantum-emitter channels, based upon the eight independent diamond waveguides available on a single diamond microchiplet. SiN waveguides provide optical input (8) and output (8) access to the diamond using 16 total channels. To ease the integration of the PIC module with a commercial optical fiber array, the input and output SiN waveguides were routed to the same side of the PIC and spaced $127\text{\,}\mathrm{\SIUnitSymbolMicro m}$ apart as shown in Fig. 7(a) of the Appendix. Two SiN waveguide loopback structures that are not routed through the diamond window were added to the same PIC facet to help facilitate alignment with the fiber array and characterize alignment drift during packaging and cryo cooling.

In addition to optical waveguides, metal electrodes were fabricated as part of the PIC module in a $0.75\text{\,}\mathrm{\SIUnitSymbolMicro m}$-thick aluminum layer. The role of the electronic capabilities on the PIC is for future microwave control of the qubit and DC strain tuning of the diamond. Ground-signal-ground coplanar microwave waveguides were routed below the diamond window in order to deliver microwave control signals to the SiV-s. In addition, DC electrodes were patterned in the same aluminum layer and interdigitated with the individual diamond waveguides (see Fig. 7(c)) for future electrostatic actuation-based strain tuning [40] of the inhomogeneously-spread color center transition frequencies. For this work, microwave loss was measured but DC bias for strain tuning was not applied.

Attachment of the commercial fiber array to the custom PIC, while maintaining alignment from room temperature down below 100 mK, required the use of thermally compatible materials. We used a common silicon substrate and a silicon spacer—bonded with cryo-compatible epoxy—to match vertical dimensions of the SiN waveguides on the PIC and the optical fibers in the fiber array as shown in Fig. 4. This majority-silicon design minimized relative motion between the fiber array and the PIC in the module during cooldown. We additionally applied UV epoxy in the interface between the fiber array and the PIC to eliminate any residual alignment drift. While we observed that UV epoxy alone is prone to failure at cryogenic temperatures, the added support from the cryo-compatible epoxy was sufficient to maintain the UV epoxy bond and keep the module aligned. Our packaging procedure compares favorably to other methods (see for example [33]). Additional details for the packaging design and procedure are described in Appendix C.

After the module was fully cured, we placed an eight-channel diamond chiplet onto the PIC (see Fig. 3(b)) using a custom-cut polydimethylsiloxane (PDMS) stamp affixed to a standard glass slide. We used a high magnification zoom lens to image through the stamp to view the diamond chiplet and the PIC simultaneously and positioned the diamond chiplet with a six-axis stage with differential micrometers [41]. Correct diamond alignment with the SiN waveguides can be confirmed at room temperature using photoluminescence (PL, see Sec. III for details). Based on the sub-micrometer width of the SiN waveguides, we estimate a diamond placement accuracy of better than 100 nm, which compares very favorably with the approximately 10 $\mu$m placement accuracy inherent to commercially available pick-and-place systems. The module was then attached mechanically to a gold-plated copper puck and wire-bonded to a custom printed circuit board as shown in Fig. 4. Custom fiber feedthroughs for up to 40 fibers (630HP)—supporting up to 16 diamond channels—through a single KF-40 flange and commercially available microwave and DC feedthroughs enabled operation of the module in our cryogenic system.

III Performance Characterization

We measured the optical and electrical properties of the quantum-emitter module using the setup shown in Fig. 5. Light traveled from two laser sources at different wavelengths, combined at a 50:50 fiber splitter/combiner, through an optical fiber and down into a dilution refrigerator (DR). Excitation light was coupled into the module via one channel of a 20-channel fiber array, into the glued PIC and then transitioned from the PIC into the diamond chiplet, driving color centers to emit into the diamond waveguide mode. This fluorescence transitioned back into the PIC waveguide, into the fiber array and out of the DR where it was filtered spectrally and sent to either an avalanche phototodiode (APD) for time-tagged photon detection, or a spectrometer for spectral characterization.

The figures of merit we considered for this architecture include the optical and microwave losses through the packaged system, the detected photon flux from the SiV-, and the linewidth of the SiV- emitters. We characterize the optical insertion loss of the PIC by using a short loopback waveguide structure that does not pass through the diamond window on the PIC. We measured approximately 7 dB round trip insertion loss at 737 nm, which included facet, propagation, and bend losses. Based upon measurements of test devices, we estimate the facet loss to be approximately 3 dB/facet at 737 nm which, crucially, is stable from room temperature down to 100 mK with no active alignment. This compares favorably to the room temperature results of Ref. [42] which employs a bi-layer SiN waveguide at 940 nm. The package was cycled from room temperature down below 100 mK multiple times with no appreciable change in transmission.

The fabricated PIC parameters were swept to explore the optimum geometry for these novel structures and to reveal the most relevant fabrication limitations which will inform future designs. Using cascaded test devices, our best performing window structures had approximately 3.0 dB loss per transition. This loss was primarily due to optical scattering as the waveguide passes directly through window etch which we found to have a rough surface. This fabrication limitation can be overcome by moving to a design with a two-layer SiN stack and adiabatically transitioning between SiN layers within the window region. This would significantly reduce the window transition loss and would also allow for useful capabilities such as polarization control and low-loss optical routing. The best performing SiN-to-diamond transition devices resulted in 6.6 dB loss per transition. Loss in these devices arises from the SiN waveguide layer thickness—which was optimized for edge coupling performance between the PIC and the cleaved fiber array—resulting in imperfect mode matching between the SiN and diamond waveguides. This limitation can again be addressed by a two-layer SiN stack, where the bottom layer thickness is optimized for cleaved fiber to PIC transmission performance and the top layer thickness is optimized for SiN-to-diamond waveguide transmission. Finally, we estimate an optimum straight waveguide propagation loss of 0.30 dB/cm at 737 nm for 600 nm wide waveguides, which could be improved by increasing the waveguide width from 600 nm up to 700 nm [43]. We note that there is increased loss near metals on the PIC, though this can be mitigated by moving the metal layer farther from the optical mode by increasing the oxide depth between the SiN and metal layer.

The microwave transmission through a typical module is shown in Fig. 6(d). This data was taken at room temperature, and we have observed minimal changes in microwave transmission characteristics between room temperature and cryogenic operation. The data shows smooth transmission properties out to 10 GHz, indicating the module can deliver distortion free microwave pulses to the SiV- color centers in the module, suitable for enabling quantum memory control operations [27]. The transmission loss is dominated by line-loss from the cables, not by the module itself, which should result in minimal heating of the diamond microchiplet; preliminary results indicate that next generation devices will be able to further reduce microwave loss for improved performance [44].

We demonstrate the functionality of our packaged module by performing optical spectroscopy of six color center emitters in separate diamond waveguides. The SiV energy levels are shown in Fig. 6(a), and Fig. 6(b) shows a typical photoluminescence (PL) spectrum of an ensemble of color centers in a single waveguide under 638 nm excitation. For these measurements, we used CW light with approximately $5.2\text{\,}\mathrm{\SIUnitSymbolMicro W}$ of power in the diamond waveguide (calculated based upon known losses) and an integration time of two minutes with a background-subtracted count rate of 2.8 kHz. The output was filtered using a long-pass interference filter at 664 nm. The scan shows two 737 nm transitions due to the excited state splitting of the SiV- as shown Fig. 6(a). Similar results were found in all six transmitting waveguides.

To further explore the optical properties of the SiV- emitters, we took high-resolution photoluminescent excitation scans of six channels, finding similar results in each as shown in Appendix D. For these scans, we used the pulse sequence shown in Fig. 5 with optical powers that optimize the signal to noise ratio and linewidth of the emitter. To begin, the repump laser initializes the SiV- electronic state with a 500 ns pulse with a peak power of $4.1\text{\,}\mathrm{\SIUnitSymbolMicro W}$ in the diamond waveguide. After a period of $1.6\text{\,}\mathrm{\SIUnitSymbolMicro s}$, a $10\text{\,}\mathrm{\SIUnitSymbolMicro s}$ resonant 737 nm pulse with a peak power of $440\text{\,}\mathrm{pW}$ in the diamond waveguide is applied to cycle the resonant transition. The optical power is calculated based upon known losses. Each full optical pulse cycle is $16.1\text{\,}\mathrm{\SIUnitSymbolMicro s}$ long and includes $10\text{\,}\mathrm{\SIUnitSymbolMicro s}$ of measurement time during the resonant pulse. The output light is filtered to collect the phonon sideband with two 46 nm bandpass filters centered at 775 nm. The resonant laser frequency is swept with emitted phonon sideband photon counts measured by an avalanche photodiode (APD) for many pulse cycles, ranging between $2.50\times 10^{5}$ and $6.21\times 10^{5}$ cycles, depending on the channel. A typical scan is shown in Fig. 6(c) with an individual SiV- resonance including a Lorentzian fit with a full width at half maximum of $108\pm 11$ MHz. These results confirm that the packaged module supports individual color center characterization for future use in quantum memory applications.

IV Discussion and Outlook

In summary, we have designed, fabricated, packaged, and tested a cryogenically-compatible photonic quantum-emitter module that has the potential to scale to many qubits. In particular, we have resolved two key issues for developing scalable memories for quantum networking—namely, a packaged optical interconnect that is both (a) temperature-stable and (b) compatible with heterogeneous integration techniques, all while maintaining low loss at the PIC-to-fiber interface.

To put the efficiency of this quantum-emitter module into context, the reported losses associated with successful networked quantum memory demonstrations ranges from tens of dB [45] to less than 1 dB [5]. This work provides an intermediate solution in terms of optical loss at 7 dB, while also demonstrating a scalable architecture with multiple spatially separated emitters. Additionally, we think that the relatively straightforward modification of using a two-layer SiN stack to avoid window transition loss, and the incorporation of lensed fibers to reduce edge coupling loss, will result in a module with approximately 1 dB of loss.

By upgrading our cryogenic setup with a vector magnet to realize a long-lived spin qubit [27], and connecting the module to our Boston area quantum network testbed [46, 47] we will be able to perform advanced system-level demonstrations across deployed fiber links. Furthermore, while we have designed and demonstrated this module’s utility using SiV- color centers at 737 nm, by modifying its design wavelength our approach can be made compatible with a range of complementary technologies spanning the range of operation of silicon nitride, from the visible to the mid-IR band. This includes other color centers in diamond [48], defects in silicon carbide  [49], and rare earth ions implanted in various high index materials  [50]. Additionally, the individual components and techniques developed here have use in enabling efficient novel emitter characterization for quantum information processing use [44], and will likely be of significant benefit to interconnects between disparate technologies for quantum [51, 52] and classical applications [53, 54, 55].

Acknowledgements.

Distribution Statement A. Approved for public release. Distribution is unlimited. This material is based upon work supported by the National Reconnaissance Office and the Under Secretary of Defense for Research and Engineering under Air Force Contract No. FA8702-15-D-0001. Any opinions, findings, conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Reconnaissance Office or the Under Secretary of Defense for Research and Engineering. © 2023 Massachusetts Institute of Technology. Delivered to the U.S. Government with Unlimited Rights, as defined in DFARS Part 252.227-7013 or 7014 (Feb 2014). Notwithstanding any copyright notice, U.S. Government rights in this work are defined by DFARS 252.227-7013 or DFARS 252.227-7014 as detailed above. Use of this work other than as specifically authorized by the U.S. Government may violate any copyrights that exist in this work. This material is based upon work supported by the Center for Quantum Networks under NSF grant 1941583. M.S. acknowledges support from the NASA Space Technology Graduate Research Fellowship Program. Work performed on MIT campus was supported in part by the Air Force Office of Scientific Research under award number FA9550-20-1-0105, supervised by Dr. Gernot Pomrenke.

APPENDIX A DIAMOND FABRICATION

The diamond micro chiplet was fabricated using a similar process to the one shown in Refs. [37, 38, 26]. The fabrication process began with an electronic grade single-crystal diamond plate from Element 6. We performed plasma etching in Ar/Cl2 followed by O2 etching to remove $7\text{\,}\mathrm{\SIUnitSymbolMicro m}$ of the diamond surface in order to relieve strain in the sample. This was followed by ion implantation of 29Si by Innovation Inc. with an effective areal dose of $10^{11}$ ion/cm2 at 175 keV for a mean depth of 115 nm. After implantation, the sample was annealed at $1200\text{\,}\mathrm{\SIUnitSymbolCelsius}$ in an ultra-high vacuum furnace at $10^{-7}$ mbar, followed by cleaning in a boiling mixture of nitric acid, sulfuric acid, and perchloric acid (1:1:1) to remove any graphite formed during the anneal.

Once this implantation process was complete, diamond microchiplets were fabricated following the methods described in Ref. [37]. The chiplet is shown in Fig. 7(c) and (d). The diamond waveguides taper up linearly from approximately 50 nm to 320 nm over $3.0\text{\,}\mathrm{\SIUnitSymbolMicro m}$. The eight diamond waveguides have a rectangular shape with a depth of 200 nm and are spaced be $3.0\text{\,}\mathrm{\SIUnitSymbolMicro m}$. The resulting suspended microchiplet was then removed with a tungsten probe and placed (smooth-side-up) onto a custom polydimethylsiloxane (PDMS) stamp to transfer (smooth-side-down) to the SiN PIC, as described in Sec. II.

APPENDIX B PIC FABRICATION

PICs were used to photonically access diamond color centers by routing optical signals at 628 nm and 737 nm from optical fiber, through SiN waveguides, and into a diamond micro-chiplet. These PICs were fabricated at wafer scale using MIT Lincoln Laboratory’s 90 nm node 200 mm wafer foundry, using a SiN-on-SiO2 plasma enhanced chemical vapor deposition (PECVD) process [43].

For our devices, an aluminum layer ($0.75\text{\,}\mathrm{\SIUnitSymbolMicro m}$ thickness) was deposited on SiO2 for future microwave and DC control of SiV- color centers, followed by $1.5\text{\,}\mathrm{\SIUnitSymbolMicro m}$ of SiO2 PECVD cladding. The oxide is then planarized via chemical-mechanical polishing to a total depth of $0.6\text{\,}\mathrm{\SIUnitSymbolMicro m}$. A 100-nm-thick SiN layer was deposited and etched to form the optical waveguides. Due to the lack of a SiN-SiO2 selective etch [56], we employed a titanium-aluminum (Ti-Al) etch-stop layer using a liftoff process. The etch-stop layer was deposited on top of selected SiN waveguides to aid in the removal of oxide cladding in regions where we employ diamond integration. This was followed by depositing $5\text{\,}\mathrm{\SIUnitSymbolMicro m}$ of SiO2 and a standard masked oxide etch to open a window down to the etch-stop layer, followed by a wet etch that removed the Ti-Al etch stop layer, leaving the SiN layer underneath. Vias were patterned and etched to access the metal layer for wire bonding, and a $150\text{\,}\mathrm{\SIUnitSymbolMicro m}$-deep and $100\text{\,}\mathrm{\SIUnitSymbolMicro m}$-wide trench was used to define the dicing trenches on four sides of the entire $4\times 5$ mm PIC. An additional $500\text{\,}\mathrm{\SIUnitSymbolMicro m}$-deep etch was done on the optical input facets of the PIC, resulting in a total etch depth at the facet of $650\text{\,}\mathrm{\SIUnitSymbolMicro m}$. This enabled the fiber array to come flush against the PIC facet during the bonding process. The resulting PICs had both clad and unclad SiN waveguides, high quality edge facets and embedded microwave and DC electrodes. The fabrication steps relevant for opening the diamond window are shown in Fig. 2.

Photonic structures on the PIC module included linear inverted tapers, bends, and evanescent couplers to get the optical mode in and out of the diamond. This latter structure is composed of two parts: (a) a “window transition region” composed of a taper from the clad SiN waveguide to the unclad SiN waveguide in the open window region of the device; and (b) a “SiN-to-diamond transition” region composed of a linear taper from an unclad SiN waveguide into a diamond waveguide. The details are shown in Fig. 7(d-e). The window transition is accomplished by tapering the SiN waveguide from a 600 nm width in the clad region—section (i) in Fig. 7(e)—to a 1000 nm width in the unclad region—section (ii). During this taper, the window tapers open gradually over a distance of $5\text{\,}\mathrm{\SIUnitSymbolMicro m}$—sections (ii) to (iii). The SiN-to-diamond transition is accomplished in the unclad window region, where the SiN waveguide is tapered down while the diamond waveguide is tapered up towards the desired width of 320 nm—section (iv). The optical mode is thus evanescently coupled from the 1000 nm-wide SiN waveguide to the diamond waveguide—section (v)—where it can interact with SiV- color centers. The losses of the window transition were measured to be 3.3 dB/transition using a variation of the cut-back method, where several back-to-back window transitions were nested together and the insertion loss over multiple window transitions was measured. The losses of the SiN-to-diamond transition were estimated to be 6.6 dB/transition by measuring total PIC insertion losses with diamond attached and back-calculating the diamond transition losses from known insertion losses of all other components. A standard parameter sweep on separate test structures allowed identification of designs with lower losses, to be used as part of the full module design in future tape-outs. We note that although Fig. 7(d) shows the layout of an ideal diamond placement onto the etched window, in practice small angular displacements of the diamond microchiplet with respect to SiN waveguides resulting from manual diamond positioning could result in higher insertion losses.

Reasonable changes to the design and fabrication of these devices can offer significant improvements to the loss in the transition to the unclad SiN and from the unclad SiN waveguide to the diamond waveguide. These improvements can be accomplished by employing two layers of SiN and optimizing the layer thicknesses and taper parameters of the SiN and diamond waveguides.

APPENDIX C PACKAGING

As shown in Fig. 4, a $725\text{\,}\mathrm{\SIUnitSymbolMicro m}$ thick silicon bench formed a common substrate for the PIC and fiber array; however, a $275\text{\,}\mathrm{\SIUnitSymbolMicro m}$ thick silicon spacer between the silicon bench and the PIC was needed to allow clearance for the fiber core to align with the facet of the PIC. We designed a custom jig to ensure precise alignment of the bench, spacer and PIC. Using this jig, along with custom cut spacers made from plastic shim stock, we were able to maintain a bond line of cryo-compatible epoxy (MasterBond EP21TCHT-1) measuring approximately $76\text{\,}\mathrm{\SIUnitSymbolMicro m}$ for each layer. Pressure was applied with a Teflon-tipped screw from above for approximately two hours to ensure that the PIC, spacer and bench were parallel.

Before the epoxy was fully cured, we moved the package to a bonding platform consisting of a three-axis translation stage and a custom designed Delrin fixture to temporarily mount the PIC stack-up. A commercial 20-channel silicon fiber array composed of 630HP single mode fiber was mounted to a six-axis translation stage with differential micrometers and a custom fabricated rigid fixture. This fixture provided strain relief to the fibers and was able to release the fiber array after curing without disturbing the alignment. A high magnification optical microscope with viewing camera was used to aid in bonding. Using a 730 nm diode laser with a polarization controller, we optimized alignment through loopback alignment structures on the PIC (see Fig. 7(b)), ensuring accurate alignment across the full length of the facet. Once aligned, the fiber array was raised out of the way and epoxy was applied to two regions: a) the cryo-compatible epoxy was applied to the silicon bench beneath the fiber array; b) UV epoxy (Norland 63) was applied to the facet of the fiber array. The fiber array was then lowered back into position, forming a bond both below the array and between the array and the PIC. The alignment was optimized and then UV light was applied to the interface for approximately 60 minutes to ensure a complete cure. Compared to other methods [33], this bonding procedure is completed without the need for a temperature controlled alignment stage. We allow the module to cure in the alignment setup for 24 hours before transferring to a dry box to complete the room temperature cure of the cryo-compatible epoxy over an additional 48 hours.

APPENDIX D OPTICAL CHARACTERIZATION

We measured PLE signals on six diamond channels as discussed in Sec. III. Data was taken using the methods discussed there, with integration times varied from 2.50 s up to 6.20 s ($2.50\times 10^{5}$–$6.21\times 10^{5}$ cycles) to ensure adequate signal-to-noise based upon the brightness of the individual emitter. The results are shown in Fig. 8 with an arbitrary vertical axis. The Lorentzian full width at half maximum $\Gamma$ as well as the shift in center frequency $\Delta$ relative to the Fig. 6(c) is shown. All emitters are within a 12 GHz range, and the linewidths vary from 108 MHz up to 229 MHz.