We thank R. Helsten for technical insights; P. Kung from QPS Photronics for the help and processing equipment; as well as QuantumOpus and N. Bertone of OptoElectronics Components for their support and for providing us with state-of-the-art photon detection equipment. This work was made possible by the following funding sources: Natural Sciences and Engineering Research Council of Canada (NSERC) (Steacie, Strategic, Discovery, and Acceleration Grants Schemes, Vanier Canada Graduate Scholarships, USRA Scholarship); Mitacs (IT06530) and PBEEE (207748); MESI PSR-SIIRI Initiative; Canada Research Chair Program; Australian Research Council Discovery Projects (DP150104327); European Union&#39;s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie grant (656607); CityU SRG-Fd program (7004189); Strategic Priority Research Program of the Chinese Academy of Sciences (XDB24030300); People Programme (Marie Curie Actions) of the European Union&#39;s FP7 Programme under REA grant agreement INCIPIT (PIOF-GA-2013-625466); Government of the Russian Federation through the ITMO Fellowship and Professorship Program (Grant 074-U 01); 1000 Talents Sichuan Program (China)

1. Generation of the High-dimensional Frequency-bin Entangled States via Pulsed Excitation
<ol>
	<li>Following the scheme outlined in Figure 2 (Generation stage), connect each component using polarization-maintaining optical fibers (for improved environmental stability).</li>
	<li>Connect a power supply to the electro-optic amplitude modulator and apply a DC voltage offset, tuning the offset value until the optical power transmitted through it is approximately halved (measured using an opt...

<ol>
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The optical frequency-domain, via QFCs, is advantageous in quantum applications for a host of reasons. Operations are global, acting on all states simultaneously, which results in a design that does not scale in size or complexity as the state dimensionality increases. This is enhanced as the components can be reconfigured on-the-fly without changing the setup and are capable of being integrated on-chip by exploiting existing and/or developing semiconductor and telecommunications infrastructures. The generation technique...

The control of quantum phenomena opens the possibility for new applications in fields as diverse as secure quantum communications1, powerful quantum information processing2, and quantum sensing3. While a variety of physical platforms are actively being researched for the realizations of quantum technologies4, optical quantum states are important candidates as they can exhibit long coherence times and stability from external noise, excellent transmission properties, as well as compatibility with existing telecommunications and silicon chip (CMOS) technologies.
Towards fully realizing the potential of photons for quantum technologies, state complexity and information content can be increased through the use of multiple entangled parties and/or high-dimensionality. However, the on-chip generation of such optical states lacks practicality as setups are complicated, not perfectly scalable, and/or use highly-specialized components. Specifically, high-dimensional path-entanglement requires <img alt="Equation 01" src="/files/ftp_upload/57517/57517eq01v3.jpg" /> coherently-excited identical sources and elaborate circuits of beam-splitters5 (where <img alt="Equation 01" src="/files/ftp_upload/57517/57517eq01v3.jpg" /> is the state dimensionality), while time-entanglement needs complex multi-arm interferometers6. Remarkably, the frequency-domain is well-suited for the scalable generation and control of complex states, as shown by its recent exploitation in quantum frequency combs (QFC)7,8 using a combination of integrated optics and telecommunication infrastructures9, and provides a promising framework for future quantum information technologies.
On-chip QFCs are generated using nonlinear optical effects in integrated micro-cavities. Using such a nonlinear micro-resonator, two entangled photons (noted as signal and idler) are produced by spontaneous four-wave mixing, via the annihilation of two excitation photons - with the resultant pair generated in a superposition of the cavity&#39;s evenly-spaced resonant frequency modes (Figure 1). If there is coherence between the individual frequency modes, a frequency-bin entangled state is formed10, which is often referred to as a mode-locked two photon state11. This state wave-function can be described by,
<img alt="Equation 02" src="/files/ftp_upload/57517/57517eq02v3.jpg" />
Here, <img alt="Equation 03" src="/files/ftp_upload/57517/57517eq03v3.jpg" /> and <img alt="Equation 04" src="/files/ftp_upload/57517/57517eq04v3.jpg" /> are the single-frequency-mode idler and signal components, respectively, and <img alt="Equation 05" src="/files/ftp_upload/57517/57517eq05v3.jpg" /> is the probability amplitude for the <img alt="Equation 06" src="/files/ftp_upload/57517/57517eq06v3.jpg" />-th signal-idler mode pair.
Previous demonstrations of on-chip QFCs highlight their versatility as viable quantum information platforms, and include combs of correlated photons12, cross-polarized photons13, entangled photons14,15,16, multi-photon states15, and frequency-bin entangled states9,17. Here, we provide a detailed overview of the QFC platform and a protocol for high-dimensional frequency-bin entangled optical state generation and control.
Future quantum applications, especially those to be interfaced with high-speed electronics (for timely information processing), demand the high-rate generation of high-purity photon states in a compact and stable setup. We use an actively mode-locked, nested cavity scheme to produce QFCs within the telecommunications S, C, and L frequency bands. A micro-ring is incorporated into a larger pulsed laser cavity, with optical gain (provided by an erbium-doped fiber amplifier, EDFA) filtered to match the micro-ring excitation bandwidth18. Mode-locking is actively realized via electro-optic modulation of the cavity losses19. An isolator ensures that pulse propagation follows a single direction. The resulting pulse train has very low root mean square (RMS) noise and exhibits tunable repetition rates and pulse powers. A high isolation notch filter separates the emitted QFC photons from the excitation field. These single photons are then guided through fibers for control and detection.
Our scheme is a step towards a high generation-rate, small-footprint QFC source, as all components used can potentially be integrated onto a photonic chip. Additionally, pulsed excitation is particularly well-suited for quantum applications. First, looking at a pair of micro-cavity resonances symmetric to the excitation, it generates two-photon states where each photon is characterized by a single-frequency mode&#8211; central for linear optical quantum computing20. As well, multi-photon states can be generated by moving to higher power excitation regimes and selecting multiple signal-idler pairs15. Second, as photons are emitted in known time windows corresponding to the pulsed excitation, post-processing and gating can be implemented to improve state detection. Perhaps most significantly, our scheme supports high generation rates of photon states using harmonic mode-locking without reducing the coincidence-to-accidental ratio (CAR) &#8211; which could pave the way for high-speed, multi-channel quantum information technologies.
To demonstrate the impact and feasibility of the frequency-domain, control of QFC states must be accomplished in targeted ways, ensuring highly efficient transformations and state coherence. To satisfy such requirements, we use cascaded programmable filters and phase modulators &#8211; established components in the telecommunications industry. Programmable filters can be used to impose an arbitrary spectral amplitude and phase mask on the single photons, with a resolution sufficient to address each frequency mode individually; and electro-optic phase modulators driven by radio-frequency (RF) signal generators facilitate the mixing of frequency components21.
The most important aspect of this control scheme is that it operates on all quantum modes of the photons simultaneously in a single spatial mode, using single control elements. Increasing the quantum state dimensionality will not lead to an increase in the setup complexity, in contrast to path- or time-bin entanglement schemes. As well, all components are externally reconfigurable (meaning the operations can be altered without amending the setup) and use existing telecommunications infrastructure. Thus, existing and upcoming developments in the field of ultrafast optical processing can be directly transferred to the scalable control of quantum states in the future.
In summary, the exploitation of the frequency-domain by QFCs supports the high-rate generation of complex quantum states and their control, and, is thus well-suited for the harnessing of complex states towards practical and scalable quantum technologies.

<table>
	<tbody>
		<tr>
			<td>Superconducting Nanowire Single-Photon Detector System</td>
			<td>Quantum Opus</td>
			<td>Opus One</td>
			<td></td>
		</tr>
		<tr>
			<td>Electro-optic phase modulator</td>
			<td>EO-Space</td>
			<td>Low loss model</td>
			<td></td>
		</tr>
		<tr>
			<td>Programmable filter</td>
			<td>Finisar&#160;</td>
			<td>WaveShaper 4000s</td>
			<td></td>
		</tr>
		<tr>
			<td>Timing electronics</td>
			<td>PicoQuant</td>
			<td>HydraHarp 400</td>
			<td></td>
		</tr>
		<tr>
			<td>Micro-ring resonator</td>
			<td></td>
			<td></td>
			<td>200 GHz FSR micro-ring resonator made from high refractive index glass. See Ref. 24 for platform details.</td>
		</tr>
		<tr>
			<td>Erbium-doped fiber amplifier</td>
			<td>Keopsys</td>
			<td>PEFA-SP-C-PM-27-B202-FA-FA</td>
			<td></td>
		</tr>
		<tr>
			<td>Electro-optic amplitude modulator</td>
			<td>Oclaro&#160;</td>
			<td>SD40</td>
			<td></td>
		</tr>
		<tr>
			<td>RF tone source</td>
			<td>Rohde &#38; Schwarz</td>
			<td>SMP 04</td>
			<td></td>
		</tr>
		<tr>
			<td>RF tone amplifier</td>
			<td>RF-Lambda</td>
			<td>RFLUPA27G34GA</td>
			<td></td>
		</tr>
		<tr>
			<td>Function generator</td>
			<td>Tetronix</td>
			<td>AFG 3251</td>
			<td></td>
		</tr>
		<tr>
			<td>Isolator</td>
			<td>General Photonics</td>
			<td>NISO-S-15-SS-FC/APF</td>
			<td></td>
		</tr>
		<tr>
			<td>Oscilloscope</td>
			<td>Tetronix&#160;</td>
			<td>TDS5052B</td>
			<td></td>
		</tr>
		<tr>
			<td>Photodiode</td>
			<td>Finisar</td>
			<td>XPDV 50 GHz</td>
			<td></td>
		</tr>
		<tr>
			<td>DWDM</td>
			<td>OptiWorks</td>
			<td>DWFUQUMD08BN</td>
			<td></td>
		</tr>
		<tr>
			<td>Power supply</td>
			<td>Madell</td>
			<td>CA18303D</td>
			<td></td>
		</tr>
	</tbody>
</table>

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.

The outlined scheme for the generation and control of high-dimensional frequency-bin states (based on the excitation of nonlinear micro-cavities, Figure 1) is shown in Figure 2. This setup uses standard telecommunications components and is highly flexible in the photon production rate and the processing operations applied. Figure 3 shows the characterization of the generation scheme through the coinc...

Watch this Scientific Journal Video about Generation and Coherent Control of Pulsed Quantum Frequency Combs at JoVE.com

Generation and Coherent Control of Pulsed Quantum Frequency Combs

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 ...

The overall goal of this protocol is to generate and coherently control pulsed quantum frequency combs which may be used for quantum information processing. This method can help us provide the tools for fundamental investigations of quantum mechanics and for realizing non-classical technologies, such as quantum communications and information processing. The main advantage of this technique is that well-established telecommunications components and protocols are used to generate and control complex optical quantum states in a reconfigurable and scalable way.We have this idea when we talk with my colleague Jose Azana who is an expert in telecommunication processing, and we realized that we could transfer these tools to the world of quantum objects. Set up the components of the system on an optical table. The system has stages for generation, control, and processing.This depiction provides an overview. All elements are connected with polarization maintaining optical fiber. For now, focus on the generation stage.This stage features an on chip micro-ring resonator embedded in a larger external cavity. The external cavity is made of an electro-optic amplitude modulator driven by a signal generator, an isolator, and an erbium-doped fiber amplifier providing optical gain. There is a narrow filter with a pass band selecting a single microcavity resonance and a notch filter routing the generated photons to the control section.With the cavity disconnected, initiate the erbium-doped fiber amplifier. Use an optical power meter after the amplitude modulator to measure the transmitted power. At the modulator, use a power supply to apply a DC offset to have the transmitted power.Reconnect the cavity and insert a fast photo diode into a different ring port. Use an oscilloscope to observe its signal in the time domain. Without the modulator activated, the output will show unstable pulse operation with a low quality pulse train.Return to the amplitude modulator and connect the function generator. Set the output frequency of the generator to a multiple of the approximate external cavity mode spacing. Selecting a rectangular or sine waveform and turn on the function generator.Tune the function generator frequency and DC offset to optimize and stabilize the pulse train on the oscilloscope. Manually adjust the gain to set the pulse intensity. The non-linear four wave mixing process inside the ring resonator now creates signal and idler photon pairs which will leave the external cavity at the notch filter.Connect the synchronization signal from the function generator to the timing electronics. The generation rate of this pulsed quantum frequency comb may be increased by driving the modulator a higher harmonics of the external cavity frequency spacing, thus entering a harmonic mode locking machine. The amplifier gain must then also be increased to ensure the same power per pulse.After the notch filter in the generation stage, the entangled photons enter the control stage. There, in order, they encounter a programmable filter, a phase modulator, and a second programmable filter. First, program the filters.Set the amplitude of the desired frequency mode channels and attenuate the others. Similarly, decide on the desired phase mask. Do this for each filter.This image represents the amplitude and phase for a coincidence measurement. To prepare the phase modulator, connect the signal generator to the RF amplifier with low loss cables. Then connect the RF amplifier to the phase modulator.Once all the RF ends are connected and terminated, bias the amplifier. Set the RF signal generator to create sidebands which overlap with the desired frequency modes, then turn it on. As a test, set up the system to send a continuous wave laser beam through the phase modulator.Use an optical spectrum analyzer to check that the input spectrum produces an output spectrum that corresponds to the intended modulation for the experiment. To continue, connect the phase modulator with the programmable filters. When setting the phase modulation pattern, it is important to determine what pattern will create the targeted frequency sidebands for the chosen operation.This will depend on the dimension of the quantum state used and on microcavity resonance spacing. The photon pairs from the generation stage enter the control stage. The first filter sets the programmed amplitude and phase.Next, the phase modulator creates the necessary frequency sidebands. The second filter selects the signal and idler pair. On input to the processing stage, separate the entangled photons with a dense wavelength division multiplexer.From there, they each go to single photon detectors. Record the arrival time of each photon using timing electronics set up for coincidence measurement. The setup allows coherent control over the photon states.Here frequency sidebands are generated via phase modulation. The sideband spacing and amplitudes are determined by the modulating signal. Coherent control of the photon state can be used for quantum state tomography.This is an example reconstruction of the state density matrix for a two photon system with a dimensionality of three for each photon. The fidelity between the measured and maximally entangled states is about 81%The pulsed high repetition rate generation technique is not limited to micro-ring resonators and may be adopted for other optical cavities, such as photonic crystal waveguides, microdisks, and second-order nonlinear cavities. With its development, the platform combines established techniques in telecommunications with quantum technologies towards potential applications, like secure communications at high rates over multiplex channels or high-dimensional quantum operations.

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8.8K Aufrufe.  Institut National de la Recherche Scientifique - Centre Énergie, Matériaux et Télécommunications (INRS-EMT). The overall goal of this protocol is to generate and coherently control pulsed quantum frequency combs which may be used for quantum information processing. This method can help us provide the tools for fundamental investigations of quantum mechanics and for realizing non-classical technologies, such as quantum communications and information processing. The main advantage of this technique is that well-established telecommunications components and protocols are used to generate and control co...