Generation and Coherent Control of Pulsed Quantum Frequency Combs

Summary

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.

Abstract

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.

Introduction

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 coherently-excited identical sources and elaborate circuits of beam-splitters⁵ (where 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'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,

Here, and are the single-frequency-mode idler and signal components, respectively, and is the probability amplitude for the -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 photons^14,15,16, multi-photon states¹⁵, and frequency-bin entangled states^9,17. 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– 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) – 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 – 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.

Protocol

1. Generation of the High-dimensional Frequency-bin Entangled States via Pulsed Excitation Following the scheme outlined in Figure 2 (Generation stage), connect each component using polarization-maintaining optical fibers (for improved environmental stability). 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…

Representative Results

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…

Discussion

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…

Materials

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