Photonic Chip Optical-Frequency Combs for Ultraprecise Measurements

Scott B. Papp

Physical Measurements Laboratory National Institute of Standards and Technology

Boulder, CO 80305 USA Email: scott.papp@nist.gov

Abstract— Optical-frequency combs are versatile tools for measuring time, sensing chemicals, and supporting quantum-information science. A recent direction is to produce miniature frequency combs – microcombs – through intriguing nonlinear behaviors of light in integrated photonics. We realize an octave bandwidth microcomb by exciting a soliton optical pulse in a Kerr microresonator implemented within the silicon-nitride platform. By carrier-envelope-offset frequency detection with the soliton microcomb, we implement a coherent microwave-to-optical connection that enables for example optical-frequency synthesis and optical-clock metrology with more than 17 digits of accuracy and precision. We will report on the nonlinear-optical interactions that govern and optimize soliton microcombs and that enable ultraprecise measurements. Moreover from detailed carrier-envelope-offset frequency noise measurements with our soliton microcombs, we assess that fundamental thermal decoherence and thermo-optic backaction are important contributions, opening the regime that microscopic physics affects ultraprecise optical-frequency metrology.

Keywords—nanophotonics, integrated photonics, optical-

frequency combs, optical clocks, metrology, optical-frequency synthesis, low phase noise signal generation

I. INTRODUCTION The realization of dissipative Kerr solitons in optical microresonators [1,2] has opened a field of new possibilities through mode-locked frequency-comb generation in chip-integrated devices. Building on decades of soliton nonlinear optics [3], this advance has led to the demonstration of such functional devices as atomic clocks [4], dual-comb spectrometers [5], and high-speed ranging [6], all in a platform with the potential for heterogeneous electronic-photonic integration. Our recent work in phase stabilizing the carrier-envelope-offset frequency ( 𝑓"#$ ) of Kerr-microresonators combs has led to the demonstration of an optical synthesizer with a fractional-frequency accuracy and precision of <3 x 10-16 [6,7] and a clockwork with accuracy and precision of less than 10-17 [8]. This level of performance, obtained with nanofabricated frequency combs, opens up a range of application opportunities to advance US national interests.

We will describe the Kerr-microresonator technology and system integration needed to realize full phase stabilization of a Kerr-microresonator frequency comb– often called a microcomb –with respect to any microwave or optical frequency reference. This includes device fabrication, group-

velocity-dispersion engineering, initiation of ultrafast soliton excitations of the microresonator and their ensemble and self-interactions, frequency-noise analysis of soliton microcombs, and frequency control of soliton microcombs. These topics present a comprehensive view of current microcomb readiness and potential for various applications, and they preview lines of next-generation developments around microcomb science, technology, and photonic integration that will push out the frontier of applications. Moreover, now through direct and high signal-to-noise f-2f nonlinear interferometry to detect 𝑓"#$, we explore the fundamental fluctuations of Kerr-microresonator frequency combs that arise from thermodynamic noise. Our observations indicate that thermal noise reflected in refractive-index fluctuations stochastically decoheres the repetition frequency and 𝑓"#$ of a Kerr-soliton microcomb. Indeed thermal noise is the leading mechanism of decoherence in our soliton microcomb, and thermo-optic backaction– laser cooling –reduces the decoherence to below that at ambient temperature. We will describe the role that microscopic thermal physics plays in frequency-comb metrology with integrated photonics.

DISTRIBUTION STATEMENT A. Approved for public release: distribution is unlimited.

Figure 1: Kerr-microresonator frequency comb system. (a) Interlocking Kerr combs that offer a wide design space for system integration, and photodetection and electronics to implement complete phase stabilization. (b) SEM image with overlays that indicate waveguide functionalities and the calculated soliton pulse eigenstate of the silicon-nitride ring resonator. (c) Optical spectrum of the interlocking Kerr comb.

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II. KERR-MICRORESONATOR FREQUENCY COMB SYSTEM Kerr microresonators offer access to parametric nonlinear optical effects for the purpose of coherently converting laser light to new colors. To implement a phase stabilized microresonator frequency comb with a microwave-rate mode spacing in the telecom C band, we utilize an interlocking pair of soliton microcombs formed with a silica wedge resonator [9] with 22 GHz free-spectral range (FSR) and a silicon-nitride ring resonator with 1.013 THz FSR [6]. This interlocking Kerr comb system is outlined in Fig. 1a, and a SEM image of the silicon-nitride device is shown in Fig. 1b. The combined spectrum of the interlocking combs is shown in Fig. 1c. Operationally, we initiate soliton microcombs in both devices, and we implement interlocking phase stabilization of the combs with respect to optical and microwave frequency references. We will describe the properties, applications, and extensions of this microcomb.

III. THERMAL DECOHERENCE AND LASER COOLING Our measurements of 𝑓"#$ indicate that its frequency

fluctuations are dominated by the microresonator’s intrinsic thermorefractive noise– thermodynamic fluctuations of the ambient environment that cause fundamental index-of-refraction jitter. While thermorefractive noise has been studied in microresonator systems [10–12], its effects have not been observed or thoroughly predicted in Kerr frequency combs.

We directly and efficiently detect 𝑓"#$ with high SNR, using the system outlined in Fig. 2a. Optical amplification of the soliton microcomb assists in f-2f detection. Our measurements of the 𝑓"#$ spectrum are shown in Fig. 2b. We will describe how we calibrate the contribution of thermorefractive noise to 𝑓"#$ noise, which demonstrates the tight correlation between 𝑓"#$ and thermorefractive noise. The calibration is performed by measuring the thermorefractive frequency noise of microresonator modes in the 1550 nm band with a ‘probe laser’ that counter-propagates the soliton pump laser; see Fig. 2a. The small size, the correspondingly rapid thermal conduction timescale, and the relatively high thermorefractive coefficient of silicon nitride explain the >1 MHz bandwidth of thermorefractive noise and the ~6 MHz linewdith of 𝑓"#$ . Therefore, 𝑓"#$ of the octave-bandwidth Kerr-soliton pulses that circulate in our microresonator are governed by thermal physics, and not on technical noise that can be traced to the pump laser as in previous experiments [13,14]. To further understand the thermorefractive-noise contributions to 𝑓"#$, we explore thermo-optic backaction [12], or what can be considered laser cooling, of this noise; see Fig. 2c. While an octave-bandwidth soliton circulates in our microresonator and monitoring 𝑓"#$ , we couple blue-detuned ‘cooling’ laser light to the same TE1 mode family that carries the soliton and pump laser, but at 1 THz higher frequency than the pump laser. This reduces fluctuations imparted to the soliton’s repetition frequency, and enables reduction of the 𝑓"#$ linewidth as shown in Fig. 2c. We will report on the details and implications of this technique.

ACKNOWLEDGMENT We thank Kerry Vahala for providing the silica device. We

thank Travis Briles, Tara Drake, Jordan Stone, Daryl Spencer, Su-Peng Yu, Erin Lamb, Hojoong Jung, David Carlson, Daniel Cole, Wei Zhang, Daniel Hickstein, Liron Stern, Qing Li, Gregory Moille, Xiyuan Lu, Daron Westly, Scott Diddams, and Kartik Srinivasan. This work

is supported by NIST and DARPA. We thank our collaborators on the CORES team.

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Figure 2: Carrier-envelope-offset frequency detection system with a silicon-nitride microcomb. The ~2 µm wavelength component of octave bandwidth comb is amplified with thulium-doped fiber and second-harmonic generation directly implements f-2f by an optical heterodyne with the ~1 µm wavelength component of the microcomb. (b) 𝑓%&' signal of the silicon-nitride microcomb obtained with high SNR. The gray trace is the noise floor of our detection system. (c) Demonstration of thermo-optic backaction laser cooling of the soliton microcomb. This cooling effect reduces the 𝑓%&' linewidth by more than a factor of ten.

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