Femtosecond optical two-way time-frequency transfer in the presence of motion

Abstract

Platform motion poses significant challenges to high-precision optical time and frequency transfer. We give a detailed description of these challenges and their solutions in comb-based optical twoway time and frequency transfer (O-TWTFT). Specifically, we discuss the breakdown in reciprocity due to relativity and due to asynchronous sampling, the impact of optical and electrical dispersion, and velocity-dependent transceiver calibration. We present a detailed derivation of the equations governing comb-based O-TWTFT in the presence of motion. We describe the implementation of real-time signal processing algorithms based on these equations and demonstrate active synchronization of two sites over turbulent air paths to below a femtosecond time deviation despite effective velocities of ±25 m/s, which is the maximum achievable with our physical setup. With the implementation of the time transfer equation derived here, we find no velocity-dependent bias between the synchronized clocks to within at two-sigma statistical uncertainty of 330 attoseconds.Work of the U.S. Government and not subject to copyright. PACS numbers. 06.30.Ft Time and frequency III.A.4 Velocity-Dependent Transceiver CalibrationIn the simplest case, the calibration constant, cal T  , in Eq. (1) reflects a time delay in the transceiver between the reference plane and the detection of the incoming pulses. However, each transceiver is far from a compact point and consists of a distributed set of optical components comprising optical oscillators, frequency combs, modulated cw lasers, optical transceivers for detecting the arrival time of frequency comb pulses, and optical transceivers for the communication-based O-TWTFT as is illustrated in Fig. 2 (and later in Fig. 4). Nevertheless, in the absence of significant Doppler shifts, as in Refs. [2][3][4], the calibration of this distributed system can still be lumped into a single overall time offset, cal T  . Here, with Doppler shifts, that is no longer the case and this calibration must be expanded to include a velocity-dependent contribution,

Femtosecond time synchronization of optical clocks off of a flying quadcopter

“…The advanced comb-based O-TWTFT demonstrated here differs significantly in hardware, calibration, and algorithms from the previous comb-based O-TWTFT described in Refs. 13-15. The full extent of the hardware and algorithms will be discussed in a follow-on article 32 . Below we provide a brief outline the hardware and an alternative derivation of a master synchronization equation to the use of the virtual calculated four time stamps of Eq.…”

“…The derivation of the four effective timestamps is lengthy and provided in Ref. 32. We briefly outline a different derivation here that leads to a single master synchronization equation but does not provide the same physical insight.…”

“…Unfortunately, the interferograms' waveform depends on the Doppler shift of the incoming light (and therefore on velocity as indicated by the superscript) and this, coupled with the relative chirp between the comb pulses, can cause an apparent and strong timing shifts. To avoid this, we calculate the ambiguity function 26 of this heterodyne signal and find its peak in real-time (<300 sec) by use of a Fourier transform algorithm and the Nelder-Mead search algorithm 32 . With this approach, we suppress this systematic to below 100 as.…”

Optical atomic clock comparison through turbulent air

“…These applications require comparisons between clocks, and they have motivated optical atomic clock comparisons both within the same laboratory [1][2][3][4][15][16][17][25][26][27][28] and over fiber-optic links between laboratories [15,16,19,20,[29][30][31]. However, recent progress in the development of high-performance portable atomic clocks [20,[32][33][34], as well as continued interest in links between airborne or spaceborne clocks [35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50], highlights the need for methods of comparing atomic clocks over free-space links. Ideally, such methods would have residual instabilities and inaccuracies below those of the clocks themselves, despite the inevitable presence of atmospheric turbulence and platform motion.…”

Measurement of the impact of turbulence anisoplanatism on precision free-space optical time transfer

“…Circ: circulator. The non-reciprocal time-of-flight, NR T , and the average time-of-flight, link T are extracted fromthe O-TWTFT at an update rate of 2 kHz by use of the equations given in Refs [13,14]…”