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Register a new userUltra stable and very low noise signal source using a cryocooled sapphire oscillator for VLBI
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Here we present the design and implementation of a novel frequency synthesizer based on low phase noise digital dividers and a direct digital synthesizer. The synthesis produces two low noise accurate and tunable signals at 10 MHz and 100 MHz. We report on the measured residual phase noise and frequency stability of the synthesizer, and estimate the total frequency stability, which can be expected from the synthesizer seeded with a signal near 11.2 GHz from an ultra-stable cryocooled sapphire oscillator. The synthesizer residual single sideband phase noise, at 1 Hz offset, on 10 MHz and 100 MHz signals, respectively, were measured to be -135 dBc/Hz and -130 dBc/Hz. Their intrinsic frequency stability contributions, on the 10 MHz and 100 MHz signals, respectively, were measured as sigma_y = 9 x 10^-15 and sigma_y = 2.2 x 10^-15, at 1 s integration time. The Allan Deviation of the total fractional frequency noise on the 10 MHz and 100 MHz signals derived from the synthesizer with the cryocooled sapphire oscillator, may be estimated as sigma_y = 5.2 x 10^-15 tau ^-1 + 3.6 x 10^-15 tau ^-1/2 + 4 x 10^-16 and sigma_y = 2 x 10^-15 tau ^-1/2 + 3 x 10^-16, respectively, for 1 s < tau < 10^4 s. We also calculate the coherence function, (a figure of merit in VLBI) for observation frequencies of 100 GHz, 230 GHz and 345 GHz, when using the cryocooled sapphire oscillator and an hydrogen maser. The results show that the cryocooled sapphire oscillator offers a significant advantage at frequencies above 100 GHz.
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Two nominally identical ultra-stable cryogenic microwave oscillators are compared. Each incorporates a dielectric-sapphire resonator cooled to near 6 K in an ultra-low vibration cryostat using a low-vibration pulse-tube cryocooler. The phase noise for a single oscillator is measured at -105 dBc/Hz at 1 Hz offset on the 11.2 GHz carrier. The oscillator fractional frequency stability is characterized in terms of Allan deviation by 5.3 x 10^-16 tau^-1/2 + 9 x 10^-17 for integration times 0.1 s < tau < 1000 s and is limited by a flicker frequency noise floor below 1 x 10^-16. This result is better than any other microwave source even those generated from an optical comb phase-locked to a room temperature ultra-stable optical cavity.
A Cryogenic Sapphire Oscillator has been implemented at 11.2 GHz using a low-vibration design pulse-tube cryocooler. Compared with a state-of-the-art liquid helium cooled CSO in the same laboratory, the square root Allan variance of their combined fractional frequency instability is $sigma_y = 1.4 times 10^{-15}tau^{-1/2}$ for integration times $1 < tau < 10$ s, dominated by white frequency noise. The minimum $sigma_y = 5.3 times 10^{-16}$ for the two oscillators was reached at $tau = 20$ s. Assuming equal contributions from both CSOs, the single oscillator phase noise $S_{phi} approx -96 ; dB ; rad^2/Hz$ at 1 Hz offset from the carrier.
We present first results from a number of experiments conducted on a 0.53 kg cylindrical dumbbell-shaped sapphire crystal. This is the first reported optomechanical experiment of this nature utilising a novel modification to the typical cylindrical architecture. Mechanical motion of the crystal structure alters the dimensions of the crystal, and the induced strain changes the permittivity. These two effects result in parametric frequency modulation of resonant microwave whispering gallery modes that are simultaneously excited within the crystal. A novel low-noise microwave readout system is implemented allowing extremely low noise measurements of this frequency modulation near our modes of interest, having a phase noise floor of -165 dBc/Hz at 100 kHz. Fine-tuning of the crystals suspension has allowed for the optimisation of mechanical quality factors in preparation for cryogenic experiments, with a value of Q=8 x 10^7 achieved at 127 kHz. This results in a Q x f product of 10^13, equivalent to the best measured values in a macroscopic sapphire mechanical system. Results are presented that demonstrate the excitation of mechanical modes via radiation pressure force, allowing an experimental method of determining the transducers displacement sensitivity df/dx, and calibrating the system. Finally, we demonstrate parametric back-action phenomenon within the system. These are all important steps towards the overall goal of the experiment; to cool a macroscopic device to the quantum ground state at millikelvin temperatures.
A low maintenance long-term operational cryogenic sapphire oscillator has been implemented at 11.2 GHz using an ultra-low-vibration cryostat and pulse-tube cryocooler. It is currently the worlds most stable microwave oscillator employing a cryocooler. Its performance is explained in terms of temperature and frequency stability. The phase noise and the Allan deviation of frequency fluctuations have been evaluated by comparing it to an ultra-stable liquid-helium cooled cryogenic sapphire oscillator in the same laboratory. Assuming both contribute equally, the Allan deviation evaluated for the cryocooled oscillator is sigma_y = 1 x 10^-15 tau^-1/2 for integration times 1 < tau < 10 s with a minimum sigma_y = 3.9 x 10^-16 at tau = 20 s. The long term frequency drift is less than 5 x 10^-14/day. From the measured power spectral density of phase fluctuations the single side band phase noise can be represented by L_phi(f) = 10^-14.0/f^4+10^-11.6/f^3+10^-10.0/f^2+10^-10.2/f+ 10^-11.0 for Fourier frequencies 10^-3<f<10^3 Hz in the single oscillator. As a result L_phi approx -97.5 dBc/Hz at 1 Hz offset from the carrier.
We demonstrate an easy to manufacture, 25 mm long ultra-stable optical reference cavity for transportable photonic microwave generation systems. Employing a rigid holding geometry that is first-order insensitive to the squeezing force and a cavity geometry that improves the thermal noise limit at room temperature, we observe a laser phase noise that is nearly thermal noise limited for three frequency decades (1 Hz to 1 kHz offset) and supports 10 GHz generation with phase noise near -100 dBc/Hz at 1 Hz offset and <-173 dBc/Hz for all offsets >600 Hz. The fractional frequency stability reaches $2times10^{-15}$ at 0.1 s of averaging.
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