Reliability and Reproducibility of the Cryogenic Sapphire Oscillator Technology

Abstract

International audienceThe cryogenic sapphire oscillator (CSO) is a highly specializedmachine, which delivers a microwave reference signal exhibiting thelowest frequency fluctuations [Allan deviation (ADEV) <span class="MathJax" id="MathJax-Element-9-Frame" tabindex="0" style=""&gt<nobr&gt<span class="math" id="MathJax-Span-57" style="width: 2.78em; display: inline-block;"&gt<span style="display: inline-block; position: relative; width: 2.315em; height: 0px; font-size: 120%;"&gt<span style="position: absolute; clip: rect(1.426em, 1002.22em, 2.749em, -1000em); top: -2.315em; left: 0em;"&gt<span class="mrow" id="MathJax-Span-58"&gt<span class="msubsup" id="MathJax-Span-59"&gt<span style="display: inline-block; position: relative; width: 0.997em; height: 0px;"&gt<span style="position: absolute; clip: rect(3.412em, 1000.57em, 4.131em, -1000em); top: -3.981em; left: 0em;"&gt<span class="mi" id="MathJax-Span-60" style="font-family: MathJax_Math; font-style: italic;"&gtσ</span&gt</span&gt<span style="position: absolute; top: -3.831em; left: 0.571em;"&gt<span class="texatom"id="MathJax-Span-61"&gt<span class="mrow" id="MathJax-Span-62"&gt<span class="mi" id="MathJax-Span-63" style="font-size: 70.7%; font-family: MathJax_Math; font-style: italic;"&gty</span&gt</span&gt</span&gt</span&gt</span&gt</span&gt<span class="mo"id="MathJax-Span-64" style="font-family: MathJax_Main;"&gt(</span&gt<span class="mi" id="MathJax-Span-65" style="font-family: MathJax_Math; font-style: italic;"&gtτ</span&gt<span class="mo"id="MathJax-Span-66" style="font-family: MathJax_Main;"&gt)</span&gt</span&gt</span&gt</span&gt</span&gt</nobr&gt</span&gt] for the integration time <span class="MathJax" id="MathJax-Element-10-Frame" tabindex="0" style=""&gt<nobr&gt<span class="math" id="MathJax-Span-67" style="width: 0.604em; display: inline-block;"&gt<span style="display: inline-block; position: relative; width: 0.509em; height: 0px; font-size: 120%;"&gt<span style="position: absolute; clip: rect(1.745em, 1000.51em, 2.467em, -1000em); top: -2.315em; left: 0em;"&gt<span class="mrow" id="MathJax-Span-68"&gt<span class="mi" id="MathJax-Span-69" style="font-family: MathJax_Math; font-style: italic;"&gtτ</span&gt</span&gt</span&gt</span&gt</span&gt</nobr&gt</span&gtbetween 1 and <span class="MathJax" id="MathJax-Element-11-Frame"tabindex="0" style=""&gt<nobr&gt<span class="math" id="MathJax-Span-70"style="width: 1.762em; display: inline-block;"&gt<span style="display: inline-block; position: relative; width: 1.435em; height: 0px; font-size: 120%;"&gt<span style="position: absolute; clip: rect(1.165em, 1001.44em, 2.337em, -1000em); top: -2.176em; left: 0em;"&gt<span class="mrow" id="MathJax-Span-71"&gt<span class="msubsup" id="MathJax-Span-72"&gt<span style="display: inline-block; position: relative; width: 1.429em; height: 0px;"&gt<span style="position: absolute; clip: rect(3.177em, 1000.96em, 4.142em, -1000em); top: -3.981em; left: 0em;"&gt<span class="mn" id="MathJax-Span-73" style="font-family: MathJax_Main;"&gt10</span&gt</span&gt<span style="position: absolute; top: -4.374em; left: 1em;"&gt<span class="texatom" id="MathJax-Span-74"&gt<span class="mrow" id="MathJax-Span-75"&gt<span class="mn" id="MathJax-Span-76" style="font-size: 70.7%; font-family: MathJax_Main;"&gt4</span&gt</span&gt</span&gt</span&gt</span&gt</span&gt</span&gt</span&gt</span&gt</span&gt</nobr&gt</span&gts, indeed four decades. In such interval, good units feature<span class="MathJax" id="MathJax-Element-12-Frame" tabindex="0"style=""&gt<nobr&gt<span class="math" id="MathJax-Span-77" style="width: 7.178em; display: inline-block;"&gt<span style="display: inline-block; position: relative; width: 5.972em; height: 0px; font-size: 120%;"&gt<span style="position: absolute; clip: rect(1.312em, 1005.97em, 2.749em, -1000em); top: -2.315em; left: 0em;"&gt<span class="mrow" id="MathJax-Span-78"&gt<span class="msubsup" id="MathJax-Span-79"&gt<span style="display: inline-block; position: relative; width: 0.997em; height: 0px;"&gt<span style="position: absolute; clip: rect(3.412em, 1000.57em, 4.131em, -1000em); top: -3.981em; left: 0em;"&gt<span class="mi" id="MathJax-Span-80" style="font-family: MathJax_Math; font-style: italic;"&gtσ</span&gt</span&gt<span style="position: absolute; top: -3.831em; left: 0.571em;"&gt<span class="texatom"id="MathJax-Span-81"&gt<span class="mrow" id="MathJax-Span-82"&gt<span class="mi" id="MathJax-Span-83" style="font-size: 70.7%; font-family: MathJax_Math; font-style: italic;"&gty</span&gt</span&gt</span&gt</span&gt</span&gt</span&gt<span class="mo"id="MathJax-Span-84" style="font-family: MathJax_Main;"&gt(</span&gt<span class="mi" id="MathJax-Span-85" style="font-family: MathJax_Math; font-style: italic;"&gtτ</span&gt<span class="mo"id="MathJax-Span-86" style="font-family: MathJax_Main;"&gt)</span&gt<span class="mo" id="MathJax-Span-87" style="font-family: MathJax_Main; padding-left: 0.278em;"&gt&lt;</span&gt<span class="msubsup"id="MathJax-Span-88" style="padding-left: 0.278em;"&gt<span style="display: inline-block; position: relative; width: 2.332em; height: 0px;"&gt<span style="position: absolute; clip: rect(3.177em, 1000.96em, 4.142em, -1000em); top: -3.981em; left: 0em;"&gt<span class="mn"id="MathJax-Span-89" style="font-family: MathJax_Main;"&gt10</span&gt</span&gt<span style="position: absolute; top: -4.374em; left: 1em;"&gt<span class="texatom" id="MathJax-Span-90"&gt<span class="mrow" id="MathJax-Span-91"&gt<span class="mo" id="MathJax-Span-92" style="font-size: 70.7%; font-family: MathJax_Main;"&gt−</span&gt<span class="mn" id="MathJax-Span-93" style="font-size: 70.7%; font-family: MathJax_Main;"&gt15</span&gt</span&gt</span&gt</span&gt</span&gt</span&gt</span&gt</span&gt</span&gt</span&gt</nobr&gt</span&gt, with <span class="MathJax" id="MathJax-Element-13-Frame"tabindex="0" style=""&gt<nobr&gt<span class="math" id="MathJax-Span-94"style="width: 4.076em; display: inline-block;"&gt<span style="display: inline-block; position: relative; width: 3.38em; height: 0px; font-size: 120%;"&gt<span style="position: absolute; clip: rect(1.212em, 1003.38em, 2.401em, -1000em); top: -2.222em; left: 0em;"&gt<span class="mrow" id="MathJax-Span-95"&gt<span class="mo" id="MathJax-Span-96" style="font-family: MathJax_Main;"&gt&lt;</span&gt<span class="msubsup" id="MathJax-Span-97" style="padding-left: 0.278em;"&gt<span style="display: inline-block; position: relative; width: 2.332em; height: 0px;"&gt<span style="position: absolute; clip: rect(3.177em, 1000.96em, 4.142em, -1000em); top: -3.981em; left: 0em;"&gt<span class="mn"id="MathJax-Span-98" style="font-family: MathJax_Main;"&gt10</span&gt</span&gt<span style="position: absolute; top: -4.374em; left: 1em;"&gt<span class="texatom" id="MathJax-Span-99"&gt<span class="mrow" id="MathJax-Span-100"&gt<span class="mo" id="MathJax-Span-101" style="font-size: 70.7%; font-family: MathJax_Main;"&gt−</span&gt<span class="mn" id="MathJax-Span-102" style="font-size: 70.7%; font-family: MathJax_Main;"&gt14</span&gt</span&gt</span&gt</span&gt</span&gt</span&gt</span&gt</span&gt</span&gt</span&gt</nobr&gt</span&gtdrift in one day. The oscillator is based on a sapphire monocrystalresonating at 10 GHz in a whispering-gallery mode, cooled at<span class="MathJax" id="MathJax-Element-14-Frame" tabindex="0"style=""&gt<nobr&gt<span class="math" id="MathJax-Span-103" style="width: 1.9em; display: inline-block;"&gt<span style="display: inline-block; position: relative; width: 1.574em; height: 0px; font-size: 120%;"&gt<span style="position: absolute; clip: rect(1.417em, 1001.53em, 2.383em, -1000em); top: -2.222em; left: 0em;"&gt<span class="mrow" id="MathJax-Span-104"&gt<span class="mo" id="MathJax-Span-105" style="font-family: MathJax_Main;"&gt≈</span&gt<span class="mn" id="MathJax-Span-106" style="font-family: MathJax_Main; padding-left: 0.278em;"&gt6</span&gt</span&gt</span&gt</span&gt</span&gt</nobr&gt</span&gtK for zero thermal coefficient and optimal quality factor<span class="MathJax" id="MathJax-Element-15-Frame" tabindex="0"style=""&gt<nobr&gt<span class="math" id="MathJax-Span-107" style="width: 0.975em; display: inline-block;"&gt<span style="display: inline-block; position: relative; width: 0.787em; height: 0px; font-size: 120%;"&gt<span style="position: absolute; clip: rect(1.472em, 1000.74em, 2.648em, -1000em); top: -2.315em; left: 0em;"&gt<span class="mrow" id="MathJax-Span-108"&gt<span class="mi" id="MathJax-Span-109" style="font-family: MathJax_Math; font-style: italic;"&gtQ</span&gt</span&gt</span&gt</span&gt</span&gt</nobr&gt</span&gt. We report on the progress accomplished in implementing 11 CSOs inabout ten years since the first sample was delivered to theMalargüe station of the European Space Agency (ESA) in Argentina.Short-term stability is improved by a factor of 3–10, depending on<span class="MathJax" id="MathJax-Element-16-Frame" tabindex="0"style=""&gt<nobr&gt<span class="math" id="MathJax-Span-110" style="width: 0.604em; display: inline-block;"&gt<span style="display: inline-block; position: relative; width: 0.509em; height: 0px; font-size: 120%;"&gt<span style="position: absolute; clip: rect(1.745em, 1000.51em, 2.467em, -1000em); top: -2.315em; left: 0em;"&gt<span class="mrow" id="MathJax-Span-111"&gt<span class="mi" id="MathJax-Span-112" style="font-family: MathJax_Math; font-style: italic;"&gtτ</span&gt</span&gt</span&gt</span&gt</span&gt</nobr&gt</span&gt, and the refrigerator’s electric power is reduced to a 3-kWsingle-phase line. Frequency stability and overall performances arereproducible, with unattended operation between scheduledmaintenance every two years. The CSO is now a semicommercialproduct suitable to scientific applications requiring extremefrequency stability with the reliable unattended long-termoperation, like the flywheel for primary frequency standards, theground segment of global navigation satellite system (GNSS),astrometry, very long baseline interferometry (VLBI), and radioastronomy stations