{"title":"SQUID 阵列中的噪声缩放","authors":"O A Nieves, K-H Müller","doi":"10.1088/1361-6668/ad70dd","DOIUrl":null,"url":null,"abstract":"We numerically investigate the noise scaling in high-<italic toggle=\"yes\">T<sub>c</sub></italic> commensurate 1D and 2D SQUID arrays. We show that the voltage noise spectral density in 1D arrays violates the scaling rule of <inline-formula>\n<tex-math><?CDATA ${\\sim}1/N_p$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mrow><mml:mo>∼</mml:mo></mml:mrow><mml:mn>1</mml:mn><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi>p</mml:mi></mml:msub></mml:mrow></mml:math><inline-graphic xlink:href=\"sustad70ddieqn1.gif\"></inline-graphic></inline-formula> for the number <italic toggle=\"yes\">N<sub>p</sub></italic> of Josephson junctions in parallel. In contrast, in 2D arrays with <italic toggle=\"yes\">N<sub>s</sub></italic> 1D arrays in series, the voltage noise spectral density follows more closely the expected scaling behaviour of <inline-formula>\n<tex-math><?CDATA ${\\sim}N_s/N_p$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mrow><mml:mo>∼</mml:mo></mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi>s</mml:mi></mml:msub><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi>p</mml:mi></mml:msub></mml:mrow></mml:math><inline-graphic xlink:href=\"sustad70ddieqn2.gif\"></inline-graphic></inline-formula>. Additionally, we reveal how the flux and magnetic field rms noise spectral densities deviate from their expected <inline-formula>\n<tex-math><?CDATA ${\\sim}(N_sN_p)^{-1/2}$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mrow><mml:mo>∼</mml:mo></mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mi>s</mml:mi></mml:msub><mml:msub><mml:mi>N</mml:mi><mml:mi>p</mml:mi></mml:msub><mml:msup><mml:mo stretchy=\"false\">)</mml:mo><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math><inline-graphic xlink:href=\"sustad70ddieqn3.gif\"></inline-graphic></inline-formula> scaling and discuss their implications for designing low noise magnetometers.","PeriodicalId":21985,"journal":{"name":"Superconductor Science and Technology","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Noise scaling in SQUID arrays\",\"authors\":\"O A Nieves, K-H Müller\",\"doi\":\"10.1088/1361-6668/ad70dd\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We numerically investigate the noise scaling in high-<italic toggle=\\\"yes\\\">T<sub>c</sub></italic> commensurate 1D and 2D SQUID arrays. We show that the voltage noise spectral density in 1D arrays violates the scaling rule of <inline-formula>\\n<tex-math><?CDATA ${\\\\sim}1/N_p$?></tex-math><mml:math overflow=\\\"scroll\\\"><mml:mrow><mml:mrow><mml:mo>∼</mml:mo></mml:mrow><mml:mn>1</mml:mn><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi>p</mml:mi></mml:msub></mml:mrow></mml:math><inline-graphic xlink:href=\\\"sustad70ddieqn1.gif\\\"></inline-graphic></inline-formula> for the number <italic toggle=\\\"yes\\\">N<sub>p</sub></italic> of Josephson junctions in parallel. In contrast, in 2D arrays with <italic toggle=\\\"yes\\\">N<sub>s</sub></italic> 1D arrays in series, the voltage noise spectral density follows more closely the expected scaling behaviour of <inline-formula>\\n<tex-math><?CDATA ${\\\\sim}N_s/N_p$?></tex-math><mml:math overflow=\\\"scroll\\\"><mml:mrow><mml:mrow><mml:mo>∼</mml:mo></mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi>s</mml:mi></mml:msub><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi>p</mml:mi></mml:msub></mml:mrow></mml:math><inline-graphic xlink:href=\\\"sustad70ddieqn2.gif\\\"></inline-graphic></inline-formula>. Additionally, we reveal how the flux and magnetic field rms noise spectral densities deviate from their expected <inline-formula>\\n<tex-math><?CDATA ${\\\\sim}(N_sN_p)^{-1/2}$?></tex-math><mml:math overflow=\\\"scroll\\\"><mml:mrow><mml:mrow><mml:mo>∼</mml:mo></mml:mrow><mml:mo stretchy=\\\"false\\\">(</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mi>s</mml:mi></mml:msub><mml:msub><mml:mi>N</mml:mi><mml:mi>p</mml:mi></mml:msub><mml:msup><mml:mo stretchy=\\\"false\\\">)</mml:mo><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math><inline-graphic xlink:href=\\\"sustad70ddieqn3.gif\\\"></inline-graphic></inline-formula> scaling and discuss their implications for designing low noise magnetometers.\",\"PeriodicalId\":21985,\"journal\":{\"name\":\"Superconductor Science and Technology\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Superconductor Science and Technology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1088/1361-6668/ad70dd\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Superconductor Science and Technology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1088/1361-6668/ad70dd","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We numerically investigate the noise scaling in high-Tc commensurate 1D and 2D SQUID arrays. We show that the voltage noise spectral density in 1D arrays violates the scaling rule of ∼1/Np for the number Np of Josephson junctions in parallel. In contrast, in 2D arrays with Ns 1D arrays in series, the voltage noise spectral density follows more closely the expected scaling behaviour of ∼Ns/Np. Additionally, we reveal how the flux and magnetic field rms noise spectral densities deviate from their expected ∼(NsNp)−1/2 scaling and discuss their implications for designing low noise magnetometers.
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