Sensitivity of parameter estimation near the exceptional point of a non-Hermitian system
The exceptional points (EPs) of non-Hermitian systems, where n different energy eigenstates merge into an identical one, have many intriguing properties that have no counterparts in Hermitian systems. In particular, the ϵ 1 n dependence of the energy level splitting on a perturbative parameter ϵ nea...
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| Veröffentlicht in: | New journal of physics 2019-08, Vol.21 (8), p.83002 |
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| creator | Chen, Chong Jin, Liang Liu, Ren-Bao |
| description | The exceptional points (EPs) of non-Hermitian systems, where n different energy eigenstates merge into an identical one, have many intriguing properties that have no counterparts in Hermitian systems. In particular, the ϵ 1 n dependence of the energy level splitting on a perturbative parameter ϵ near an nth order EP stimulates the idea of metrology with arbitrarily high sensitivity, since the susceptibility dϵ1/n/dϵ diverges at the EP. Here we theoretically study the sensitivity of parameter estimation near the EPs, using the exact formalism of quantum Fisher information (QFI). The QFI formalism allows the highest sensitivity to be determined without specifying a specific measurement approach. We find that the EP bears no dramatic enhancement of the sensitivity. Instead, the coalescence of the eigenstates exactly counteracts the eigenvalue susceptibility divergence and makes the sensitivity a smooth function of the perturbative parameter. |
| doi_str_mv | 10.1088/1367-2630/ab32ab |
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In particular, the ϵ 1 n dependence of the energy level splitting on a perturbative parameter ϵ near an nth order EP stimulates the idea of metrology with arbitrarily high sensitivity, since the susceptibility dϵ1/n/dϵ diverges at the EP. Here we theoretically study the sensitivity of parameter estimation near the EPs, using the exact formalism of quantum Fisher information (QFI). The QFI formalism allows the highest sensitivity to be determined without specifying a specific measurement approach. We find that the EP bears no dramatic enhancement of the sensitivity. Instead, the coalescence of the eigenstates exactly counteracts the eigenvalue susceptibility divergence and makes the sensitivity a smooth function of the perturbative parameter.</description><identifier>ISSN: 1367-2630</identifier><identifier>EISSN: 1367-2630</identifier><identifier>DOI: 10.1088/1367-2630/ab32ab</identifier><identifier>CODEN: NJOPFM</identifier><language>eng</language><publisher>Bristol: IOP Publishing</publisher><subject>Coalescing ; Eigenvalues ; Eigenvectors ; Energy levels ; exceptional point ; Fisher information ; Formalism ; non-Hermitian system ; Parameter estimation ; Parameter sensitivity ; Physics ; quantum Fisher information ; sensitivity ; Sensitivity enhancement</subject><ispartof>New journal of physics, 2019-08, Vol.21 (8), p.83002</ispartof><rights>2019 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft</rights><rights>2019. 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Phys</addtitle><description>The exceptional points (EPs) of non-Hermitian systems, where n different energy eigenstates merge into an identical one, have many intriguing properties that have no counterparts in Hermitian systems. In particular, the ϵ 1 n dependence of the energy level splitting on a perturbative parameter ϵ near an nth order EP stimulates the idea of metrology with arbitrarily high sensitivity, since the susceptibility dϵ1/n/dϵ diverges at the EP. Here we theoretically study the sensitivity of parameter estimation near the EPs, using the exact formalism of quantum Fisher information (QFI). The QFI formalism allows the highest sensitivity to be determined without specifying a specific measurement approach. We find that the EP bears no dramatic enhancement of the sensitivity. Instead, the coalescence of the eigenstates exactly counteracts the eigenvalue susceptibility divergence and makes the sensitivity a smooth function of the perturbative parameter.</description><subject>Coalescing</subject><subject>Eigenvalues</subject><subject>Eigenvectors</subject><subject>Energy levels</subject><subject>exceptional point</subject><subject>Fisher information</subject><subject>Formalism</subject><subject>non-Hermitian system</subject><subject>Parameter estimation</subject><subject>Parameter sensitivity</subject><subject>Physics</subject><subject>quantum Fisher information</subject><subject>sensitivity</subject><subject>Sensitivity enhancement</subject><issn>1367-2630</issn><issn>1367-2630</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><sourceid>O3W</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>DOA</sourceid><recordid>eNp9kc1L5TAUxYs44MfM3mXAhRuryU1emi5F_ALBhTMwu3DT3moe7zU1ieL7722ng7oQVwmHc365ObcoDgQ_EdyYUyF1VYKW_BSdBHRbxe67tP3pvlPspbTkXAgDsFv8vac--exffN6w0LEBI64pU2SUsl9j9qFnPWFk-ZEYvTY0TBKu2BB8n6cIsj705TXF9cjBnqVNyrT-WfzocJXo1_9zv_hzefH7_Lq8vbu6OT-7LZuFULlUuuW6wdbVTSU7cmZRS16BJlCV7oxaYEt1bTRQ22FjuHbGaVmJ1kAjpEC5X9zM3Dbg0g5xnDlubEBv_wkhPliM2TcrspwUALhKYE1KKHSoQGveubbStFA0sg5n1hDD0_NYgF2G5zh-NlmQAmRluIHRxWdXE0NKkbr3VwW30y7sVLadyrbzLsbI8RzxYfhgfmM_-sLeLwcLwhrLjeQc7NB28g3YKJg1</recordid><startdate>20190802</startdate><enddate>20190802</enddate><creator>Chen, Chong</creator><creator>Jin, Liang</creator><creator>Liu, Ren-Bao</creator><general>IOP Publishing</general><scope>O3W</scope><scope>TSCCA</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>8FD</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>H8D</scope><scope>L7M</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>DOA</scope></search><sort><creationdate>20190802</creationdate><title>Sensitivity of parameter estimation near the exceptional point of a non-Hermitian system</title><author>Chen, Chong ; Jin, Liang ; Liu, Ren-Bao</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c514t-46d06cadb9c73feb85930726e2476f845ade99862edfac806b8b6371d82c131a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Coalescing</topic><topic>Eigenvalues</topic><topic>Eigenvectors</topic><topic>Energy levels</topic><topic>exceptional point</topic><topic>Fisher information</topic><topic>Formalism</topic><topic>non-Hermitian system</topic><topic>Parameter estimation</topic><topic>Parameter sensitivity</topic><topic>Physics</topic><topic>quantum Fisher information</topic><topic>sensitivity</topic><topic>Sensitivity enhancement</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Chen, Chong</creatorcontrib><creatorcontrib>Jin, Liang</creatorcontrib><creatorcontrib>Liu, Ren-Bao</creatorcontrib><collection>Institute of Physics Open Access Journal Titles</collection><collection>IOPscience (Open Access)</collection><collection>CrossRef</collection><collection>Technology Research Database</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>DOAJ Directory of Open Access Journals</collection><jtitle>New journal of physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Chen, Chong</au><au>Jin, Liang</au><au>Liu, Ren-Bao</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Sensitivity of parameter estimation near the exceptional point of a non-Hermitian system</atitle><jtitle>New journal of physics</jtitle><stitle>NJP</stitle><addtitle>New J. 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Instead, the coalescence of the eigenstates exactly counteracts the eigenvalue susceptibility divergence and makes the sensitivity a smooth function of the perturbative parameter.</abstract><cop>Bristol</cop><pub>IOP Publishing</pub><doi>10.1088/1367-2630/ab32ab</doi><tpages>15</tpages><oa>free_for_read</oa></addata></record> |
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| subjects | Coalescing Eigenvalues Eigenvectors Energy levels exceptional point Fisher information Formalism non-Hermitian system Parameter estimation Parameter sensitivity Physics quantum Fisher information sensitivity Sensitivity enhancement |
| title | Sensitivity of parameter estimation near the exceptional point of a non-Hermitian system |
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