Fundamental limits to frequency estimation: a comprehensive microscopic perspective
We consider a metrology scenario in which qubit-like probes are used to sense an external field that affects their energy splitting in a linear fashion. Following the frequency estimation approach in which one optimizes the state and sensing time of the probes to maximize the sensitivity, we provide...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2018-01-01
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| Series: | New Journal of Physics |
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| Online Access: | https://doi.org/10.1088/1367-2630/aab67f |
| _version_ | 1797750772090273792 |
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| author | J F Haase A Smirne J Kołodyński R Demkowicz-Dobrzański S F Huelga |
| author_facet | J F Haase A Smirne J Kołodyński R Demkowicz-Dobrzański S F Huelga |
| author_sort | J F Haase |
| collection | DOAJ |
| description | We consider a metrology scenario in which qubit-like probes are used to sense an external field that affects their energy splitting in a linear fashion. Following the frequency estimation approach in which one optimizes the state and sensing time of the probes to maximize the sensitivity, we provide a systematic study of the attainable precision under the impact of noise originating from independent bosonic baths. Specifically, we invoke an explicit microscopic derivation of the probe dynamics using the spin-boson model with weak coupling of arbitrary geometry. We clarify how the secular approximation leads to a phase-covariant (PC) dynamics, where the noise terms commute with the field Hamiltonian, while the inclusion of non-secular contributions breaks the PC. Moreover, unless one restricts to a particular (i.e., Ohmic) spectral density of the bath modes, the noise terms may contain relevant information about the frequency to be estimated. Thus, by considering general evolutions of a single probe, we study regimes in which these two effects have a non-negligible impact on the achievable precision. We then consider baths of Ohmic spectral density yet fully accounting for the lack of PC, in order to characterize the ultimate attainable scaling of precision when N probes are used in parallel. Crucially, we show that beyond the semigroup (Lindbladian) regime the Zeno limit imposing the 1/ N ^3/2 scaling of the mean squared error, recently derived assuming PC, generalises to any dynamics of the probes, unless the latter are coupled to the baths in the direction perfectly transversal to the frequency encoding—when a novel scaling of 1/ N ^7/4 arises. As our microscopic approach covers all classes of dissipative dynamics, from semigroup to non-Markovian ones (each of them potentially non-phase-covariant), it provides an exhaustive picture, in which all the different asymptotic scalings of precision naturally emerge. |
| first_indexed | 2024-03-12T16:37:44Z |
| format | Article |
| id | doaj.art-aed721ac5f7a4ee5845dc84f3e738434 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:37:44Z |
| publishDate | 2018-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-aed721ac5f7a4ee5845dc84f3e7384342023-08-08T14:48:06ZengIOP PublishingNew Journal of Physics1367-26302018-01-0120505300910.1088/1367-2630/aab67fFundamental limits to frequency estimation: a comprehensive microscopic perspectiveJ F Haase0A Smirne1J Kołodyński2https://orcid.org/0000-0001-8211-0016R Demkowicz-Dobrzański3S F Huelga4Institut für Theoretische Physik, Albert-Einstein-Allee 11, Universität Ulm , D-89069 Ulm, GermanyInstitut für Theoretische Physik, Albert-Einstein-Allee 11, Universität Ulm , D-89069 Ulm, GermanyICFO-Institut de Ciènces Fotòniques, The Barcelona Institute of Science and Technology, E-08860 Castelldefels (Barcelona), SpainFaculty of Physics, University of Warsaw , 02-093 Warszawa, PolandInstitut für Theoretische Physik, Albert-Einstein-Allee 11, Universität Ulm , D-89069 Ulm, GermanyWe consider a metrology scenario in which qubit-like probes are used to sense an external field that affects their energy splitting in a linear fashion. Following the frequency estimation approach in which one optimizes the state and sensing time of the probes to maximize the sensitivity, we provide a systematic study of the attainable precision under the impact of noise originating from independent bosonic baths. Specifically, we invoke an explicit microscopic derivation of the probe dynamics using the spin-boson model with weak coupling of arbitrary geometry. We clarify how the secular approximation leads to a phase-covariant (PC) dynamics, where the noise terms commute with the field Hamiltonian, while the inclusion of non-secular contributions breaks the PC. Moreover, unless one restricts to a particular (i.e., Ohmic) spectral density of the bath modes, the noise terms may contain relevant information about the frequency to be estimated. Thus, by considering general evolutions of a single probe, we study regimes in which these two effects have a non-negligible impact on the achievable precision. We then consider baths of Ohmic spectral density yet fully accounting for the lack of PC, in order to characterize the ultimate attainable scaling of precision when N probes are used in parallel. Crucially, we show that beyond the semigroup (Lindbladian) regime the Zeno limit imposing the 1/ N ^3/2 scaling of the mean squared error, recently derived assuming PC, generalises to any dynamics of the probes, unless the latter are coupled to the baths in the direction perfectly transversal to the frequency encoding—when a novel scaling of 1/ N ^7/4 arises. As our microscopic approach covers all classes of dissipative dynamics, from semigroup to non-Markovian ones (each of them potentially non-phase-covariant), it provides an exhaustive picture, in which all the different asymptotic scalings of precision naturally emerge.https://doi.org/10.1088/1367-2630/aab67fnoisy quantum metrologyopen quantum systemsmicroscopic derivationultimate estimation precision limits |
| spellingShingle | J F Haase A Smirne J Kołodyński R Demkowicz-Dobrzański S F Huelga Fundamental limits to frequency estimation: a comprehensive microscopic perspective New Journal of Physics noisy quantum metrology open quantum systems microscopic derivation ultimate estimation precision limits |
| title | Fundamental limits to frequency estimation: a comprehensive microscopic perspective |
| title_full | Fundamental limits to frequency estimation: a comprehensive microscopic perspective |
| title_fullStr | Fundamental limits to frequency estimation: a comprehensive microscopic perspective |
| title_full_unstemmed | Fundamental limits to frequency estimation: a comprehensive microscopic perspective |
| title_short | Fundamental limits to frequency estimation: a comprehensive microscopic perspective |
| title_sort | fundamental limits to frequency estimation a comprehensive microscopic perspective |
| topic | noisy quantum metrology open quantum systems microscopic derivation ultimate estimation precision limits |
| url | https://doi.org/10.1088/1367-2630/aab67f |
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