{"id":{"repo_id":"auckland-ms","oai_identifier":"oai:researchspace.auckland.ac.nz:2292/66282"},"canonical_url":"https://search.dev.ndltd.org/etd/auckland-ms/oai:researchspace.auckland.ac.nz:2292/66282","repository":{"repo_id":"auckland-ms","name":"University of Auckland","base_url":"https://researchspace.auckland.ac.nz/server/oai/request"},"display":{"title":"Frequency-Filtered Photon Correlations","abstract":"In quantum optics, the standard approach for measuring and calculating frequency-filtered photon correlations is to filter the source field of interest with a Lorentzian-type filter, e.g., a tunable single-mode cavity or detector atom. However, given the inverse relation between a filter’s bandwidth and temporal response, there is trade-off between the frequency isolation and temporal response of the filter. A broad bandwidth results in a faster temporal response with more accurately measured photon correlations, yet the slow decaying tails of a Lorentzian distribution can allow for non-target frequency photons to pass through the filter. Conversely, a narrow filter bandwidth results in more effective frequency isolation, yet a slow temporal response, potentially changing the nature of the emitted photon correlations. The aim of this work is to develop a theoretical filtering technique that is simple to implement and offers an effective method of calculating frequency-filtered photon correlations. We model our filter as a multi-mode array filter, which consists of an array of tunable single-mode cavities that are equally spaced in frequency. By introducing a mode-dependent phase modulation, we produce a near rectangular frequency response, allowing us to increase the filter bandwidth – and thus the temporal response – without sacrificing frequency isolation. To ensure the filter has no effect on the evolution of the source system, we couple the source system using a cascaded quantum open systems approach. The complete lack of back-action of the filter onto the source system allows us to derive a closed set of operator moment equations for source and filter system operators. This provides an extremely effective and computationally efficient way to calculate frequency-filtered first- and second-order correlation functions. By coupling the target field into two multi-mode array filters, we can set the resonance of the two filters to two different transitions, and thus calculate frequency-filtered cross-correlation functions. We demonstrate this novel filtering method by applying it to two different driven quantum systems: a resonantly driven two-level atom and a three-level ladder-type atom driven at two-photon resonance. We present results of frequency-filtered power spectrum to demonstrate the improved frequency isolation of the multi-mode array filter over the single-mode filter. We then present results for the single-mode and multi-mode array filtered second-order auto- and cross-correlation functions. These are compared against expressions derived in the secular approximation. The improved frequency isolation of the multi-mode array filter allows us to investigate new areas of frequency-filtered photon correlations, such as two-photon leapfrog processes, and the effect of vanishing bandwidth on filtered auto-correlation functions.","abstract_html":"In quantum optics, the standard approach for measuring and calculating frequency-filtered photon correlations is to filter the source field of interest with a Lorentzian-type filter, e.g., a tunable single-mode cavity or detector atom. However, given the inverse relation between a filter’s bandwidth and temporal response, there is trade-off between the frequency isolation and temporal response of the filter. A broad bandwidth results in a faster temporal response with more accurately measured photon correlations, yet the slow decaying tails of a Lorentzian distribution can allow for non-target frequency photons to pass through the filter. Conversely, a narrow filter bandwidth results in more effective frequency isolation, yet a slow temporal response, potentially changing the nature of the emitted photon correlations. The aim of this work is to develop a theoretical filtering technique that is simple to implement and offers an effective method of calculating frequency-filtered photon correlations. We model our filter as a multi-mode array filter, which consists of an array of tunable single-mode cavities that are equally spaced in frequency. By introducing a mode-dependent phase modulation, we produce a near rectangular frequency response, allowing us to increase the filter bandwidth – and thus the temporal response – without sacrificing frequency isolation. To ensure the filter has no effect on the evolution of the source system, we couple the source system using a cascaded quantum open systems approach. The complete lack of back-action of the filter onto the source system allows us to derive a closed set of operator moment equations for source and filter system operators. This provides an extremely effective and computationally efficient way to calculate frequency-filtered first- and second-order correlation functions. By coupling the target field into two multi-mode array filters, we can set the resonance of the two filters to two different transitions, and thus calculate frequency-filtered cross-correlation functions. We demonstrate this novel filtering method by applying it to two different driven quantum systems: a resonantly driven two-level atom and a three-level ladder-type atom driven at two-photon resonance. We present results of frequency-filtered power spectrum to demonstrate the improved frequency isolation of the multi-mode array filter over the single-mode filter. We then present results for the single-mode and multi-mode array filtered second-order auto- and cross-correlation functions. These are compared against expressions derived in the secular approximation. The improved frequency isolation of the multi-mode array filter allows us to investigate new areas of frequency-filtered photon correlations, such as two-photon leapfrog processes, and the effect of vanishing bandwidth on filtered auto-correlation functions.","abstract_has_math":false,"creators":["Ngaha, Jacob Peter Kia"],"institution":"ResearchSpace@Auckland","degree_name":"PhD","degree_level":"Doctoral","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":[],"advisors":["Carmichael, Howard","Parkins, Scott"],"committee_chairs":[],"committee_members":[],"year":2023,"date_issued":"2023","date_published":"2023","updated_at":"2026-07-24T01:03:37Z","subjects":[],"languages":[],"rights":["Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated."],"rights_urls":["https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm"],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2292/66282","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Carmichael, Howard","Parkins, Scott"]},{"key":"dc:creator","label":"Author","values":["Ngaha, Jacob Peter Kia"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2023-10-12T21:17:38Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2023-10-12T21:17:38Z"]},{"key":"dc:date.issued","label":"Date","values":["2023"]},{"key":"dc:publisher","label":"Institution","values":["ResearchSpace@Auckland"]},{"key":"dc:relation.isreferencedby","label":"Dc Relation Isreferencedby","values":["UoA99265572640802091"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Physics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["PhD"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["The University of Auckland"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated."]},{"key":"dc:rights.uri","label":"Rights URI","values":["https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/2292/66282"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In quantum optics, the standard approach for measuring and calculating frequency-filtered photon correlations is to filter the source field of interest with a Lorentzian-type filter, e.g., a tunable single-mode cavity or detector atom. However, given the inverse relation between a filter’s bandwidth and temporal response, there is trade-off between the frequency isolation and temporal response of the filter. A broad bandwidth results in a faster temporal response with more accurately measured photon correlations, yet the slow decaying tails of a Lorentzian distribution can allow for non-target frequency photons to pass through the filter. Conversely, a narrow filter bandwidth results in more effective frequency isolation, yet a slow temporal response, potentially changing the nature of the emitted photon correlations. The aim of this work is to develop a theoretical filtering technique that is simple to implement and offers an effective method of calculating frequency-filtered photon correlations. We model our filter as a multi-mode array filter, which consists of an array of tunable single-mode cavities that are equally spaced in frequency. By introducing a mode-dependent phase modulation, we produce a near rectangular frequency response, allowing us to increase the filter bandwidth – and thus the temporal response – without sacrificing frequency isolation. To ensure the filter has no effect on the evolution of the source system, we couple the source system using a cascaded quantum open systems approach. The complete lack of back-action of the filter onto the source system allows us to derive a closed set of operator moment equations for source and filter system operators. This provides an extremely effective and computationally efficient way to calculate frequency-filtered first- and second-order correlation functions. By coupling the target field into two multi-mode array filters, we can set the resonance of the two filters to two different transitions, and thus calculate frequency-filtered cross-correlation functions. We demonstrate this novel filtering method by applying it to two different driven quantum systems: a resonantly driven two-level atom and a three-level ladder-type atom driven at two-photon resonance. We present results of frequency-filtered power spectrum to demonstrate the improved frequency isolation of the multi-mode array filter over the single-mode filter. We then present results for the single-mode and multi-mode array filtered second-order auto- and cross-correlation functions. These are compared against expressions derived in the secular approximation. The improved frequency isolation of the multi-mode array filter allows us to investigate new areas of frequency-filtered photon correlations, such as two-photon leapfrog processes, and the effect of vanishing bandwidth on filtered auto-correlation functions."]},{"key":"dc:title","label":"Title","values":["Frequency-Filtered Photon Correlations"]}]}],"canonical_facts":{"dc:contributor.advisor":["Carmichael, Howard","Parkins, Scott"],"dc:creator":["Ngaha, Jacob Peter Kia"],"dc:date.accessioned":["2023-10-12T21:17:38Z"],"dc:date.available":["2023-10-12T21:17:38Z"],"dc:date.issued":["2023"],"dc:description.abstract":["In quantum optics, the standard approach for measuring and calculating frequency-filtered photon correlations is to filter the source field of interest with a Lorentzian-type filter, e.g., a tunable single-mode cavity or detector atom. However, given the inverse relation between a filter’s bandwidth and temporal response, there is trade-off between the frequency isolation and temporal response of the filter. A broad bandwidth results in a faster temporal response with more accurately measured photon correlations, yet the slow decaying tails of a Lorentzian distribution can allow for non-target frequency photons to pass through the filter. Conversely, a narrow filter bandwidth results in more effective frequency isolation, yet a slow temporal response, potentially changing the nature of the emitted photon correlations. The aim of this work is to develop a theoretical filtering technique that is simple to implement and offers an effective method of calculating frequency-filtered photon correlations. We model our filter as a multi-mode array filter, which consists of an array of tunable single-mode cavities that are equally spaced in frequency. By introducing a mode-dependent phase modulation, we produce a near rectangular frequency response, allowing us to increase the filter bandwidth – and thus the temporal response – without sacrificing frequency isolation. To ensure the filter has no effect on the evolution of the source system, we couple the source system using a cascaded quantum open systems approach. The complete lack of back-action of the filter onto the source system allows us to derive a closed set of operator moment equations for source and filter system operators. This provides an extremely effective and computationally efficient way to calculate frequency-filtered first- and second-order correlation functions. By coupling the target field into two multi-mode array filters, we can set the resonance of the two filters to two different transitions, and thus calculate frequency-filtered cross-correlation functions. We demonstrate this novel filtering method by applying it to two different driven quantum systems: a resonantly driven two-level atom and a three-level ladder-type atom driven at two-photon resonance. We present results of frequency-filtered power spectrum to demonstrate the improved frequency isolation of the multi-mode array filter over the single-mode filter. We then present results for the single-mode and multi-mode array filtered second-order auto- and cross-correlation functions. These are compared against expressions derived in the secular approximation. The improved frequency isolation of the multi-mode array filter allows us to investigate new areas of frequency-filtered photon correlations, such as two-photon leapfrog processes, and the effect of vanishing bandwidth on filtered auto-correlation functions."],"dc:identifier.uri":["https://hdl.handle.net/2292/66282"],"dc:publisher":["ResearchSpace@Auckland"],"dc:relation.isreferencedby":["UoA99265572640802091"],"dc:rights":["Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated."],"dc:rights.uri":["https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm"],"dc:title":["Frequency-Filtered Photon Correlations"],"dc:type":["Thesis"],"thesis:degree_discipline":["Physics"],"thesis:degree_level":["Doctoral"],"thesis:degree_name":["PhD"],"thesis:institution_name":["The University of Auckland"]},"updated_at":"2026-07-24T01:03:37Z"}