Quantum theory of optical temporal phase and instantaneous frequency. II. Continuous-time
We consider the continuous-time version of our recently proposed quantum theory of optical temporal phase and instantaneous frequency [M. Tsang et al., Phys. Rev. A 78, 053820 (2008)]. Using a state-variable approach to estimation, we design homodyne phase-locked loops that can measure the temporal...
| Main Authors: | , , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
American Physical Society
2010
|
| Online Access: | http://hdl.handle.net/1721.1/51033 https://orcid.org/0000-0001-7173-1239 https://orcid.org/0000-0002-6094-5861 |
| _version_ | 1811081547056414720 |
|---|---|
| author | Tsang, Mankei Shapiro, Jeffrey H. Lloyd, Seth |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Tsang, Mankei Shapiro, Jeffrey H. Lloyd, Seth |
| author_sort | Tsang, Mankei |
| collection | MIT |
| description | We consider the continuous-time version of our recently proposed quantum theory of optical temporal phase and instantaneous frequency [M. Tsang et al., Phys. Rev. A 78, 053820 (2008)]. Using a state-variable approach to estimation, we design homodyne phase-locked loops that can measure the temporal phase with quantum-limited accuracy. We show that postprocessing can further improve the estimation performance if delay is allowed in the estimation. We also investigate the fundamental uncertainties in the simultaneous estimation of harmonic-oscillator position and momentum via continuous optical phase measurements from the classical estimation theory perspective. In the case of delayed estimation, we find that the inferred uncertainty product can drop below that allowed by the Heisenberg uncertainty relation. Although this result seems counterintuitive, we argue that it does not violate any basic principle of quantum mechanics. |
| first_indexed | 2024-09-23T11:48:16Z |
| format | Article |
| id | mit-1721.1/51033 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T11:48:16Z |
| publishDate | 2010 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/510332022-09-27T22:00:23Z Quantum theory of optical temporal phase and instantaneous frequency. II. Continuous-time Tsang, Mankei Shapiro, Jeffrey H. Lloyd, Seth Massachusetts Institute of Technology. Department of Mechanical Engineering Massachusetts Institute of Technology. Research Laboratory of Electronics Shapiro, Jeffrey H. Tsang, Mankei Shapiro, Jeffrey H. Lloyd, Seth We consider the continuous-time version of our recently proposed quantum theory of optical temporal phase and instantaneous frequency [M. Tsang et al., Phys. Rev. A 78, 053820 (2008)]. Using a state-variable approach to estimation, we design homodyne phase-locked loops that can measure the temporal phase with quantum-limited accuracy. We show that postprocessing can further improve the estimation performance if delay is allowed in the estimation. We also investigate the fundamental uncertainties in the simultaneous estimation of harmonic-oscillator position and momentum via continuous optical phase measurements from the classical estimation theory perspective. In the case of delayed estimation, we find that the inferred uncertainty product can drop below that allowed by the Heisenberg uncertainty relation. Although this result seems counterintuitive, we argue that it does not violate any basic principle of quantum mechanics. W. M. Keck Foundation Center for Extreme Quantum Information Theory 2010-01-29T18:18:40Z 2010-01-29T18:18:40Z 2009-05 2009-02 Article http://purl.org/eprint/type/JournalArticle 1094-1622 1050-2947 http://hdl.handle.net/1721.1/51033 Tsang, Mankei , Jeffrey H. Shapiro, and Seth Lloyd. “Quantum theory of optical temporal phase and instantaneous frequency. II. Continuous-time limit and state-variable approach to phase-locked loop design.” Physical Review A 79.5 (2009): 053843. (C) 2010 The American Physical Society. https://orcid.org/0000-0001-7173-1239 https://orcid.org/0000-0002-6094-5861 en_US http://dx.doi.org/10.1103/PhysRevA.79.053843 Physical Review A Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Physical Society APS |
| spellingShingle | Tsang, Mankei Shapiro, Jeffrey H. Lloyd, Seth Quantum theory of optical temporal phase and instantaneous frequency. II. Continuous-time |
| title | Quantum theory of optical temporal phase and instantaneous frequency. II. Continuous-time |
| title_full | Quantum theory of optical temporal phase and instantaneous frequency. II. Continuous-time |
| title_fullStr | Quantum theory of optical temporal phase and instantaneous frequency. II. Continuous-time |
| title_full_unstemmed | Quantum theory of optical temporal phase and instantaneous frequency. II. Continuous-time |
| title_short | Quantum theory of optical temporal phase and instantaneous frequency. II. Continuous-time |
| title_sort | quantum theory of optical temporal phase and instantaneous frequency ii continuous time |
| url | http://hdl.handle.net/1721.1/51033 https://orcid.org/0000-0001-7173-1239 https://orcid.org/0000-0002-6094-5861 |
| work_keys_str_mv | AT tsangmankei quantumtheoryofopticaltemporalphaseandinstantaneousfrequencyiicontinuoustime AT shapirojeffreyh quantumtheoryofopticaltemporalphaseandinstantaneousfrequencyiicontinuoustime AT lloydseth quantumtheoryofopticaltemporalphaseandinstantaneousfrequencyiicontinuoustime |