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Pancharatnam-Berry Phase in Quantum Optics

Relation to Bargmann Invariants and Geodesics

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Abstract

A quantum system, when subjected to an adiabatic cyclic evolution of parameters governing its Hamiltonian, gains a phase factor known as the geometric phase. One of its most celebrated formulations in the regime of quantum optics is the Pancharatnam-Berry phase. It is said to be acquired by a beam of light undergoing an evolution of its polarization state. This article builds on the background and notion of the Pancharatnam-Berry phase in quantum optics. A convenient tool for visualizing the evolution of polarization states is the Poincaré sphere, which has been briefly discussed here. The close relation of the phase to a few other important concepts, such as Bargmann invariants and geodesics, has also been discussed in this article.

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Suggested Reading

  1. S. Pancharatnam, Generalized theory of interference, and its applications, Proceedings of Indian Academy of Sciences, Vol.44, pp.247–262, 1956, https://doi.org/10.1007/BF03046050.

    Article  MathSciNet  Google Scholar 

  2. Michael V. Berry, Quantal phase factors accompanying adiabatic changes, Proceedings of Royal Society, Vol.392, No.1802, pp.45–57, 1984, https://doi.org/10.1098/rspa.1984.0023.

    MathSciNet  ADS  Google Scholar 

  3. S. Ramaseshan and R. Nityananda, The interference of polarized light as an early example of Berry’s phase, Current Science, Vol.55, No.24, pp.1225–1226, 1986, https://www.jstor.org/stable/24090242.

    Google Scholar 

  4. R. Bhandari and J. Samuel, Observation of topological phase by use of a laser interferometer, Physical Review Letters, Vol.60, No.13, pp.1211–1213, 1988, https://doi.org/10.1103/PhysRevLett.60.1211.

    Article  CAS  PubMed  ADS  Google Scholar 

  5. J. Samuel and R. Bhandari, General setting of Berry’s phase, Physical Review Letters, Vol.60, No.23, pp.2339–2342, 1988, https://doi.org/10.1103/PhysRevLett.60.2339.

    Article  MathSciNet  CAS  PubMed  ADS  Google Scholar 

  6. F. Wilczek, and A. Shapere, Geometric phases in physics, World Scientific, Vol.5, 1989, https://doi.org/10.1142/0613.

  7. Barry Simon, Holonomy, the quantum adiabatic theorem, and Berry’s phase, Physical Review Letters, Vol.51, No.24, pp.2167–2170, 1983, https://doi.org/10.1103/PhysRevLett.51.2167.

    Article  MathSciNet  ADS  Google Scholar 

  8. Y. Aharonov and J. Anandan, Phase change during a cyclic quantum evolution, Physical Review Letters, Vol.58, No.16, pp.1593–1596, 1987, https://doi.org/10.1103/PhysRevLett.58.1593.

    Article  MathSciNet  CAS  PubMed  ADS  Google Scholar 

  9. N. Mukunda and R. Simon, Quantum kinematic approach to the geometric phase. 1. General formalism, Annals of Physics, Vol.228, No.2, pp.205–268, 1993, https://doi.org/10.1006/aphy.1993.1093.

    Article  MathSciNet  ADS  Google Scholar 

  10. Rajaram Nityananda, The interference of polarised light - The Pancharatnam phase, Resonance, Vol.18, No.4, pp.309–322, 2013, https://doi.org/10.1007/s12045-013-0048-9.

    Article  CAS  Google Scholar 

  11. John M. Lee, Introduction to Riemannian Manifolds, Second Edition, Springer, 2019, eBook ISBN 978-3-319-91755-9, https://doi.org/10.1007/978-3-319-91755-9.

  12. Eqab M. Rabei, Arvind et.al., Bargmann invariants and geometric phases - A generalised connection, Physical Review A, Vol.60, No.5, pp.3397–3409, 1999, https://doi.org/10.1103/PhysRevA.60.3397.

    Article  MathSciNet  CAS  ADS  Google Scholar 

  13. Francisco De Zela, The Pancharatnam–Berry phase: Theoretical and experimental aspects, Theoretical Aspects of Quantum Mechanics, 2012, https://doi.org/10.5772/34882.

  14. Eliahu Cohen, Hugo Larocque et.al., Geometric phase from Aharonov—Bohm to Pancharatnam—Berry and beyond, Nature Reviews Physics, Vol.1, pp.437–449, 2019, https://doi.org/10.1038/s42254-019-0071-1.

    Article  Google Scholar 

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Acknowledgement

Sarbani Chatterjee would like to gratefully thank Prof. Arvind and Prof. N. Mukunda for invaluable discussions on the subject. She also thanks Prof. Joseph Samuel for insightful comments on the manuscript and the Prime Minister’s Research Fellowship (PMRF) scheme, GoI, for financial support.

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Authors and Affiliations

  1. Department of Physical Sciences, Indian Institute of Science Education and Research (IISER) Mohali, Knowledge City, SAS Nagar, Sector 81, Mohali, Punjab, 140 306, India

    Sarbani Chatterjee

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  1. Sarbani Chatterjee
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Correspondence to Sarbani Chatterjee.

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Sarbani Chatterjee is an Integrated PhD student at the Indian Institute of Science Education and Research (IISER) Mohali. She is presently pursuing her PhD under the supervision of Prof. Arvind. Her research interests include quantum optics, quantum computation and communication.

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Chatterjee, S. Pancharatnam-Berry Phase in Quantum Optics. Reson 28, 1669–1683 (2023). https://doi.org/10.1007/s12045-023-1705-2

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  • DOI: https://doi.org/10.1007/s12045-023-1705-2

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