Photon wave functions, wave-packet quantization of light, and coherence theory
The monochromatic Dirac and polychromatic Titulaer-Glauber quantized field theories (QFTs) of electromagnetism are derived from a photonenergy wave function in much the same way that one derives QFT for electrons, i.e., by quantization of a single-particle wave function. The photon wave function and...
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| Format: | Journal article |
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IOP Publishing
2007
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| _version_ | 1826260819368738816 |
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| author | Smith, B Raymer, MG |
| author_facet | Smith, B Raymer, MG |
| author_sort | Smith, B |
| collection | OXFORD |
| description | The monochromatic Dirac and polychromatic Titulaer-Glauber quantized field theories (QFTs) of electromagnetism are derived from a photonenergy wave function in much the same way that one derives QFT for electrons, i.e., by quantization of a single-particle wave function. The photon wave function and its equation of motion are established from the Einstein energy-momentum-mass relation, assuming a local energy density. This yields a theory of photon wave mechanics (PWM). The proper Lorentz-invariant singlephoton scalar product is found to be non-local in coordinate space, and is shown to correspond to orthogonalization of the Titulaer-Glauber wave-packet modes. The wave functions of PWM and mode functions of QFT are shown to be equivalent, evolving via identical equations of motion, and completely describe photonic states. We generalize PWM to two or more photons, and show how to switch between the PWM and QFT viewpoints. The second-order coherence tensors of classical coherence theory and the two-photon wave functions are shown to propagate equivalently. We give examples of beam-like states, which can be used as photon wave functions in PWM, or modes in QFT. We propose a practical mode converter based on spectral filtering to convert between wave packets and their corresponding biorthogonal dual wave packets. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. |
| first_indexed | 2024-03-06T19:11:46Z |
| format | Journal article |
| id | oxford-uuid:17034736-d9a5-455b-b7d4-07f5078f2542 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T19:11:46Z |
| publishDate | 2007 |
| publisher | IOP Publishing |
| record_format | dspace |
| spelling | oxford-uuid:17034736-d9a5-455b-b7d4-07f5078f25422022-03-26T10:34:39ZPhoton wave functions, wave-packet quantization of light, and coherence theoryJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:17034736-d9a5-455b-b7d4-07f5078f2542Symplectic Elements at OxfordIOP Publishing2007Smith, BRaymer, MGThe monochromatic Dirac and polychromatic Titulaer-Glauber quantized field theories (QFTs) of electromagnetism are derived from a photonenergy wave function in much the same way that one derives QFT for electrons, i.e., by quantization of a single-particle wave function. The photon wave function and its equation of motion are established from the Einstein energy-momentum-mass relation, assuming a local energy density. This yields a theory of photon wave mechanics (PWM). The proper Lorentz-invariant singlephoton scalar product is found to be non-local in coordinate space, and is shown to correspond to orthogonalization of the Titulaer-Glauber wave-packet modes. The wave functions of PWM and mode functions of QFT are shown to be equivalent, evolving via identical equations of motion, and completely describe photonic states. We generalize PWM to two or more photons, and show how to switch between the PWM and QFT viewpoints. The second-order coherence tensors of classical coherence theory and the two-photon wave functions are shown to propagate equivalently. We give examples of beam-like states, which can be used as photon wave functions in PWM, or modes in QFT. We propose a practical mode converter based on spectral filtering to convert between wave packets and their corresponding biorthogonal dual wave packets. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. |
| spellingShingle | Smith, B Raymer, MG Photon wave functions, wave-packet quantization of light, and coherence theory |
| title | Photon wave functions, wave-packet quantization of light, and coherence theory |
| title_full | Photon wave functions, wave-packet quantization of light, and coherence theory |
| title_fullStr | Photon wave functions, wave-packet quantization of light, and coherence theory |
| title_full_unstemmed | Photon wave functions, wave-packet quantization of light, and coherence theory |
| title_short | Photon wave functions, wave-packet quantization of light, and coherence theory |
| title_sort | photon wave functions wave packet quantization of light and coherence theory |
| work_keys_str_mv | AT smithb photonwavefunctionswavepacketquantizationoflightandcoherencetheory AT raymermg photonwavefunctionswavepacketquantizationoflightandcoherencetheory |