Relevance of the statistical nature of the radiation to the time evolution of atomic variables View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1976-04

AUTHORS

H. P. Baltes, P. Meystre, A. Quattropani

ABSTRACT

We present the genral and rigorous equation of motion for the reduced density matrix (RDM) describing the time evolution of a systemA coupled to a systemB for any initial statistical state. We derive the corresponding perturbation expansion up to the second order in the interaction and discuss it for a variety of physical initial conditions. We apply the formalism to the interaction of radiation with matter in terms of a single-mode field coupled to a two-level atomic system through electric-dipole interaction. We solve the equations of motion for the dynamical variables describing the atomic system interacting with i) thermal and ii) coherent incident radiation or coupled to iii) a field produced by classical currents. We show that the «effective» semi-classical Hamiltonian can be established in the case ii), whereas the semi-classical approximation (SCA) is meaningless in the case i). We discuss the range of validity of the SCA in terms of the exactly solvable rotating-wave version of the dipole coupling. We report drastic deviations from the SCA results even in the limit of high intensity of the incident coherent field unless the coupling is very weak or the interaction time elapsed is very short. We analyse the relevance of the initial photon statistics by comparing the SCA with the exact RDM. We discuss the validity of the SCA for various spectroscopic techniques. More... »

PAGES

303-323

References to SciGraph publications

  • 1973-02. Destruction of coherence by scattering of radiation on atoms in LETTERE AL NUOVO CIMENTO (1971-1985)
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bf02727641

    DOI

    http://dx.doi.org/10.1007/bf02727641

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1040189957


    Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
    Incoming Citations Browse incoming citations for this publication using opencitations.net

    JSON-LD is the canonical representation for SciGraph data.

    TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

    [
      {
        "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
        "about": [
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/02", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Physical Sciences", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0299", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Other Physical Sciences", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Zentrale Forschung und Entwicklung, Landis and Gyr Zug A.G., CH-6300, Zug, Switzerland", 
              "id": "http://www.grid.ac/institutes/None", 
              "name": [
                "Zentrale Forschung und Entwicklung, Landis and Gyr Zug A.G., CH-6300, Zug, Switzerland"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Baltes", 
            "givenName": "H. P.", 
            "id": "sg:person.0736632363.32", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0736632363.32"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Optical Science Center, University of Arizona, 85721, Tucson, Ariz., USA", 
              "id": "http://www.grid.ac/institutes/grid.134563.6", 
              "name": [
                "Optical Science Center, University of Arizona, 85721, Tucson, Ariz., USA"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Meystre", 
            "givenName": "P.", 
            "id": "sg:person.010042543335.11", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010042543335.11"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Laboratoire de Physique Th\u00e9orique, Ecole Polytechnique F\u00e9d\u00e9rale, CH-1006, Lausanne, Switzerland", 
              "id": "http://www.grid.ac/institutes/grid.5333.6", 
              "name": [
                "Laboratoire de Physique Th\u00e9orique, Ecole Polytechnique F\u00e9d\u00e9rale, CH-1006, Lausanne, Switzerland"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Quattropani", 
            "givenName": "A.", 
            "id": "sg:person.012337260034.33", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012337260034.33"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/bf02743631", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1033694898", 
              "https://doi.org/10.1007/bf02743631"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "1976-04", 
        "datePublishedReg": "1976-04-01", 
        "description": "We present the genral and rigorous equation of motion for the reduced density matrix (RDM) describing the time evolution of a systemA coupled to a systemB for any initial statistical state. We derive the corresponding perturbation expansion up to the second order in the interaction and discuss it for a variety of physical initial conditions. We apply the formalism to the interaction of radiation with matter in terms of a single-mode field coupled to a two-level atomic system through electric-dipole interaction. We solve the equations of motion for the dynamical variables describing the atomic system interacting with i) thermal and ii) coherent incident radiation or coupled to iii) a field produced by classical currents. We show that the \u00abeffective\u00bb semi-classical Hamiltonian can be established in the case ii), whereas the semi-classical approximation (SCA) is meaningless in the case i). We discuss the range of validity of the SCA in terms of the exactly solvable rotating-wave version of the dipole coupling. We report drastic deviations from the SCA results even in the limit of high intensity of the incident coherent field unless the coupling is very weak or the interaction time elapsed is very short. We analyse the relevance of the initial photon statistics by comparing the SCA with the exact RDM. We discuss the validity of the SCA for various spectroscopic techniques.", 
        "genre": "article", 
        "id": "sg:pub.10.1007/bf02727641", 
        "inLanguage": "en", 
        "isAccessibleForFree": false, 
        "isPartOf": [
          {
            "id": "sg:journal.1336108", 
            "issn": [
              "1826-9877"
            ], 
            "name": "Il Nuovo Cimento B (1971-1996)", 
            "publisher": "Springer Nature", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "2", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "32"
          }
        ], 
        "keywords": [
          "semi-classical approximation", 
          "corresponding perturbation expansions", 
          "physical initial conditions", 
          "equations of motion", 
          "time evolution", 
          "statistical state", 
          "dynamical variables", 
          "statistical nature", 
          "range of validity", 
          "initial conditions", 
          "classical current", 
          "atomic system", 
          "rigorous equations", 
          "second order", 
          "density matrix", 
          "atomic variables", 
          "perturbation expansion", 
          "two-level atomic system", 
          "electric-dipole interaction", 
          "photon statistics", 
          "single-mode field", 
          "equations", 
          "interaction of radiation", 
          "coherent field", 
          "incident radiation", 
          "dipole coupling", 
          "variables", 
          "interaction time", 
          "approximation", 
          "motion", 
          "Hamiltonian", 
          "radiation", 
          "statistics", 
          "spectroscopic techniques", 
          "formalism", 
          "drastic deviations", 
          "high intensity", 
          "validity", 
          "terms", 
          "system", 
          "Case II", 
          "matrix", 
          "field", 
          "coupling", 
          "version", 
          "Systema", 
          "interaction", 
          "case I", 
          "expansion", 
          "evolution", 
          "technique", 
          "order", 
          "limit", 
          "intensity", 
          "deviation", 
          "RDM", 
          "current", 
          "conditions", 
          "matter", 
          "state", 
          "variety", 
          "range", 
          "time", 
          "nature", 
          "relevance", 
          "systemB", 
          "initial statistical state", 
          "coherent incident radiation", 
          "semi-classical Hamiltonian", 
          "solvable rotating-wave version", 
          "rotating-wave version", 
          "incident coherent field", 
          "initial photon statistics", 
          "exact RDM"
        ], 
        "name": "Relevance of the statistical nature of the radiation to the time evolution of atomic variables", 
        "pagination": "303-323", 
        "productId": [
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1040189957"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/bf02727641"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/bf02727641", 
          "https://app.dimensions.ai/details/publication/pub.1040189957"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2022-01-01T18:01", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-springernature-scigraph/baseset/20220101/entities/gbq_results/article/article_136.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://doi.org/10.1007/bf02727641"
      }
    ]
     

    Download the RDF metadata as:  json-ld nt turtle xml License info

    HOW TO GET THIS DATA PROGRAMMATICALLY:

    JSON-LD is a popular format for linked data which is fully compatible with JSON.

    curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/bf02727641'

    N-Triples is a line-based linked data format ideal for batch operations.

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/bf02727641'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/bf02727641'

    RDF/XML is a standard XML format for linked data.

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/bf02727641'


     

    This table displays all metadata directly associated to this object as RDF triples.

    155 TRIPLES      22 PREDICATES      101 URIs      92 LITERALS      6 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/bf02727641 schema:about anzsrc-for:02
    2 anzsrc-for:0299
    3 schema:author Na160748a81ea45da9b835f849533fa1a
    4 schema:citation sg:pub.10.1007/bf02743631
    5 schema:datePublished 1976-04
    6 schema:datePublishedReg 1976-04-01
    7 schema:description We present the genral and rigorous equation of motion for the reduced density matrix (RDM) describing the time evolution of a systemA coupled to a systemB for any initial statistical state. We derive the corresponding perturbation expansion up to the second order in the interaction and discuss it for a variety of physical initial conditions. We apply the formalism to the interaction of radiation with matter in terms of a single-mode field coupled to a two-level atomic system through electric-dipole interaction. We solve the equations of motion for the dynamical variables describing the atomic system interacting with i) thermal and ii) coherent incident radiation or coupled to iii) a field produced by classical currents. We show that the «effective» semi-classical Hamiltonian can be established in the case ii), whereas the semi-classical approximation (SCA) is meaningless in the case i). We discuss the range of validity of the SCA in terms of the exactly solvable rotating-wave version of the dipole coupling. We report drastic deviations from the SCA results even in the limit of high intensity of the incident coherent field unless the coupling is very weak or the interaction time elapsed is very short. We analyse the relevance of the initial photon statistics by comparing the SCA with the exact RDM. We discuss the validity of the SCA for various spectroscopic techniques.
    8 schema:genre article
    9 schema:inLanguage en
    10 schema:isAccessibleForFree false
    11 schema:isPartOf N65505864047b4159af7673597b047f27
    12 Nf1c41e1506a84509a56f6c8ed607883b
    13 sg:journal.1336108
    14 schema:keywords Case II
    15 Hamiltonian
    16 RDM
    17 Systema
    18 approximation
    19 atomic system
    20 atomic variables
    21 case I
    22 classical current
    23 coherent field
    24 coherent incident radiation
    25 conditions
    26 corresponding perturbation expansions
    27 coupling
    28 current
    29 density matrix
    30 deviation
    31 dipole coupling
    32 drastic deviations
    33 dynamical variables
    34 electric-dipole interaction
    35 equations
    36 equations of motion
    37 evolution
    38 exact RDM
    39 expansion
    40 field
    41 formalism
    42 high intensity
    43 incident coherent field
    44 incident radiation
    45 initial conditions
    46 initial photon statistics
    47 initial statistical state
    48 intensity
    49 interaction
    50 interaction of radiation
    51 interaction time
    52 limit
    53 matrix
    54 matter
    55 motion
    56 nature
    57 order
    58 perturbation expansion
    59 photon statistics
    60 physical initial conditions
    61 radiation
    62 range
    63 range of validity
    64 relevance
    65 rigorous equations
    66 rotating-wave version
    67 second order
    68 semi-classical Hamiltonian
    69 semi-classical approximation
    70 single-mode field
    71 solvable rotating-wave version
    72 spectroscopic techniques
    73 state
    74 statistical nature
    75 statistical state
    76 statistics
    77 system
    78 systemB
    79 technique
    80 terms
    81 time
    82 time evolution
    83 two-level atomic system
    84 validity
    85 variables
    86 variety
    87 version
    88 schema:name Relevance of the statistical nature of the radiation to the time evolution of atomic variables
    89 schema:pagination 303-323
    90 schema:productId N0773151e343a44a5bc055f4d07421b07
    91 Nea37f21e07c6408ead8ca26b8e44f4fc
    92 schema:sameAs https://app.dimensions.ai/details/publication/pub.1040189957
    93 https://doi.org/10.1007/bf02727641
    94 schema:sdDatePublished 2022-01-01T18:01
    95 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    96 schema:sdPublisher N8a6da52254a14b60ac35fb8f68e808be
    97 schema:url https://doi.org/10.1007/bf02727641
    98 sgo:license sg:explorer/license/
    99 sgo:sdDataset articles
    100 rdf:type schema:ScholarlyArticle
    101 N0773151e343a44a5bc055f4d07421b07 schema:name dimensions_id
    102 schema:value pub.1040189957
    103 rdf:type schema:PropertyValue
    104 N65505864047b4159af7673597b047f27 schema:issueNumber 2
    105 rdf:type schema:PublicationIssue
    106 N8a6da52254a14b60ac35fb8f68e808be schema:name Springer Nature - SN SciGraph project
    107 rdf:type schema:Organization
    108 Na160748a81ea45da9b835f849533fa1a rdf:first sg:person.0736632363.32
    109 rdf:rest Nf988e1d8a367448c9017b855c4335593
    110 Nc1ba53a804e243ca850e31b6dcfc1449 rdf:first sg:person.012337260034.33
    111 rdf:rest rdf:nil
    112 Nea37f21e07c6408ead8ca26b8e44f4fc schema:name doi
    113 schema:value 10.1007/bf02727641
    114 rdf:type schema:PropertyValue
    115 Nf1c41e1506a84509a56f6c8ed607883b schema:volumeNumber 32
    116 rdf:type schema:PublicationVolume
    117 Nf988e1d8a367448c9017b855c4335593 rdf:first sg:person.010042543335.11
    118 rdf:rest Nc1ba53a804e243ca850e31b6dcfc1449
    119 anzsrc-for:02 schema:inDefinedTermSet anzsrc-for:
    120 schema:name Physical Sciences
    121 rdf:type schema:DefinedTerm
    122 anzsrc-for:0299 schema:inDefinedTermSet anzsrc-for:
    123 schema:name Other Physical Sciences
    124 rdf:type schema:DefinedTerm
    125 sg:journal.1336108 schema:issn 1826-9877
    126 schema:name Il Nuovo Cimento B (1971-1996)
    127 schema:publisher Springer Nature
    128 rdf:type schema:Periodical
    129 sg:person.010042543335.11 schema:affiliation grid-institutes:grid.134563.6
    130 schema:familyName Meystre
    131 schema:givenName P.
    132 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010042543335.11
    133 rdf:type schema:Person
    134 sg:person.012337260034.33 schema:affiliation grid-institutes:grid.5333.6
    135 schema:familyName Quattropani
    136 schema:givenName A.
    137 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012337260034.33
    138 rdf:type schema:Person
    139 sg:person.0736632363.32 schema:affiliation grid-institutes:None
    140 schema:familyName Baltes
    141 schema:givenName H. P.
    142 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0736632363.32
    143 rdf:type schema:Person
    144 sg:pub.10.1007/bf02743631 schema:sameAs https://app.dimensions.ai/details/publication/pub.1033694898
    145 https://doi.org/10.1007/bf02743631
    146 rdf:type schema:CreativeWork
    147 grid-institutes:None schema:alternateName Zentrale Forschung und Entwicklung, Landis and Gyr Zug A.G., CH-6300, Zug, Switzerland
    148 schema:name Zentrale Forschung und Entwicklung, Landis and Gyr Zug A.G., CH-6300, Zug, Switzerland
    149 rdf:type schema:Organization
    150 grid-institutes:grid.134563.6 schema:alternateName Optical Science Center, University of Arizona, 85721, Tucson, Ariz., USA
    151 schema:name Optical Science Center, University of Arizona, 85721, Tucson, Ariz., USA
    152 rdf:type schema:Organization
    153 grid-institutes:grid.5333.6 schema:alternateName Laboratoire de Physique Théorique, Ecole Polytechnique Fédérale, CH-1006, Lausanne, Switzerland
    154 schema:name Laboratoire de Physique Théorique, Ecole Polytechnique Fédérale, CH-1006, Lausanne, Switzerland
    155 rdf:type schema:Organization
     




    Preview window. Press ESC to close (or click here)


    ...