Is the photon pair generated from the electron-positron annihilation entangled?











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Is the photon pair generated from the electron-positron annihilation entangled?



And would they work as a source of entangled photons suitable for experiments in quantum optics?










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    up vote
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    down vote

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    Is the photon pair generated from the electron-positron annihilation entangled?



    And would they work as a source of entangled photons suitable for experiments in quantum optics?










    share|cite|improve this question


























      up vote
      17
      down vote

      favorite
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      down vote

      favorite
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      Is the photon pair generated from the electron-positron annihilation entangled?



      And would they work as a source of entangled photons suitable for experiments in quantum optics?










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      Is the photon pair generated from the electron-positron annihilation entangled?



      And would they work as a source of entangled photons suitable for experiments in quantum optics?







      quantum-mechanics particle-physics photons quantum-entanglement






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      edited Nov 19 at 17:56









      Peter Mortensen

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      asked Nov 19 at 11:23









      E.phy

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          2 Answers
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          up vote
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          Yes, they are definitely entangled. Their combined energy will exactly equal the combined energy of the original electron-positron pair, for example. The same is true for combined momentum and combined spin.






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          • "Combined spin" should also include any orbital angular momentum if the electron and positron briefly orbited each other (positronium) before annihilating.
            – Andreas Blass
            Nov 19 at 16:08










          • That is correct--
            – S. McGrew
            Nov 19 at 16:13










          • And from what I understand about these things (only a layman as far as physics goes), the angular momentum of the electron-positron pair will almost always be non-zero.
            – EvilSnack
            Nov 20 at 0:57


















          up vote
          4
          down vote













          The photon-pair is definitely entangled. It is produced from an $S$-wave state of the electron-positron system and as such has orbital angular momentum $L=0$. But it's not useful for quantum optics, the photons' energy is too high for your usual mirrors to reflect. See fig 33.15 on p. 23 of this http://pdg.lbl.gov/2018/reviews/rpp2018-rev-passage-particles-matter.pdf to get an idea what happens to a 511 keV photon from two-photon annihilation of an electron-positron pair at rest once it hits matter: ionization by Compton scattering dominates the interaction, that's not what you want to happen in a mirror or lense.



          It's worth keeping in mind though, that the electron-positron system (Positronium) can decay to any number of photons $>1$, though numbers higher than three are very rare. An even number of photons can be produced for decays of the singlet ground state ${}^1S_0$ (where the electron and positron are in an anti-symmetric spin state
          $frac{1}{sqrt{2}}left( left|uparrow downarrow rightrangle - left|downarrow uparrow rightrangleright)$, "Parapositronium"). This defines the spin entanglement in the case you had in mind, and it has actually been measured and found to agree with full entanglement, see e.g. here http://adsabs.harvard.edu/abs/2009APS..HAW.GB108S



          An uneven number can be produced from the triplet ${}^3S_0$ ("Orthopositronium"). The triplet is much longer-lived than the singlet state (roughly thousand times), but since it consists of three states and because symmetries ($CP$) prevent the positronium from going from the triplet to the singlet state, an appreciable number of electron-positron pairs decays to three photons.



          In fact, also the $S$ states of higher energy levels can decay to photons directly, but usually they will decay to the ground state first, emitting photons of energies $O(10 - 100 emathrm{V})$ before the actual decay to the high-energy pair or to the three continuous spectrum photons.






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            protected by David Z Nov 20 at 9:58



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            2 Answers
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            active

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            2 Answers
            2






            active

            oldest

            votes









            active

            oldest

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            active

            oldest

            votes








            up vote
            22
            down vote













            Yes, they are definitely entangled. Their combined energy will exactly equal the combined energy of the original electron-positron pair, for example. The same is true for combined momentum and combined spin.






            share|cite|improve this answer





















            • "Combined spin" should also include any orbital angular momentum if the electron and positron briefly orbited each other (positronium) before annihilating.
              – Andreas Blass
              Nov 19 at 16:08










            • That is correct--
              – S. McGrew
              Nov 19 at 16:13










            • And from what I understand about these things (only a layman as far as physics goes), the angular momentum of the electron-positron pair will almost always be non-zero.
              – EvilSnack
              Nov 20 at 0:57















            up vote
            22
            down vote













            Yes, they are definitely entangled. Their combined energy will exactly equal the combined energy of the original electron-positron pair, for example. The same is true for combined momentum and combined spin.






            share|cite|improve this answer





















            • "Combined spin" should also include any orbital angular momentum if the electron and positron briefly orbited each other (positronium) before annihilating.
              – Andreas Blass
              Nov 19 at 16:08










            • That is correct--
              – S. McGrew
              Nov 19 at 16:13










            • And from what I understand about these things (only a layman as far as physics goes), the angular momentum of the electron-positron pair will almost always be non-zero.
              – EvilSnack
              Nov 20 at 0:57













            up vote
            22
            down vote










            up vote
            22
            down vote









            Yes, they are definitely entangled. Their combined energy will exactly equal the combined energy of the original electron-positron pair, for example. The same is true for combined momentum and combined spin.






            share|cite|improve this answer












            Yes, they are definitely entangled. Their combined energy will exactly equal the combined energy of the original electron-positron pair, for example. The same is true for combined momentum and combined spin.







            share|cite|improve this answer












            share|cite|improve this answer



            share|cite|improve this answer










            answered Nov 19 at 11:40









            S. McGrew

            5,4152923




            5,4152923












            • "Combined spin" should also include any orbital angular momentum if the electron and positron briefly orbited each other (positronium) before annihilating.
              – Andreas Blass
              Nov 19 at 16:08










            • That is correct--
              – S. McGrew
              Nov 19 at 16:13










            • And from what I understand about these things (only a layman as far as physics goes), the angular momentum of the electron-positron pair will almost always be non-zero.
              – EvilSnack
              Nov 20 at 0:57


















            • "Combined spin" should also include any orbital angular momentum if the electron and positron briefly orbited each other (positronium) before annihilating.
              – Andreas Blass
              Nov 19 at 16:08










            • That is correct--
              – S. McGrew
              Nov 19 at 16:13










            • And from what I understand about these things (only a layman as far as physics goes), the angular momentum of the electron-positron pair will almost always be non-zero.
              – EvilSnack
              Nov 20 at 0:57
















            "Combined spin" should also include any orbital angular momentum if the electron and positron briefly orbited each other (positronium) before annihilating.
            – Andreas Blass
            Nov 19 at 16:08




            "Combined spin" should also include any orbital angular momentum if the electron and positron briefly orbited each other (positronium) before annihilating.
            – Andreas Blass
            Nov 19 at 16:08












            That is correct--
            – S. McGrew
            Nov 19 at 16:13




            That is correct--
            – S. McGrew
            Nov 19 at 16:13












            And from what I understand about these things (only a layman as far as physics goes), the angular momentum of the electron-positron pair will almost always be non-zero.
            – EvilSnack
            Nov 20 at 0:57




            And from what I understand about these things (only a layman as far as physics goes), the angular momentum of the electron-positron pair will almost always be non-zero.
            – EvilSnack
            Nov 20 at 0:57










            up vote
            4
            down vote













            The photon-pair is definitely entangled. It is produced from an $S$-wave state of the electron-positron system and as such has orbital angular momentum $L=0$. But it's not useful for quantum optics, the photons' energy is too high for your usual mirrors to reflect. See fig 33.15 on p. 23 of this http://pdg.lbl.gov/2018/reviews/rpp2018-rev-passage-particles-matter.pdf to get an idea what happens to a 511 keV photon from two-photon annihilation of an electron-positron pair at rest once it hits matter: ionization by Compton scattering dominates the interaction, that's not what you want to happen in a mirror or lense.



            It's worth keeping in mind though, that the electron-positron system (Positronium) can decay to any number of photons $>1$, though numbers higher than three are very rare. An even number of photons can be produced for decays of the singlet ground state ${}^1S_0$ (where the electron and positron are in an anti-symmetric spin state
            $frac{1}{sqrt{2}}left( left|uparrow downarrow rightrangle - left|downarrow uparrow rightrangleright)$, "Parapositronium"). This defines the spin entanglement in the case you had in mind, and it has actually been measured and found to agree with full entanglement, see e.g. here http://adsabs.harvard.edu/abs/2009APS..HAW.GB108S



            An uneven number can be produced from the triplet ${}^3S_0$ ("Orthopositronium"). The triplet is much longer-lived than the singlet state (roughly thousand times), but since it consists of three states and because symmetries ($CP$) prevent the positronium from going from the triplet to the singlet state, an appreciable number of electron-positron pairs decays to three photons.



            In fact, also the $S$ states of higher energy levels can decay to photons directly, but usually they will decay to the ground state first, emitting photons of energies $O(10 - 100 emathrm{V})$ before the actual decay to the high-energy pair or to the three continuous spectrum photons.






            share|cite|improve this answer



























              up vote
              4
              down vote













              The photon-pair is definitely entangled. It is produced from an $S$-wave state of the electron-positron system and as such has orbital angular momentum $L=0$. But it's not useful for quantum optics, the photons' energy is too high for your usual mirrors to reflect. See fig 33.15 on p. 23 of this http://pdg.lbl.gov/2018/reviews/rpp2018-rev-passage-particles-matter.pdf to get an idea what happens to a 511 keV photon from two-photon annihilation of an electron-positron pair at rest once it hits matter: ionization by Compton scattering dominates the interaction, that's not what you want to happen in a mirror or lense.



              It's worth keeping in mind though, that the electron-positron system (Positronium) can decay to any number of photons $>1$, though numbers higher than three are very rare. An even number of photons can be produced for decays of the singlet ground state ${}^1S_0$ (where the electron and positron are in an anti-symmetric spin state
              $frac{1}{sqrt{2}}left( left|uparrow downarrow rightrangle - left|downarrow uparrow rightrangleright)$, "Parapositronium"). This defines the spin entanglement in the case you had in mind, and it has actually been measured and found to agree with full entanglement, see e.g. here http://adsabs.harvard.edu/abs/2009APS..HAW.GB108S



              An uneven number can be produced from the triplet ${}^3S_0$ ("Orthopositronium"). The triplet is much longer-lived than the singlet state (roughly thousand times), but since it consists of three states and because symmetries ($CP$) prevent the positronium from going from the triplet to the singlet state, an appreciable number of electron-positron pairs decays to three photons.



              In fact, also the $S$ states of higher energy levels can decay to photons directly, but usually they will decay to the ground state first, emitting photons of energies $O(10 - 100 emathrm{V})$ before the actual decay to the high-energy pair or to the three continuous spectrum photons.






              share|cite|improve this answer

























                up vote
                4
                down vote










                up vote
                4
                down vote









                The photon-pair is definitely entangled. It is produced from an $S$-wave state of the electron-positron system and as such has orbital angular momentum $L=0$. But it's not useful for quantum optics, the photons' energy is too high for your usual mirrors to reflect. See fig 33.15 on p. 23 of this http://pdg.lbl.gov/2018/reviews/rpp2018-rev-passage-particles-matter.pdf to get an idea what happens to a 511 keV photon from two-photon annihilation of an electron-positron pair at rest once it hits matter: ionization by Compton scattering dominates the interaction, that's not what you want to happen in a mirror or lense.



                It's worth keeping in mind though, that the electron-positron system (Positronium) can decay to any number of photons $>1$, though numbers higher than three are very rare. An even number of photons can be produced for decays of the singlet ground state ${}^1S_0$ (where the electron and positron are in an anti-symmetric spin state
                $frac{1}{sqrt{2}}left( left|uparrow downarrow rightrangle - left|downarrow uparrow rightrangleright)$, "Parapositronium"). This defines the spin entanglement in the case you had in mind, and it has actually been measured and found to agree with full entanglement, see e.g. here http://adsabs.harvard.edu/abs/2009APS..HAW.GB108S



                An uneven number can be produced from the triplet ${}^3S_0$ ("Orthopositronium"). The triplet is much longer-lived than the singlet state (roughly thousand times), but since it consists of three states and because symmetries ($CP$) prevent the positronium from going from the triplet to the singlet state, an appreciable number of electron-positron pairs decays to three photons.



                In fact, also the $S$ states of higher energy levels can decay to photons directly, but usually they will decay to the ground state first, emitting photons of energies $O(10 - 100 emathrm{V})$ before the actual decay to the high-energy pair or to the three continuous spectrum photons.






                share|cite|improve this answer














                The photon-pair is definitely entangled. It is produced from an $S$-wave state of the electron-positron system and as such has orbital angular momentum $L=0$. But it's not useful for quantum optics, the photons' energy is too high for your usual mirrors to reflect. See fig 33.15 on p. 23 of this http://pdg.lbl.gov/2018/reviews/rpp2018-rev-passage-particles-matter.pdf to get an idea what happens to a 511 keV photon from two-photon annihilation of an electron-positron pair at rest once it hits matter: ionization by Compton scattering dominates the interaction, that's not what you want to happen in a mirror or lense.



                It's worth keeping in mind though, that the electron-positron system (Positronium) can decay to any number of photons $>1$, though numbers higher than three are very rare. An even number of photons can be produced for decays of the singlet ground state ${}^1S_0$ (where the electron and positron are in an anti-symmetric spin state
                $frac{1}{sqrt{2}}left( left|uparrow downarrow rightrangle - left|downarrow uparrow rightrangleright)$, "Parapositronium"). This defines the spin entanglement in the case you had in mind, and it has actually been measured and found to agree with full entanglement, see e.g. here http://adsabs.harvard.edu/abs/2009APS..HAW.GB108S



                An uneven number can be produced from the triplet ${}^3S_0$ ("Orthopositronium"). The triplet is much longer-lived than the singlet state (roughly thousand times), but since it consists of three states and because symmetries ($CP$) prevent the positronium from going from the triplet to the singlet state, an appreciable number of electron-positron pairs decays to three photons.



                In fact, also the $S$ states of higher energy levels can decay to photons directly, but usually they will decay to the ground state first, emitting photons of energies $O(10 - 100 emathrm{V})$ before the actual decay to the high-energy pair or to the three continuous spectrum photons.







                share|cite|improve this answer














                share|cite|improve this answer



                share|cite|improve this answer








                edited Nov 20 at 9:31

























                answered Nov 20 at 6:54









                tobi_s

                1812




                1812

















                    protected by David Z Nov 20 at 9:58



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