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Casimir-Polder force between two uniformly accelerating atoms and the Unruh effect

DIPARTIMENTO DI SCIENZE FISICHE ED ASTRONOMICHE PALERMO, ITALY . Casimir-Polder force between two uniformly accelerating atoms and the Unruh effect. Quantum Field Theory under external conditions (QFEXT09), Norman, September 2009. J. Marino and R. Passante.

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Casimir-Polder force between two uniformly accelerating atoms and the Unruh effect

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  1. DIPARTIMENTO DI SCIENZE FISICHE ED ASTRONOMICHE PALERMO, ITALY Casimir-Polderforcebetweentwouniformlyacceleratingatoms and the Unruh effect Quantum FieldTheory under externalconditions (QFEXT09), Norman, September 2009 J. Marino and R. Passante Dipartimento di Scienze Fisiche ed Astronomiche, Palermo, Italy

  2. In thistalk… …Iwilldiscuss the Casimir-Polderforcebetweentwoacceleratingatomsfor • smallaccelerations • high accelerations atomictransitionfrequency I will show how Unruh Effectchanges the scalingwith R of the interatomicenergy

  3. The Unruh effect Rindler coordinate transformation Rindlerspacetimeinterval

  4. Expectationvaluesofparticlenumbers ActionofMinkowskioperators on Minkowskivacuum Actionof right Rindleroperators on Minkowskivacuum An acceleratedobserverassociates a thermalbathoffictiousparticlesto the Minkowskivacuum

  5. Acceleratedhydrogenatom and the Unruh effect in QED MultipolarGauge Linear couplingbetweenfield and atom propertimeof the atom We separate vacuumfluctuations and reactionradiationcontributionsto the energylevelshifts R. Passante, Phys. Rev. A, 57, 3 (1998)

  6. Vacuumfluctuationscontributionto radiative levelshifts • Unruh effect can bedetectedforatomicaccelerations • The termisrelevant at accelerationsof the sameorder • Thereisno equivalencebetween scalar Unruh effect and QED Unruh effect

  7. LambShiftof a uniformlyacceleratedatom near a conductingplate (1) • Scalar Case • Forthere are onlysmallcorrectionsto the staticatom-plate Casimir force. • Forthe LambShiftisreminescentof the LambShiftofaninertialatom, in itsexcited state, in frontof a plate L. Rizzuto Phys. Rev. A 76, 062114 (2007)

  8. LambShiftof a uniformlyacceleratedatom near a conductingplate (2) • EM Case • Westillrequire high atomicaccelerationtodetect Unruh effect. • We can useanisotropiesofatomicpolarizabilitiestoweaken or increase the atom-wallforce (for high atomicaccelerations). QED vacuum L. Rizzuto, S. Spagnolo Phys. Rev. A 79, 062110 (2009)

  9. Ourphysicalsystem… The twoatomshave the sameacceleration The twoatomssee the sameUnruh bath

  10. Goedecke’s method Casimir-Polderinteraction at finite temperature Weconsider the T=0 interactionpotential For a thermalbathwehave . Goedeckesubstitues the averageparticlenumber in the T=0 - interactionpotential G. H. Goedecke, R. C. Wood, Phys. Rev. A 60, 3 (1999)

  11. Casimir-Polderinteraction at finite temperature In the high temperature limit In the low temperature limit Near zone Far zone

  12. We compare the radiative vacuumshiftofanacceleratedhydrogenatom with the radiative vacuumshiftofanhydrogenatom in a thermalbath Fromthiscomparison, weguess the expression for the average mode numberforanacceleratedatom

  13. withthisaverageparticlenumber, we can write the Casimir-Polderpotentialbetweentwoacceleratedatoms : negligibletransitionprobabilitytoexcitedstates

  14. Extensionof V(R) to the compexplane Weperform a rotation of the integrationline in the first quadrantof the complexplane Poles on the immaginaryaxis:

  15. Near zone Far zone • In far zone the Unruh effectintroduces a correctionto the interactionenergy • The accelerationdependentterms are in bothcasescomparableto the stationariesoneswhen

  16. Thisresultholdsboth in near and in far zone; • itisrelevantonlyto high accelerations; • itissimilarto high temperature limitofthe Casimir-Polderinteraction at finite temperature

  17. Casimir-Polderforcebetweentwouniformlyacceleratingatoms in the highaccelerationlimit Spontaneousexcitation Inertialintermolecularpotentialforexcitedmolecules E. A. Power, T. Thirunamachandran, 48, 6 (1993). Resonancefrequencyof the atomictransition Resonantcontributionofaverage mode number

  18. For a characteristicatomictransition, and high accelerations are againrequired. Reminescentof the exchangeofrealphotonswhichoccurswhen the twomolecules are excited. Far zone

  19. Foundationsof the method Non-relativisticdynamics: Under theseapproximationswe can use the staticpotentialand the averageparticlenumber in the sameexpression

  20. Conclusions • The Casimir-Polderforcebetweentwoacceleratedatomscontainstermsderivingfrom the Unruh effect, relevantonly at . • In far zone theUnruh effectintroduces a term, thatscaleswith the fifthpowerof R. • Usinganheuristicmethod, wefindforanpowerlaw in far zone.

  21. Future developments Actually, we are workingto a IV ordermethodthatseparatesvacuumfluctuations and reactionradiationcontributions in the interactionenergyof the twomolecules. Thisapproachhas the advantageto solve from first principles the problemofCasimir-Polderforcebetweentwouniformlyacceleratingatoms. Acknowledgments This talk hasbeensupportedby a grant from the International AdvisoryCommitteeof the QFEXT09

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