Electromagnetic And Gravitational Casimir-Polder Interaction In The Presence Of External Fields

In a quantum sense,there inevitably exist quantum fluctuations of the field in vacuum,which may induce some novel effects which can be observable in principle.One of the most famous examples is the electromagnetic Casimir-Polder interaction.In general,fluctuating electromagnetic fields in vacuum induce instantaneous electric dipole moments in neutral atoms or molecules,which then couple with each other via the exchange of virtual photons to yield an interaction energy.Likewise,one may also expect a gravitational Casimir-Polder-like interaction(i.e.,quantum gravitational quadrupole-quadrupole interaction)if one accepts that basic quantum principles are also applicable to gravity.Unfortunately,a full theory of quantum gravity is elusive at present.Even though,one may still study quantum gravitational effects at low energies in the framework of linearized quantum gravity,the basic idea of which is to express the spacetime metric as a sum of the flat background spacetime metric and a linearized perturbation,and quantize the perturbation part in the canonical approach.In this dissertation,we on the one hand study the interatomic electromagnetic Casimir-Polder interaction in the presence of external electrostatic fields utilizing the methods in quantum electrodynamics,on the other hand,based on the theory of linearized quantum gravity,we investigate respectively the gravitational Casimir-Polder interaction between two non point-like entangled objects in vacuum,as well as two non point-like ground-state objects in external gravitational radiation fields.Our conclusion are as follows:1.We study,in the presence of an external electrostatic field,the interatomic interaction between two ground-state atoms coupled with vacuum electromagnetic fluctuations within the dipole coupling approximation based on the perturbation theory.We show that,in the fourth-order,the electrostatic field-induced interatomic interaction is just the classical dipole-dipole interaction,which disagrees with the recent result in[Phys.Rev.Lett.124,013604(2020)].However,to higher orders,there exist two different ways that can give rise to the electrostatic field-induced modifications of the interatomic Casimir-Polder interactions.In the sixth-order,the external field effectively modifies the atomic polarizability to influence the two-photon exchange Casimir-Polder interactions,while in the eighth-order,the electrostatic field enables an additional process of a three-photon exchange which generates a r-11 term in the interaction potential in the far zone,where r is the interatomic separation.Numerical estimations show that these external field-related quantum corrections are much smaller than the two-photon exchange Casimir-Polder interaction.2.We investigate the gravitational Casimir-Polder interaction between two entangled non point-like objects induced by a bath of fluctuating quantum gravitational fields in vacuum.Our result shows that,the interaction energy behaves as r-5 in the near regime,and oscillates with a decreasing amplitude proportional to r-1 in the far regime,where r is the distance between the two objects.Compared to the case when the two objects are in their ground states,the quantum gravitational interaction is significantly enhanced when the objects are in an entangled state.Moreover,in the far regime,the gravitational Casimir-Polder interaction between two entangled objects can give the dominating quantum correction to the Newtonian potential,since the extremum is much greater than the monopole-monopole quantum gravitational interaction.3.We explore the gravitational Casimir-Polder interaction between two non point-like objects(non-polar)in their ground states,which are subjected to an external quantized gravitational radiation field.Our result shows that,the interaction energy decreases as r-5 in the near regime,and oscillates with a decreasing amplitude proportional to r-1 in the far regime.The interaction can be either attractive or repulsive depending on the propagation direction,polarization and frequency of the external gravitational field.That is,such an interobject gravitational Casimir-Polder interaction can be manipulated by varying the relative direction between the orientation of the objects with respect to the propagation direction of the incident gravitational radiation.4.We investigate the gravitational Casimir-Polder interaction between two ground-state objects with permanent quadrupole moments,which are subjected to an external gravitational radiation field.Compared with the non-polar case,there exists an additional term in the leading-order interobject gravitational CasimirPolder interaction between two polar objects,which is relevant to the number density of gravitons,the frequency and polarization of the external gravitational field,as well as the permanent quadrupoles of the objects.Due to the existence of such an additional term,the gravitational Casimir-Polder interaction between two polar objects can be significantly different from that between non-polar ones when the interobject distance is much smaller than the wavelength of the external gravitational radiation field.