We investigate the dispersive Casimir-Polder interaction between a rubidium atom and a suspended graphene sheet subjected to an external magnetic field B. We demonstrate that this concrete physical system allows for an unprecedented control of dispersive interactions at micro-and nanoscales. Indeed, we show that the application of an external magnetic field can induce an 80% reduction in the Casimir-Polder energy relative to its value without the field. We also show that sharp discontinuities emerge in the Casimir-Polder interaction energy for certain values of the applied magnetic field at low temperatures. Moreover, for sufficiently large distances, these discontinuities show up as a plateau-like pattern with a quantized Casimir-Polder interaction energy, in a phenomenon that can be explained in terms of the quantum Hall effect. In addition, we point out the importance of thermal effects in the Casimir-Polder interaction, which we show must be taken into account even for considerably short distances. In this case, the discontinuities in the atom-graphene dispersive interaction do not occur, which by no means prevents the tuning of the interaction in ∼50% by the application of the external magnetic field.

We derive the radiation pressure force on a non-relativistic moving plate in 1+1 dimensions. We assume that a massless scalar field satisfies either Dirichlet or Neumann boundary conditions (BC) at the instantaneous position of the plate. We show that when the state of the field is invariant under time translations, the results derived for Dirichlet and Neumann BC are equal. We discuss the force for a thermal field state as an example for this case. On the other hand, a coherent state introduces a phase reference, and the two types of BC lead to different results.

We present three methods for calculating the Feynman propagator for the nonrelativistic harmonic oscillator. The first method was employed by Schwinger a half a century ago, but has rarely been used in non-relativistic problems since. Also discussed is an algebraic method and a path integral method so that the reader can compare the advantages and disadvantages of each method.

We investigate the spontaneous emission rate of a two-level quantum emitter near a graphene-coated substrate under the influence of an external magnetic field or strain induced pseudo-magnetic field. We demonstrate that the application of the magnetic field can substantially increase or decrease the decay rate. We show that a suppression as large as 99% in the Purcell factor is achieved even for moderate magnetic fields. The emitter's lifetime is a discontinuous function of |B|, which is a direct consequence of the occurrence of discrete Landau levels in graphene. We demonstrate that, in the near-field regime, the magnetic field enables an unprecedented control of the decay pathways into which the photon/polariton can be emitted. Our findings strongly suggest that a magnetic field could act as an efficient agent for on-demand, active control of light-matter interactions in graphene at the quantum level.The possibility of tailoring light-matter interactions at a quantum level has been a sought-after goal in optics since the pioneer work of Purcell 1 , where it was first shown that the environment can strongly modify the spontaneous emission (SE) rate of a quantum emitter. To achieve such objective, several approaches have been proposed so far. One of them is to investigate SE in different system geometries [2][3][4][5][6][7][8][9][10][11] . Advances in nanofabrication techniques have not only allowed the increase of the spectroscopic resolution of molecules in complex environments 12 , but have also led to the use of nanometric objects, such as antennas and tips, to modify the lifetime, and enhance the fluorescence of single molecules [13][14][15][16] . The presence of metamaterials may also strongly affect quantum emitters' radiative processes. For instance, the impact of negative refraction and of the hyperbolic dispersion on the SE have been investigated [17][18][19] . Also, the influence of cloaking devices on the SE of atoms has been recently addressed 20 .Progress in plasmonics has also allowed for a unprecedented control of light-matter interactions at a quantum level. When the emitter is located near a plasmonic structure it may experience a strong enhancement of the local field. This effect can be exploited in the development of important applications in nanoplasmonics [21][22][23][24][25] . However, structures made of noble metals are hardly tunable, which unavoidably limit their application in photonic devices. To circumvent these limitations, graphene has emerged as an alternative plasmonic material due to its extraordinary electronic and optical properties [26][27][28][29][30][31] . Indeed, graphene hosts extremely confined plasmons, facilitating strong light-matter interactions [28][29][30][31] . In addition, the plasmon spectrum in doped graphene is highly tunable through electrical or chemical modification of the charge carrier density. Due to these properties, graphene is a promising material platform for several photonic applications, specially in the THz frequency range 30 . At the quantum leve...

We consider a real massless scalar field in 1+1 dimensions satisfying time-dependent Robin boundary condition at a static mirror. This condition can simulate moving reflecting mirrors whose motions are determined by the time-dependence of the Robin parameter. We show that particles can be created from vacuum, characterizing in this way a dynamical Casimir effect.