Quantum optics in static spacetimes: How to sense a cosmic string

Abstract

We study the influence of static gravitational fields on the spontaneous emission and the Lamb shift of atoms. To illustrate the procedure we consider a two-level atom coupled by a dipole interaction to a massless scalar quantum field in a general static Riemann space and work out the Einstein coefficient and the radiative energy shift. To treat an example, the general scheme is applied to a cosmic string spacetime. The possibility is discussed to detect, at least in principle, the cosmic string via the modified spontaneous emission. PACS number(s): 42.50.-p, 04.62.+v, 98.80.Cq I. I N T R O D U C T I O NIt is well known that the decay rate for spontaneous emission, and accordingly the respective Einstein coefficient, is not a n inherent property of the atom but depends on the particular vacuum in which the atom is located. Similarly the shift of the atom's energy level, the Lamb shift, depends on the surroundings. In a confined space, for example, realized by a cavity, for mirrors causing boundary conditions and in dielectric media the mode structure of the electromagnetic field is modified as compared to the empty Minkowski space. Consequently, the decay rate and Lamb shift differ from their free-space values. These values refer to atoms a t rest or in uniform motion. For accelerated atoms, spontaneous excitation and radiative energy shifts have been worked out in [l] and [2] with the intention to analyze quantitatively the distinct contribution of vacuum fluctuations and radiation reaction.The basis of all the considerations mentioned above was a flat spacetime. The inclusion of the influence of inhomogeneous gravitational fields amounts to the transition to a curved Riemann space. In the following we restrict ourselves t o static gravitational fields or spacetimes, respectively. We will give a general discussion of the spontaneous decay and Lamb shift in this physical situation. An important application could be found in the astrophysical context where the Einstein coefficient is modified for example in the strong gravitational field of collapsed stars. This modification enters the interpretation of the spectroscopical data.Below we will study a simpler application of our general scheme in choosing as static Riemann space the spacetime of a straight cosmic string which is flat everywhere outside the string but shows a conical topology. This demonstrates how a nontrivial topology influences spontaneous emission and Lamb shift. A cosmic string could, only in principle, of course, be sensed this way. 'Electronic address:We shall consider a model consisting of a two-level atom and a scalar quantum field interacting via a coupling of dipole type. The more realistic calculation based on a n electromagnetic vector potential would follow the same lines. We are interested in the total amount of considered effects only. Therefore, we do not discuss the contributions of vacuum fluctuations and radiation reaction separately.The structure of the paper is as follows. In Sec. I1 we quantize in the canonical way a Klein-Gor...

Boundarylike behaviors of the resonance interatomic energy in a cosmic string spacetime

“…The aforementioned examples are concerned with the atomic radiative properties in a Minkowski spacetime. In recent years, investigations concerning the atomic radiative properties in curved spacetimes have been carried out [15][16][17][18][19][20][21][22][23][24][25], and it is found that in certain curved spacetimes, behaviors of the atomic radiative properties similar to those in a bounded Minkowski spacetime occur, even when boundaries are absent.…”

“…The cosmic string spacetime is characterized by its nontrivial topological structure, and many quantum effects such as the vacuum fluctuations [39][40][41][42][43][44][45], atomic transition rates [15,22,44,46,47] and energy shifts [48] in this spacetime exhibit behaviors similar to those in a bounded flat spacetime. Here, we are interested in how the resonance interatomic energy is affected by the presence of a cosmic string and whether some boundarylike effects show up in the resonance interatomic energy.…”

Spontaneous excitation of a static atom in a thermal bath in cosmic string spacetime

“…Recently, a number of authors have studied the Casimir effect and Casimir-Polder force in a more realistic situation where the atom interacts with electromagnetic vacuum fluctuations in the geometry of a straight cosmic string [35][36][37]. In this paper, we plan to study the spontaneous excitation and emission of a static atom immersed in a thermal bath of electromagnetic radiation in the vicinity of a straight cosmic string, where the atom is coupled to quantum electromagnetic fields rather than scalar fields in [38].…”

Entanglement dynamics for static two-level atoms in cosmic string spacetime

“…The simplest cosmic string spacetime is that of a static, straight and infinitely thin cosmic string, which can be regarded as a flat spacetime with a planar angle deficit. Quantum fields propagating in the cosmic string spacetime are inevitably influenced by the nontrivial topology, and many quantum effects, such as the vacuum expectations of stress-energy tensor [26][27][28][29][30][31], the Casimir-Polder effect [32], atomic transition rate [33][34][35][36], resonance interaction [37], and lightcone fluctuations [38,39] have been studied, which exhibit behaviors similar to those in a flat spacetime with a boundary. Therefore, it is also of interest to investigate the entanglement dynamics of two static atoms coupled with the vacuum fluctuations of massless scalar fields in the cosmic string spacetime, and compare the result with that in the Minkowski spacetime with a reflecting boundary [10,17,24].…”