Decoherence and recoherence from vacuum fluctuations near a conducting plate

Abstract

The interaction between particles and the electromagnetic field induces decoherence generating a small suppression of fringes in an interference experiment. We show that if a double slit-like experiment is performed in the vicinity of a conducting plane, the fringe visibility depends on the position (and orientation) of the experiment relative to the conductor's plane. This phenomenon is due to the change in the structure of vacuum induced by the conductor and is closely related to the Casimir effect. We estimate the fringe visibility both for charged and for neutral particles with a permanent dipole moment. The presence of the conductor may tend to increase decoherence in some cases and to reduce it in others. A simple explanation for this peculiar behavior is presented.The interaction of a quantum system with its environment is responsible for the process of decoherence, which is one of the main ingredients to understand the quantum-classical transition [1]. In some cases, the interaction with the environment cannot be switched off. This is the case for charged particles that unavoidably interact with the electromagnetic field. As this interaction is fundamental, its effect is present in any interference experiment. In this letter we will analyze the influence of a conducting boundary in the decay of the visibility of interference fringes in a double slit experiment performed with charged particles (or neutral particles with a dipole moment). The reduction of fringe visibility is induced by the interaction between the particles and the electromagnetic field. Some aspects of this problem have been analyzed before. In fact, it is known that for charged particles, the interaction between the system (the particle) and the environment (the electromagnetic field) induces a rather small decoherence effect even if the initial state of the field is the vacuum [2,3,4,5,6,7,8]. A particularly simple expression for the decay in the fringe visibility was obtained in [2,3]: Assuming an electron in harmonic motion (with frequency Ω) along the relevant trajectories of the double slit experiment, the fringe visibility decays by a factor (1− P ) 2 where P is the probability that a dipole p = eR oscillating at frequency Ω emits a photon (R is the characteristic size of the trajectory). This result is in accordance with the idea that decoherence becomes effective when a record of the state of the system is irreversibly imprinted in the environment. In this case, after photon emission, if the electron follows the trajectory X 1 (t) of the double slit experiment (see Figure 1) it becomes correlated with a state of the environment |E 1 (t) . This state is different from the one with which the electron correlates if it follows the trajectory X 2 (t). The absolute value of the overlap between these two different states is precisely given by (1 − P )2 .In this letter we will analyze how the fringe visibility is modified when performing a double slit interference experiment in the vicinity of a conducting plane. Our analysis will serve ...

Decoherence of electron waves due to induced charges moving through a nearby resistive material

“…5. There are other mechanisms which can also cause decoherence in this experiment: Vacuum fluctuations near a (perfect) conductor [24,25] and emission of bremsstrahlung even in free space [26]. But both of these effects are much smaller than decoherence due to dissipation to the induced current in a poor conductor.…”

Decoherence induced by Smith-Purcell radiation

“…If an interference experiment is performed with charged particles, the unavoidable interaction with the vacuum fluctuations of the electromagnetic field induces decoherence, and therefore affects the visibility of the fringes [2]- [4]. Indeed, in previous papers it has been shown that the presence of a perfectly conducting plane surface has a small influence on the contrast of the fringes.…”

“…[4]. The interaction with the vacuum fluctuations of the electromagnetic field can enhance or suppress the contrast with respect to the visibility in vacuum (absence of conducting plane), depending on the relative orientation of the conducting plane and the plane of the trajectories of the particles [4]. The modification of the visibility of the fringes can be understood in very simple terms [5]: if an electron moves with a typical frequency Ω along the trajectory of the experiment, and if the two trajectories are separated by a distance R, the fringes visibility decays a factor (1 − P ) 2 , where P is the probability that a dipole p = eR oscillating at a frequency Ω emits a photon.…”

“…[3], and the results were subsequently revised and generalized in Ref. [4]. The interaction with the vacuum fluctuations of the electromagnetic field can enhance or suppress the contrast with respect to the visibility in vacuum (absence of conducting plane), depending on the relative orientation of the conducting plane and the plane of the trajectories of the particles [4].…”

Loss of coherence and dressing in QED

“…In the case of a particle, either free or in a potential, linearly coupled to the environment modelled as a bath of harmonic oscillators at temperature T , several studies of decoherence processes have already been reported [10,11,12,13,14,15]. In these studies both the Hamiltonian approach and functional techniques have been used.…”