“…In this case, the state of the system before the change is no longer an eigenstate of the new Hamiltonian, and thus a time-evolution of the Casimir-Polder force is obtained [22]. Very recently these studies have been extended to the cases of a real surface, where the excitation of surface plasmons plays an important role in the dynamical interaction [23] or to the case of an atom in a cavity with a dielectric medium [24] or a chiral molecule near a chiral plate [25]. All these studies show that, in the dynamical case, the Casimir-Polder force can be much stronger compared with the static case around the round-trip time, that is the time taken by a light signal emitted by the atom to go back to the atom after reflection on the plate; they also highlight a new transient repulsive character (on the contrary, static electric atom-surface Casimir-Polder forces are attractive).…”
We consider the dynamical atom-surface Casimir-Polder force in the non-equilibrium configuration of an atom near a perfectly conducting wall, initially prepared in an excited state with the field in its vacuum state. We evaluate the time-dependent Casimir-Polder force on the atom, and find that it shows an oscillatory behavior from attractive to repulsive both in time and in space. We also investigate the asymptotic behavior in time of the dynamical force and of related local field quantities, showing that the static value of the force, as obtained by a time-independent approach, is recovered for times much larger than the timescale of the atomic self-dressing, but smaller than the atomic decay time. We then discuss the evolution of global quantities such as atomic and field energies, and their asymptotic behavior. We also compare our results for the dynamical force on the excited atom with analogous results recently obtained for an initially bare ground-state atom. We show that new relevant features are obtained in the case of an initially excited atom, for example much larger values of the dynamical force with respect to the static one, allowing for an easier way to single-out and observe the dynamical Casimir-Polder effect.
“…In this case, the state of the system before the change is no longer an eigenstate of the new Hamiltonian, and thus a time-evolution of the Casimir-Polder force is obtained [22]. Very recently these studies have been extended to the cases of a real surface, where the excitation of surface plasmons plays an important role in the dynamical interaction [23] or to the case of an atom in a cavity with a dielectric medium [24] or a chiral molecule near a chiral plate [25]. All these studies show that, in the dynamical case, the Casimir-Polder force can be much stronger compared with the static case around the round-trip time, that is the time taken by a light signal emitted by the atom to go back to the atom after reflection on the plate; they also highlight a new transient repulsive character (on the contrary, static electric atom-surface Casimir-Polder forces are attractive).…”
We consider the dynamical atom-surface Casimir-Polder force in the non-equilibrium configuration of an atom near a perfectly conducting wall, initially prepared in an excited state with the field in its vacuum state. We evaluate the time-dependent Casimir-Polder force on the atom, and find that it shows an oscillatory behavior from attractive to repulsive both in time and in space. We also investigate the asymptotic behavior in time of the dynamical force and of related local field quantities, showing that the static value of the force, as obtained by a time-independent approach, is recovered for times much larger than the timescale of the atomic self-dressing, but smaller than the atomic decay time. We then discuss the evolution of global quantities such as atomic and field energies, and their asymptotic behavior. We also compare our results for the dynamical force on the excited atom with analogous results recently obtained for an initially bare ground-state atom. We show that new relevant features are obtained in the case of an initially excited atom, for example much larger values of the dynamical force with respect to the static one, allowing for an easier way to single-out and observe the dynamical Casimir-Polder effect.
“…It is noted that we have neglected the effect of the resonant cavity on the CP interaction of a two-level system near a cavity wall. This is a good approximation when the cavity length L is large enough, i.e., of the order of centimeters, and as a result the change of the density of states of the electromagnetic field inside the cavity does not significantly alter the CP force [97].In addition, the dynamical CP effect between an atomic gas and a conducting wall due to the dissipation of the electromagnetic fields inside the cavity can be neglected safely with a large enough optical cavity [98,99].…”
Section: Model and Hamiltonian Of The Hybrid Optomechanical Systemmentioning
We investigate a hybrid optomechanical system consisting of an ensemble of quantum emitters inside a standard optomechanical cavity with a moving end mirror, in which the motion of the mirror changes the transition rate of each emitter and therefore leads to a direct coupling between the internal state of the quantum emitter and the mechanical mode. We analyzed the steady-state characteristics of the optomechanical system and found that the bistability of the system depends strongly on the distance between the emitter ensemble and the mirror. Further, we also analyze in detail the influences of the distance and other system parameters, i.e., the effective detunings, the driving power, the decay rates of the cavity, and the emitter ensemble and the thermal phonons on the steady-state entanglement by considering fluctuation of the mechanical oscillator, the cavity field, and the emitter ensemble. It is found that the degree of the steady-state entanglement can be greatly enhanced in a certain range of parameters by increasing the vacuum-induced emitter–mirror coupling, which can be realized by decreasing the emitter–mirror distance and increasing properly the free-space spontaneous emission rate of the emitter.
“…A two-level atom is located at x 0 in the cavity. The Hamiltonian for the system within the dipole approximation can be written as [32][33][34] We can defined the parameter g j in Eq. (3) where µ is the dipole operator component in the polarization of the field.…”
Section: Model and Hamiltonianmentioning
confidence: 99%
“…A two-level atom is located at in the cavity. The Hamiltonian for the system within the dipole approximation can be written as 32 – 34 Figure 1 (Color online) The schematic diagram of the structure of a two-level atom located in the one-dimensional dielectric cavity (Region 1). The cavity is embedded in a larger ideal cavity with ideal conductor plates at both ends.…”
We study the dynamical Casimir-Polder force on a two-level atom with different initial states in the one-dimensional dielectric cavity with output coupling, and obtain the analytical expression of the expectation value of dynamical Casimir-Polder force. Results show that the expectation values of dynamical Casimir-Polder force may be affected by the initial states of the atom. Moreover, the expectation value of Casimir-Polder force may vanish at some special atomic positions by properly selecting the initial state of the system. The effects of different relative dielectric constants and the cavity size on the expectation value of Casimir-Polder force are also discussed. The existence of electromagnetic vacuum fluctuations has caused many quantum effects, such as Casimir-Polder force 1,2. The Casimir-Polder force is the long-range interaction between neutral polarizable particles and macroscopic objects, which is successfully observed in experiments 3 and has received considerable attentions 4-7 due to its potential application in basic physics and designing of quantum devices 6,8-11. For instance, the Casimir-Polder force has covered various configurations such as trapping cold atoms near surfaces 12-16 , quantum reflection 17-20 , graphene 21 , Bose-Einstein condensates 17,22 , and carbon nanotubes 23-25. At finite temperatures, the key correlations between these interactions and the topological and magnetoelectric properties of interacting objects are highlighted 26,27. In recent years, many studies have focused on the Casimir-Polder force on atoms when they start from ground or excited states 28-31. In Ref. 31 and 4 , the authors investigate the dynamcial Casimir-Polder force on a two level atom placed before a ideal metal plate starting from the ground state and the excited state, respectively. Results show that the static Casimir-Polder force is always attractive for the ground state condition, while the static Casimir-Polder force is either attractive or repulsive for the excited condition. At some special atom-wall distances, the static Casimir-Polder force can vanish for the excited condition. Besides, the static Casimir-Polder force for the excited-atom condition is much greater than that of the ground-atom condition. In this paper, we will investigate the effect of initial states on the dynamical Casimir-Polder force acting on a two-level atom in a caivity with output coupling 32. The analytical expression of the expectation value of dynamical Casimir-Polder force on atom starting from the superposition state will be obtained. And the effects of the dielectric and cavity size will be discussed. The paper is organized as follows: in "Model and Hamiltonian" section, we describe the model and the Hamiltonian of the system. In "Calculation of the expectation value of dynamical Casimir-Polder force" section we will calculate the expectation value of dynamical Casimir-Polder force. In "Dynamical Casimir-Polder force on an initially general superposition state atom" section we will discuss the dynamical Casimi...
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