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Physical Review A

Casimir-Polder force on a V -type three-level atom near a structure containing left-handed materials

Jingping Xu, Shenglong Chang, Yaping Yang, M. Al-Amri

Published Jan 21, 2016• 5 citations
Publisher

Abstract

The Casimir-Polder (CP) force acting on a $\mathsf{V}$-type three-level atom which is initially prepared in two different kinds of superposition states, i.e., subradiant and superradiant states, is investigated. The influence of quantum interference on force evolution due to two-dipole transitions is analyzed in detail. It is found that the orientation of the atomic dipole moment has significant influence on the Casimir-Polder force and consequently its evolution. For the ideal degenerate $\mathsf{V}$-type atom with two parallel dipoles, quantum interference leads to population trapping as well as the cancellation of the CP force when the atom is prepared initially in a subradiant state. However, the result changes when we consider the practical Zeeman $\mathsf{V}$-type atom whose two dipole moments are perpendicular to each other. Since quantum interference in such an atom must occur in an anisotropic environment, it is possible to trap atomic population and enhance the CP force simultaneously by preparing the atom initially in sub-radiant states. In principle, our results can be found in an arbitrary anisotropic environment, and here we describe a structure containing left-handed materials to highlight our findings.

DOI
10.1103/physreva.93.012514

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The Casimir-Polder (CP) force acting on a V\mathsf{V}V-type three-level atom which is initially prepared in two different kinds of superposition states, i.e., subradiant and superradiant states, is investigated. The influence of quantum interference on force evolution due to two-dipole transitions is analyzed in detail. It is found that the orientation of the atomic dipole moment has significant influence on the Casimir-Polder force and consequently its evolution. For the ideal degenerate V\mathsf{V}V-type atom with two parallel dipoles, quantum interference leads to population trapping as well as the cancellation of the CP force when the atom is prepared initially in a subradiant state. However, the result changes when we consider the practical Zeeman V\mathsf{V}V-type atom whose two dipole moments are perpendicular to each other. Since quantum interference in such an atom must occur in an anisotropic environment, it is possible to trap atomic population and enhance the CP force simultaneously by preparing the atom initially in sub-radiant states. In principle, our results can be found in an arbitrary anisotropic environment, and here we describe a structure containing left-handed materials to highlight our findings.
We study the thermal Casimir-Polder (CP) forces on a V-type three-level atom. The competition between the thermal effect and the quantum interference of the two transition dipoles on the force is investigated. To shed light onto the role of the quantum interference, we analyze two kinds of initial states of the atom, i.e., the superradiant state and the subradiant state. Considering the atom being in the thermal reservoir, the resonant CP force arising from the real photon emission dominates in the evolution of the CP force. Under the zero-temperature condition, the quantum interference can effectively modify the amplitude and the evolution of the force, leading to a long-time force or even the cancellation of the force. Our results reveal that in the finite-temperature case, the thermal photons can enhance the amplitude of all force elements, but have no influence on the net resonant CP force in the steady state, which means that the second law of thermodynamics still works. For the ideal degenerate V-type atom with parallel dipoles under the initial subradiant state, the robust destructive quantum interference overrides the thermal fluctuations, leading to the trapping of the atom in the subradiant state and the disappearance of the CP force. However, in terms of a realistic Zeeman atom, the thermal photons play a significant role during the evolution of the CP force. The thermal fluctuations can enhance the amplitude of the initial CP force by increasing the temperature, and weaken the influence of the quantum interference on the evolution of the CP force from the initial superradiant (subradiant) state to the steady state.
Influence of the Casimir-Polder force on a slowly moving atom near a left-handed slab is discussed.We focus on an initially excited atom and its dynamic evolution during the spontaneous decay process.The left-haned slab is adopted based on two factors:(1) It provides a relatively stronger Casimir-Polder force on the excited atom far away from the interface,and(2) it can lead to an inhibited spontaneous decay rate within such a region.Therefore,we can discuss the dynamic evolution of atoms acted only by the Casimir-Polder force.The dynamic evolution discussed here includes both the evolution of atomic population and the atomic displacement.As the Casimir-Polder force depends on the atomic population,while the decay rate is related to the atomic positions,the atomic dynamic evolution is determined by its initial conditions,i.e.its position and volecity.We choose two initial positions for discussion,i.e.(1) the position with the maximum resonant Casimir-Polder force,and(2) the edge of the resonant Casimir-Polder force of the atom with dipole parallel to the interface.Furthermore,we also consider two kinds of orientations of atomic dipole,i.e.parallel and normal to the interface.It is found that the atom can be repulsed away from a surface by the Casimir-Polder force with a proper initial velocity in certain dipole orientaion during the sponatneous decay process.As the atomic dynamics depends on the orientation of the atom dipole momentum,our result can be used as a reference to distinguish atoms with different dipole momenta.Though the force discussed here exists during the spontaneous decay process,it is much different from the recoil force of the atom when it emits a photon during the spontaneous decay.The statistical average of the recoil force is null,but that of the resonant Casimir-Polder force is not.After reasonable estimation,such a Casimir-Polder force can counteract the thermal fluctuation of temperature of 15 μK during sponatneous decay.If combined with other constraint methods,it is helpful to control the dynamics of an atom more efficiently.
We address quantum interference of the Zeeman atom embedded in two kinds of structures containing left-handed materials (LHM), which are a single LHM layer mounted on a single mirror (SLSM) and Fabry-P\'erot cavity filled with a LHM layer by half (FPCLH). Especially, the influence of the dissipation of LHM on quantum interference has been studied in detail. Though dissipation weakens quantum interference in general, it holds nearly complete quantum interference when the thickness of the cavity is small for FPCLH. Moreover, with equivalence of left- and right- rotation polarized dipoles to two spatial orthogonal dipoles, we found the optimum orientation of two orthogonal dipoles which can realize the maximum quantum interference in a certain anisotropic environment. Our research may have potential applications in the designing of microsize devices.
Influence of the Casimir-Polder force on a slowly moving atom near a left-handed slab is discussed. We focus on an initially excited atom and its dynamic evolution during the spontaneous decay process. The left-haned slab is adopted based on two factors: (1) It provides a relatively stronger Casimir-Polder force on the excited atom far away from the interface, and (2) it can lead to an inhibited spontaneous decay rate within such a region. Therefore, we can discuss the dynamic evolution of atoms acted only by the Casimir-Polder force. The dynamic evolution discussed here includes both the evolution of atomic population and the atomic displacement. As the Casimir-Polder force depends on the atomic population, while the decay rate is related to the atomic positions, the atomic dynamic evolution is determined by its initial conditions, i.e. its position and volecity. We choose two initial positions for discussion, i.e. (1) the position with the maximum resonant Casimir-Polder force, and (2) the edge of the resonant Casimir-Polder force of the atom with dipole parallel to the interface. Furthermore, we also consider two kinds of orientations of atomic dipole, i. e. parallel and normal to the interface. It is found that the atom can be repulsed away from a surface by the Casimir-Polder force with a proper initial velocity in certain dipole orientaion during the sponatneous decay process. As the atomic dynamics depends on the orientation of the atom dipole momentum, our result can be used as a reference to distinguish atoms with different dipole momenta. Though the force discussed here exists during the spontaneous decay process, it is much different from the recoil force of the atom when it emits a photon during the spontaneous decay. The statistical average of the recoil force is null, but that of the resonant Casimir-Polder force is not. After reasonable estimation, such a Casimir-Polder force can counteract the thermal fluctuation of temperature of 15 μupK during sponatneous decay. If combined with other constraint methods, it is helpful to control the dynamics of an atom more efficiently.
The spontaneous emission of a V-type Zeeman atom in a Fabry–Perot cavity containing left-handed materials (LHMs) is investigated. Because of the strong indirect quantum interference induced by the refocusing and phase compensation of LHMs, the population evolution and the emission spectrum are much different from that in isotropic environments at different initial conditions. For the degenerate cases, by preparing different initial states, the population decays much faster or slower than that in free vacuum, while the spontaneous emission spectra are narrowed or broadened, respectively. For large detuning cases, the population exchange between two upper levels could be weakened, and the Fano minimum appears in the emission spectrum. In addition, the influence of the dipole orientation on the spectrum is discussed.
This study proposes a nanophotonic structure that supports the generation and enhancement of the lateral Casimir-Polder (CP) force acting on atoms. By applying the two-dimensional anisotropic material, we demonstrate that both the spontaneous decay rate and the emission pattern of the atom exhibit distinct features by manipulating the parameters of the system. In particular, the exact numerical solutions of population dynamics reveal the occurrence of Rabi oscillations in the strong atom-field coupling case, where the Markovian results fail to describe this phenomenon. We also show that the asymmetric spatial distribution of the in-plane dipole radiation into surface plasmon modes is achievable for the system under consideration. Based on these intriguing properties, we predict the generation of the lateral CP force, where the transient evolution of the force indicates the periodical variation in both the direction and the amplitude under strong light-atom interaction conditions. Our findings have potential applications for novel optical nanotechnologies and devices, which provide a method for atom manipulation and trapping.