Two-level atom systems

Luminescence is, in some ways, the inverse process to absorption. We have seen in the previous section how a simple two-level atomic system shifts to the excited state after photons of appropriate frequency are absorbed. This atomic system can return to the ground state by spontaneous emission of photons. This de-excitation process is called luminescence. However, the absorption of light is only one of the multiple mechanisms by which a system can be excited. In a general sense, luminescence is the emission of light from a system that is excited by some form of energy. Table 1.2 lists the most important types of luminescence according to the excitation mechanism. 

This model may describe, for example, a spin -particle confined to move in a one-dimensional harmonic potential whose spin is subject to a harmonic magnetic field or a two-level atomic system interacting with a single mode of a cavity field. It is of interest here as example of an interaction between a discrete- and a continuous-variable system. 

Here, we rq>ort related trapped-ion research at NIST on (1) the study of the dynamics of a two-level atomic system coupled to harmonic atomic motion, (2) the creation and characterization of nonclassical states of motion such as Schrodinger-cat superposition states, and (3) quantum logic for the generation of highly entangled states and for the investigation of scaling in a quantum computer. 

Fluorescence is spontaneous radiation that arises because of the stimulation of an atomic or molecular system to energies higher than equilibrium. This is illustrated in Figure 1 for a simple two-level atom. The atom is excited by absorption of a photon of energy hv. If the fluorescence is observed at 90° to a collimated excitation source, then a very small focal volume may be defined resulting in fine spatial resolution. The fluorescence power an optical system will collect is... 

We consider a two-level atom with excited and ground states e) and g) when in a photonic crystal coupled to the field of a discrete (or defect) mode and to the photonic band structure in the vacuum state. The hamiltonian of the system in the rotating-wave approximation assumes the form [Kofman 1994]... 

Tire SA phenomenon can be described within the framework of a two-level atomic model [69]. When the medium can be assimilated to a coherent ensemble of identical two-level systems all having the same response - that is, when the broadening of the transition is purely homogeneous -, the absorption coefficient is related to the incident light intensity I through... 

It is apparent from Eq. (106) that transitions from the state 0,1V) to the dressed states of the manifold below are allowed only if the dipole moments are not parallel. The transitions occur with significantly reduced rates, proportional to (1 — cosO), giving very narrow lines when 0 0°. For parallel dipole moments the transitions to the state 0,N) are allowed from the dressed states of the manifold above, but are forbidden to the states of the manifold below. Therefore, the state 0, N) is a trapping state such that the population can flow into this state, but cannot leave it resulting in the disappearance of the fluorescence from the driven atom. The nonzero transition rates to the state 10,1V) are proportional to a and are allowed only when A 0. Otherwise, for A = 0, the state 0,1V) is completely decoupled from the remaining dressed states. In this case the three-level system reduces to that equivalent to a two-level atom. 

It is evident that the antisymmetric state is populated by the coherent coupling to the symmetric state. Since the decay rate of the antisymmetric state, T(1 — p), is very small for p 1, the population stays in this state for a long time. If A = 0 the state is decoupled from the symmetric state and is zero if its initial value is zero. In the latter case the system reduces to a two-level atom. In the former case the transfer of the population to a slowly decaying state leaves the symmetric state almost unpopulated even if the driving field is strong. This is shown in Fig. 17, where we plot the steady-state populations pss as a... 

Transitions with parallel or antiparallel dipole moments can be created not only in multilevel systems but also in a two-level system driven by a polychromatic field [63]. In order to show this, we consider a two-level atom driven by a bichromatic field composed of a strong resonant laser field and a weaker laser field detuned from the atomic resonance by the Rabi frequency of the strong field. The effect of the strong field alone is to produce dressed states [35]... 

The formalism of FD quantum-optical states is applicable to other systems described by the FD models as well, such as spin systems or ensembles of two-level atoms or quantum dots. In such cases we should talk about, for instance the z component of the spin and its azimuthal orientation rather than about the photon number and phase. However, the states studied here were first discussed in the quantum-optical papers and we also will keep the terminology of quantum optics. 

It has been shown [31] that a system of two identical two-level atoms may be prepared in the symmetric state s) by a short laser pulse. The conditions for a selective excitation of the collective atomic states can be analyzed from the interaction Hamiltonian of the laser field with the two-atom system. We make the unitary transformation... 

In the model experiment under consideration, the field is represented by the outgoing and incoming spherical waves of photons, which are specified by a continuous distribution of k or of co = ck. Assume that the two identical atoms are the two-level atoms of the type of (34) with the electric dipole transition. Because of the simple geometry of the problem (Fig. 17), it can be considered as a quasiunidimensional integrable system [69]. The effective spatial dependence of the photon operators can be introduced with the aid of the Fourier transformation... 

An entangled quantum state is one where the wave function of the overall system cannot be written as a product of the wave functions of the subsystems. In this case, a measurement on one of the subsystems will affect the state of the other subsystems. For example, consider a two-level atom bound in a 1-D harmonic well. Suppose we can create the state... 

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