Quantum interference atomic transitions

X-ray absorption spectroscopy combining x-ray absorption near edge fine structure (XANES) and extended x-ray absorption fine structure (EXAFS) was used to extensively characterize Pt on Cabosll catalysts. XANES Is the result of electron transitions to bound states of the absorbing atom and thereby maps the symmetry - selected empty manifold of electron states. It Is sensitive to the electronic configuration of the absorbing atom. When the photoelectron has sufficient kinetic energy to be ejected from the atom It can be backscattered by neighboring atoms. The quantum Interference of the Initial... 

In NaxW03-yFy Doumerc (1978) observed a transition that has all the characteristics of an Anderson transition similar phenomena are observed in NaxTayW3 y03. The results are shown in Fig. 7.14. It is unlikely that this transition is generated by the overlap of two Hubbard bands with tails (Chapter 1, Section 4) this could only occur if it took place in an uncompensated alkali-metal impurity band, which seems inconsistent with the comparatively small electron mass. We think rather that in the tungsten (or tungsten-tantalum) 5d-band an Anderson transition caused by the random positions of Na (and F or Ta) atoms occurs. The apparent occurrence of amiD must, as explained elsewhere, indicate that a at the temperature of the experiments. Work below 100 K, to look for quantum interference effects, does not seem to have been carried out. 

The interest in quantum interference stems from the early 1970s when Agarwal [4] showed that the ordinary spontaneous decay of an excited degenerate V-type three-level atom can be modified due to interference between the two atomic transitions. The analysis of quantum interference has since been extended to other configurations of three- and multilevel atoms and many interesting effects have been predicted, which can be used to control optical properties of quantum systems, such as high-contrast resonances [5,6], electro-magnetically induced transparency [7], amplification without population inversion [8], and enhancement of the index of refraction without absorption [9]. 

The effect of quantum interference on spontaneous emission in atomic and molecular systems is the generation of superposition states that can be manipulated, to reduce the interaction with the environment, by adjusting the polarizations of the transition dipole moments, or the amplitudes and phases of the external driving fields. With a suitable choice of parameters, the superposition states can decay with controlled and significantly reduced rates. This modification can lead to subnatural linewidths in the fluorescence and absorption spectra [5,10]. Furthermore, as will be shown in this review, the superposition states can even be decoupled from the environment and the population can be trapped in these states without decaying to the lower levels. These states, known as dark or trapped states, were predicted in many configurations of multilevel systems [11], as well as in multiatom systems [12],... 

In the transformed form the T - and Fn-dependent terms are accompanied by a phase-dependent term, exp( 8< )). These terms are also accompanied by the time-dependent terms exp co — ffiijf], which oscillate with the difference of the laser frequencies. This shows that in any attempt to calculate phase-dependent effects, it is important to assume that the lasers have equal frequencies. Otherwise, for unequal frequencies the time-dependent terms rapidly oscillate in time and average out over a long period of the detection time. Furthermore, we note from Eq. (75) that in the case of q = 1 a phase dependence can be observed even in the absence of the vacuum induced quantum interference terms (I)2 = 0). Only for q = 0, that is, when each laser couples to only one of the transitions, the phase terms solely depend on the vacuum induced quantum interference. However, this condition can be achieved only for an imperfect interference (p =/= 1) between the atomic transitions that the dipole... 

The dressed-atom predictions clearly explain the origin of the cancellation of the spectral line arising from the cancellation of the transition dipole moment due to quantum interference between the two atomic transitions. 

Another area of interest in quantum interference effects, which has been studied extensively, is the response of a V-type three-level atom to a coherent laser field directly coupled to the decaying transitions. This was studied by Cardimona et al. [36], who found that the system can be driven into a trapping state in which quantum interference prevents any fluorescence from the excited levels, regardless of the intensity of the driving laser. Similar predictions have been reported by Zhou and Swain [5], who have shown that ultrasharp spectral lines can be predicted in the fluorescence spectrum when the dipole moments of the atomic transitions are nearly parallel and the fluorescence can be completely quenched when the dipole moments are exactly parallel. 

The narrow resonances produced by quantum interference may also be observed in the absorption spectrum of a three-level atom probed by a weak field of the frequency o> ). Zhou and Swain [10] have calculated the absorption spectrum of a probe field monitoring E-type three-level atoms with degenerate (A = 0) as well as nondegenerate (A / 0) transitions and have demonstrated that quantum... 

The CPT effect and its dependence on quantum interference can be easily explained by examining the population dynamics in terms of the superposition states. v) and a). Assume that a three-level A-type atom is composed of a single upper state 3) and two ground states 1) and 2). The upper state is connected to the lower states by transition dipole moments p31 and p32. After introducing superposition operators 5+ = (S ) = 3)(.v and 5+ = (Sa) = 3)(a, where. v) and a) are the superposition states of the same form as Eqs. (107) and (108), the Hamiltonian (65) can be written as... 

Consider the Menon-Agarwal approach to the Autler-Townes spectrum of a V-type three-level atom. The atom is composed of two excited states, 1) and 3), and the ground state 2) coupled by transition dipole moments with matrix elements p12 and p32, but with no dipole coupling between the excited states. The excited states are separated in frequency by A. The spontaneous emission rates from 1) and 3) to the ground state 2) are Tj and T2, respectively. The atom is driven by a strong laser field of the Rabi frequency il, coupled solely to the 1) —> 2) transition. This is a crucial assumption, which would be difficult to realize in practice since quantum interference requires almost parallel dipole moments. However, the difficulty can be overcome in atomic systems with specific selection rules for the transition dipole moments, or by applying fields with specific polarization properties [26]. 

We concentrate on the role of quantum interference in the correlation of photons emitted from a coherently driven V-type atom, recently analyzed by Swain et al. [58]. We calculate the normalized second-order two-time correlation function g (R, t R, t + x) for the fluorescent field emitted from a three-level V-type atom driven by a coherent laser field coupled to both atomic transitions. The fluorescence field is observed by a single detector located at a point R = RR, where R is the unit vector in the direction of the observation. 

IY In their case the atom prefers to stay in the transition with the larger decay rate (strong transition) and there is a small probability of finding the system in the other (weak) transition. The extended dark periods, predicted for the V-type atom with almost parallel dipole moments, appear simultaneously on both transitions independent of the decay rates. This indicates that in the presence of quantum interference the atomic states 1) and 3) are not the preferred radiative states of the atom. 

This represents a formidable practical problem, as one is very unlikely to find isolated atoms with two nonorthogonal dipole moments and quantum states close in energy. Consider, for example, a V-type atom with the upper states 11), 3) and the ground state 2). The evaluation of the dipole matrix elements produces the following selection rules in terms of the angular momentum quantum numbers J — J2 = 1,0, J3 — J2 = 1,0, and Mi — M2 = M3 — M2 = 1,0. Since Mi / M3, in many atomic systems, p12 is perpendicular to p32 and the atomic transitions are independent. Xia et al. [62] have found transitions with parallel and antiparallel dipole moments in sodium molecules (dimers) and have demonstrated experimentally the effect of quantum interference on the fluorescence intensity. We discuss the experiment in more details in the next section. Here, we point out that the transitions with parallel and antiparallel dipole moments in the sodium dimers result from a mixing of the molecular states due to the spin-orbit coupling. 

We now can calculate the transition dipole moments (in n between the doubly dressed states, corresponding to the transitions at (Do, and find that the dipole moments are equal to zero. Thus, in the doubly driven atom the effective dipole moments at (Do are zero due to quantum interference between the two... 

Here we extend the simple three-level EIT system to mote complicated and versatile configurations in a multi-level atomic system coupled by multiple laser fields. We show that with multiple excitation paths provided by different laser fields, phase-dependent quantum interference is induced either constractive or destractive interfereiKe can be realized by varying the relative phases among the laser fields. Two specific examples are discussed. One is a three-level system coupled by bichromatic coupling and probe fields, in which the phase dependent interference between the resonant two-photon Raman transitions can be initiated and controlled. Another is a four-level system coupled by two coupling fields and two probe fields, in which a double-EIT confignration is created by the phase-dependent interference between three-photon and one-photon excitation processes. We analyze the coherently coupled multi-level atomic system and discuss the control parameters for the onset of constructive or destructive quantum interference. We describe two experiments performed with cold Rb atoms that can be approximately treated as the coherently coupled three-level and four-level atomic systems respectively. The experimental results show the phase-dependent quantum coherence and interference in the multi-level Rb atomic system, and agree with the theoretical calculations based on the coherently coupled three-level or four-level model system. 

Rabi frequeney of the eoupling laser and result in two transition paths ( l> +> and 1>—> ->) for the probe laser (Fig. 1(b)). On the resonance frequency of the bare state transition 1> —> 3>, the quantum interferenee between the two transition paths is destructive due to the opposite frequency detuning and leads to the suppression of the probe light absorption, rendering the three-level atomic medium transparent to the probe laser. Since the two transitions are linear and are connected by the same probe laser field, the quantum interference is independent of the probe laser phase and is destructive only. 

The atomic coherence and interference phenomenon in the simple three-level system sueh as EIT can be extended to more eomplicated multi-level atomic systems. A variety of other phenomena and applications involving three or four-level EIT systems have been studied in reeent years. In particular, phase-dependent atomic coherence and interference has been explored [52-66]. These studies show that in multi-level atomic systems coupled by multiple laser fields, there are often various types of nonlinear optical transitions involving multiple laser fields and the quantum interference among these transition paths may exhibit complicated spectral and dynamic features that can be manipulated with the system parameters such as the laser field amplitudes and phases. Here we present two examples of such coherently coupled multi-level atomic systems in which the quantum interference is induced between two nonlinear transition paths and can be eontrolled by the relative phase of the laser fields. 

We observed the phase-dependent quantum interference in the double A system realized with cold Rb atoms coupled by four laser fields. The coherently coupled four-level double A-type system realized with the laser coupling scheme for the Rb Di transitions is shown in Fig. 8 and the simplified experimental set up is depicted in Fig. 4(b). An extended-cavity diode laser with a beam diameter 3 mm and output power 50 mW is used as the coupling laser. The driving electric current to the diode laser is modulated at 5=181 MHz with a modulation index -0.5, which produces two first-order frequency sidebands separated by 362 MHz. The two sidebands are tuned to the Rb Di F=3—>F =2 and F=3 F =3 transitions respectively and serve as the two coupling fields due to a tt phase difference between the two sidebands). Another... 

Phase-dependent coherence and interference can be induced in a multi-level atomic system coupled by multiple laser fields. Two simple examples are presented here, a three-level A-type system coupled by four laser fields and a four-level double A-type system coupled also by four laser fields. The four laser fields induce the coherent nonlinear optical processes and open multiple transitions channels. The quantum interference among the multiple channels depends on the relative phase difference of the laser fields. Simple experiments show that constructive or destructive interference associated with multiple two-photon Raman channels in the two coherently coupled systems can be controlled by the relative phase of the laser fields. Rich spectral features exhibiting multiple transparency windows and absorption peaks are observed. The multicolor EIT-type system may be useful for a variety of application in coherent nonlinear optics and quantum optics such as manipulation of group velocities of multicolor, multiple light pulses, for optical switching at ultra-low light intensities, for precision spectroscopic measurements, and for phase control of the quantum state manipulation and quantum memory. 

There is a strong analogy between these interference structures and the so-called quantum beats that are observed in photon emission studies when atoms are coherently excited into different states by beam-foil, laser excitation, or other methods. Both phenomena are due to time-dependent interferences of transitions from different states. In quantum-beat studies... 

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