Quantum interference phase control

In this contribution recent results [13] on the control of the quantum mechanical phase of an atomic state in strong laser fields studied using the Autler-Townes (AT) effect [14] in the photoionization of the K (4p) state are discussed. We demonstrate quantum control beyond (i) population control and (ii) spectral interference, (i) We show, that for suitable combinations of the laser intensity of the first pulse and the time delay the second resonant intense laser pulse leaves the excited state population unchanged. However, the knowledge of the... 

We demonstrate coherent control in strong fields beyond (i) population control and (ii) spectral interference, since (i) control is achieved without altering the population during the second intense laser pulse, i.e., the population during the second laser pulse is frozen, and (ii) the quantum mechanical phase is controlled without changing the spectrum of the pulse sequence. The control mechanism relies on the interplay of the quantum mechanical phase set by the intensity of the first pulse and the phase of the second pulse determined by the time delay. 

Two lines of inquiry will be important in future work in photochemistry. First, both the traditional and the new methods for studying photochemical processes will continue to be used to obtain information about the subtle ways in which the character of the excited state and the molecular dynamics defines the course of a reaction. Second, there will be extension and elaboration of recent work that has provided a first stage in the development of methods to control, at the level of the molecular dynamics, the ratio of products formed in a branching chemical reaction. These control methods are based on exploitation of quantum interference effects. One scheme achieves control over the ratio of products by manipulating the phase difference between two excitation pathways between the same initial and final states. Another scheme achieves control over the ratio of products by manipulating the time interval between two pulses that connect various states of the molecule. These schemes are special cases of a general methodology that determines the pulse duration and spectral content that maximizes the yield of a desired product. Experimental verifications of the first two schemes mentioned have been reported. Consequently, it is appropriate to state that control of quantum many-body dynamics is both in principle possible and is... 

Control of the type discussed above, in which quantum interference effects are used to constructively or destructively alter product properties, is called coherent control (CC). Photodissociation of a superposition state, the scenario described above, will be seen to be just one particular implementation of a general principle of coherent control Coherently driving a state with phase coherence through multiple, coherent,... 

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 Fig. 2, we present the steady-state population inversion between the upper state 1) and the ground state 2), computed from the master equation (73), for r = 0 and different values of the phase difference 5<(> and the interference parameter p. It is seen that in the presence of quantum interference the population can be inverted on the 1) —> 2) transition and the inversion can be controlled by the phase difference between the driving laser fields [27],... 

Paspalakis and Knight [28] have considered a V-type three-level system driven from an auxiliary level by two laser fields of the same frequencies. They have predicted linewidth narrowing and cancellation of the fluorescenc, which can be controlled via the phase difference between the two laser fields used for the excitation. Ghafoor et al. [29] have considered a four-level system in which quantum interference can be generated by three driving fields and have shown that the linewidths and intensities of the spectral lines can be controlled by the phases and amplitudes of the driving fields. 

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. 

The phase-dependent interference is revealed by measuring the weak laser transmission versus the control laser phase. Fig. 10 ((a) and (b)) plots the transmitted signal and control beams versus the control laser phase Oo as Oo is varied by a sinusoidal voltage applied to the EOM. Fig. 10(a) plots the light transmission versus Oo at Ap=Ac 0 and Fig. 10(b) plots the light transmission versus Oc at Ap=Ac= Q. The data show that there is a ti phase difference in the interference pattern between the two cases, illustrating the phase and frequency control of the light transmission by the quantum interference. 

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. 

Two main approaches to the control of molecules using wave interference in quantum systems have been proposed and developed in different languages . The first approach (Tannor and Rice 1985 Tannor et al. 1986) uses pairs of ultrashort coherent pulses to manipulate quantum mechanical wave packets in excited electronic states of molecules. These laser pulses are shorter than the coherence lifetime and the inverse rate of the vibrational-energy redistribution in molecules. An ultrashort pulse excites vibrational wave packets, which evolve freely until the desired spacing of the excited molecular bond is reached at some specified instant of time on a subpicosecond timescale. The second approach is based on the wave properties of molecules as quantum systems and uses quantum interference between various photoexcitation pathways (Brumer and Shapiro 1986). Shaped laser pulses can be used to control this interference with a view to achieving the necessary final quantum state of the molecule. The probability of production of the necessary excited quantum state and the required final product depends, for example, on the phase difference between two CW lasers. Both these methods are based on the existence of multiple interfering pathways from the initial... 

By making use of classical or quantum-mechanical interferences, one can use light to control the temporal evolution of nuclear wavepackets in crystals. An appropriately timed sequence of femtosecond light pulses can selectively excite a vibrational mode. The ultimate goal of such optical control is to prepare an extremely nonequilibrium vibrational state in crystals and to drive it into a novel structural and electromagnetic phase. 

Here we describe the development of the coherent-control toolbox with gas-phase iodine molecules [37 1, 48]. The gas-phase molecules are isolated from each other, so that they have long coherence lifetime, serving as an ideal platform to observe and control quantum coherence. First, we describe our experiments to observe and control the temporal evolution of the WP interference. Second, the eigenstate picture of the WP interference is presented. Finally, we demonstrate the application of WPI to ultrafast molecular computing. 

A note of caution must be inserted at this point. It appears, at first sight, that there is a meaning that can be attached to the absolute phase of the field and to the phases of the molecular expectation values. However, it must be remembered that the phase of the molecular quantity is induced by the radiation field prior to the present time. Therefore all phases must be related to the phase of a previous pulse that synchronizes the molecular clock with the field clock. With this synchronization it is possible to understand how quantum mechanical interference between events induced in the past propagates and can be used to control energy and/or population transfer at a later time. 

The stability matrix carries the necessary information related to the vicinity of the trajectory and provides an efficient numerical procedure for computing the response function. It plays an important role in the field of classical chaos the sign of its eigenvalues (related to the Lyapunov exponents) controls the chaotic nature of the system. Interference effects in classical response functions have a different origin than their quantum counterparts. For each initial phase-space point we need to launch two trajectories with very close initial conditions. [For 5(n) we need n trajectories.] The nonlinear response is obtained by adding the contributions of these trajectories and letting them interfere. 

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