Laser light has been used as a probe of atoms, molecules, and solids since the invention of the laser. The use of laser light in a more active role, to modify and process surfaces, and initiate chemical reactions, followed shortly thereafter. But usually it is the intensity and the directionality of the laser light that is employed, not necessarily its coherence, and not particularly the fact that it has a well-defined phase. 'Coherence control' can be broadly understood as the set of processes whereby light modifies matter in a way that is critically dependent on the incident light beams possessing well-defined phases. While in a laser matter is manipulated to produce light of the desired properties, in coherent control light is manipulated -- in particular, its phase and intensity is adjusted -- to produce a material response of the desired type. Of the various coherent control processes that are currently being investigated, some involve a transition in the material medium from an initial state to a final state by two or more possible processes. With each of these is associated a quantum mechanical amplitude, and hence the probability for the transition can show interference effects between the two amplitudes, just as in the familiar two-slit interference experiment the probability for the electron to be observed at a given position involves a probability that is the square of the sum of two amplitudes. In quantum interference control (QUIC), the relative phase of the two amplitudes is adjusted by adjusting the relative phase of two polarizations of a single beam, or the relative phase of two beams at different frequencies. It is this particular type of coherent control that is of interest in this communication.
Laser light has been used as a probe of atoms, molecules, and solids since the invention of the laser. The use of laser light in a more active role, to modify and process surfaces, and initiate chemical reactions, followed shortly thereafter. But usually it is the intensity and the directionality of the laser light that is employed, not necessarily its coherence, and not particularly the fact that it has a well-defined phase. 'Coherence control' can be broadly understood as the set of processes whereby light modifies matter in a way that is critically dependent on the incident light beams possessing well-defined phases. While in a laser matter is manipulated to produce light of the desired properties, in coherent control light is manipulated -- in particular, its phase and intensity is adjusted -- to produce a material response of the desired type. Of the various coherent control processes that are currently being investigated, some involve a transition in the material medium from an initial state to a final state by two or more possible processes. With each of these is associated a quantum mechanical amplitude, and hence the probability for the transition can show interference effects between the two amplitudes, just as in the familiar two-slit interference experiment the probability for the electron to be observed at a given position involves a probability that is the square of the sum of two amplitudes. In quantum interference control (QUIC), the relative phase of the two amplitudes is adjusted by adjusting the relative phase of two polarizations of a single beam, or the relative phase of two beams at different frequencies. It is this particular type of coherent control that is of interest in this communication.
T hink about coherent systems, and odds are that the first example to cross your mind will be a laser: a device that emits monochromatic light homogenized so that the photons propagate with their phase in lockstep. The well-defined wavefront of the laser beam makes it possible to focus the light to spot sizes on the order of the wavelength of the light without the aberrations usually observed with the random wavefront of incoherent light. The well-defined phase also provides a medium capable of storing and carrying information more efficiently than the intensity-modulated signals typical of incoherent sources. These useful properties of coherence have made lasers almost ubiquitous in science and technology, and that “almost” is shrinking by the day.
In general, coherence comes about when individual components of a system act in unison, either in phase or with a fixed phase difference between the components. More accurately, the system can be described as a local oscillator whose wavefunction contains phase and amplitude terms that define how the system evolves in space and time. The collection of articles in this special issue describes the recent progress and developments of coherence in optical, atomic, and semiconductor systems, and how manipulating that coherence may lead to useful applications and to experimental systems for studying the elements of quantum mechanics.
Since the first demonstration of the laser in 1960, progress in improving the extent of the spatial and temporal coherence of laser light has been steady. Psaltis (p. [1359][1]) reviews developments in optical coherence and highlights examples of the key role coherence has played in applications in imaging, communication, and information processing and storage. Just as lasers revolutionized the field of optics, many researchers have high expectations that other coherent systems will provide similar advances in their respective fields. Exploiting the fundamental tenet of quantum mechanics whereby particles have the properties of waves, Kasevich (p. [1363][2]) reviews coherence effects in collections of cold atoms and describes how the shorter wavelengths associated with atoms and the recent accessibility of bright coherent atom sources may lead to precision measurements beyond anything currently available to the optical regime. For integration and potential applications, the ideal system would be based in semiconductors. Snoke (p. [1368][3]) describes recent work toward the formation of coherent semiconductor systems.
With coherence in the atomic and optical systems generally comprising macroscopic systems, Mabuchi and Doherty (p. [1372][4]) look at coherence effects at the quantum limit, probing the interactions between single atoms and single photons confined to high-quality cavities. In addition to providing invaluable information on the limits of quantum mechanics, such effects might also shed new light on information science in the quantum regime.
The section opens with a pair of News features by staff writers Charles Seife and Robert Service. Seife presents a smattering of common applications that scientists and engineers have found for coherent waves, whether in light, sound, or subatomic particles. Service describes efforts to create new coherent sources of the type of radiation known as “hard” x-rays—a long-sought range of high frequencies with enormous potential for scientific research, technology, and medicine.
[1]: /lookup/doi/10.1126/science.1078823
[2]: /lookup/doi/10.1126/science.1079430
[3]: /lookup/doi/10.1126/science.1078082
[4]: /lookup/doi/10.1126/science.1078446
Quantum mechanics, though a probabilistic theory, gives a 'deterministic' answer to the question of how the present determines the future. In essence, in order to predict future probabilities, we need to (numerically) propagate the time-dependent Schrödinger equation from the present to the future. It is interesting to note that classical mechanics of macroscopic bodies, though reputed to be a deterministic theory, does not allow, due to chaos (which unfortunately is more prevalent than integrability), such clear insights into the future. In contrast, small (e.g., atomic, molecular and photonic) systems which are best understood using the tools of quantum mechanics, do not suffer from chaos, rendering the prediction of the probability-distributions of future events possible. The field of quantum control deals with an important modification of this task, namely, it asks: given a wave function in the present, what dynamics, i.e. what Hamiltonian, guarantees a desired outcome or 'objective' in the future? In practice one may achieve this goal of modifying and finding the desired Hamiltonian by introducing external fields, e.g. laser light. It is then possible to reach the objective in a 'trial-and-error' fashion, performed either numerically or in the laboratory. We can guess or build a Hamiltonian, do an experiment, or propagate the initial wave function to the future, compare the result with the desirable objective, and correct the guess for the Hamiltonian until satisfactory agreement with the objective is reached. A systematic way of executing this procedure is the sub-field called 'optimal control'. The trial-and-error method is often very time consuming and rarely provides mechanistic insight. There are situations where analytical solutions exist, rendering the control strategies more transparent. This is especially so when one can identify quantum interferences as the heart of quantum control, the essence of the field called 'coherent control'. The experience accumulated so far by many groups is that quantum interferences are the mechanism underlying most successful control scenarios and control experiments. The identification of the control mechanism is especially facile when the time-dependence of the Hamiltonian merely serves to prepare a state which then evolves in the absence of external fields. Analytical theories also exist when the explicit time dependence of the Hamiltonian can be treated adiabatically. Under these circumstances one can identify the quantum interfering pathways that lead to control, allowing for the simultaneous exploration of entire 'landscapes' (and not just a single 'desirable' objective) resulting from varying all the experimental 'knobs' at our disposal, e.g., relative- and envelope-phases, intensities, polarizations, and pulse-sequencing. Such 'pulse-shaping' knobs are now available down to the sub-femtosecond regime in broad spectral regions ranging from the UV to the IR. We expect that comprehensive investigations of the quantum interference required to control dynamical processes will result in a more detailed understanding of the dynamics themselves. Together with experimental progress---the stage is now set for many exciting applications in fundamental and applied sciences by 'tailoring' light--matter interactions essentially at will.
Quantum interference [1] is a cornerstone phenomenon in quantum mechanics, arising when the probability amplitudes associated with different quantum pathways combine, leading to patterns of constructive or destructive interference. Coherent control [2] leverages this phenomenon by using external optical or electromagnetic pulses to steer the outcome of quantum interference. Through careful adjustment of the phase, amplitude, and frequency of these external pulses, it is possible to selectively enhance or suppress specific quantum transitions. This selective manipulation enables researchers to direct quantum pathways toward desired outcomes, making coherent control a powerful tool for exploring and utilizing quantum systems.
Coherent control is a technique to manipulate the amplitudes and phases of wave functions by exploiting the coherent property of light. It is of great importance for the development of quantum technologies including quantum information processing and chemical reaction control as well as for addressing fundamental problems in quantum mechanics such as the quantum–classical boundary. In this chapter, we describe the development and applications of coherent control based on wave-packet interferometry with attosecond precision, which has been made possible by tuning the delay between two laser pulses on the attosecond time scale. This technique has been applied to several different hierarchies from simple to complex quantum systems: (i) isolated iodine molecules in the gas phase, (ii) molecular crystals of para-hydrogen, and (iii) single crystals of bismuth. In system (i), we have controlled and visualized the interference of vibrational wave packets in the isolated iodine molecules, and that wave-packet interference has been utilized to develop a molecular computer, which executes ultrafast Fourier transform. In system (ii), we have manipulated vibrational wave-functions delocalized in a para-hydrogen crystal. The long coherence lifetime of para-hydrogen crystals is a promising resource to preserve quantum information in bulk solids. In system (iii), we have controlled the excitation ratio of two orthogonal coherent phonon modes, whose coherent superposition has allowed for active control of ultrafast two-dimensional atomic motions in a single crystal of bismuth. Those atomic motions have been visualized by density functional theory calculations. Finally, the coherent control of an ensemble of ultracold Rydberg atoms is briefly discussed as future perspectives for exploring the quantum–classical boundary.
Coherent control provides a quantum interference based method for controlling atomic and molecular dynamics. We report two experimental observations of different ways to achieve such a control in atomic photoionization continuum. One is the photoionization of sodium atoms, initially prepared in the 3P1/2 excited state, by a non resonant three-photon interaction with 1064-nm laser light and by a one-photon interaction with the third-harmonic field, at 355 nm. Interference between the two transition paths allows the control of the total ionization rate by varying the relative phase of the laser fields. The second experiment is the observation of the modification of the ionization continua of xenon through laser induced continuum structure (LICS). The multiphoton radiative decay of the xenon ground state into the two electronic continua, that correspond to the two fine structure levels of the ground state of the xenon ion, is varied by electromagnetically embedding a bound state of the atom into the two continua. Both experiments are performed on an atomic beam apparatus which uses a time-of-flight spectrometer for energy analyzing the emitted photoelectrons.
Optical Transient Experiments allow one to probe the coherent interaction of light with matter, as well as measure the time for energy transfer, T1, and loss of phase coherence, T2, in atoms, molecules and solids. Coherent optical transients are induced when the interaction of light with the sample is changed in a time which is short compared to T2. The interaction can be modified by changing the amplitude, frequency or phase of the existing laser light. This can be accomplished with an electro-optic modulator which makes it possible to electronically control a wide variety of laser experiments. The method of electro-optic laser phase and frequency switching with an extra-cavity modulator is discussed below.