Control quantum

In this section we discuss quantum control in the frequency domain. In Section 8.3 we discuss control in the time domain 

From quantum mechanics we need an idea that has already played a central role superposition of states and the resulting interference. 

by our definition of control we aim to favor one particular outcome. So obviously there needs to be more titan one possible outcome. Say that there are two. To make it very simple, say two final quantum states, each one being a separate outcome. In Section 4.3.2 we showed how the wave function of the collision is specified in terms of the initial state and the Hamiltonian of the system. On the molecular level time runs just as well forward as backward. Therefore, a wave function can just as well be specified in terms of the final state it will evolve into For our problem we have two wave functions, at the same energy, each evolving exclusively into a different final state. An arbitrary wave function will be a superposition of these two target states. If we can experimentally alter the contribution of these two states we can vary the branching ratio. 

A more technical but stUl simple analysis suggests that we have two control parameters. Say that experimentally we can prepare two different wave functions  

The probability of getting products in state a is the overlap of the wave function f that we prepared with the target state if a. 

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Pausch R, Held M, Chen T, Schwoerer H and Kiefer W 2000 Quantum control by stimulated Raman scattering J. Raman Spectrosc. 31 7... 

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Bardeen C J, Che J, WIson K R, Yakovlev V V, Cong P, Kohler B, Krause J L and Messina M 1997 Quantum control of Nal photodissociation reaction product states by ultrafast tailored light pulses J. Phys. Chem. A 101 3815-22... 

Krause J L, Messina M, Wilson K R and Van Y J 1995 Quantum control of molecular dynamics—the strong response regime J. Phys. Chem. 99 13 736... 

The purpose of this work is to demonstrate that the techniques of quantum control, which were developed originally to study atoms and molecules, can be applied to the solid state. Previous work considered a simple example, the asymmetric double quantum well (ADQW). Results for this system showed that both the wave paeket dynamics and the THz emission can be controlled with simple, experimentally feasible laser pulses. This work extends the previous results to superlattices and chirped superlattices. These systems are considerably more complicated, because their dynamic phase space is much larger. They also have potential applications as solid-state devices, such as ultrafast switches or detectors. 

Calculating the exact response of a semiconductor heterostructure to an ultrafast laser pulse poses a daunting challenge. Fortunately, several approximate methods have been developed that encompass most of the dominant physical effects. In this work a model Hamiltonian approach is adopted to make contact with previous advances in quantum control theory. This method can be systematically improved to obtain agreement with existing experimental results. One of the main goals of this research is to evaluate the validity of the model, and to discover the conditions under which it can be reliably applied. 

The theory discussed in this paper treats the biased superlattices as onedimensional systems in a single particle envelope approximation in which the electrons and holes act independently. Scattering mechanisms, which cause a loss of coherence, have not yet been included in the formalism. Loss of coherence represents a significant obstacle to quantum control in... 

In summary, this work has shown that superlattices are promising systems for investigation of quantum control in the solid state. The examples presented here show that the dynamics of charge carriers can be controlled using relatively simple, experimentally laser fields. Superlattices are ideal candidates for quantum control precisely because their complexity does not allow for simple, intuition-guided experiments, and because their dynamics are largely unknown. 

M. Shapiro and R Bmmer, Principles of the Quantum Control of Molecular Processes, John Wiley Sons, Canada, Ltd., 2003. 

M. Shapiro and P. Brumer, Quantum control of bound and continuum state dynamics, Phys. Rep. 425, 195 (2006). 

Krause, J. L., Whitnell, R. M., Wilson, K. E. and Yan, Y. J. (1994) "Classical quantum control with application to solution reaction dynamics,in Gauduel, Y. and Rossky, P. J.(eds.), Ultrafast reaction dynamics and solvent effects, AIP Press, New York,pp.3- 15. 

Brixner, T., and Gerber, G. 2003. Quantum control of gas-phase and liquid-phase femtochem-istry. Chem. Phys. Chem. 4(5) 418-38. 

Herek, J. L., Wohlleben, W., Cogdell, R. J., Zeidler, D., and Motzkus, M. 2002. Quantum control of energy flow in light harvesting. Nature 417(6888) 533-35. 

Meshulach, D., and Silberberg, Y. 1998. Coherent quantum control of two-photon transitions by a femtosecond laser pulse. Nature 396(6708) 239 2. 

Ando, T., Urakami, T., Itoh, H., and Tsuchiya, Y. 2002. Optimization of resonant two-photon absorption with adaptive quantum control. Appl. Phys. Lett. 80 4265-67. 

Coherent excitation of quantum systems by external fields is a versatile and powerful tool for application in quantum control. In particular, adiabatic evolution has been widely used to produce population transfer between discrete quantum states. Eor two states the control is by means of a varying detuning (a chirp), while for three states the change is induced, for example, by a pair of pulses, offset in time, that implement stimulated Raman adiabatic passage (STIRAP) [1-3]. STIRAP produces complete population transfer between the two end states 11) and 3) of a chain linked by two fields. In the adiabatic limit, the process places no temporary population in the middle state 2), even though the two driving fields - pump and Stokes-may be on exact resonance with their respective transitions, 1) 2)and... 

In contrast to weak-held (perturbative) quantum control schemes where the population of the initial state is approximately constant during the interaction with the external light held, the strong-held (nonperturbative) regime is characterized by efficient population transfer. Adiabatic strong-held techniques such as rapid... 

Achieving control over microscopic dynamics of molecules with external fields has long been a major goal in chemical reaction dynamics. This goal stimulated the development of quantum control schemes, which have been applied with spectacular results to unimolecular reactions, such as photodissociation or isomerization reactions. Attaining control over bimolecular reactions in a gas has proven to be a much bigger challenge. 

As discussed by M. Shapiro and R Brumer in the book Quantum Control of Molecular Processes, there are two general control strategies that can be applied to harness and direct molecular dynamics optimal control and coherent control. The optimal control schemes aim to find a sef of external field parameters that conspire - through quantum interferences or by incoherent addition - to yield the best possible outcome for a specific, desired evolution of a quantum system. Coherent control relies on interferences, constructive or destructive, that prohibit or enhance certain reaction pathways. Both of these control strategies meet with challenges when applied to molecular collisions. 

The important feature of resonances is that when the widths of states in Q are larger than their associated level spacing, such states, termed now overlapping resonances, can interfere with one another. The quantum dynamics of systems with overlapping resonances show a rich variety of interesting physical phenomena furthermore, in such systems there is potential for quantum control... 

M. Shapiro and P. Brumer. Principles of Quantum Control of Molecular Processes. Wiley-Interscience, New York (2003) Quantum Control of Molecular Processes, 2nd edition, Wiley-VCH Verlag GmbH, Weinheim, 2012). 

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