Coherent quantum control

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

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... 

We first survey in Section 4.2 the Kurizki-Shapiro-Brumer scheme [5-7] of phase-coherent photocurrent control and focus on its robustness to decoherence, relaxation, and quantum (Langevin) noise induced by the environment. We then... 

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... 

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. 

A fundamental issue concerns how to define control mechanism in the context of coherent quantum dynamics. Mechanism will likely be understood in a variety of ways, depending on the particular circumstances and control goals. However, an attractive perspective is to consider mechanism defined in terms of the amplitudes connecting the initial and final states, as depicted... 

Equation (7.75) defines what is meant by a so-called coherent sum of quantum states. The diagonal terms resemble the incoherent sum in Eq. (7.74) the values of the populations cn 2 are, however, determined by the laser pulse. The off-diagonal terms are called interference terms these terms are the key to quantum control. They are time dependent and we use the term coherent dynamics for the motion associated with the coherent excitation of quantum states. A particular simple form of Eq. (7.75) is obtained in the special case of two states. Then... 

The underlying principle of coherent phase control is that the probability of an event occurring is given by the square of the sum of the quantum mechanical amplitudes... 

All of the quantum control scenarios involve a host of laser and system parameters. To obtain maximal control in any scenario necessitates a means of tuning the system and laser parameters to optimally achieve the desired objective. This topic, optimal control, is introduced and discussed in Chapters 4 and 13. The role of quantum interference effects in optimal control are discussed as well, providing a uniform picture of control via optimal pulse shaping and coherent control. 

By definition, quantum control relies upon the unique quantum properties of light and matter, principally the wavelilce nature of both. As such, maintenance of the phase information contained in both the matter and light is central to the success of the control scenarios. Chapter 5 deals with decoherence, that is, the loss of phase information due to the influence of the external environment in reducing the system coherence. Methods of countering decoherence are also discussed. 

Yet it has been shown that OK may be attainable in a finite number of finite operations (perhaps even in one) via quantum-control-refrigeration (QCR) methods, specifically, employing quantum coherence [1], This challenges the strongest-mode unattainability... 

Scully MO, Aharonov Y, Kapale KT, Tannor DJ, Sussmann G, Walther H. Sharpening accepted thermodynamic wisdom via quantum control or cooling to an internal temperature of zero by external coherent control fields without spontaneous emission. Journal of Modem Optics. 2002 49 2297-2307. DOI 10.1080/0950034021000011392... 

TOWARDS QUANTUM CONTROL OF LIGHT SHAPING QUANTUM PULSES OF LIGHT VIA COHERENT ATOMIC MEMORY... 

For the last decade or so, a new method has been developed to control chemical reactions that it is based on the wave nature of atoms and molecules. The new methodology is called quantum control , or coherent control of chemical reactions, and is based on the coherent excitation of the molecule by a laser. Generally speaking, an ultra-short laser pulse creates a wave packet whose time evolution describes the molecular evolution in the superposition of excited states. Quantum control tries to modify the superposition of such an ensemble of excited states and, therefore, influences the motion of the wave... 

As mentioned above, the temporal coherence of the laser light has revolutionized the investigation of chemical processes in real time because it has made possible the preparation, and subsequent evolution, of wave packets in molecular and atomic systems. This coherent character of laser light is currently used for quantum control of chemical processes. Although this field is still in its infancy, important scientific and technological applications are expected in the near future and will undoubtedly extend beyond chemistry. 

Gorshkov, A.V., Jiang, L., Greiner, M., Zoller, R, and Lukin, M.D., Coherent Quantum Optical Control with Subwavelength Resolution, arXiv quant-ph/0706.3879. 

Experimental demonstration of fully coherent quantum feedback - This paper of 1999 by Nelson and co-workers describes a quantum circuit which implements a coherent quantum feedback by NMR [15]. The idea is to transmit a quantum state with its correlations from a quantum register to a target. A classical feedback can be used to control quantum states, but it involves a measurement step, which destroys quantum correlations. On the contrary, quantum feedback control is able to transmit full quantum states with correlations altogether. The experiment involves three spins (qubits) A, B, and C. The proposal is to use the quantum feedback control circuit to transmit the quantum correlations, initially between B and C, to A and C. Starting from the equilibrium state, a sequence of pulses applied over qubits B and C creates a density matrix proportional to the spin operators -1 + 21 if - Such a density matrix describes a thermal... 

Zadoyan R, Kohen D, Lidar D, Apkarian VA (2001) The manipulation of massive ro-vibronic superpositions using time-frequency-resolved coherent anti-stokes raman scattering (tfrcars) from quantum control to quantum computing. Chem Phys 266 323... 

The situation with molecules is much more involved for several reasons. First, for polyatomic molecules, the intramolecular relaxation processes that occur on a subpicosecond timescale are essential. It was for exactly this reason that the first successful experiments were conducted on the noncoherent laser control of polyatomic molecules with intermolecular selectivity. Second, the phase relaxation time in a condensed medium is also on a subpicosecond scale because of the interaction between the quantum system and its surroundings. Therefore, it was only the creation of relatively simple and inexpensive femtosecond lasers that made it possible to set about realizing the ideas of the coherent laser control of unimolecular processes (Tannor and Rice 1985 Brumer and Shapiro 1986 Judson and Rabitz 1992), particularly the... 

New concepts of coherent femtosecond control, quantum learning, and feedback control of molecules have been proposed and demonstrated successfully in several laboratories for the past two decades. Moreover, significant advances have been made toward establishing broad foundations and laboratory implementation of control over quantum phenomena in various quantum systems, from atoms to complex molecules. 

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