Quantum Coherent Control
It is control that turns scientific knowledge into technology. The general goal of quantum control is to manipulate dynamical processes at the atomic or molecular scale, typically using external electromagnetic field. The objective of quantum optimal control is to devise and implement shapes of pulses of external field or sequences of such pulses, that accomplish a given task in a quantum system in the best possible manner.
The challenge of manipulating nature at the quantum level has a huge potential for current and future applications. Quantum optimal control is a part of the effort to engineer quantum technologies from the bottom up. Currently the emerging quantum technologies are based on superposition, entanglement and many-body quantum states. Quantum control is thus a strategic cross-sectional field of research, enabling and leveraging current and future quantum technology applications.
The field of quantum control has been initiated by the idea of controlling chemical reactions [1–5]. It was soon realised that the principles of quantum control through interfering pathways is universal and spread to other fields such as quantum information [6,7]. A recent overview has been published which emphasises the future prospects of the field [8]. Coherent control can be applied directly to controlling matter waves using a BEC as a source of matter waves. We have pioneered this idea.
Despite the success and proliferation of coherent control the dream of controlling chemical reactions has not been achieved. To fill this gap our recent efforts concentrated on control of binary reactions. As a first step in coherent control of binary-chemical reactions we studied both experimentally and theoretically the photoassociation of hot Mg2[9]. We were able to identify two mechanisms of coherent control. The first is based on multiphoton interference pathways. The second is vibrationally assisted [10]. The pulse shaping was carried out by a spatial light modulator in the frequency domain. The other extreme case is coherent control of photoassociation of ultracold Rb2[11]. The duration of the control pulse is four orders of magnitude longer than the pulse used for Mg2 photoassociation. For the Rb2 case the pulse shaping was carried out in the time domain. In both the photoassociation of the Mg2 and the Rb2 the reaction leads to a significant reduction of translational entropy. The next step in control of binary reactions should be devoted to processes of the type AB + C → A + BC → AC + B. This will require a combined experimental and theoretical effort.
Photoassociation of hot Mg2
A natural meeting point between Quantum thermodynamics and coherent control is to develop method to cool internal degrees of freedom of molecules [12]. We originated this quest of cooling internal degrees of freedom of molecules by broad band excitations [13–14]. This scheme has been realised experimentally in broad band cooling the vibrations of Cs2 [15–18] and rotational cooling of trapped molecular ions [19]. The current challenge is a simultaneous cooling of both vibrational and rotational degrees of freedom [20]. The difficulty emerges from the large separation of time scales.
The coherent control required to achieve these tasks is of an open quantum system. It would seem that decoherence in open systems will destroy the interference required to generated control. Nevertheless in some cases the the environment allows control which otherwise could not be achieved [21, 22]. An outstanding issue is coherent control in weak field. For isolated systems for target operators that commute with the system hamiltonian phase only coherent control is impossible [23]. We were able to extend this theorem of no phase control to Markovian evolution of open systems [24]. Nevertheless there is unpublished experimental data indicating asymmetry between positive and negative chirp in weak field absorption. If verified, it would indicate to an experimental procedure to unravel non-Markovian dynamics.
The issue of controllability has not been resolved. What can be controlled by interference? What is the minimal time to achieve such a control? What is the optimal control protocol? These issues deserve further study in the context of open quantum systems. An important issue is the influence of noise. In particular the unavoidable noise on the controller. Such noise is fast relative to the timescale of the controlled system. Can one circumvent the influence of this noise by cooling the system? In the context of quantum information this is known as adding an ancilla qubit.
Coherent Control has become an essential component in achieving quantum gates [6]. What is unique is the requirement of extremely high fidelity. A related issue is how to obtain a quantum gate under noisy conditions [7]. The same type of gates for example swap gates can be used for quantum heat engines.
All practical engines require active control to achieve their goals. Quantum heat engines are no exception, they require monitoring and feedback. But in quantum mechanics constant monitoring can change the state of the working medium, for example measuring energy will destroy coherence. We only started to tackle this issue [27] which is related to quantum measurement and control [25].
Active quantum control requires measurement and feedback [27]. This issue has not been studied in a thermodynamical context. Quantum thermodynamics and quantum control are natural mates. Quantum control is the enabler of the coherent manipulations required in a truly quantum heat device. Advance in one field has immediate consequence in the other.
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