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A Markovian master equation describing the evolution of open quantum systems in the presence of a time-dependent external field is derived within the Bloch-Redfield formalism. It leads to a system-bath interaction which depends on the control field. Optimal control theory is used to select control fields which allow accelerated or decelerated system relaxation, or suppression of relaxation (dissipation) altogether, depending on the dynamics we impose on the quantum system. The control-dissipation correlation and the non-perturbative treatment of the control field are essential for reaching this goal. The optimal control problem is formulated within Pontryagin's minimum principle and the resulting optimal differential system is solved numerically. As an application, we study the dynamics of a spin-boson model in the strong coupling regime under the influence of an external control field. We show how trapping the system in unstable quantum states and transfer of population can be achieved by optimized control of the dissipative quantum system. We also used optimal control theory to find the driving field that generates the quantum Z-gate. In several cases studied, we find that the selected optimal field which reduces the purity loss significatively is a multi-component low-frequency field including higher harmonics, all of which lie below the phonon cutoff frequency. Finally, in the undriven case we present an analytic result for the Lamb shift at zero temperature.

We suggest a closed form expression for the path integral of quantum transition amplitudes. We introduce a quantum action with renormalized parameters. We present numerical results for the V ∼ x 4 potential. The renormalized action is relevant for quantum chaos and quantum instantons.

We construct an effective Hamiltonian via Monte Carlo from a given action. This Hamiltonian describes physics in the low energy regime. We test it by computing spectrum, wave functions and thermodynamical observables (average energy and specific heat) for the free system and the harmonic oscillator. The method is shown to work also for other local potentials.Comment: LaTeX file (text) + 9 PS files (figures + tables

We develop an efficient and general method for optimizing the microwave field that achieves magnetization switching with a smaller static field. This method is based on optimal control and renders an exact solution for the 3D microwave field that triggers the switching of a nanomagnet with a given anisotropy and in an oblique static field. Applying this technique to the particular case of uniaxial anisotropy, we show that the optimal microwave field, that achieves switching with minimal absorbed energy, is modulated both in frequency and in magnitude. Its role is to drive the magnetization from the metastable equilibrium position towards the saddle point and then damping induces the relaxation to the stable equilibrium position. For the pumping to be efficient, the microwave field frequency must match at the early stage of the switching process the proper precession frequency of the magnetization, which depends on the magnitude and direction of the static field. We investigate the effect of the static field (in amplitude and direction) and of damping on the characteristics of the microwave field. We have computed the switching curves in the presence of the optimal microwave field. The results are in qualitative agreement with micro-SQUID experiments on isolated nanoclusters. The strong dependence of the microwave field and that of the switching curve on the damping parameter may be useful in probing damping in various nanoclusters.Comment: 9 pages, 8 figure

We consider a current-biased dc SQUID in the presence of an applied time-dependent bias current or magnetic flux. The phase dynamics of such a Josephson device is equivalent to that of a quantum particle trapped in a 1−D anharmonic potential, subject to external timedependent control fields, i.e. a driven multilevel quantum system. The problem of finding the required time-dependent control field that will steer the system from a given initial state to a desired final state at a specified final time is formulated in the framework of optimal control theory. Using the spectral filter technique, we show that the selected optimal field which induces a coherent population transfer between quantum states is represented by a carrier signal having a constant frequency but which is time-varied both in amplitude and phase. The sensitivity of the optimal solution to parameter perturbations is also addressed.

No abstract

We investigate optimal control of a single qubit coupled to an ohmic heat bath. For the weak bath coupling regime, we derive a Bloch-Redfield master equation describing the evolution of the qubit state parameterized by vectors in the Bloch sphere. By use of the optimal control methodology, we determine a field that generates a single-qubit rotation. We use techniques of automatic differentiation to compute the gradient for the cost functional.