Atom-laser coherence and its control via feedback

Abstract

We present a quantum-mechanical treatment of the coherence properties of a single-mode atom laser. Specifically, we focus on the quantum phase noise of the atomic field as expressed by the first-order coherence function, for which we derive analytical expressions in various regimes. The decay of this function is characterized by the coherence time, or its reciprocal, the linewidth. A crucial contributor to the linewidth is the collisional interaction of the atoms. We find four distinct regimes for the linewidth with increasing interaction strength. These range from the standard laser linewidth, through quadratic and linear regimes, to another constant regime due to quantum revivals of the coherence function. The laser output is only coherent (Bose degenerate) up to the linear regime. However, we show that application of a quantum nondemolition measurement and feedback scheme will increase, by many orders of magnitude, the range of interaction strengths for which it remains coherent.

Quantum Dissipative Systems and Feedback Control Design by Interconnection

“…Indeed, in what follows we describe a control design procedure that extends classical methods including passivitybased control (PBC), "energy shaping" control, interconnection and damping assignment (IDA) PBC, and "control as interconnection", [26], [32], [27], [28], [35], [36], [31], [30], [38].…”

“…We allow the exosystem to vary in a class of such exosystems, and the dissipation inequality we define is expressed in these terms. This network description turns out to be very appropriate and efficient, and was inspired by the behavioral "control as interconnection" perspective in Willems' more recent work, [35], [36] (also [31], [30], [38]). We provide an infinitesimal characterization of the dissipation property, and this important tool is used indispensably in this paper.…”

Number-phase Wigner representation for scalable stochastic simulations of controlled quantum systems

“…(5) is not simply due to a coordinate transformation, but rather, it originates from a fundamental difference in the construction of the representations. Evolution of transformed quasidistributions has been considered in the Q representation [34], and for the tomographic Wigner distribution [39], however, these approaches would not help in this situation as they cannot fix the non-semi-positive-definite diffusion in Eq. (5).…”

“…Equation (34) has non-positivesemi-definite diffusion and, as such, requires a doubling of the phase space. We, therefore, convert this evolution into the following set of SPDEs:…”

“…Measurements that are lower order with respect to the field operators do not conserve the number and may be suited to traditional coherentstate representations, but in many cases, these systems may be treated using analytic techniques, such as the Kalman filter, making simulation less important. Number-conserving measurements are quite common in engineered monitoring of BECs [14,15,[33][34][35][36][37][38]. Typically, off-resonant light is used to image the density moments of a BEC.…”