Non-holonomic Quantum Devices

We analyze the possibility and efficiency of non-holonomic control over quantum devices with exponentially large number of Hilbert space dimensions. We show that completely controllable devices of this type can be assembled from elementary units of arbitrary physical nature, and can be employed efficiently for universal quantum computations and simulation of quantum field dynamics.Comment: 8 revtex pages, 4 postscript figure

Population Dynamics in Cold Gases Resulting from the Long-Range Dipole-Dipole Interaction

We consider the effect of the long range dipole-dipole interaction on the excitation exchange dynamics of cold two-level atomic gase in the conditions where the size of the atomic cloud is large as compared to the wavelength of the dipole transition. We show that this interaction results in population redistribution across the atomic cloud and in specific spectra of the spontaneous photons emitted at different angles with respect to the direction of atomic polarization.Comment: 6 pages, 8 figure

Quantum compiling with diffusive sets of gates

Given a set of quantum gates and a target unitary operation, the most elementary task of quantum compiling is the identification of a sequence of the gates that approximates the target unitary to a determined precision $\varepsilon$. Solovay-Kitaev theorem provides an elegant solution which is based on the construction of successively tighter `nets' around the unity comprised by successively longer sequences of gates. The procedure for the construction of the nets, according to this theorem, requires accessibility to the inverse of the gates as well. In this work, we propose a method for constructing nets around unity without this requirement. The algorithmic procedure is applicable to sets of gates which are diffusive enough, in the sense that sequences of moderate length cover the space of unitary matrices in a uniform way. We prove that the number of gates sufficient for reaching a precision $\varepsilon$ scales as $\log (1/\varepsilon )^{\log 3 / log 2}$ while the pre-compilation time is increased as compared to thatof the Solovay-Kitaev algorithm by the exponential factor 3/2.Comment: 6 pages, several corrections in text, figures & bibliograph

Description of Quantum Entanglement with Nilpotent Polynomials

We propose a general method for introducing extensive characteristics of quantum entanglement. The method relies on polynomials of nilpotent raising operators that create entangled states acting on a reference vacuum state. By introducing the notion of tanglemeter, the logarithm of the state vector represented in a special canonical form and expressed via polynomials of nilpotent variables, we show how this description provides a simple criterion for entanglement as well as a universal method for constructing the invariants characterizing entanglement. We compare the existing measures and classes of entanglement with those emerging from our approach. We derive the equation of motion for the tanglemeter and, in representative examples of up to four-qubit systems, show how the known classes appear in a natural way within our framework. We extend our approach to qutrits and higher-dimensional systems, and make contact with the recently introduced idea of generalized entanglement. Possible future developments and applications of the method are discussed.Comment: 40 pages, 7 figures, 1 table, submitted for publication. v2: section II.E has been changed and the Appendix on "Four qubit sl-entanglement measure" has been removed. There are changes in the notation of section IV. Typos and language mistakes has been corrected. A figure has been added and a figure has been replaced. The references have been update

Subthreshold Ionization of Weakly Bound Complexes: StochasticAnalysis of the Role of the Rydberg Quasicontinuum

Recent evidence for subthreshold ionization (i.e. electron loss at energies less than anticipated from vertical transitions assuming adiabatic separation of nuclear motion) points at the role of nonadiabatic coupling of high Rydberg terms of molecules. Sinai's billiard model for the chaotic motion of the Rydberg electron, that leads to a diffusion over the energy ladder as a result of electronic–vibrational exchange, is suggested as the classical mechanism of autoionization. A quantum expression for the branching ratio between autoionization and spontaneous fluorescence is obtained and discussed with reference to experimental results on associative ionization in atomic collisions and on laser ionization of van der Waals diatomics

Cooperative behavior of qutrits with dipole-dipole interactions

We have identified a class of many body problems with analytic solution beyond the mean-field approximation. This is the case where each body can be considered as an element of an assembly of interacting particles that are translationally frozen multi-level quantum systems and that do not change significantly their initial quantum states during the evolution. In contrast, the entangled collective state of the assembly experiences an appreciable change. We apply this approach to interacting three-level systems.Comment: 5 pages, 3 figures. Minor correction