Optimal estimation of one-parameter quantum channels

We explore the task of optimal quantum channel identification and in particular, the estimation of a general one-parameter quantum process. We derive new characterizations of optimality and apply the results to several examples including the qubit depolarizing channel and the harmonic oscillator damping channel. We also discuss the geometry of the problem and illustrate the usefulness of using entanglement in process estimation.

Macroscopic test of quantum mechanics versus stochastic electrodynamics

We identify a test of quantum mechanics versus macroscopic local realism in the form of stochastic electrodynamics. The test uses the steady-state triple quadrature correlations of a parametric oscillator below threshold.

On the construction of integrable closed chains with quantum supersymmetry

We present a general prescription for the construction of integrable one-dimensional systems with closed boundary conditions and quantum supersymmetry.

Quantum Lie algebras, their existence, uniqueness and q-antisymmetry

Quantum Lie algebras are generalizations of Lie algebras which have the quantum parameter h built into their structure. They have been defined concretely as certain submodules L-h(g) of the quantized enveloping algebras U-h(g). On them the quantum Lie product is given by the quantum adjoint action. Here we define for any finite-dimensional simple complex Lie algebra g an abstract quantum Lie algebra g(h) independent of any concrete realization. Its h-dependent structure constants are given in terms of inverse quantum Clebsch-Gordan coefficients. We then show that all concrete quantum Lie algebras L-h(g) are isomorphic to an abstract quantum Lie algebra g(h). In this way we prove two important properties of quantum Lie algebras: 1) all quantum Lie algebras L-h(g) associated to the same g are isomorphic, 2) the quantum Lie product of any Ch(B) is q-antisymmetric. We also describe a construction of L-h(g) which establishes their existence.

Quantum dynamics of an atomic Bose-Einstein condensate in a double-well potential

We consider the quantum dynamics of a neutral atom Bose-Einstein condensate in a double-well potential, including many-body hard-sphere interactions. Using a mean-field factorization we show that the coherent oscillations due to tunneling are suppressed when the number of atoms exceeds a critical value. An exact quantum solution, in a two-mode approximation, shows that the mean-field solution is modulated by a quantum collapse and revival sequence.

Classical and quantum signatures of competing chi((2)) nonlinearities

We report the observation of the quantum effects of competing chi((2)) nonlinearities. We also report classical signatures of competition, namely, clamping of the second-harmonic power and production of nondegenerate frequencies in the visible. Theory is presented that describes the observations as resulting from competition between various chi((2)) up-conversion and down-conversion processes. We show that competition imposes hitherto unsuspected limits to both power generation and squeezing. The observed signatures are expected to be significant effects in practical systems.

Twisted quantum affine superalgebra U-q[sl(2/2)((2))], U-q[osp(2/2)] invariant R-matrices and a new integrable electronic model

We describe the twisted affine superalgebra sl(2\2)((2)) and its quantized version U-q[sl(2\2)((2))]. We investigate the tensor product representation of the four-dimensional grade star representation for the fixed-point sub superalgebra U-q[osp(2\2)]. We work out the tensor product decomposition explicitly and find that the decomposition is not completely reducible. Associated with this four-dimensional grade star representation we derive two U-q[osp(2\2)] invariant R-matrices: one of them corresponds to U-q [sl(2\2)(2)] and the other to U-q [osp(2\2)((1))]. Using the R-matrix for U-q[sl(2\2)((2))], we construct a new U-q[osp(2\2)] invariant strongly correlated electronic model, which is integrable in one dimension. Interestingly this model reduces in the q = 1 limit, to the one proposed by Essler et al which has a larger sl(2\2) symmetry.

Quantum chaos in the atomic gravitational cavity

We report quantum chaos phenomena in the atomic gravitational cavity. We consider the reflection of cold atoms from a temporally modulated evanescent wave. In the globally chaotic regime, for small modulation, the squared energy distribution as a function of time demonstrates dynamical localization. However, for larger modulation delocalization occurs.

Quantum signatures of chaos in the dynamics of a trapped ion

We show how a nonlinear chaotic system, the parametrically kicked nonlinear oscillator, may be realized in the dynamics of a trapped, laser-cooled ion, interacting with a sequence of standing-wave pulses. Unlike the original optical scheme [G. J. Milburn and C.A. Holmes, Phys. Rev. A 44, 4704 (1991)], the trapped ion enables strongly quantum dynamics with minimal dissipation. This should permit an experimental test of one of the quantum signatures of chaos: irregular collapse and revival dynamics of the average vibrational energy.

Comments on the Drinfeld realization of the quantum affine superalgebra U-q[gl(m backslash n)(1)] and its Hopf algebra structure

By generalizing the Reshetikhin and Semenov-Tian-Shansky construction to supersymmetric cases, we obtain the Drinfeld current realization for the quantum affine superalgebra U-q[gl(m\n)((1))]. We find a simple coproduct for the quantum current generators and establish the Hopf algebra structure of this super current algebra.

Renormalizing the kinetic energy operator in elementary quantum mechanics

In this paper, we consider solutions to the three-dimensional Schrodinger equation of the form psi(r) = u(r)/r, where u(0) not equal 0. The expectation value of the kinetic energy operator for such wavefunctions diverges. We show that it is possible to introduce a potential energy with an expectation value that also diverges, exactly cancelling the kinetic energy divergence. This renormalization procedure produces a self-adjoint Hamiltonian. We solve some problems with this new Hamiltonian to illustrate its usefulness.