Simulating Hamiltonian dynamics using many-qudit Hamiltonians and local unitary control

When can a quantum system of finite dimension be used to simulate another quantum system of finite dimension? What restricts the capacity of one system to simulate another? In this paper we complete the program of studying what simulations can be done with entangling many-qudit Hamiltonians and local unitary control. By entangling we mean that every qudit is coupled to every other qudit, at least indirectly. We demonstrate that the only class of finite-dimensional entangling Hamiltonians that are not universal for simulation is the class of entangling Hamiltonians on qubits whose Pauli operator expansion contains only terms coupling an odd number of systems, as identified by Bremner [Phys. Rev. A 69, 012313 (2004)]. We show that in all other cases entangling many-qudit Hamiltonians are universal for simulation.

Bifurcations in the non-dissipative dynamics of ultra cold atoms

We present the first experimental observation of several bifurcations in a controllable non-linear Hamiltonian system. Dynamics of cold atoms are used to test predictions of non-linear, non-dissipative Hamiltonian dynamics.

Nonlinear dynamics of a satellite with deployable solar panel arrays

The multibody dynamics of a satellite in circular orbit, modeled as a central body with two hinge-connected deployable solar panel arrays, is investigated. Typically, the solar panel arrays are deployed in orbit using preloaded torsional springs at the hinges in a near symmetrical accordion manner, to minimize the shock loads at the hinges. There are five degrees of freedom of the interconnected rigid bodies, composed of coupled attitude motions (pitch, yaw and roll) of the central body plus relative rotations of the solar panel arrays. The dynamical equations of motion of the satellite system are derived using Kane's equations. These are then used to investigate the dynamic behavior of the system during solar panel deployment via the 7-8th-order Runge-Kutta integration algorithms and results are compared with approximate analytical solutions. Chaotic attitude motions of the completely deployed satellite in circular orbit under the influence of the gravity-gradient torques are subsequently investigated analytically using Melnikov's method and confirmed via numerical integration. The Hamiltonian equations in terms of Deprit's variables are used to facilitate the analysis. (C) 2003 Published by Elsevier Ltd.

Fungible dynamics: There are only two types of entangling multiple-qubit interactions

What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? It has been shown that all two-body Hamiltonian evolutions can be simulated using any fixed two-body entangling n-qubit Hamiltonian and fast local unitaries. By entangling we mean that every qubit is coupled to every other qubit, if not directly, then indirectly via intermediate qubits. We extend this study to the case where interactions may involve more than two qubits at a time. We find necessary and sufficient conditions for an arbitrary n-qubit Hamiltonian to be dynamically universal, that is, able to simulate any other Hamiltonian acting on n qubits, possibly in an inefficient manner. We prove that an entangling Hamiltonian is dynamically universal if and only if it contains at least one coupling term involving an even number of interacting qubits. For odd entangling Hamiltonians, i.e., Hamiltonians with couplings that involve only an odd number of qubits, we prove that dynamic universality is possible on an encoded set of n-1 logical qubits. We further prove that an odd entangling Hamiltonian can simulate any other odd Hamiltonian and classify the algebras that such Hamiltonians generate. Thus, our results show that up to local unitary operations, there are only two fundamentally different types of entangling Hamiltonian on n qubits. We also demonstrate that, provided the number of qubits directly coupled by the Hamiltonian is bounded above by a constant, our techniques can be made efficient.

Quantum dynamics of a model for two Josephson-coupled Bose-Einstein condensates

In this work, we investigate the quantum dynamics of a model for two singlemode Bose-Einstein condensates which are coupled via Josephson tunnelling. Using direct numerical diagonalization of the Hamiltonian, we compute the time evolution of the expectation value for the relative particle number across a wide range of couplings. Our analysis shows that the system exhibits rich and complex behaviours varying between harmonic and non-harmonic oscillations, particularly around the threshold coupling between the delocalized and selftrapping phases. We show that these behaviours are dependent on both the initial state of the system and regime of the coupling. In addition, a study of the dynamics for the variance of the relative particle number expectation and the entanglement for different initial states is presented in detail.