Quantum dynamics with stochastic gauge simulations

The general idea of a stochastic gauge representation is introduced and compared with more traditional phase-space expansions, like the Wigner expansion. Stochastic gauges can be used to obtain an infinite class of positive-definite stochastic time-evolution equations, equivalent to master equations, for many systems including quantum time evolution. The method is illustrated with a variety of simple examples ranging from astrophysical molecular hydrogen production, through to the topical problem of Bose-Einstein condensation in an optical trap and the resulting quantum dynamics.

Exact solution, scaling behaviour and quantum dynamics of a model of an atom-molecule Bose-Einstein condensate

0We study the exact solution for a two-mode model describing coherent coupling between atomic and molecular Bose-Einstein condensates (BEC), in the context of the Bethe ansatz. By combining an asymptotic and numerical analysis, we identify the scaling behaviour of the model and determine the zero temperature expectation value for the coherence and average atomic occupation. The threshold coupling for production of the molecular BEC is identified as the point at which the energy gap is minimum. Our numerical results indicate a parity effect for the energy gap between ground and first excited state depending on whether the total atomic number is odd or even. The numerical calculations for the quantum dynamics reveals a smooth transition from the atomic to the molecular BEC.

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.

Characterization of complex quantum dynamics with a scalable NMR information processor

We present experimental results on the measurement of fidelity decay under contrasting system dynamics using a nuclear magnetic resonance quantum information processor. The measurements were performed by implementing a scalable circuit in the model of deterministic quantum computation with only one quantum bit. The results show measurable differences between regular and complex behavior and for complex dynamics are faithful to the expected theoretical decay rate. Moreover, we illustrate how the experimental method can be seen as an efficient way for either extracting coarse-grained information about the dynamics of a large system or measuring the decoherence rate from engineered environments.

Classical and quantum dynamics of a model for atomic-molecular Bose-Einstein condensates

We study a model for a two-mode atomic-molecular Bose-Einstein condensate. Starting with a classical analysis we determine the phase space fixed points of the system. It is found that bifurcations of the fixed points naturally separate the coupling parameter space into four regions. The different regions give rise to qualitatively different dynamics. We then show that this classification holds true for the quantum dynamics.

First-principles quantum dynamics in interacting Bose gases II: stochastic gauges

First principles simulations of the quantum dynamics of interacting Bose gases using the stochastic gauge representation are analysed. In a companion paper, we showed how the positive-P representation can be applied to these problems using stochastic differential equations. That method, however, is limited by increased sampling error as time evolves. Here, we show how the sampling error can be greatly reduced and the simulation time significantly extended using stochastic gauges. In particular, local stochastic gauges (a subset) are investigated. Improvements are confirmed in numerical calculations of single-, double- and multi-mode systems in the weak-mode coupling regime. Convergence issues are investigated, including the recognition of two modes by which stochastic equations produced by phase-space methods in general can diverge: movable singularities and a noise-weight relationship. The example calculated here displays wave-like behaviour in spatial correlation functions propagating in a uniform 1D gas after a sudden change in the coupling constant. This could in principle be tested experimentally using Feshbach resonance methods.

First-principles quantum dynamics in interacting Bose gases: I. The positive P representation

The performance of the positive P phase-space representation for exact many- body quantum dynamics is investigated. Gases of interacting bosons are considered, where the full quantum equations to simulate are of a Gross-Pitaevskii form with added Gaussian noise. This method gives tractable simulations of many-body systems because the number of variables scales linearly with the spatial lattice size. An expression for the useful simulation time is obtained, and checked in numerical simulations. The dynamics of first-, second- and third-order spatial correlations are calculated for a uniform interacting 1D Bose gas subjected to a change in scattering length. Propagation of correlations is seen. A comparison is made with other recent methods. The positive P method is particularly well suited to open systems as no conservation laws are hard-wired into the calculation. It also differs from most other recent approaches in that there is no truncation of any kind.

Many-body quantum dynamics of polarization squeezing in optical fibers

We report new experiments that test quantum dynamical predictions of polarization squeezing for ultrashort photonic pulses in a birefringent fiber, including all relevant dissipative effects. This exponentially complex many-body problem is solved by means of a stochastic phase-space method. The squeezing is calculated and compared to experimental data, resulting in excellent quantitative agreement. From the simulations, we identify the physical limits to quantum noise reduction in optical fibers. The research represents a significant experimental test of first-principles time-domain quantum dynamics in a one-dimensional interacting Bose gas coupled to dissipative reservoirs.

Divisible quantum dynamics satisfies temporal Tsirelson's bound

We show that divisibility of qubit quantum processes implies temporal Tsirelson's bound. We also prove that the classical bound of the temporal Bell's inequality holds for dynamics that can be described by entanglement-breaking channels---a more general class of dynamics than that allowed by classical physics.

Multipartite entanglement in harmonic oscillators subjected to dissipative quantum dynamics

Una detallada descripción de la dinámica de bajas energías del entrelazamiento multipartito es proporcionada para sistemas armónicos en una gran variedad de escenarios disipativos. Sin hacer ninguna aproximación central, esta descripción yace principalmente sobre un conjunto razonable de hipótesis acerca del entorno e interacción entorno-sistema, ambas consistente con un análisis lineal de la dinámica disipativa. En la primera parte se deriva un criterio de inseparabilidad capaz de detectar el entrelazamiento k-partito de una extensa clase de estados gausianos y no-gausianos en sistemas de variable continua. Este criterio se emplea para monitorizar la dinámica transitiva del entrelazamiento, mostrando que los estados no-gausianos pueden ser tan robustos frente a los efectos disipativos como los gausianos. Especial atención se dedicada a la dinámica estacionaria del entrelazamiento entre tres osciladores interaccionando con el mismo entorno o diferentes entornos a distintas temperaturas. Este estudio contribuye a dilucidar el papel de las correlaciones cuánticas en el comportamiento de la corrientes energéticas.

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.

Dynamics of a mesoscopic charge quantum bit under continuous quantum measurement

We present the conditional quantum dynamics of an electron tunneling between two quantum dots subject to a measurement using a low transparency point contact or tunnel junction. The double dot system forms a single qubit and the measurement corresponds to a continuous in time readout of the occupancy of the quantum dot. We illustrate the difference between conditional and unconditional dynamics of the qubit. The conditional dynamics is discussed in two regimes depending on the rate of tunneling through the point contact: quantum jumps, in which individual electron tunneling current events can be distinguished, and a diffusive dynamics in which individual events are ignored, and the time-averaged current is considered as a continuous diffusive variable. We include the effect of inefficient measurement and the influence of the relative phase between the two tunneling amplitudes of the double dot/point contact system.

Universal simulation of Hamiltonian dynamics for quantum systems with finite-dimensional state spaces

What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? Dodd [Phys. Rev. A 65, 040301(R) (2002)] provided a partial solution to this problem in the form of an efficient algorithm to simulate any desired two-body Hamiltonian evolution using any fixed two-body entangling N-qubit Hamiltonian, and local unitaries. We extend this result to the case where the component systems are qudits, that is, have D dimensions. As a consequence we explain how universal quantum computation can be performed with any fixed two-body entangling N-qudit Hamiltonian, and local unitaries.

Performance Analysis of Two Quantum Reaction Dynamics Codes: Time-Dependent and Time-Independent Strategies

The computer simulation of reaction dynamics has nowadays reached a remarkable degree of accuracy. Triatomic elementary reactions are rigorously studied with great detail on a straightforward basis using a considerable variety of Quantum Dynamics computational tools available to the scientific community. In our contribution we compare the performance of two quantum scattering codes in the computation of reaction cross sections of a triatomic benchmark reaction such as the gas phase reaction Ne + H2+ %12. NeH++ H. The computational codes are selected as representative of time-dependent (Real Wave Packet [ ]) and time-independent (ABC [ ]) methodologies. The main conclusion to be drawn from our study is that both strategies are, to a great extent, not competing but rather complementary. While time-dependent calculations advantages with respect to the energy range that can be covered in a single simulation, time-independent approaches offer much more detailed information from each single energy calculation. Further details such as the calculation of reactivity at very low collision energies or the computational effort related to account for the Coriolis couplings are analyzed in this paper.