arXiv subjects

Ray Ng

Publications and source records attributed to Ray Ng.

4 recordsLinked to original sources

arXiv2013

Exact Real Time Dynamics of Quantum Spin Systems Using the Positive-P Representation

We discuss a scheme for simulating the real time quantum quench dynamics of interacting quantum spin systems within the positive-P formalism. As model systems we study the transverse field Ising model as well as the Heisenberg model undergoing a quench away from the classical ferromagnetic ordered state and antiferromagnetic Neel state, depending on the sign of the Heisenberg exchange interaction. The connection to the positive-P formalism as it is used in quantum optics is established by mapping the spin operators on to Schwinger bosons. In doing so, the dynamics of the interacting quantum spin system is mapped onto a set of Ito stochastic differential equations (SDEs) the number of which scales linearly with the number of spins, N, compared to an exact solution through diagonalization that in the case of the Heisenberg model would require matrices exponentially large in N . This mapping is exact and can be extended to higher dimensional interacting systems as well as to systems with an explicit coupling to the environment.

cond-mat.stat-mech↗

arXiv2013

Simulation of the Dynamics of Many-Body Quantum Spin Systems Using Phase-Space Techniques

We reformulate the full quantum dynamics of spin systems using a phase space representation based on SU(2) coherent states which generates an exact mapping of the dynamics of any spin system onto a set of stochastic differential equations. The new representation is superior in practice to an earlier phase space approach based on Schwinger bosons, with the numerical effort scaling only linearly with system size. By also implementing extrapolation techniques from quasiclassical equations to the full quantum limit, we are able to extend useful simulation times several fold. This approach is applicable in any dimension including cases where frustration is present in the spin system. The method is demonstrated by simulating quenches in the transverse field Ising model in one and two dimensions

cond-mat.stat-mech↗

arXiv2005

Non-Markovian Quantum State Diffusion: Application to Quantum Jumps in $^{24}$Mg$^+$

Non-Markovian quantum state diffusion (NMQSD) is an exact method for calculating the reduced density matrix of an arbitrary subsystem interacting linearly with the radiation field. Applications of the theory have however been few due to the intractable nature of the variational-differential NMQSD evolution equation. Recently, we argued that the variational-differential equation can be rewritten as an integrodifferential equation which can be readily solved numerically. This manuscript provides an explicit derivation of the modified equations. Applications to intermittent fluorescence in $^{24}$Mg$^+$ are discussed in detail. Earlier speculations that quantum jumps occur on all time scales are verified on a picosecond timescale. We show that a plot of the probability density of the signal vs signal strength shows the two characteristic peaks associated with the bright and dark manifolds, and that the ratio of the areas under the peaks is 16 as observed experimentally. We also show that the shape of this distribution is sensitive to bath memory, but has a mathematical form common to both the Markovian and non-Markovian cases.

quant-ph↗

arXiv2005

Numerical Implementation of Non-Markovian Quantum State Diffusion

Non-Markovian quantum state diffusion (NMQSD) is a non-relativistic but otherwise exact theory which expresses the reduced density matrix of an arbitrary subsystem, interacting linearly with an uncoupled harmonic oscillator bath, as an average of diadics formed from state vectors which obey stochastic variational-differential equations. The vacuum radiation field can be represented as such an oscillator bath, and so this model is in widespread use in quantum optics. Prior to the development of NMQSD, exact subsystem solutions could only be obtained in a few special cases (e.g. spin-1/2, harmonic oscillator). Unfortunately, it has not yet been possible to obtain exact solutions to new problems using NMQSD due to the difficulty of solving the variational-differential equations. Here we show that these equations can be transformed into a pair of coupled nonlinear integrodifferential equations. We develop exact numerical methods for the integrodifferential equations and show that solutions can be readily obtained to good accuracy for quite general subsystems. We exactly solve various examples including tunneling in a double well representing molecular isomerization or racemization, suppression of fluorescence from a two-level atom in a band gap, and intermittent fluorescence from a driven three level system representing electronic states of singly ionized magnesium.

quant-ph↗