Initial correlations in open system's dynamics: The Jaynes-Cummings model

Employing the trace distance as a measure for the distinguishability of quantum states, we study the influence of initial correlations on the dynamics of open systems. We concentrate on the Jaynes-Cummings model for which the knowledge of the exact joint dynamics of system and reservoir allows the treatment of initial states with arbitrary correlations. As a measure for the correlations in the initial state we consider the trace distance between the system-environment state and the product of its marginal states. In particular, we examine the correlations contained in the thermal equilibrium state for the total system, analyze their dependence on the temperature and on the coupling strength, and demonstrate their connection to the entanglement properties of the eigenstates of the Hamiltonian. A detailed study of the time dependence of the distinguishability of the open system states evolving from the thermal equilibrium state and its corresponding uncorrelated product state shows that the open system dynamically uncovers typical features of the initial correlations.Comment: 12 pages, 7 figure

Initial state preparation with dynamically generated system-environment correlations

The dependence of the dynamics of open quantum systems upon initial correlations between the system and environment is an utterly important yet poorly understood subject. For technical convenience most prior studies assume factorizable initial states where the system and its environments are uncorrelated, but these conditions are not very realistic and give rise to peculiar behaviors. One distinct feature is the rapid build up or a sudden jolt of physical quantities immediately after the system is brought in contact with its environments. The ultimate cause of this is an initial imbalance between system-environment correlations and coupling. In this note we demonstrate explicitly how to avoid these unphysical behaviors by proper adjustments of correlations and/or the coupling, for setups of both theoretical and experimental interest. We provide simple analytical results in terms of quantities that appear in linear (as opposed to affine) master equations derived for factorized initial states.Comment: 6 pages, 2 figure

Magnetism of the LTT phase of Eu doped La_{2-x}Sr_xCuO_4

The ESR signal of Gd spin probes (0.5 at %) as well as the static normal state susceptibility of Eu (J(Eu^{3+})=0) doped La_{2-x-y}Sr_xEu_yCuO_4 reveal pronounced changes of the Cu magnetism at the structural transition from the orthorhombic to the low temperature tetragonal phase for all non-superconducting compositions. Both a jumplike decrease of \chi as well as the ESR data show an increase of the in-plane magnetic correlation length in the LTT phase. From the Gd^{3+} ESR linewidth we find that for specific Eu and Sr concentrations in the LTT phase the correlation length increases up to more than 100 lattice constants and the fluctuation frequency of the CuO_2 spin system slows down to 10^{10}- 10^{11}sec^{-1}. However, there is no static order above T ~ 8K in contrast to the LTT phase of Nd doped La_{2-x}Sr_xCuO_4 with pinned stripe correlations.Comment: 7 pages, RevTex, 3 eps figures. To appear in the Proceedings of the International Conference "Stripes, Lattice Instabilities and High Tc Superconductivity", (Rome, Dec. 1996

The equilibrium states of open quantum systems in the strong coupling regime

In this work we investigate the late-time stationary states of open quantum systems coupled to a thermal reservoir in the strong coupling regime. In general such systems do not necessarily relax to a Boltzmann distribution if the coupling to the thermal reservoir is non-vanishing or equivalently if the relaxation timescales are finite. Using a variety of non-equilibrium formalisms valid for non-Markovian processes, we show that starting from a product state of the closed system = system + environment, with the environment in its thermal state, the open system which results from coarse graining the environment will evolve towards an equilibrium state at late-times. This state can be expressed as the reduced state of the closed system thermal state at the temperature of the environment. For a linear (harmonic) system and environment, which is exactly solvable, we are able to show in a rigorous way that all multi-time correlations of the open system evolve towards those of the closed system thermal state. Multi-time correlations are especially relevant in the non-Markovian regime, since they cannot be generated by the dynamics of the single-time correlations. For more general systems, which cannot be exactly solved, we are able to provide a general proof that all single-time correlations of the open system evolve to those of the closed system thermal state, to first order in the relaxation rates. For the special case of a zero-temperature reservoir, we are able to explicitly construct the reduced closed system thermal state in terms of the environmental correlations.Comment: 20 pages, 2 figure

Dynamic entanglement in oscillating molecules and potential biological implications

We demonstrate that entanglement can persistently recur in an oscillating two-spin molecule that is coupled to a hot and noisy environment, in which no static entanglement can survive. The system represents a non-equilibrium quantum system which, driven through the oscillatory motion, is prevented from reaching its (separable) thermal equilibrium state. Environmental noise, together with the driven motion, plays a constructive role by periodically resetting the system, even though it will destroy entanglement as usual. As a building block, the present simple mechanism supports the perspective that entanglement can exist also in systems which are exposed to a hot environment and to high levels of de-coherence, which we expect e.g. for biological systems. Our results furthermore suggest that entanglement plays a role in the heat exchange between molecular machines and environment. Experimental simulation of our model with trapped ions is within reach of the current state-of-the-art quantum technologies.Comment: Extended version, including supplementary information. 9 pages, 8 figure

Environment-dependent dissipation in quantum Brownian motion

The dissipative dynamics of a quantum Brownian particle is studied for different types of environment. We derive analytic results for the time evolution of the mean energy of the system for Ohmic, sub-Ohmic and super-Ohmic environments, without performing the Markovian approximation. Our results allow to establish a direct link between the form of the environmental spectrum and the thermalization dynamics. This in turn leads to a natural explanation of the microscopic physical processes ruling the system time evolution both in the short-time non-Markovian region and in the long-time Markovian one. Our comparative study of thermalization for different environments sheds light on the physical contexts in which non-Markovian dissipation effects are dominant.Comment: 10 pages, 6 figures, v2: added new references and paragraph

New method to simulate quantum interference using deterministic processes and application to event-based simulation of quantum computation

We demonstrate that networks of locally connected processing units with a primitive learning capability exhibit behavior that is usually only attributed to quantum systems. We describe networks that simulate single-photon beam-splitter and Mach-Zehnder interferometer experiments on a causal, event-by-event basis and demonstrate that the simulation results are in excellent agreement with quantum theory. We also show that this approach can be generalized to simulate universal quantum computers.Comment: J. Phys. Soc. Jpn. (in press) http://www.compphys.net/dl

Entanglement in the adiabatic limit of a two-atom Tavis-Cummings model

We study the adiabatic limit for the sequential passage of atoms through a high-Q cavity, in the presence of frequency chirps. Despite the fact that the adiabatic approximation might be expected to fail, we were able to show that for proper choice of Stark-pulses this is not the case. Instead, a connection to the resonant limit is established, where the robust creation of entanglement is demonstrated. Recent developments in the fabrication of high-Q cavities allow fidelities for a maximally entangled state up to 97%.Comment: 12 pages, 5 figures, Submitted to Physica Scripta as part of the Proceedings of the 15th CEWQO 200

Stochastic wave function approach to the calculation of multitime correlation functions of open quantum systems

Within the framework of probability distributions on projective Hilbert space a scheme for the calculation of multitime correlation functions is developed. The starting point is the Markovian stochastic wave function description of an open quantum system coupled to an environment consisting of an ensemble of harmonic oscillators in arbitrary pure or mixed states. It is shown that matrix elements of reduced Heisenberg picture operators and general time-ordered correlation functions can be expressed by time-symmetric expectation values of extended operators in a doubled Hilbert space. This representation allows the construction of a stochastic process in the doubled Hilbert space which enables the determination of arbitrary matrix elements and correlation functions. The numerical efficiency of the resulting stochastic simulation algorithm is investigated and compared with an alternative Monte Carlo wave function method proposed first by Dalibard et al. [Phys. Rev. Lett. {\bf 68}, 580 (1992)]. By means of a standard example the suggested algorithm is shown to be more efficient numerically and to converge faster. Finally, some specific examples from quantum optics are presented in order to illustrate the proposed method, such as the coupling of a system to a vacuum, a squeezed vacuum within a finite solid angle, and a thermal mixture of coherent states.Comment: RevTex, 19 pages, 3 figures, uses multico

Stochastic wave function method for non-Markovian quantum master equations

A generalization of the stochastic wave function method to quantum master equations which are not in Lindblad form is developed. The proposed stochastic unravelling is based on a description of the reduced system in a doubled Hilbert space and it is shown, that this method is capable of simulating quantum master equations with negative transition rates. Non-Markovian effects in the reduced systems dynamics can be treated within this approach by employing the time-convolutionless projection operator technique. This ansatz yields a systematic perturbative expansion of the reduced systems dynamics in the coupling strength. Several examples such as the damped Jaynes Cummings model and the spontaneous decay of a two-level system into a photonic band gap are discussed. The power as well as the limitations of the method are demonstrated.Comment: RevTex, 14 pages, 9 figures, uses multico