Decoherence of quantum wavepackets due to interaction with conformal spacetime fluctuations

One of the biggest problems faced by those attempting to combine quantum theory and general relativity is the experimental inaccessibility of the unification scale. In this paper we show how incoherent conformal waves in the gravitational field, which may be produced by quantum mechanical zero-point fluctuations, interact with the wavepackets of massive particles. The result of this interaction is to produce decoherence within the wavepackets which could be accessible in experiments at the atomic scale. Using a simple model for the coherence properties of the gravitational field we derive an equation for the evolution of the density matrix of such a wavepacket. Following the primary state diffusion programme, the most promising source of spacetime fluctuations for detection are the above zero-point energy fluctuations. According to our model, the absence of intrinsic irremoveable decoherence in matter interferometry experiments puts bounds on some of the parameters of quantum gravity theories. Current experiments give \lambda > 18. , where \lambda t_{Planck} is an effective cut-off for the validity of low-energy quantum gravity theories.Comment: REVTeX forma

From Heisenberg matrix mechanics to EBK quantization: theory and first applications

Despite the seminal connection between classical multiply-periodic motion and Heisenberg matrix mechanics and the massive amount of work done on the associated problem of semiclassical (EBK) quantization of bound states, we show that there are, nevertheless, a number of previously unexploited aspects of this relationship that bear on the quantum-classical correspondence. In particular, we emphasize a quantum variational principle that implies the classical variational principle for invariant tori. We also expose the more indirect connection between commutation relations and quantization of action variables. With the help of several standard models with one or two degrees of freedom, we then illustrate how the methods of Heisenberg matrix mechanics described in this paper may be used to obtain quantum solutions with a modest increase in effort compared to semiclassical calculations. We also describe and apply a method for obtaining leading quantum corrections to EBK results. Finally, we suggest several new or modified applications of EBK quantization.Comment: 37 pages including 3 poscript figures, submitted to Phys. Rev.

Conditions for the Quantum to Classical Transition: Trajectories vs. Phase Space Distributions

We contrast two sets of conditions that govern the transition in which classical dynamics emerges from the evolution of a quantum system. The first was derived by considering the trajectories seen by an observer (dubbed the ``strong'' transition) [Bhattacharya, et al., Phys. Rev. Lett. 85: 4852 (2000)], and the second by considering phase-space densities (the ``weak'' transition) [Greenbaum, et al., Chaos 15, 033302 (2005)]. On the face of it these conditions appear rather different. We show, however, that in the semiclassical regime, in which the action of the system is large compared to $\hbar$, and the measurement noise is small, they both offer an essentially equivalent local picture. Within this regime, the weak conditions dominate while in the opposite regime where the action is not much larger than Planck's constant, the strong conditions dominate.Comment: 8 pages, 2 eps figure

Mechanical Translation

Contains reports on three research projects.National Science Foundation (Grant G-24047

The quantum-classical crossover of a field mode

We explore the quantum-classical crossover in the behaviour of a quantum field mode. The quantum behaviour of a two-state system - a qubit - coupled to the field is used as a probe. Collapse and revival of the qubit inversion form the signature for quantum behaviour of the field and continuous Rabi oscillations form the signature for classical behaviour of the field. We demonstrate both limits in a single model for the full coupled system, for states with the same average field strength, and so for qubits with the same Rabi frequency.Comment: 6 pages, 3 figures (in this version the figures, text and references have all been expanded

Continuous stochastic Schrodinger equations and localization

The set of continuous norm-preserving stochastic Schrodinger equations associated with the Lindblad master equation is introduced. This set is used to describe the localization properties of the state vector toward eigenstates of the environment operator. Particular focus is placed on determining the stochastic equation which exhibits the highest rate of localization for wide open systems. An equation having such a property is proposed in the case of a single non-hermitian environment operator. This result is relevant to numerical simulations of quantum trajectories where localization properties are used to reduce the number of basis states needed to represent the system state, and thereby increase the speed of calculation.Comment: 18 pages in LaTeX + 6 figures (postscript), uses ioplppt.sty. To appear in J. Phys.

Control of Integrable Hamiltonian Systems and Degenerate Bifurcations

We discuss control of low-dimensional systems which, when uncontrolled, are integrable in the Hamiltonian sense. The controller targets an exact solution of the system in a region where the uncontrolled dynamics has invariant tori. Both dissipative and conservative controllers are considered. We show that the shear flow structure of the undriven system causes a Takens-Bogdanov birfurcation to occur when control is applied. This implies extreme noise sensitivity. We then consider an example of these results using the driven nonlinear Schrodinger equation.Comment: 25 pages, 11 figures, resubmitted to Physical Review E March 2004 (originally submitted June 2003), added content and reference

Predictability sieve, pointer states, and the classicality of quantum trajectories

We study various measures of classicality of the states of open quantum systems subject to decoherence. Classical states are expected to be stable in spite of decoherence, and are thought to leave conspicuous imprints on the environment. Here these expected features of environment-induced superselection (einselection) are quantified using four different criteria: predictability sieve (which selects states that produce least entropy), purification time (which looks for states that are the easiest to find out from the imprint they leave on the environment), efficiency threshold (which finds states that can be deduced from measurements on a smallest fraction of the environment), and purity loss time (that looks for states for which it takes the longest to lose a set fraction of their initial purity). We show that when pointer states -- the most predictable states of an open quantum system selected by the predictability sieve -- are well defined, all four criteria agree that they are indeed the most classical states. We illustrate this with two examples: an underdamped harmonic oscillator, for which coherent states are unanimously chosen by all criteria, and a free particle undergoing quantum Brownian motion, for which most criteria select almost identical Gaussian states (although, in this case, predictability sieve does not select well defined pointer states.)Comment: 10 pages, 13 figure