Self-induced decoherence approach: Strong limitations on its validity in a simple spin bath model and on its general physical relevance

The "self-induced decoherence" (SID) approach suggests that (1) the expectation value of any observable becomes diagonal in the eigenstates of the total Hamiltonian for systems endowed with a continuous energy spectrum, and (2), that this process can be interpreted as decoherence. We evaluate the first claim in the context of a simple spin bath model. We find that even for large environments, corresponding to an approximately continuous energy spectrum, diagonalization of the expectation value of random observables does in general not occur. We explain this result and conjecture that SID is likely to fail also in other systems composed of discrete subsystems. Regarding the second claim, we emphasize that SID does not describe a physically meaningful decoherence process for individual measurements, but only involves destructive interference that occurs collectively within an ensemble of presupposed "values" of measurements. This leads us to question the relevance of SID for treating observed decoherence effects.Comment: 11 pages, 4 figures. Final published versio

Decoherence of coupled electron spins via nuclear spin dynamics in quantum dots

In double quantum dots, the exchange interaction between two electron spins renormalizes the excitation energy of pair-flips in the nuclear spin bath, which in turn modifies the non-Markovian bath dynamics. As the energy renormalization varies with the Overhauser field mismatch between the quantum dots, the electron singlet-triplet decoherence resulting from the bath dynamics depends on sampling of nuclear spin states from an ensemble, leading to the transition from exponential decoherence in single-sample dynamics to power-law decay under ensemble averaging. In contrast, the decoherence of a single electron spin in one dot is essentially the same for different choices of the nuclear spin configuration.Comment: 4 pages 3 figure

Quantum dynamics of the avian compass

The ability of migratory birds to orient relative to the Earth's magnetic field is believed to involve a coherent superposition of two spin states of a radical electron pair. However, the mechanism by which this coherence can be maintained in the face of strong interactions with the cellular environment has remained unclear. This Letter addresses the problem of decoherence between two electron spins due to hyperfine interaction with a bath of spin 1/2 nuclei. Dynamics of the radical pair density matrix are derived and shown to yield a simple mechanism for sensing magnetic field orientation. Rates of dephasing and decoherence are calculated ab initio and found to yield millisecond coherence times, consistent with behavioral experiments

On Zurek's derivation of the Born rule

Recently, W. H. Zurek presented a novel derivation of the Born rule based on a mechanism termed environment-assisted invariance, or "envariance" [W. H. Zurek, Phys. Rev. Lett. 90(2), 120404 (2003)]. We review this approach and identify fundamental assumptions that have implicitly entered into it, emphasizing issues that any such derivation is likely to face.Comment: 8 pages; v2: minor clarifications added; v3: reference to Zurek's quant-ph/0405161 added. To appear in Foundations of Physics (Cushing Volume

Collective versus Single--Particle Motion in Quantum Many--Body Systems: Spreading and its Semiclassical Interpretation

We study the interplay between collective and incoherent single-particle motion in a model of two chains of particles whose interaction comprises a non-integrable part. In the perturbative regime, but for a general form of the interaction, we calculate the spectral density for collective excitations. We obtain the remarkable result that it always has a unique semiclassical interpretation. We show this by a proper renormalization procedure which allows us to map our system to a Caldeira-Leggett--type of model in which the bath is part of the system.Comment: 4 page

Systematic Perturbation Theory for Dynamical Coarse-Graining

We demonstrate how the dynamical coarse-graining approach can be systematically extended to higher orders in the coupling between system and reservoir. Up to second order in the coupling constant we explicitly show that dynamical coarse-graining unconditionally preserves positivity of the density matrix -- even for bath density matrices that are not in equilibrium and also for time-dependent system Hamiltonians. By construction, the approach correctly captures the short-time dynamics, i.e., it is suitable to analyze non-Markovian effects. We compare the dynamics with the exact solution for highly non-Markovian systems and find a remarkable quality of the coarse-graining approach. The extension to higher orders is straightforward but rather tedious. The approach is especially useful for bath correlation functions of simple structure and for small system dimensions.Comment: 17 pages, 5 figures, version accepted for publication in PR

Spatial Degrees of Freedom in Everett Quantum Mechanics

Stapp claims that, when spatial degrees of freedom are taken into account, Everett quantum mechanics is ambiguous due to a "core basis problem." To examine an aspect of this claim I generalize the ideal measurement model to include translational degrees of freedom for both the measured system and the measuring apparatus. Analysis of this generalized model using the Everett interpretation in the Heisenberg picture shows that it makes unambiguous predictions for the possible results of measurements and their respective probabilities. The presence of translational degrees of freedom for the measuring apparatus affects the probabilities of measurement outcomes in the same way that a mixed state for the measured system would. Examination of a measurement scenario involving several observers illustrates the consistency of the model with perceived spatial localization of the measuring apparatus.Comment: 34 pp., no figs. Introduction, discussion revised. Material tangential to main point remove

Generalized quantum measurements. Part I: Information properties of soft quantum measurements

A special class of soft quantum measurements as a physical model of the fuzzy measurements widely used in physics is introduced and its information properties are studied in detail.Comment: 25 pages, 3 figures, 25 ref

Evading quantum mechanics

Quantum mechanics is potentially advantageous for certain information-processing tasks, but its probabilistic nature and requirement of measurement back action often limit the precision of conventional classical information-processing devices, such as sensors and atomic clocks. Here we show that by engineering the dynamics of coupled quantum systems, it is possible to construct a subsystem that evades the measurement back action of quantum mechanics, at all times of interest, and obeys any classical dynamics, linear or nonlinear, that we choose. We call such a system a quantum-mechanics-free subsystem (QMFS). All of the observables of a QMFS are quantum-nondemolition (QND) observables; moreover, they are dynamical QND observables, thus demolishing the widely held belief that QND observables are constants of motion. QMFSs point to a new strategy for designing classical information-processing devices in regimes where quantum noise is detrimental, unifying previous approaches that employ QND observables, back-action evasion, and quantum noise cancellation. Potential applications include gravitational-wave detection, optomechanical force sensing, atomic magnetometry, and classical computing. Demonstrations of dynamical QMFSs include the generation of broad-band squeezed light for use in interferometric gravitational-wave detection, experiments using entangled atomic spin ensembles, and implementations of the quantum Toffoli gate.Comment: v2: changed the title, added a figure, and made some minor update

Electronic coherence dynamics in trans-polyacetylene oligomers

Electronic decoherence processes in trans-polyacetylene oligomers are considered by explicitly computing the time dependent molecular polarization from the coupled dynamics of electronic and vibrational degrees of freedom in a mean-field mixed quantum-classical approximation. The oligomers are described by the SSH Hamiltonian and the effect of decoherence is incorporated by propagating an ensemble of quantum-classical trajectories with initial conditions obtained by sampling the Wigner distribution of the nuclear degrees of freedom. The decoherence for superpositions between the ground and excited and between pairs of excited states is considered for chains of different length, and the dynamics is discussed in terms of the nuclear overlap function that appears in the off-diagonal elements of the electronic reduced density matrix. For long oligomers the loss of coherence occurs in tens of femtoseconds. This timescale is determined by the initial decay of the nuclear overlap and by the decay of population into other electronic states, and is relatively insensitive to the type and class of superposition considered. By contrast, for smaller oligomers the decoherence timescale depends strongly on the initially selected superposition, with superpositions that can decay as fast as 50 fs and as slow as 250 fs. The long-lived superpositions are such that little population is transferred to other electronic states and for which the vibronic dynamics is relatively harmonic.Comment: Accepted for J. Chem. Phy