Revealing the Emergence of Classicality Using Nitrogen-Vacancy Centers.

The origin of classical reality in our quantum world is a long-standing mystery. Here, we examine a nitrogen-vacancy center in diamond evolving in the presence of its magnetic nuclear spin environment which is formed by the natural appearance of carbon ^{13}C atoms in the diamond lattice, to study quantum Darwinism-the proliferation of information about preferred quantum states throughout the world via the environment. This redundantly imprinted information accounts for the perception of objective reality, as it is independently accessible by many without perturbing the system of interest. To observe this process, we implement a novel dynamical decoupling scheme that enables the measurement and control of several nuclear spins (the environment E) interacting with a nitrogen vacancy (the system S). Our experiment demonstrates that, in the course of the decoherence of S, redundant information is indeed imprinted onto E, giving rise to incipient classical objectivity-a consensus recorded in redundant copies, and available from the fragments of the nuclear spin environment E, about the state of S. This provides the first laboratory verification of the process responsible for the emergence of the objective classical world from the underlying quantum substrate.

Topological relics of symmetry breaking: winding numbers and scaling tilts from random vortex-antivortex pairs.

I show that random distributions of vortex-antivortex pairs (rather than of individual vortices) lead to scaling of typical winding numbers W trapped inside a loop of circumference C with the square root of that circumference, W ≈√C, when the expected winding numbers are large, |W| ≫ 1. Such scaling is consistent with the Kibble-Zurek mechanism (KZM), with inversely proportional to ξ, the typical size of the domain that can break symmetry in unison. (The dependence of ξ on quench rate is predicted by KZM from critical exponents of the phase transition.) Thus, according to KZM, the dispersion √ scales as √C/ξ for large W. By contrast, a distribution of individual vortices with randomly assigned topological charges would result in the dispersion scaling with the square root of the area inside C (i.e., ≈√ ≈C). Scaling of the dispersion of W as well as of the probability of detection of non-zero W with C and ξ can be also studied for loops so small that non-zero windings are rare. In this case I show that dispersion varies not as 1/√ξ, but as 1/ξ, which results in a doubling of the scaling of dispersion with the quench rate when compared to the large |W| regime. Moreover, the probability of trapping of non-zero W becomes approximately equal to , and scales as 1/ξ2. This quadruples--as compared with √≃ √C/ ξ valid for large W--the exponent in the power law dependence of the frequency of trapping of |W| = 1 on ξ when the probability of |W| > 1 is negligible. This change of the power law exponent by a factor of four--from 1√ξ for the dispersion of large W to 1/ξ2 for the frequency of non-zero W when |W| > 1 is negligibly rare--is of paramount importance for experimental tests of KZM.

Causality and non-equilibrium second-order phase transitions in inhomogeneous systems.

When a second-order phase transition is crossed at a finite rate, the evolution of the system stops being adiabatic as a result of the critical slowing down in the neighborhood of the critical point. In systems with a topologically nontrivial vacuum manifold, disparate local choices of the ground state lead to the formation of topological defects. The universality class of the transition imprints a signature on the resulting density of topological defects: it obeys a power law in the quench rate, with an exponent dictated by a combination of the critical exponents of the transition. In inhomogeneous systems the situation is more complicated, as the spontaneous symmetry breaking competes with bias caused by the influence of the nearby regions that already chose the new vacuum. As a result, the choice of the broken symmetry vacuum may be inherited from the neighboring regions that have already entered the new phase. This competition between the inherited and spontaneous symmetry breaking enhances the role of causality, as the defect formation is restricted to a fraction of the system where the front velocity surpasses the relevant sound velocity and phase transition remains effectively homogeneous. As a consequence, the overall number of topological defects can be substantially suppressed. When the fraction of the system is small, the resulting total number of defects is still given by a power law related to the universality class of the transition, but exhibits a more pronounced dependence on the quench rate. This enhanced dependence complicates the analysis but may also facilitate experimental testing of defect formation theories.

Topological defect formation and spontaneous symmetry breaking in ion Coulomb crystals.

Symmetry breaking phase transitions play an important role in nature. When a system traverses such a transition at a finite rate, its causally disconnected regions choose the new broken symmetry state independently. Where such local choices are incompatible, topological defects can form. The Kibble-Zurek mechanism predicts the defect densities to follow a power law that scales with the rate of the transition. Owing to its ubiquitous nature, this theory finds application in a wide field of systems ranging from cosmology to condensed matter. Here we present the successful creation of defects in ion Coulomb crystals by a controlled quench of the confining potential, and observe an enhanced power law scaling in accordance with numerical simulations and recent predictions. This simple system with well-defined critical exponents opens up ways to investigate the physics of non-equilibrium dynamics from the classical to the quantum regime.

Measurement of energy eigenstates by a slow detector.

We propose a method for a weak continuous measurement of the energy eigenstates of a fast quantum system by means of a slow detector. Such a detector is sensitive only to slowly changing variables, e.g., energy, while its backaction can be limited solely to decoherence of the eigenstate superpositions. We apply this scheme to the problem of detection of quantum jumps between energy eigenstates in a harmonic oscillator.

Decoherence and the Loschmidt echo.

Decoherence causes entropy increase that can be quantified using, e.g., the purity sigma=Trrho(2). When the Hamiltonian of a quantum system is perturbed, its sensitivity to such perturbation can be measured by the Loschmidt echo M(t). It is given by the squared overlap between the perturbed and unperturbed state. We describe the relation between the temporal behavior of sigma(t) and the average Mmacr;(t). In this way we show that the decay of the Loschmidt echo can be analyzed using tools developed in the study of decoherence. In particular, for systems with a classically chaotic Hamiltonian the decay of sigma and Mmacr; has a regime where it is dominated by the Lyapunov exponents.

Critical dynamics of gauge systems: spontaneous vortex formation in 2D superconductors.

We examine the formation of vortices during the nonequilibrium relaxation of a high-temperature initial state of an Abelian-Higgs system. We equilibrate the scalar and gauge fields using gauge-invariant Langevin equations and relax the system by instantaneously removing thermal fluctuations. For couplings near critical, kappa(c) = square root[lambda]/e = 1, we observe the formation of large clusters of like-sign magnetic vortices. Their appearance has implications for the dynamics of the phase transition, for the distribution of topological defects, and for late-time phase ordering kinetics. We offer explanations for both the observed vortex densities and vortex configurations.

Dynamics of quantum phase transition in an array of Josephson junctions.

We study the dynamics of the Mott insulator-superfluid quantum phase transition in a periodic 1D array of Josephson junctions. We show that crossing the critical point at a finite rate with a quench time tau(Q) induces finite quantum fluctuations of the current around the loop proportional to tau(-1/6)(Q). This scaling could be experimentally verified with an array of weakly coupled Bose-Einstein condensates or superconducting grains.

Sub-Planck structure in phase space and its relevance for quantum decoherence.

Heisenberg's principle states that the product of uncertainties of position and momentum should be no less than the limit set by Planck's constant, Planck's over 2pi/2. This is usually taken to imply that phase space structures associated with sub-Planck scales (<

Unconditional pointer states from conditional master equations.

When part of the environment responsible for decoherence is used to extract information about the decohering system, the preferred pointer states remain unchanged. This conclusion--reached for a specific class of models--is investigated in a general setting of conditional master equations using suitable generalizations of predictability sieve. We also find indications that the einselected states are easiest to infer from the measurements carried out on the environment.

Dissipative optical flow in a nonlinear Fabry-Pérot cavity.

We describe a classical nonlinear optical system that displays superfluidity and its breakdown. The system consists of a self-defocusing refractive medium inside a Fabry-Pérot cavity with a cylindrical obstacle. We have numerically solved for the transmitted beam when an incident plane wave strikes the cavity at an oblique angle. The presence of the incident beam pins the steady-state phase of the output, preventing the formation of vortices or time-dependent flow. When the incident beam is switched off, a transient wake of moving optical vortices is produced. This is analogous to the breakdown of superfluidity above a critical velocity.