Quantum integrability and nonintegrability in the spin-boson model

We study the spectral properties of a spin-boson Hamiltonian that depends on two continuous parameters $0\leq\Lambda<\infty$ (interaction strength) and $0\leq\alpha\leq\pi/2$ (integrability switch). In the classical limit this system has two distinct integrable regimes, $\alpha=0$ and $\alpha=\pi/2$. For each integrable regime we can express the quantum Hamiltonian as a function of two action operators. Their eigenvalues (multiples of $\hbar$) are the natural quantum numbers for the complete level spectrum. This functional dependence cannot be extended into the nonintegrable regime $(0<\alpha<\pi/2)$. Here level crossings are prohibited and the level spectrum is naturally described by a single (energy sorting) quantum number. In consequence, the tracking of individual eigenstates along closed paths through both regimes leads to conflicting assignments of quantum numbers. This effect is a useful and reliable indicator of quantum chaos -- a diagnostic tool that is independent of any level-statistical analysis

Entanglement, fidelity, and quantum-classical correlations with an atom walking in a quantized cavity field

Stability and instability of quantum evolution are studied in the interaction between a two-level atom with photon recoil and a quantized field mode in an ideal cavity, the basic model of cavity quantum electrodynamics (QED). It is shown that the Jaynes-Cummings dynamics can be unstable in the regime of chaotic walking of the atomic center-of-mass in the quantized field of a standing wave in the absence of any kind of interaction with environment. This kind of quantum instability manifests itself in strong variations of reduced quantum purity and entropy, correlating with the respective classical Lyapunov exponent, and in exponential sensitivity of fidelity of quantum states to small variations in the atom-field detuning. The connection between quantum entanglement and fidelity and the center-of-mass motion is clarified analytically and numerically for a few regimes of that motion. The results are illustrated with two specific initial field states: the Fock and coherent ones. Numerical experiments demonstrate various manifestations of the quantum-classical correspondence, including dynamical chaos and fractals, which can be, in principle, observed in real experiments with atoms and photons in high finesse cavities

Dipolar ground state of planar spins on triangular lattices

An infinite triangular lattice of classical dipolar spins is usually considered to have a ferromagnetic ground state. We examine the validity of this statement for finite lattices and in the limit of large lattices. We find that the ground state of rectangular arrays is strongly dependent on size and aspect ratio. Three results emerge that are significant for understanding the ground state properties: i) formation of domain walls is energetically favored for aspect ratios below a critical valu e; ii) the vortex state is always energetically favored in the thermodynamic limit of an infinite number of spins, but nevertheless such a configuration may not be observed even in very large lattices if the aspect ratio is large; iii) finite range approximations to actual dipole sums may not provide the correct ground sta te configuration because the ferromagnetic state is linearly unstable and the domain wall energy is negative for any finite range cutoff.Comment: Several short parts have been rewritten. Accepted for publication as a Rapid Communication in Phys. Rev.

Spin melting and refreezing driven by uniaxial compression on a dipolar hexagonal plate

We investigate freezing characteristics of a finite dipolar hexagonal plate by the Monte Carlo simulation. The hexagonal plate is cut out from a piled triangular lattice of three layers with FCC-like (ABCABC) stacking structure. In the present study an annealing simulation is performed for the dipolar plate uniaxially compressed in the direction of layer-piling. We find spin melting and refreezing driven by the uniaxial compression. Each of the melting and refreezing corresponds one-to-one with a change of the ground states induced by compression. The freezing temperatures of the ground-state orders differ significantly from each other, which gives rise to the spin melting and refreezing of the present interest. We argue that these phenomena are originated by a finite size effect combined with peculiar anisotropic nature of the dipole-dipole interaction.Comment: Proceedings of the Highly Frustrated Magnetism (HFM2006) conference. To appear in a special issue of J. Phys. Condens. Matte

Synchronization and bistability of qubit coupled to a driven dissipative oscillator

We study numerically the behavior of qubit coupled to a quantum dissipative driven oscillator (resonator). Above a critical coupling strength the qubit rotations become synchronized with the oscillator phase. In the synchronized regime, at certain parameters, the qubit exhibits tunneling between two orientations with a macroscopic change of number of photons in the resonator. The life times in these metastable states can be enormously large. The synchronization leads to a drastic change of qubit radiation spectrum with appearance of narrow lines corresponding to recently observed single artificial-atom lasing [O. Astafiev {\it et al.} Nature {\bf 449}, 588 (2007)].Comment: revtex 4 pages, 6 figs, research at http://www.quantware.ups-tlse.fr

Peculiar from-Edge-to-Interior Spin Freezing in a Magnetic Dipolar Cube

By molecular dynamics simulation, we have investigated classical Heisenberg spins, which are arrayed on a finite simple cubic lattice and interact with each other only by the dipole-dipole interaction, and have found its peculiar it from-Edge-to-interior freezing process. As the temperature is decreased, spins on each edge predominantly start to freeze in a ferromagnetic alignment parallel to the edge around the corresponding bulk transition temperature, then from each edges grow domains with short-range orders similar to the corresponding bulk orders, and the system ends up with a unique multi-domain ground state at the lowest temperature. We interpret this freezing characteristics is attributed to the anisotropic and long-range nature of the dipole-dipole interaction combined with a finite-size effect.Comment: 11 pages 5 figure

The transition to classical chaos in a coupled quantum system through continuous measurement

Continuous observation of a quantum system yields a measurement record that faithfully reproduces the classically predicted trajectory provided that the measurement is sufficiently strong to localize the state in phase space but weak enough that quantum backaction noise is negligible. We investigate the conditions under which classical dynamics emerges, via continuous position measurement, for a particle moving in a harmonic well with its position coupled to internal spin. As a consequence of this coupling we find that classical dynamics emerges only when the position and spin actions are both large compared to $\hbar$. These conditions are quantified by placing bounds on the size of the covariance matrix which describes the delocalized quantum coherence over extended regions of phase space. From this result it follows that a mixed quantum-classical regime (where one subsystem can be treated classically and the other not) does not exist for a continuously observed spin 1/2 particle. When the conditions for classicallity are satisfied (in the large-spin limit), the quantum trajectories reproduce both the classical periodic orbits as well as the classically chaotic phase space regions. As a quantitative test of this convergence we compute the largest Lyapunov exponent directly from the measured quantum trajectories and show that it agrees with the classical value.Comment: 8 pages, 5 figure

Magnetic Properties of 2-Dimensional Dipolar Squares: Boundary Geometry Dependence

By means of the molecular dynamics simulation on gradual cooling processes, we investigate magnetic properties of classical spin systems only with the magnetic dipole-dipole interaction, which we call dipolar systems. Focusing on their finite-size effect, particularly their boundary geometry dependence, we study two finite dipolar squares cut out from a square lattice with $\Phi=0$ and $\pi/4$, where $\Phi$ is an angle between the direction of the lattice axis and that of the square boundary. Distinctly different results are obtained in the two dipolar squares. In the $\Phi=0$ square, the ``from-edge-to-interior freezing'' of spins is observed. Its ground state has a multi-domain structure whose domains consist of the two among infinitely (continuously) degenerated Luttinger-Tisza (LT) ground-state orders on a bulk square lattice, i.e., the two antiferromagnetically aligned ferromagnetic chains (af-FMC) orders directed in parallel to the two lattice axes. In the $\Phi=\pi/4$ square, on the other hand, the freezing starts from the interior of the square, and its ground state is nearly in a single domain with one of the two af-FMC orders. These geometry effects are argued to originate from the anisotropic nature of the dipole-dipole interaction which depends on the relative direction of sites in a real space of the interacting spins.Comment: 21 pages, 13 figures, submitted to Journal of Physical Society Japa

Semiclassical chaos, the uncertainty principle, and quantum dissipation

Article on semiclassical chaos, the uncertainty principle, and quantum dissipation