Electron Spin Relaxation in a Semiconductor Quantum Well

A fully microscopic theory of electron spin relaxation by the D'yakonov-Perel' type spin-orbit coupling is developed for a semiconductor quantum well with a magnetic field applied in the growth direction of the well. We derive the Bloch equations for an electron spin in the well and define microscopic expressions for the spin relaxation times. The dependencies of the electron spin relaxation rate on the lowest quantum well subband energy, magnetic field and temperature are analyzed.Comment: Revised version as will appear in Physical Review

Decoherence and Relaxation of a Quantum Bit in the Presence of Rabi Oscillations

Dissipative dynamics of a quantum bit driven by a strong resonant field and interacting with a heat bath is investigated. We derive generalized Bloch equations and find modifications of the qubit's damping rates caused by Rabi oscillations. Nonequilibrium decoherence of a phase qubit inductively coupled to a LC-circuit is considered as an illustration of the general results. It is argued that recent experimental results give a clear evidence of effective suppression of decoherence in a strongly driven flux qubit.Comment: 14 pages; misprints correcte

Theory of weak continuous measurements in a strongly driven quantum bit

Continuous spectroscopic measurements of a strongly driven superconducting qubit by means of a high-quality tank circuit (a linear detector) are under study. Output functions of the detector, namely, a spectrum of voltage fluctuations and an impedance, are expressed in terms of the qubit spectrum and magnetic susceptibility. The nonequilibrium spectrum of the current fluctuations in the qubit loop and the linear response function of the driven qubit coupled to a heat bath are calculated with Bloch-Redfield and rotating wave approximations. Backaction effects of the qubit on the tank and the tank on the qubit are analyzed quantitatively. We show that the voltage spectrum of the tank provides detailed information about a frequency and a decay rate of Rabi oscillations in the qubit. It is found that both an efficiency of spectroscopic measurement and measurement-induced decoherence of the qubit demonstrate a resonant behaviour as the Rabi frequency approaches the resonant frequency of the tank. We determine conditions when the spectroscopic observation of the Rabi oscillations in the flux qubit with the tank circuit can be considered as a weak continuous quantum measurement.Comment: 28 page

Collective excitations in trapped boson-fermion mixtures: from demixing to collapse

We calculate the spectrum of low-lying collective excitations in a gaseous cloud formed by a Bose-Einstein condensate and a spin-polarized Fermi gas over a range of the boson-fermion coupling strength extending from strongly repulsive to strongly attractive. Increasing boson-fermion repulsions drive the system towards spatial separation of its components (``demixing''), whereas boson-fermion attractions drive it towards implosion (``collapse''). The dynamics of the system is treated in the experimentally relevant collisionless regime by means of a Random-Phase approximation and the behavior of a mesoscopic cloud under isotropic harmonic confinement is contrasted with that of a macroscopic mixture at given average particle densities. In the latter case the locations of both the demixing and the collapse phase transitions are sharply defined by the same stability condition, which is determined by the softening of an eigenmode of either fermionic or bosonic origin. In contrast, the transitions to either demixing or collapse in a mesoscopic cloud at fixed confinement and particle numbers are spread out over a range of boson-fermion coupling strength, and some initial decrease of the frequencies of a set of collective modes is followed by hardening as evidenced by blue shifts of most eigenmodes. The spectral hardening can serve as a signal of the impending transition and is most evident when the number of bosons in the cloud is relatively large. We propose physical interpretations for these dynamical behaviors with the help of suitably defined partial compressibilities for the gaseous cloud under confinement.Comment: 16 pages, 7 figures, revtex

A Generalized Fluctuation-Dissipation Theorem for Nonlinear Response Functions

A nonlinear generalization of the Fluctuation-Dissipation Theorem (FDT) for the n-point Green functions and the amputated 1PI vertex functions at finite temperature is derived in the framework of the Closed Time Path formalism. We verify that this generalized FDT coincides with known results for n=2 and 3. New explicit relations among the 4-point nonlinear response and correlation (fluctuation) functions are presented.Comment: 34 pages, Revte

Coherent QCD phenomena in the Coherent Pion-Nucleon and Pion-Nucleus Production of Two Jets at High Relative Momenta

We use QCD to compute the cross section for coherent production of a di-jet (treated as a $q\bar q$ moving at high relative transverse momentum,$\kappa_t$). In the target rest frame,the space-time evolution of this reaction is dominated by the process in which the high $\kappa_t$ $q\bar q$ component of the pion wave function is formed before reaching the target. It then interacts through two gluon exchange. In the approximation of keeping the leading order in powers of $\alpha_s$ and all orders in $\alpha_{s}\ln(\kappa_{t}^2/k_{0}^2),$ the amplitudes for other processes are shown to be smaller at least by a power of $\alpha_{s}$. The resulting dominant amplitude is proportional to $z(1-z) \kappa_t^{-4}$ ($z$ is the fraction light-cone(+)momentum carried by the quark in the final state) times the skewed gluon distribution of the target. For the pion scattering by a nuclear target, this means that at fixed $x_{N}= 2\kappa_{t}^2/s$ (but $\kappa_{t}^2\to \infty$) the nuclear process in which there is only a single interaction is the most important one to contribute to the reaction. Thus in this limit color transparency phenomena should occur.These findings are in accord with E971 experiment at FNAL. We also re-examine a potentially important nuclear multiple scattering correction which is positive and $\propto A^{1/3}/\kappa_t^4$. The meaning of the signal obtained from the experimental measurement of pion diffraction into two jets is also critically examined and significant corrections are identified.We show also that for values of $\kappa_t$ achieved at fixed target energies, di-jet production by the e.m. field of the nucleus leads to an insignificant correction which gets more important as $\kappa_t$ increases.Comment: 23 pages, 9 figure

Sum rules and dualities for generalized parton distributions: is there a holographic principle?

To leading order approximation, the physical content of generalized parton distributions (GPDs) that is accessible in deep virtual electroproduction of photons or mesons is contained in their value on the cross-over trajectory. This trajectory separates the t-channel and s-channel dominated GPD regions. The underlying Lorentz covariance implies correspondence between these two regions through their relation to GPDs on the cross-over trajectory. This point of view leads to a family of GPD sum rules which are a quark analogue of finite energy sum rules and it guides us to a new phenomenological GPD concept. As an example, we discuss the constraints from the JLab/Hall A data on the dominant u-quark GPD H. The question arises whether GPDs are governed by some kind of holographic principle.Comment: 45 pages, 4 figures, Sect. 2 reorganized for clarity. Typos in Eq. (20) corrected. 4 new refs. Matches published versio