Canonically conjugate pairs and phase operators

For quantum mechanics on a lattice the position (``particle number'') operator and the quasi-momentum (``phase'') operator obey canonical commutation relations (CCR) only on a dense set of the Hilbert space. We compare exact numerical results for a particle in simple potentials on the lattice with the expectations, when the CCR are assumed to be strictly obeyed. Only for sufficiently smooth eigenfunctions this leads to reasonable results. In the long time limit the use of the CCR can lead to a qualitativel wrong dynamics even if the initial state is in the dense set.Comment: 4 pages, 5 figures. Phys. Rev. A, in pres

Bound State and Order Parameter Mixing Effect by Nonmagnetic Impurity Scattering in Two-band Superconductors

We investigate nonmagnetic impurity effects in two-band superconductors, focusing on the effects of interband scatterings. Within the Born approximation, it is known that interband scatterings mix order parameters in the two bands. In particular, only one averaged energy gap appears in the excitation spectrum in the dirty limit. [G. Gusman: J. Phys. Chem. Solids {\bf 28} (1967) 2327.] In this paper, we take into account the interband scattering within the $t$-matrix approximation beyond the Born approximation in the previous work. We show that, although the interband scattering is responsible for the mixing effect, this effect becomes weak when the interband scattering becomes very strong. In the strong interband scattering limit, a two-gap structure corresponding to two order parameters recovers in the superconducting density of states. We also show that a bound state appears around a nonmagnetic impurity depending on the phase of interband scattering potential.Comment: 28pages, 10 figure

Vortex nucleation through edge states in finite Bose-Einstein condensates

We study the vortex nucleation in a finite Bose-Einstein condensate. Using a set of non-local and chiral boundary conditions to solve the Schr$\ddot{o}$dinger equation of non-interacting bosons in a rotating trap, we obtain a quantitative expression for the characteristic angular velocity for vortex nucleation in a condensate which is found to be 35% of the transverse harmonic trapping frequency.Comment: 24 pages, 8 figures. Both figures and the text have been revise

C-axis resistivity and high Tc superconductivity

Recently we had proposed a mechanism for the normal-state C-axis resistivity of the high-T$_c$ layered cuprates that involved blocking of the single-particle tunneling between the weakly coupled planes by strong intra-planar electron-electron scattering. This gave a C-axis resistivity that tracks the ab-plane T-linear resistivity, as observed in the high-temperature limit. In this work this mechanism is examined further for its implication for the ground-state energy and superconductivity of the layered cuprates. It is now argued that, unlike the single-particle tunneling, the tunneling of a boson-like pair between the planes prepared in the BCS-type coherent trial state remains unblocked inasmuch as the latter is by construction an eigenstate of the pair annihilation operator. The resulting pair-delocalization along the C-axis offers energetically a comparative advantage to the paired-up trial state, and, thus stabilizes superconductivity. In this scheme the strongly correlated nature of the layered system enters only through the blocking effect, namely that a given electron is effectively repeatedly monitored (intra-planarly scattered) by the other electrons acting as an environment, on a time-scale shorter than the inter-planar tunneling time. Possible relationship to other inter-layer pairing mechanisms proposed by several workers in the field is also briefly discussed.Comment: typos in equations corrected, contents unchange

Laser-induced collective excitations in a two-component Fermi gas

We consider the linear density response of a two-component (superfluid) Fermi gas of atoms when the perturbation is caused by laser light. We show that various types of laser excitation schemes can be transformed into linear density perturbations, however, a Bragg spectroscopy scheme is needed for transferring energy and momentum into a collective mode. This makes other types of laser probing schemes insensitive for collective excitations and therefore well suited for the detection of the superfluid order parameter. We show that for the special case when laser light is coupled between the two components of the Fermi gas, density response is always absent in a homogeneous system.Comment: 6 pages, no figure

A Method for Modeling Decoherence on a Quantum Information Processor

We develop and implement a method for modeling decoherence processes on an N-dimensional quantum system that requires only an $N^2$-dimensional quantum environment and random classical fields. This model offers the advantage that it may be implemented on small quantum information processors in order to explore the intermediate regime between semiclassical and fully quantum models. We consider in particular $\sigma_z\sigma_z$ system-environment couplings which induce coherence (phase) damping, though the model is directly extendable to other coupling Hamiltonians. Effective, irreversible phase-damping of the system is obtained by applying an additional stochastic Hamiltonian on the environment alone, periodically redressing it and thereby irreversibliy randomizing the system phase information that has leaked into the environment as a result of the coupling. This model is exactly solvable in the case of phase-damping, and we use this solution to describe the model's behavior in some limiting cases. In the limit of small stochastic phase kicks the system's coherence decays exponentially at a rate which increases linearly with the kick frequency. In the case of strong kicks we observe an effective decoupling of the system from the environment. We present a detailed implementation of the method on an nuclear magnetic resonance quantum information processor.Comment: 12 pages, 9 figure

Tunneling in Λ\Lambda Decaying Cosmologies and the Cosmological Constant Problem

The tunneling rate, with exact prefactor, is calculated to first order in $\hbar$ for an empty closed Friedmann-Robertson-Walker (FRW) universe with decaying cosmological term $\Lambda \sim R^{-m}$ ($R$ is the scale factor and $m$ is a parameter $0\leq m \leq 2$). This model is equivalent to a cosmology with the equation of state $p_{\chi}=(m/3 -1)\rho_{\chi}$. The calculations are performed by applying the dilute-instanton approximation on the corresponding Duru-Kleinert path integral. It is shown that the highest tunneling rate occurs for $m=2$ corresponding to the cosmic string matter universe. The obtained most probable cosmological term, like one obtained by Strominger, accounts for a possible solution to the cosmological constant problem.Comment: 21 pages, REVTEX, The section 3 is considerably completed including some physical mechanisms supporting the time variation of the cosmological constant, added references for the section 3. Accepted to be published in Phys. Rev.

Interference of Bose-Einstein condensates in momentum space

We suggest an experiment to investigate the linear superposition of two spatially separated Bose-Einstein condensates. Due to the coherent combination of the two wave functions, the dynamic structure factor, measurable through inelastic photon scattering at high momentum transfer $q$, is predicted to exhibit interference fringes with frequency period $\Delta\nu = q/md$ where $d$ is the distance between the condensates. We show that the coherent configuration corresponds to an eigenstate of the physical observable measured in the experiment and that the relative phase of the condensates is hence created through the measurement process.Comment: 4 pages and 2 eps figure

Strong-coupling expansion for the Hubbard model in arbitrary dimension using slave bosons

A strong-coupling expansion for the antiferromagnetic phase of the Hubbard model is derived in the framework of the slave-boson mean-field approximation. The expansion can be obtained in terms of moments of the density of states of freely hopping electrons on a lattice, which in turn are obtained for hypercubic lattices in arbitrary dimension. The expansion is given for the case of half-filling and for the energy up to fifth order in the ratio of hopping integral $t$ over on-site interaction $U$, but can straightforwardly be generalized to the non-half-filled case and be extended to higher orders in $t/U$. For the energy the expansion is found to have an accuracy of better than $1 \%$ for $U/t \geq 8$. A comparison is given with an earlier perturbation expansion based on the Linear Spin Wave approximation and with a similar expansion based on the Hartree-Fock approximation. The case of an infinite number of spatial dimensions is discussed.Comment: 12 pages, LaTeX2e, to be published in Phys. Rev.

Quantum-state control in optical lattices

We study the means to prepare and coherently manipulate atomic wave packets in optical lattices, with particular emphasis on alkali atoms in the far-detuned limit. We derive a general, basis independent expression for the lattice operator, and show that its off-diagonal elements can be tailored to couple the vibrational manifolds of separate magnetic sublevels. Using these couplings one can evolve the state of a trapped atom in a quantum coherent fashion, and prepare pure quantum states by resolved-sideband Raman cooling. We explore the use of atoms bound in optical lattices to study quantum tunneling and the generation of macroscopic superposition states in a double-well potential. Far-off-resonance optical potentials lend themselves particularly well to reservoir engineering via well controlled fluctuations in the potential, making the atom/lattice system attractive for the study of decoherence and the connection between classical and quantum physics.Comment: 35 pages including 8 figures. To appear in Phys. Rev. A. March 199