Thermal Properties of Interacting Bose Fields and Imaginary-Time Stochastic Differential Equations

Matsubara Green's functions for interacting bosons are expressed as classical statistical averages corresponding to a linear imaginary-time stochastic differential equation. This makes direct numerical simulations applicable to the study of equilibrium quantum properties of bosons in the non-perturbative regime. To verify our results we discuss an oscillator with quartic anharmonicity as a prototype model for an interacting Bose gas. An analytic expression for the characteristic function in a thermal state is derived and a Higgs-type phase transition discussed, which occurs when the oscillator frequency becomes negative.Comment: Published versio

Unconditional two-mode squeezing of separated atomic ensembles

We propose schemes for the unconditional preparation of a two-mode squeezed state of effective bosonic modes realized in a pair of atomic ensembles interacting collectively with optical cavity and laser fields. The scheme uses Raman transitions between stable atomic ground states and under ideal conditions produces pure entangled states in the steady state. The scheme works both for ensembles confined within a single cavity and for ensembles confined in separate, cascaded cavities.Comment: 4 pages, 2 figure

Effect of the Coriolis Force on the Hydrodynamics of Colliding Wind Binaries

Using fully three-dimensional hydrodynamic simulations, we investigate the effect of the Coriolis force on the hydrodynamic and observable properties of colliding wind binary systems. To make the calculations tractable, we assume adiabatic, constant velocity winds. The neglect of radiative driving, gravitational deceleration, and cooling limit the application of our models to real systems. However, these assumptions allow us to isolate the effect of the Coriolis force, and by simplifying the calculations, allow us to use a higher resolution (up to 640^3) and to conduct a larger survey of parameter space. We study the dynamics of collidng winds with equal mass loss rates and velocities emanating from equal mass stars on circular orbits, with a range of values for the ratio of the wind to orbital velocity. We also study the dynamics of winds from stars on elliptical orbits and with unequal strength winds. Orbital motion of the stars sweeps the shocked wind gas into an Archimedean spiral, with asymmetric shock strengths and therefore unequal postshock temperatures and densities in the leading and trailing edges of the spiral. We observe the Kelvin-Helmholtz instability at the contact surface between the shocked winds in systems with orbital motion even when the winds are identical. The change in shock strengths caused by orbital motion increases the volume of X-ray emitting post-shock gas with T > 0.59 keV by 63% for a typical system as the ratio of wind velocity to orbital velocity decreases to V_w/V_o = 2.5. This causes increased free-free emission from systems with shorter orbital periods and an altered time-dependence of the wind attenuation. We comment on the importance of the effects of orbital motion on the observable properties of colliding wind binaries.Comment: 12 pages, 17 figures, accepted for publication in Ap

Decoherence of number states in phase-sensitive reservoirs

The non-unitary evolution of initial number states in general Gaussian environments is solved analytically. Decoherence in the channels is quantified by determining explicitly the purity of the state at any time. The influence of the squeezing of the bath on decoherence is discussed. The behavior of coherent superpositions of number states is addressed as well.Comment: 5 pages, 2 figures, minor changes, references adde

Commuting Heisenberg operators as the quantum response problem: Time-normal averages in the truncated Wigner representation

The applicability of the so-called truncated Wigner approximation (-W) is extended to multitime averages of Heisenberg field operators. This task splits naturally in two. Firstly, what class of multitime averages the -W approximates, and, secondly, how to proceed if the average in question does not belong to this class. To answer the first question we develop an (in principle, exact) path-integral approach in phase-space based on the symmetric (Weyl) ordering of creation and annihilation operators. These techniques calculate a new class of averages which we call time-symmetric. The -W equations emerge as an approximation within this path-integral techniques. We then show that the answer to the second question is associated with response properties of the system. In fact, for two-time averages Kubo's renowned formula relating the linear response function to two-time commutators suffices. The -W is trivially generalised to the response properties of the system allowing one to calculate approximate time-normally ordered two-time correlation functions with surprising ease. The techniques we develop are demonstrated for the Bose-Hubbard model.Comment: 20 pages, 6 figure

Semiclassical Spectrum of Small Bose-Hubbard Chains: A Normal Form Approach

We analyze the spectrum of the 3-site Bose-Hubbard model with periodic boundary conditions using a semiclassical method. The Bohr-Sommerfeld quantization is applied to an effective classical Hamiltonian which we derive using resonance normal form theory. The derivation takes into account the 1:1 resonance between frequencies of a linearized classical system, and brings nonlinear terms into a corresponding normal form. The obtained expressions reproduce the exact low-energy spectrum of the system remarkably well even for a small number of particles N corresponding to fillings of just two particles per site. Such small fillings are often used in current experiments, and it is inspiring to get insight into this quantum regime using essentially classical calculations.Comment: Minor corrections to the coefficients of the effective Hamiltonian in Eqs 14,15,18,19. Figs 1,2 are slightly modified, correspondingl

Quantum trajectory approach to circuit QED: Quantum jumps and the Zeno effect

We present a theoretical study of a superconducting charge qubit dispersively coupled to a transmission line resonator. Starting from a master equation description of this coupled system and using a polaron transformation, we obtain an exact effective master equation for the qubit. We then use quantum trajectory theory to investigate the measurement of the qubit by continuous homodyne measurement of the resonator out-field. Using the same porlaron transformation, a stochastic master equation for the conditional state of the qubit is obtained. From this result, various definitions of the measurement time are studied. Furthermore, we find that in the limit of strong homodyne measurement, typical quantum trajectories for the qubit exhibit a crossover from diffusive to jump-like behavior. Finally, in the presence of Rabi drive on the qubit, the qubit dynamics is shown to exhibit quantum Zeno behavior.Comment: 20 pages, 12 figure