Influence of External Fields and Environment on the Dynamics of Phase Qubit-Resonator System

We analyze the dynamics of a qubit-resonator system coupled with a thermal bath and external electromagnetic fields. Using the evolution equations for the set of Heisenberg operators, that describe the whole system, we derive an expression for the resonator field, accounting for the resonator-drive,-bath, and -qubit interaction. The renormalization of the resonator frequency, caused by the qubit-resonator interaction, is accounted for. Using solutions for the resonator field, we derive the equation describing qubit dynamics. The influence of the qubit evolution during the measurement time on the fidelity of a single-shot measurement is studied. The relation between the fidelity and measurement time is shown explicitly. Also, an expression describing relaxation of the superposition qubit state towards its stationary value is derived. The possibility of controlling this state, by varying the amplitude and frequency of drive, is shown.Comment: 15 page

Normal mode splitting in a coupled system of nanomechanical oscillator and parametric amplifier cavity

We study how an optical parametric amplifier inside the cavity can affect the normal mode splitting behavior of the coupled movable mirror and the cavity field. We work in the resolved sideband regime. The spectra exhibit a double-peak structure as the parametric gain is increased. Moreover, for a fixed parametric gain, the double-peak structure of the spectrum is more pronounced with increasing the input laser power. We give results for mode splitting. The widths of the split lines are sensitive to parametric gain.Comment: 7 pages,9 figure

Quantum dynamics in single spin measurement

We study the quantum dynamics of a model for the single-spin measurement in magnetic-resonance force microscopy. We consider an oscillating driven cantilever coupled with the magnetic moment of the sample. Then, the cantilever is damped through an external bath and its readout is provided by a radiation field. Conditions for reliable measurements will be discussed.Comment: 7 pages, 3 figure

Four-level and two-qubit systems, sub-algebras, and unitary integration

Four-level systems in quantum optics, and for representing two qubits in quantum computing, are difficult to solve for general time-dependent Hamiltonians. A systematic procedure is presented which combines analytical handling of the algebraic operator aspects with simple solutions of classical, first-order differential equations. In particular, by exploiting $su(2) \oplus su(2)$ and $su(2) \oplus su(2) \oplus u(1)$ sub-algebras of the full SU(4) dynamical group of the system, the non-trivial part of the final calculation is reduced to a single Riccati (first order, quadratically nonlinear) equation, itself simply solved. Examples are provided of two-qubit problems from the recent literature, including implementation of two-qubit gates with Josephson junctions.Comment: 1 gzip file with 1 tex and 9 eps figure files. Unpack with command: gunzip RSU05.tar.g

Giant optical Faraday rotation induced by a single electron spin in a quantum dot: Applications to entangling remote spins via a single photon

We propose a quantum non-demolition method - giant Faraday rotation - to detect a single electron spin in a quantum dot inside a microcavity where negatively-charged exciton strongly couples to the cavity mode. Left- and right-circularly polarized light reflected from the cavity feels different phase shifts due to cavity quantum electrodynamics and the optical spin selection rule. This yields giant and tunable Faraday rotation which can be easily detected experimentally. Based on this spin-detection technique, a scalable scheme to create an arbitrary amount of entanglement between two or more remote spins via a single photon is proposed.Comment: 5 pages, 3 figure

Three-body recombination of ultracold Bose gases using the truncated Wigner method

We apply the truncated Wigner method to the process of three-body recombination in ultracold Bose gases. We find that within the validity regime of the Wigner truncation for two-body scattering, three-body recombination can be treated using a set of coupled stochastic differential equations that include diffusion terms, and can be simulated using known numerical methods. As an example we investigate the behaviour of a simple homogeneous Bose gas.Comment: Replaced paper same as original; correction to author list on cond-mat mad

A Model for the Production of Regular Fluorescent Light from Coherently Driven Atoms

It has been shown in recent years that incoherent pumping through multiple atomic levels provides a mechanism for the production of highly anti-bunched light, and that as the number of incoherent steps is increased the light becomes increasingly regular. We show that in a resonance fluorescence situation, a multi-level atom may be multiply coherently driven so that the fluorescent light is highly anti-bunched. We show that as the number of coherently driven levels is increased, the spontaneous emissions may be made increasingly more regular. We present a systematic method for designing the level structure and driving required to produce highly anti-bunched light in this manner for an arbitrary even number of levels.Comment: 6 pages multicol revtex, including figure

Generation of Squeezed States of Nanomechanical Resonators by Reservoir Engineering

An experimental demonstration of a non-classical state of a nanomechanical resonator is still an outstanding task. In this paper we show how the resonator can be cooled and driven into a squeezed state by a bichromatic microwave coupling to a charge qubit. The stationary oscillator state exhibits a reduced noise in one of the quadrature components by a factor of 0.5 - 0.2. These values are obtained for a 100 MHz resonator with a Q-value of 10$^4$ to 10$^5$ and for support temperatures of T $\approx$ 25 mK. We show that the coupling to the charge qubit can also be used to detect the squeezed state via measurements of the excited state population. Furthermore, by extending this measurement procedure a complete quantum state tomography of the resonator state can be performed. This provides a universal tool to detect a large variety of different states and to prove the quantum nature of a nanomechanical oscillator.Comment: 13 pages,9 figure

Non-equilibrium dynamics: Studies of reflection of Bose-Einstein condensates

The study of the non-equilibrium dynamics in Bose-Einstein condensed gases has been dominated by the zero-temperature, mean field Gross-Pitaevskii formalism. Motivated by recent experiments on the reflection of condensates from silicon surfaces, we revisit the so-called {\em classical field} description of condensate dynamics, which incorporates the effects of quantum noise and can also be generalized to include thermal effects. The noise is included in a stochastic manner through the initial conditions. We show that the inclusion of such noise is important in the quantitative description of the recent reflection experiments

Enhancement of Cavity Cooling of a Micromechanical Mirror Using Parametric Interactions

It is shown that an optical parametric amplifier inside a cavity can considerably improve the cooling of the micromechanical mirror by radiation pressure. The micromechanical mirror can be cooled from room temperature 300 K to sub-Kelvin temperatures, which is much lower than what is achievable in the absence of the parametric amplifier. Further if in case of a precooled mirror one can reach millikelvin temperatures starting with about 1 K. Our work demonstrates the fundamental dependence of radiation pressure effects on photon statistics.Comment: 14 pages, 7 figure