Well-posedness and convergence of the Lindblad master equation for a quantum harmonic oscillator with multi-photon drive and damping

We consider the model of a quantum harmonic oscillator governed by a Lindblad master equation where the typical drive and loss channels are multi-photon processes instead of single-photon ones; this implies a dissipation operator of order 2k with integer k>1 for a k-photon process. We prove that the corresponding PDE makes the state converge, for large time, to an invariant subspace spanned by a set of k selected basis vectors; the latter physically correspond to so-called coherent states with the same amplitude and uniformly distributed phases. We also show that this convergence features a finite set of bounded invariant functionals of the state (physical observables), such that the final state in the invariant subspace can be directly predicted from the initial state. The proof includes the full arguments towards the well-posedness of the corresponding dynamics in proper Banach spaces of Hermitian trace-class operators equipped with adapted nuclear norms. It relies on the Hille-Yosida theorem and Lyapunov convergence analysis.Comment: 20 pages, submitte

Adiabatic elimination for open quantum systems with effective Lindblad master equations

We consider an open quantum system described by a Lindblad-type master equation with two times-scales. The fast time-scale is strongly dissipative and drives the system towards a low-dimensional decoherence-free space. To perform the adiabatic elimination of this fast relaxation, we propose a geometric asymptotic expansion based on the small positive parameter describing the time-scale separation. This expansion exploits geometric singular perturbation theory and center-manifold techniques. We conjecture that, at any order, it provides an effective slow Lindblad master equation and a completely positive parameterization of the slow invariant sub-manifold associated to the low-dimensional decoherence-free space. By preserving complete positivity and trace, two important structural properties attached to open quantum dynamics, we obtain a reduced-order model that directly conveys a physical interpretation since it relies on effective Lindbladian descriptions of the slow evolution. At the first order, we derive simple formulae for the effective Lindblad master equation. For a specific type of fast dissipation, we show how any Hamiltonian perturbation yields Lindbladian second-order corrections to the first-order slow evolution governed by the Zeno-Hamiltonian. These results are illustrated on a composite system made of a strongly dissipative harmonic oscillator, the ancilla, weakly coupled to another quantum system.Comment: 9 pages, one figur

Convergence and adiabatic elimination for a driven dissipative quantum harmonic oscillator

We prove that a harmonic oscillator driven by Lindblad dynamics where the typical drive and loss channels are two-photon processes instead of single-photon ones, converges to a protected subspace spanned by two coherent states of opposite amplitude. We then characterize the slow dynamics induced by a perturbative single-photon loss on this protected subspace, by performing adiabatic elimination in the Lindbladian dynamics.Comment: submitted to IEEE-CDC 201

Robustness under saturated feedback: Strong iISS for a class of nonlinear systems

International audienceThis note proposes sufficient conditions under which a nonlinear system can be made Strongly iISS in the presence of actuator saturation. This property, recently proposed as a compromise between the strength of ISS and the generality of iISS, ensures boundedness of all solutions provided that the disturbance magnitude is below a certain threshold. We also show that, under a growth rate condition, the bounded feedback law proposed by Lin and Sontag for the stabilization of the disturbance-free system based on the knowledge of a control Lyapunov function, ensures Strong iISS in the presence of perturbations. We illustrate our findings on the angular velocity control of a spacecraft with limited-power thrusters

First whole atmosphere night-time seeing measurements at Dome C, Antarctica

We report site testing results obtained in night-time during the polar autumn and winter at Dome C. These results were collected during the first Concordia winterover by A. Agabi. They are based upon seeing and isoplanatic angle monitoring, as well as in-situ balloon measurements 2 of the refractive index structure constant profiles Cn (h). Atmosphere is divided into two regions: (i) a 36 m high surface layer responsible of 87% of the turbulence and (ii) a very stable free atmosphere above with a median seeing of 0.36+-0.19 arcsec at an elevation of h = 30 m. The median seeing measured with a DIMM placed on top of a 8.5 m high tower is 1.3+-0.8 arcsec.Comment: accepted for publication in PASP (oct 2005

Atmospheric coherence times in interferometry: definition and measurement

Current and future ground-based interferometers require knowledge of the atmospheric time constant t_0, but this parameter has diverse definitions. Moreover, adequate techniques for monitoring t_0 still have to be implemented. We derive a new formula for the structure function of the fringe phase (piston) in a long-baseline interferometer, and review available techniques for measuring the atmospheric time constant and the shortcomings. It is shown that the standard adaptive-optics atmospheric time constant is sufficient for quantifying the piston coherence time, with only minor modifications. The residual error of a fast fringe tracker and the loss of fringe visibility in a finite exposure time are calculated in terms of the same parameter. A new method based on the fast variations of defocus is proposed. The formula for relating the defocus speed to the time constant is derived. Simulations of a 35-cm telescope demonstrate the feasibility of this new technique for site testing.Comment: 8 pages, 6 figures, A&A in pres

Optical turbulence vertical distribution with standard and high resolution at Mt. Graham

A characterization of the optical turbulence vertical distribution (Cn2 profiles) and all the main integrated astroclimatic parameters derived from the Cn2 and the wind speed profiles above the site of the Large Binocular Telescope (Mt. Graham, Arizona, US) is presented. The statistic includes measurements related to 43 nights done with a Generalized Scidar (GS) used in standard configuration with a vertical resolution Delta(H)~1 km on the whole 20 km and with the new technique (HVR-GS) in the first kilometer. The latter achieves a resolution Delta(H)~20-30 m in this region of the atmosphere. Measurements done in different periods of the year permit us to provide a seasonal variation analysis of the Cn2. A discretized distribution of Cn2 useful for the Ground Layer Adaptive Optics (GLAO) simulations is provided and a specific analysis for the LBT Laser Guide Star system ARGOS (running in GLAO configuration) case is done including the calculation of the 'gray zones' for J, H and K bands. Mt. Graham confirms to be an excellent site with median values of the seeing without dome contribution epsilon = 0.72", the isoplanatic angle theta0 = 2.5" and the wavefront coherence time tau0= 4.8 msec. We find that the optical turbulence vertical distribution decreases in a much sharper way than what has been believed so far in proximity of the ground above astronomical sites. We find that 50% of the whole turbulence develops in the first 80+/-15 m from the ground. We finally prove that the error in the normalization of the scintillation that has been recently put in evidence in the principle of the GS technique, affects these measurements with an absolutely negligible quantity (0.04").Comment: 11 figures. MNRAS, accepte

State Initialization of a Hot Spin Qubit in a Double Quantum Dot by Measurement-Based Quantum Feedback Control

A measurement-based quantum feedback protocol is developed for spin state initialization in a gate-defined double quantum dot spin qubit coupled to a superconducting resonator. The protocol improves qubit state initialization as it is able to robustly prepare the spin in shorter time and reach a higher fidelity, which can be pre-set. Being able to pre-set the fidelity aimed at is a highly desired feature enabling qubit initialization to be more deterministic. The protocol developed herein is also effective at high temperatures, which is critical for the current efforts towards scaling up the number of qubits in quantum computers.Comment: 11 pages, 8 figure

Site testing in summer at Dome C, Antarctica

We present summer site testing results based on DIMM data obtained at Dome C, Antarctica. These data have been collected on the bright star Canopus during two 3-months summer campaigns in 2003-2004 and 2004-2005. We performed continuous monitoring of the seeing a nd the isoplanatic angle in the visible. We found a median seeing of 0.54 \arcsec and a median isoplanatic angle of 6.8 \arcsec. The seeing appears to have a deep minimum around 0.4 \arcsec almost every day in late afternoon