Quantum trajectories of interacting pseudo-spin networks

Received: 12 June 1998     

Heisenberg picture operators in the stochastic wave function approach to open quantum systems

A fast simulation algorithm for the calculation of multitime correlation functions of open quantum systems is presented. It is demonstrated that any stochastic process which “unravels” the quantum Master equation can be used for the calculation of matrix elements of reduced Heisenberg picture operators, and thus for the calculation of multitime correlation functions, by extending the stochastic process to a doubled Hilbert space. The numerical performance of the stochastic simulation algorithm is investigated by means of a standard example. Received: 30 May 1997 / Revised: 4 November 1997 / Accepted: 7 November 1997     

Effects of quantum interference on the spontaneous emission in a coherently driven three-level atom

A new scheme of the influence of quantum interference on the spontaneous emission in a coherently driven three-level medium is presented in this paper. The results are the same with that discussed by [S.-Y. Zhu, L.M. Narducci, M.O. Scully, Phys. Rev. A 52, 4791 (1995)] under resonance conditions, but they are different when the driven field is detuned. Received 8 September 1999 and Received in final form 13 January 2000     

Spatial and temporal properties of parametric fluorescence around degeneracy in a type I LBO crystal

We present a theoretical and experimental study of the spatio-temporal properties of the spontaneous parametric emission generated in a type I LBO crystal around degeneracy. The number of quasi-phase-matched modes is shown to be equal to the number of spatio-temporal degrees of freedom of the image that can be parametrically amplified. From this number, we demonstrate the possibility of predicting the total number of photons generated by parametric fluorescence. Correlation is observed between spatial intensity fluctuations corresponding to pairs of signal-idler modes. Received 18 February 1999 and Received in final form 9 June 1999     

Superradiant laser: First-order phase transition and non-stationary regime

We solve the superradiant laser model in two limiting cases. First the stationary low-pumping regime is considered where a first-order phase transition in the semiclassical solution occurs. This discontinuity is smeared out in the quantum regime. Second, we solve the model in the non-stationary regime where we find a temporally periodic solution. For a certain parameter range well-separated pulses may occur. Received: 19 June 1998 / Accepted: 19 October 1998     

Dependence on crystal parameters of the correlation time between signal and idler beams in parametric down conversion calculated in the Wigner representation

The theory of parametric down conversion within the framework of the Wigner representation has been treated recently in a series of papers using the standard model Hamiltonian. Here we take a more fundamental point of view studying the mechanism, inside the crystal, for the production of the signal and idler beams. We begin from the evolution equations for the quantum field operators, pass to the Wigner function and solve the resulting (Maxwell) equations with the use of the Green's function method. We derive the time dependence of the coincidence detection probability as a function of the parameters of the nonlinear crystal (in particular the length) the radius of the pumping beam, and the bandwidth of the filters in front of the detectors. Received 24 January 2000 and Received in final form 24 March 2000     

Quantum-state diffusion with adaptive noise

We present a scheme for stochastic quantum-state diffusion (QSD) with adaptive noise to calculate the time evolution of an arbitrary observable of an open system. The method is based on the fact that the observable is much less sensitive to adaptive noise than to noise with a random phase. Hence, the individual realisations of the expectation value of the observable stay closer to the average evolution and fewer realisations are required to obtain the ensemble average. This is illustrated by applying QSD to a driven two-level system using both randomly phased and adaptive noise. Applying QSD with adaptive noise to an undriven two-level system enables us to derive a deterministic Schr?dinger equation that produces the exact evolution of an arbitrary observable. Received: 31 July 1997 / Received in final form: 12 February 1998 / Accepted: 13 March 1998     

Spectrum of the parametric down converted radiation calculated in the Wigner function formalism

We continue the study of parametric down conversion within the framework of the Wigner representation, by using a Maxwellian approach developed in a recent paper [A. Casado et al., Eur. Phys. J. D 11, 465 (2000)]. This gives a mechanism, inside the crystal, for the production of the down-converted radiation. We obtain the electric field to second order in the coupling constant by using the Green's function method, and compare our treatment with the standard Hamiltonian approach. The spectrum of the down-converted radiation is calculated as a function of the parameters of the nonlinear crystal (in particular the length) and the radius of the pumping beam. Received 15 May 2000     

Noiseless amplification of images in a confocal cavity

We study the noiseless amplification of an optical image by means of a confocal cavity containing a parametric medium. We demonstrate, in the ideal situation, the possibility of preserving the signal-to-noise ratio while amplifying uniformly the entire image. Some specific effects, which may degrade the performances of the scheme, are taken into account. Received 23 March 2000     

Colored noise in a two-dimensional nonlinear system

A two-dimensional decoupling theory is developed when colored noise is included in a nonlinear dynamical system. By a functional analysis, the colored noise is transformed to an effective noise that includes the noise correlation time, the mean dynamical variable, and the original noise strength. When the two-dimensional decoupling theory is applied to single-mode and two-mode dye laser systems, the mean, variance, and effective eigenvalue of laser intensity are calculated. Excellent agreement between theoretical analysis, numerical simulations, and experimental measurements are obtained. It is seen that the increase of noise correlation time can reduce the fluctuations in the laser system. It is also shown that there is relatively large fluctuation in the phase when the laser undergoes from thermal light to coherent light when the theory is applied to a single mode dye laser. Received 20 August 2001 and Received in final form 4 December 2001     

Frequency up-converted radiation from a cavity moving in vacuum

We calculate the photon emission of a high finesse cavity moving in vacuum. The cavity is treated as an open system. The field initially in the vacuum state accumulates a dephasing depending on the mirrors motion when bouncing back and forth inside the cavity. The dephasing is not linearized in our calculation, so that qualitatively new effects like pulse shaping in the time domain and frequency up-conversion in the spectrum are found. Furthermore we predict the existence of a threshold above which the system should show self-sustained oscillations. Received: 10 December 1997 / Received in final form: 27 March 1998 / Accepted: 27 March 1998     

Twin-correlations in atoms

We discuss the possibility of preparing an atomic sample of atoms with minimum fluctuations in the difference between populations of two levels. A first scheme involves absorption of twin beams of light, and it presents a variant of a recent proposal for atomic spin squeezing within an excited state manifold [Kuzmich et al., Phys. Rev. Lett. 79, 4782 (1997)]. A second scheme involves atoms with two stable states, and we suggest that by use of quantum non-demolition detection and feed-back optical pumping, we may ensure a perfect agreement between the number of atoms in these two states. Received: 14 May 1998 / Revised: 10 August 1998 / Accepted: 8 October 1998     

Casimir force between metallic mirrors

We study the influence of finite conductivity of metals on the Casimir effect. We put the emphasis on explicit theoretical evaluations which can help comparing experimental results with theory. The reduction of the Casimir force is evaluated for plane metallic plates. The reduction of the Casimir energy in the same configuration is also calculated. It can be used to infer the reduction of the force in the plane-sphere geometry through the “proximity theorem”. Frequency dependent dielectric response functions of the metals are represented either by the simple plasma model or, more accurately, by using the optical data known for the metals used in recent experiments, that is Al, Au and Cu. In the two latter cases, the results obtained here differ significantly from those published recently. Received 30 July 1999     

Quantum derivation of the excess noise factor in lasers with non-orthogonal eigenmodes

By generalizing recently obtained results we calculate the excess noise factor (Petermann factor) for a laser system with non-orthogonal eigenmodes. The quantum consistency of the calculation is shown through the explicit conservation of input-output commutation rules. As a result of the calculation, the excess noise in the lasing mode is shown to depend on the laser gain below threshold, and on the noise analysis frequency below and above threshold. Received: 27 October 1998 / Received in final form: 11 March 1999     

Spontaneous emission of an excited two-level atom without both rotating-wave and Markovian approximation

The spontaneous emission of an excited atom is analyzed by quantum stochastic trajectory approach without both rotating-wave approximation and Markovian approximation. The atom finite size effect is also taken into account. We show by an example that the correction due to the counter-rotating wave term is rather small, even for the largest atomic number of real nuclei. Received 10 July 2002 / Received in final form 12 November 2002 Published online 4 February 2003     

Photochemistry in rare gas clusters

We introduce a novel control method for a delayed dynamical system exhibiting high-dimensional chaos. The control is based on a negative feedback loop with an adaptive filtering, consisting of a selective filter, centered at the frequency of the orbit to be stabilized, with the addition of a time derivative correction. The validity of the method is also discussed in the framework of a space-like representation adopted to study the analogies between delayed dynamical systems and spatially extended systems. Received: 12 April 1999     

Quantum theory of fluctuations in a cold damped accelerometer

We present a quantum network approach to real high sensitivity measurements. Thermal and quantum fluctuations due to active as well as passive elements are taken into account. The method is applied to the analysis of the capacitive accelerometer using the cold damping technique, developed for fundamental physics in space by ONERA and the ultimate limits of this instrument are discussed. It is confirmed in this quantum analysis that the cold damping technique allows one to control efficiently the test mass motion without degrading the noise level. Received 20 April 1999 and Received in final form 2 July 1999     

Numerical simulation of spatial fluctuations in parametric image amplification

We study the properties of the spatial fluctuations in the far-field parametric fluorescence output of a type 1 degenerate traveling-wave parametric amplifier. Results of a semi-classical simulation are compared with experiments in a LBO crystal. This simulation is then used to predict amplified images of a continuous background, in a phase-sensitive as well as in a phase-insensitive configuration. Received 12 March 2001     

Spectral linewidth of inversionless and Raman lasers in V-type three-level systems

A theoretical analysis of the spectral linewidth of V-type inversionless and Raman lasers is presented. First, we examine the effects of the atomic coherence between dressed states and the Autler-Townes splitting on the linewidth. It is demonstrated that near above threshold, the V inversionless laser has a narrower linewidth than that of the two-level laser. Instead of the dressed coherence, it is the Autler-Townes splitting that is responsible for the linewidth reduction though the dressed coherence determines the laser gain. Next, we explore the effects of the generated laser intensity on the linewidth. It is shown that the linewidths of the V inversionless and Raman lasers follow the usual 1/I decrease for smaller laser intensity I, but a slower decrease than 1/I for larger laser intensity. For the V Raman laser, even more surprisingly, with the laser intensity increasing, the linewidth appreciably increases as well. As a result, well above threshold, the V inversionless and Raman lasers may have a larger linewidth than that of the two-level laser. Finally, a comparison is made between the V lasers and the Λ lasers. It is found that the linewidth of the Λ inversionless laser shows a fast 1/I ² decay under optimum conditions. Received 25 October 1999 and Received in final form 10 March 2000