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     

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     

Zero-point momentum in complex media

In this work we apply field regularization techniques to formulate a number of new phenomena related to momentum induced by electromagnetic zero-point fluctuations. We discuss the zero-point momentum associated with magneto-electric media, with moving media, and with magneto-chiral media.     

Vortices in quantum spin systems

We examine spin vortices in ferromagnetic quantum Heisenberg models with planar anisotropy on two-dimensional lattices. The symmetry properties and the time evolution of vortices built up from spin-coherent states are studied in detail. Although these states show a dispersion typical for wave packets, important features of classical vortices are conserved. Moreover, the results on symmetry properties provide a construction scheme for vortex-like excitations from exact eigenstates, which have a well-controlled time evolution. Our approach works for arbitrary spin length both on triangular and square lattices. Received 2 October 1998     

Low temperature thermodynamics of inverse square spin models in one dimension

We present a field-theoretic renormalization group calculation in two loop order for classical O(N)-models with an inverse square interaction in the vicinity of their lower critical dimensionality one. The magnetic susceptibility at low temperatures is shown to diverge like with a=(N-2)/(N-1) and . From a comparison with the exactly solvable Haldane-Shastry model we find that the same temperature dependence applies also to ferromagnetic quantum spin chains. Received: 20 February 1998 / Revised: 27 April 1998 / Accepted: 30 April 1998     

Electron-phonon interaction in carbon clathrate hex- $\mathsf{C_{40}}$

We investigate an extended spin ladder with diagonal frustrated exchanges in a wide parameter regime. By representing the model as a sum of semidefinite positive projection operators, we prove that this model has exactly a dimer ground state. Smoothly changing parameters may lead the model cover several exactly known models. Starting from this ladder model, we proposed two two-dimensional net models with exact ground states. The quantum phase transition of the ground state, due to the change of exchange strengths along perpendicular rungs, is also discussed. Received 13 October 2002 Published online 27 January 2003 RID="a" ID="a"e-mail: schen@thphy.uni.duesseldorf.de     

Energy-transfer and quantum trajectories in quasi-molecular networks

Continuous measurement models are conveniently based on master equations specified by the respective Hamiltonian and appropriate environment operators. As demonstrated by stochastic unraveling, the latter specify the dynamical process rather than static detection modes. We show that certain environment operators acting on a simple system may, in fact, require extended networks for implementation: Their Hamilton parameters re-appear in the effective environment operators of the reduced model. The resulting quantum trajectories typically involve competing paths, which may give rise to different fluctuation and noise properties even when the corresponding ensemble behavior is practically the same. Received: 21 July 1997 / Received in final form: 10 November 1997 / Accepted: 27 October 1997     

Far-infrared probe of size dispersion and population fluctuations in doped self-assembled quantum dots

We investigate the FIR magneto-optical transitions in doped self-assembled InAs quantum dots with an average filling ranging from 0.6 to 6 electrons per dot. Significant changes in the magnetic field dispersion, the line-width and the amplitude of the transitions are observed as the doping level is varied, in agreement with our theoretical calculations. We show that our technique is an effective tool to obtain informations regarding the dot size homogeneity and the electron filling uniformity.Received: 22 July 2003, Published online: 2 October 2003PACS: 73.21.La Quantum dots - 78.20.Ls Magnetooptical effects - 78.30.Fs III-V and II-VI semiconductors - 78.67.Hc Quantum dotsE. Deleporte: Present address: Laboratoire de Photonique Quantique et Moleculaire, École Normale Superieure de Cachan, 94235 Cachan Cedex, FranceJ.M. Gérard: Present address: CEA-Grenoble DRFMC/SP2M/PSC, Laboratoire de Physique des semiconducteurs, 38054 Grenoble, France     

Magnetic excitations in charge ordered a' - {N_a}{V_2}{O_5}

An investigation of the spin excitation spectrum of charge ordered (CO) NaV₂O₅ is presented. We discuss several different exchange models which may be relevant for this compound, namely in-line and zig-zag chain models with weak as well as strong inter-chain coupling and also a ladder model and a CO/MV (mixed valent) model. We put special emphasis on the importance of large additional exchange across the diagonals of V-ladders and the presence of exchange anisotropies on the excitation spectrum. It is shown that the observed splitting of transverse dispersion branches may both be interpreted as anisotropy effect as well as acoustic-optic mode splitting in the weakly coupled chain models. In addition we calculate the field dependence of excitation modes in these models. Furthermore we show that for strong inter-chain coupling, as suggested by recent LDA + U results, an additional high energy optical excitation appears and the spin gap is determined by anisotropies. The most promising CO/MV model predicts a spin wave dispersion perpendicular to the chains which agrees very well with recent results obtained by inelastic neutron scattering. Received 30 April 1999 and Received in final form 5 October 1999     

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     

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     

Exact ground state of the generalized three-dimensional Shastry-Sutherland model

We generalize the Shastry-Sutherland model to three dimensions. By representing the model as a sum of the semidefinite positive projection operators, we exactly prove that the model has exact dimer ground state. Several schemes for constructing the three-dimensional Shastry-Sutherland model are proposed. Received 20 February 2002 / Received in final form 27 May 2002 Published online 17 September 2002     

Exactly solvable spin ladder model with degenerate ferromagnetic and singlet states

We study the spin ladder model with interactions between spins on neighboring rungs. The model Hamiltonian with the exact singlet ground state degenerated with ferromagnetic state is obtained. The singlet ground state wave function has a special recurrent form and depends on two parameters. Spin correlations in the singlet ground state show double-spiral structure with period of spirals equals to the system size. For special values of parameters they have exponential decay. The spectrum of the model is gapless and there are asymptotically degenerated excited states for special values of parameters in the thermodynamic limit. Received 7 May 1999     

Quantum spin-{3 \over 2} models on the Cayley tree - optimum ground state approach

We present a class of optimum ground states for quantum spin- models on the Cayley tree with coordination number 3. The interaction is restricted to nearest neighbours and contains 5 continuous parameters. For all values of these parameters the Hamiltonian has parity invariance, spin-flip invariance, and rotational symmetry in the xy-plane of spin space. The global ground states are constructed in terms of a 1-parametric vertex state model, which is a direct generalization of the well-known matrix product ground state approach. By using recursion relations and the transfer matrix technique we derive exact analytical expressions for local fluctuations and longitudinal and transversal two-point correlation functions. Received 1 March 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     

Quantum state transfer from light to molecules via coherent two-color photo-association in an atomic Bose-Einstein condensate

By using a quantized input light, we theoretically revisit the coherent two-color photo-association process in an atomic Bose-Einstein condensate. Under the single-mode approximations, we show two interesting regimes of the light transmission and the molecular generation. The quantum state transfer from light to molecules is exhibited, without or with the depletion of trapped atoms.     

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     

Quasiclassical Hamiltonians for large-spin systems

We extend and apply a previously developed method for a semiclassical treatment of a system with large spin S. A multisite Heisenberg Hamiltonian is transformed into an effective classical Hamilton function which can be treated by standard methods for classical systems. Quantum effects enter in form of multispin interactions in the Hamilton function. The latter is written in the form of an expansion in powers of J/(TS), where J is the coupling constant. Main ingredients of our method are spin coherent states and cumulants. Rules and diagrams are derived for computing cumulants of groups of operators entering the Hamiltonian. The theory is illustrated by calculating the quantum corrections to the free energy of a Heisenberg chain which were previously computed by a Wigner-Kirkwood expansion. Received 5 May 1999 and received in final form 24 September 1999     

Quantum rotors with regular frustration and the quantum Lifshitz point

We have discussed the zero-temperature quantum phase transition in n-component quantum rotor Hamiltonian in the presence of regular frustration in the interaction. The phase diagram consists of ferromagnetic, helical and quantum paramagnetic phase, where the ferro-para and the helical-para phase boundary meets at a multicritical point called a (d,m) quantum Lifshitz point where (d,m) indicates that the m of the d spatial dimensions incorporate frustration. We have studied the Hamiltonian in the vicinity of the quantum Lifshitz point in the spherical limit and also studied the renormalisation group flow behaviour using standard momentum space renormalisation technique (for finite n). In the spherical limit ()one finds that the helical phase does not exist in the presence of any nonvanishing quantum fluctuation for m =d though the quantum Lifshitz point exists for all d > 1+m/2, and the upper critical dimensionality is given by d _u = 3 +m/2. The scaling behaviour in the neighbourhood of a quantum Lifshitz point in d dimensions is consistent with the behaviour near the classical Lifshitz point in (d+z) dimensions. The dynamical exponent of the quantum Hamiltonian z is unity in the case of anisotropic Lifshitz point (d>m) whereas z=2 in the case of isotropic Lifshitz point (d=m). We have evaluated all the exponents using the renormalisation flow equations along-with the scaling relations near the quantum Lifshitz point. We have also obtained the exponents in the spherical limit (). It has also been shown that the exponents in the spherical model are all related to those of the corresponding Gaussian model by Fisher renormalisation. Received: 23 December 1997 / Received in final form: 6 January 1998 / Accepted: 7 January 1998     

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