Decoherence and the conditions for the classical control of quantum systems

We find the conditions for one quantum system to function as a classical controller of another quantum system: the controller must be an open system and rapidly diagonalised in the basis of the controller variable that is coupled to the controlled system. This causes decoherence in the controlled system that can be made small if the rate of diagonalisation is fast. We give a detailed example based on the quantum optomechanical control of a mechanical resonator. The resulting equations are similar in structure to recently proposed models for consistently combining quantum and classical stochastic dynamics

Optomechanical trapping and cooling of partially transparent mirrors

We consider the radiative trapping and cooling of a partially transmitting mirror suspended inside an optical cavity, generalizing the case of a perfectly reflecting mirror previously considered [M. Bhattacharya and P. Meystre, Phys. Rev. Lett. \textbf{99}, 073601 (2007)]. This configuration was recently used in an experiment to cool a nanometers-thick membrane [Thompson \textit{et al.}, arXiv:0707.1724v2, 2007]. The self-consistent cavity field modes of this system depend strongly on the position of the middle mirror, leading to important qualitative differences in the radiation pressure effects: in one case, the situation is similar that of a perfectly reflecting middle mirror, with only minor quantitative modifications. In addition, we also identify a range of mirror positions for which the radiation-mirror coupling becomes purely dispersive and the back-action effects that usually lead to cooling are absent, although the mirror can still be optically trapped. The existence of these two regimes leads us to propose a bichromatic scheme that optimizes the cooling and trapping of partially transmissive mirrors.Comment: Submitted to Phys.Rev.

Nonlinear response theory for Markov processes: Simple models for glassy relaxation

The theory of nonlinear response for Markov processes obeying a master equation is formulated in terms of time-dependent perturbation theory for the Green's functions and general expressions for the response functions up to third order in the external field are given. The nonlinear response is calculated for a model of dipole reorientations in an asymmetric double well potential, a standard model in the field of dielectric spectroscopy. The static nonlinear response is finite with the exception of a certain temperature $T_0$ determined by the value of the asymmetry. In a narrow temperature range around $T_0$, the modulus of the frequency-dependent cubic response shows a peak at a frequency on the order of the relaxation rate and it vanishes for both, low frequencies and high frequencies. At temperatures at which the static response is finite (lower and higher than $T_0$), the modulus is found to decay monotonously from the static limit to zero at high frequencies. In addition, results of calculations for a trap model with a Gaussian density of states are presented. In this case, the cubic response depends on the specific dynamical variable considered and also on the way the external field is coupled to the kinetics of the model. In particular, a set of different dynamical variables is considered that gives rise to identical shapes of the linear susceptibility and only to different temperature dependencies of the relaxation times. It is found that the frequency dependence of the nonlinear response functions, however, strongly depends on the particular choice of the variables. The results are discussed in the context of recent theoretical and experimental findings regarding the nonlinear response of supercooled liquids and glasses.Comment: 23 pages, 10 figure

The dynamics of loop formation in a semiflexible polymer

The dynamics of loop formation by linear polymer chains has been a topic of several theoretical/experimental studies. Formation of loops and their opening are key processes in many important biological processes. Loop formation in flexible chains has been extensively studied by many groups. However, in the more realistic case of semiflexible polymers, not much results are available. In a recent study (K. P. Santo and K. L. Sebastian, Phys. Rev. E, \textbf{73}, 031293 (2006)), we investigated opening dynamics of semiflexible loops in the short chain limit and presented results for opening rates as a function of the length of the chain. We presented an approximate model for a semiflexible polymer in the rod limit, based on a semiclassical expansion of the bending energy of the chain. The model provided an easy way to describe the dynamics. In this paper, using this model, we investigate the reverse process, i.e., the loop formation dynamics of a semiflexible polymer chain by describing the process as a diffusion-controlled reaction. We perform a detailed multidimensional analysis of the problem and calculate closing times for a semiflexible chain which leads to results that are physically expected. Such a multidimensional analysis leading to these results does not seem to exist in the literature so far.Comment: 37 pages 4 figure

Detection of high-power two-mode squeezing by sum-frequency generation

We introduce sum-frequency generation (SFG) as an effective physical two-photon detector for high power two-mode squeezed coherent states with arbitrary frequency separation, as produced by parametric oscillators well above the threshold. Using a formalism of "collective modes", we describe both two-mode squeezing and degenerate squeezing on equal footing and derive simple relations between the input degree of squeezing and the measured SFG quadrature noise. We compare the proposed SFG detection to standard homodyne measurement, and show advantages in robustness to detection inefficiency (loss of SFG photons) and acceptance bandwidth.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

On the Correct Convergence of Complex Langevin Simulations for Polynomial Actions

There are problems in physics and particularly in field theory which are defined by complex valued weight functions $e^{-S}$ where $S$ is a polynomial action $S: R^n \rightarrow C$. The conditions under which a convergent complex Langevin calculation correctly simulates such integrals are discussed. All conditions on the process which are used to prove proper convergence are defined in the stationary limit.Comment: 8 pages, LaTeX file, preprint UNIGRAZ-UTP 29-09-9

Anharmonic effects on a phonon number measurement of a quantum mesoscopic mechanical oscillator

We generalize a proposal for detecting single phonon transitions in a single nanoelectromechanical system (NEMS) to include the intrinsic anharmonicity of each mechanical oscillator. In this scheme two NEMS oscillators are coupled via a term quadratic in the amplitude of oscillation for each oscillator. One NEMS oscillator is driven and strongly damped and becomes a transducer for phonon number in the other measured oscillator. We derive the conditions for this measurement scheme to be quantum limited and find a condition on the size of the anharmonicity. We also derive the relation between the phase diffusion back-action noise due to number measurement and the localization time for the measured system to enter a phonon number eigenstate. We relate both these time scales to the strength of the measured signal, which is an induced current proportional to the position of the readout oscillator.Comment: 13 pages, 2 figure

Opacity of electromagnetically induced transparency for quantum fluctuations

We analyze the propagation of a pair of quantized fields inside a medium of three-level atoms in $\Lambda$ configuration. We calculate the stationary quadrature noise spectrum of the field after propagating through the medium, in the case where the probe field is in a squeezed state and the atoms show electromagnetically induced transparency (EIT). We find an oscillatory transfer of the initial quantum properties between the probe and pump fields which is most strongly pronounced when both fields have comparable Rabi frequencies. This implies that the quantum state measured after propagation can be completely different from the initial state, even though the mean values of the field are unaltered

Time-resolved extinction rates of stochastic populations

Extinction of a long-lived isolated stochastic population can be described as an exponentially slow decay of quasi-stationary probability distribution of the population size. We address extinction of a population in a two-population system in the case when the population turnover -- renewal and removal -- is much slower than all other processes. In this case there is a time scale separation in the system which enables one to introduce a short-time quasi-stationary extinction rate W_1 and a long-time quasi-stationary extinction rate W_2, and develop a time-dependent theory of the transition between the two rates. It is shown that W_1 and W_2 coincide with the extinction rates when the population turnover is absent, and present but very slow, respectively. The exponentially large disparity between the two rates reflects fragility of the extinction rate in the population dynamics without turnover.Comment: 8 pages, 4 figure