Input and output in damped quantum systems III: Formulation of damped systems driven by Fermion fields

A comprehensive input-output theory is developed for Fermionic input fields. Quantum stochastic differential equations are developed in both the Ito and Stratonovich forms. The major technical issue is the development of a formalism which takes account of anticommutation relations between the Fermionic driving field and those system operators which can change the number of Fermions within the system

All-optical versus electro-optical quantum-limited feedback

All-optical feedback can be effected by putting the output of a source cavity through a Faraday isolator and into a second cavity which is coupled to the source cavity by a nonlinear crystal. If the driven cavity is heavily damped, then it can be adiabatically eliminated and a master equation or quantum Langevin equation derived for the first cavity alone. This is done for an input bath in an arbitrary state, and for an arbitrary nonlinear coupling. If the intercavity coupling involves only the intensity (or one quadrature) of the driven cavity, then the effect on the source cavity is identical to that which can be obtained from electro-optical feedback using direct (or homodyne) detection. If the coupling involves both quadratures, this equivalence no longer holds, and a coupling linear in the source amplitude can produce a nonclassical state in the source cavity. The analogous electro-optic scheme using heterodyne detection introduces extra noise which prevents the production of nonclassical light. Unlike the electro-optic case, the all-optical feedback loop has an output beam (reflected from the second cavity). We show that this may be squeezed, even if the source cavity remains in a classical state.Comment: 21 pages. This is an old (1994) paper, but one which I thought was worth posting because in addition to what is described in abstract it has: (1) the first formulation (to my knowledge) of quantum trajectories for an arbitrary (i.e. squeezed, thermal etc.) broadband bath; (2) the prediction of a periodic modification to the detuning and damping of an oscillator for the simplest sort of all-optical feedback (i.e. a mirror) as seen in the recent experiment "Forces between a Single Atom and Its Distant Mirror Image", P. Bushev et al, Phys. Rev. Lett. 92, 223602 (2004

Quantum Kinetic Theory V: Quantum kinetic master equation for mutual interaction of condensate and noncondensate

A detailed quantum kinetic master equation is developed which couples the kinetics of a trapped condensate to the vapor of non-condensed particles. This generalizes previous work which treated the vapor as being undepleted.Comment: RevTeX, 26 pages and 5 eps figure

Robust unravelings for resonance fluorescence

Monitoring the fluorescent radiation of an atom unravels the master equation evolution by collapsing the atomic state into a pure state which evolves stochastically. A robust unraveling is one that gives pure states that, on average, are relatively unaffected by the master equation evolution (which applies once the monitoring ceases). The ensemble of pure states arising from the maximally robust unraveling has been suggested to be the most natural way of representing the system [H.M. Wiseman and J.A. Vaccaro, Phys. Lett. A {\bf 250}, 241 (1998)]. We find that the maximally robust unraveling of a resonantly driven atom requires an adaptive interferometric measurement proposed by Wiseman and Toombes [Phys. Rev. A {\bf 60}, 2474 (1999)]. The resultant ensemble consists of just two pure states which, in the high driving limit, are close to the eigenstates of the driving Hamiltonian $\Omega\sigma_{x}/2$. This ensemble is the closest thing to a classical limit for a strongly driven atom. We also find that it is possible to reasonably approximate this ensemble using just homodyne detection, an example of a continuous Markovian unraveling. This has implications for other systems, for which it may be necessary in practice to consider only continuous Markovian unravelings.Comment: 12 pages including 5 .eps figures, plus one .jpg figur

Continuous Non-Demolition Observation, Quantum Filtering and Optimal Estimation

A quantum stochastic model for an open dynamical system (quantum receiver) and output multi-channel of observation with an additive nonvacuum quantum noise is given. A quantum stochastic Master equation for the corresponding instrument is derived and quantum stochastic filtering equations both for the Heisenberg operators and the reduced density matrix of the system under the nondemolition observation are found. Thus the dynamical problem of quantum filtering is generalized for a noncommutative output process, and a quantum stochastic model and optimal filtering equation for the dynamical estimation of an input Markovian process is found. The results are illustrated on an example of optimal estimation of an input Gaussian diffusion signal, an unknown gravitational force say in a quantum optical or Weber's antenna for detection and filtering a gravitational waves.Comment: A revised version of the paper published in the Proceedings of the 1st QCMC conference, Paris 199

Spatial Correlation Functions of one-dimensional Bose gases at Equilibrium

The dependence of the three lowest order spatial correlation functions of a harmonically confined Bose gas on temperature and interaction strength is presented at equilibrium. Our analysis is based on a stochastic Langevin equation for the order parameter of a weakly-interacting gas. Comparison of the predicted first order correlation functions to those of appropriate mean field theories demonstrates the potentially crucial role of density fluctuations on the equilibrium coherence length. Furthermore,the change in both coherence length and shape of the correlation function, from gaussian to exponential, with increasing temperature is quantified. Moreover, the presented results for higher order correlation functions are shown to be in agreeement with existing predictions. Appropriate consideration of density-density correlations is shown to facilitate a precise determination of quasi-condensate density profiles, providing an alternative approach to the bimodal density fits typically used experimentally

Colon cryptogenesis: Asymmetric budding

The process of crypt formation and the roles of Wnt and cell-cell adhesion signaling in cryptogenesis are not well described; but are important to the understanding of both normal and cancer colon crypt biology. A quantitative 3D-microscopy and image analysis technique is used to study the frequency, morphology and molecular topography associated with crypt formation. Measurements along the colon reveal the details of crypt formation and some key underlying biochemical signals regulating normal colon biology. Our measurements revealed an asymmetrical crypt budding process, contrary to the previously reported symmetrical fission of crypts. 3D immunofluorescence analyses reveals heterogeneity in the subcellular distribution of E-cadherin and β-catenin in distinct crypt populations. This heterogeneity was also found in asymmetrical budding crypts. Singular crypt formation (i.e. no multiple new crypts forming from one parent crypt) were observed in crypts isolated from the normal colon mucosa, suggestive of a singular constraint mechanism to prevent aberrant crypt production. The technique presented improves our understanding of cryptogenesis and suggests that excess colon crypt formation occurs when Wnt signaling is perturbed (e.g. by truncation of adenomatous polyposis coli, APC protein) in most colon cancers

Quantum Kinetic Theory III: Quantum kinetic master equation for strongly condensed trapped systems

We extend quantum kinetic theory to deal with a strongly Bose-condensed atomic vapor in a trap. The method assumes that the majority of the vapor is not condensed, and acts as a bath of heat and atoms for the condensate. The condensate is described by the particle number conserving Bogoliubov method developed by one of the authors. We derive equations which describe the fluctuations of particle number and phase, and the growth of the Bose-Einstein condensate. The equilibrium state of the condensate is a mixture of states with different numbers of particles and quasiparticles. It is not a quantum superposition of states with different numbers of particles---nevertheless, the stationary state exhibits the property of off-diagonal long range order, to the extent that this concept makes sense in a tightly trapped condensate.Comment: 3 figures submitted to Physical Review

Functional Methods in Stochastic Systems

Field-theoretic construction of functional representations of solutions of stochastic differential equations and master equations is reviewed. A generic expression for the generating function of Green functions of stochastic systems is put forward. Relation of ambiguities in stochastic differential equations and in the functional representations is discussed. Ordinary differential equations for expectation values and correlation functions are inferred with the aid of a variational approach.Comment: Plenary talk presented at Mathematical Modeling and Computational Science. International Conference, MMCP 2011, Star\'a Lesn\'a, Slovakia, July 4-8, 201

Dynamics of evaporative cooling in magnetically trapped atomic hydrogen

We study the evaporative cooling of magnetically trapped atomic hydrogen on the basis of the kinetic theory of a Bose gas. The dynamics of trapped atoms is described by the coupled differential equations, considering both the evaporation and dipolar spin relaxation processes. The numerical time-evolution calculations quantitatively agree with the recent experiment of Bose-Einstein condensation with atomic hydrogen. It is demonstrated that the balance between evaporative cooling and heating due to dipolar relaxation limits the number of condensates to 9x10^8 and the corresponding condensate fraction to a small value of 4% as observed experimentally.Comment: 5 pages, REVTeX, 3 eps figures, Phys. Rev. A in pres