Optical micro-manipulation techniques has evolved into powerful tools to efficiently steer the motion of microscopical particles on periodic and quasi-periodic potentials, driven by the external electromagnetic field. Here, the dynamics of molecular diffusion on optical lattices is analysed within the framework of the theory of open systems, for polar molecules coupled to a transient electromagnetic field. Using the normal mode expansion of the field, we derive an effective, generalised Langevin equation which describes the motion of the system along the molecular degrees of freedom. The present approach is universally applicable (for molecules with non-vanishing permanent dipole moment) and it opens a wide spectrum of applications in the control of the molecular transport mechanisms on optical lattices. The numerical analysis of suitable model external fields demonstrates the feasibility of neglecting memory terms in the resulting Langevin equation.
Optical micro-manipulation techniques has evolved into powerful tools to efficiently steer the motion of microscopical particles on periodic and quasi-periodic potentials, driven by the external electromagnetic field. Here, the dynamics of molecular diffusion on optical lattices is analysed within the framework of the theory of open systems, for polar molecules coupled to a transient electromagnetic field. Using the normal mode expansion of the field, we derive an effective, generalised Langevin equation which describes the motion of the system along the molecular degrees of freedom. The present approach is universally applicable (for molecules with non-vanishing permanent dipole moment) and it opens a wide spectrum of applications in the control of the molecular transport mechanisms on optical lattices. The numerical analysis of suitable model external fields demonstrates the feasibility of neglecting memory terms in the resulting Langevin equation.
The present study focuses in the investigation of the diffusion of polar molecules on the structures known as optical lattices (a periodic generalization of optical traps); and in the assessment of the influence of a time dependent electromagnetic field on the motion of molecule. To study this phenomenon, the particle is considered to move under the influence of a one-dimensional potential which reproduces the main characteristics of the optical lattice. Starting from the canonical representation of the electromagnetic field, it has been introduce an equivalence between this field and an ensemble of harmonics oscillators. This allows deriving an effective Langevin equation to describe the motion of the particle interacting with the bath oscillators. We analyze the influence, on the diffusion dynamics, of the parameters which determine the shape of the electromagnetic pulses, which constitutes a key ingredient for the design of optimal fields that enable an efficient control of molecular dynamics.
This thesis includes both experimental and theoretical investigations of fluctuation-induced transport phenomena, presented in a series of nine papers, by studies of the dynamics of cold atoms in dissipative optical lattices. With standard laser cooling techniques about 108 cesium atoms are accumulated, cooled to a few μK, and transferred into a dissipative optical lattice. An optical lattice is a periodic light-shift potential, and in dissipative optical lattice the light field is sufficiently close to resonance for incoherent light scattering to be of importance. This provides the system with a diffusive force, but also with a friction through laser cooling mechanisms. In the dissipative optical lattices the friction and the diffusive force will eventually reach a steady state. At steady state, the thermal energy is low enough, compared to the potential depth, for the atoms to be localized close to the potential minima, but high enough for the atoms to occasionally make inter-well flights. This leads to a Brownian motion of the atoms in the optical lattices. In the normal case these random walks average to zero, leading to a symmetric, isotropic diffusion of the atoms. If the optical lattices are tilted, the symmetry is broken and the diffusion will be biased. This leads to a fluctuation-induced drift of the atoms. In this thesis an investigation of such drifts, for an optical lattice tilted by the gravitational force, is presented. We show that even though the tilt over a potential period is small compared to the potential depth, it clearly affect the dynamics of the atoms, and despite the complex details of the system it can, to a good approximation, be described by the Langevin equation formalism for a particle in a periodic potential. The linear drifts give evidence of stop-and-go dynamics where the atoms escape the potential wells and travel over one or more wells before being recaptured. Brownian motors open the possibility of creating fluctuation-induced drifts in the absence of bias forces, if two requirements are fulfilled: the symmetry has to be broken and the system has to be brought out of thermal equilibrium. By utilizing two distinguishable optical lattices, with a relative spatial phase and unequal transfer rates between them, these requirements can be fulfilled. In this thesis, such a Brownian motor is realized, and drifts in arbitrary directions in 3D are demonstrated. We also demonstrate a real-time steering of the transport as well as drifts along pre-designed paths. Moreover, we present measurements and discussions of performance characteristics of the motor, and we show that the required asymmetry can be obtained in multiple ways.
Analysis of the trapped and untrapped motion of particles, combined with direct numerical simulation of the 1D non-stationary Boltzmann equation, demonstrates that atoms and molecules initially at room temperature can be accelerated to velocities in the 10 to 100 km/s range over distances of 100's microns using an optical lattice. The quantity, final velocity, and velocity/energy spread of the accelerated distribution controlled by tailoring the fluence, duration and frequency chirp of the laser beam that make the lattice, indicating the potential for a compact, versatile, and configurable hyper-thermal accelerator/decelerator. Using similar lattice potentials, differential transport of atomic and molecular species with different polarizability/mass ratios leads towards the possibility of gas mixture separation in short pulses or in hollow fibers. A bulk drift can be induced in a gas by the lattice forces, even when the mean kinetic energy is much greater that the maximum dipole potential of the optical field. In this process the transfer of energy from the slowly traveling optical lattice to the gas is analogous to Landau damping of a plasma wave by charged particles.
We present a non-equilibrium quantum master equation for a driven open quantum system in the presence of a continuously applied electromagnetic field. Starting from a driven Caldeira-Leggett (CL) model in which the external electromagnetic field couples simultaneously to the subsystem and reservoir degrees of freedom, the canonical fluctuation-dissipation theorem (FDT) relations that encode the coefficients of the master equation can no longer be expected to hold. The bath statistics acquire an explicit dependence on the two-time autocorrelation function of the applied field, leading to drive-biased noise correlations and the potential for non-Markovian dynamics. By eliminating the reservoir degrees of freedom at the operator level, we obtain a modified Hu-Paz-Zhang (HPZ) master equation, in which the diffusion coefficients and coherent forces inherit an explicit memory dependence on the external field. We demonstrate that the physically observable resonant frequency remains encoded in the homogeneous Green's function of the Generalized Langevin equation (GLE), while the drive-induced corrections manifest exclusively through modified diffusion and drift terms, should the drive be treated classically. The resultant field-modified HPZ master provides a unified microscopic framework for understanding field-biased open quantum systems with direct pertinence to a wide variety of experiments in quantum optics and microscopic quantum circuits.
It is shown that the effective Hamiltonian representation, as it is formulated in author’s papers, serves as a basis for distinguishing, in a broadband environment of an open quantum system, independent noise sources that determine, in terms of the stationary quantum Wiener and Poisson processes in the Markov approximation, the effective Hamiltonian and the equation for the evolution operator of the open system and its environment. General stochastic differential equations of generalized Langevin (non-Wiener) type for the evolution operator and the kinetic equation for the density matrix of an open system are obtained, which allow one to analyze the dynamics of a wide class of localized open systems in the Markov approximation. The main distinctive features of the dynamics of open quantum systems described in this way are the stabilization of excited states with respect to collective processes and an additional frequency shift of the spectrum of the open system. As an illustration of the general approach developed, the photon dynamics in a single-mode cavity without losses on the mirrors is considered, which contains identical intracavity atoms coupled to the external vacuum electromagnetic field. For some atomic densities, the photons of the cavity mode are “locked” inside the cavity, thus exhibiting a new phenomenon of radiation trapping and non-Wiener dynamics.
Phase-space methods are powerful tools for the treatment of Markovian open quantum systems: they map the reduced dynamics of a system S, in interaction with an environment E, exactly onto Langevin equations for c-number stochastic variables, as opposed to Heisenberg-Langevin equations for operators. Langevin equations provide analytical insight in key regimes and excel at handling strong nonlinearities and couplings, where other methods often falter. Extending phase-space methods to non-Markovian dynamics, however, has remained a long-standing challenge. Here we address this gap by applying phase-space representations to the full S+E system; integrating out the environmental degrees of freedom then yields a general Langevin framework for S that incorporates both deterministic and stochastic contributions from E. Normally ordered representations, such as the Glauber-Sudarshan P representation and its positive variant due to Drummond and Gardiner, lead to Langevin equations in which (i) non-Markovian effects emerge exclusively in the deterministic terms, via a memory kernel, and (ii) noise contributions vanish when E is initially in the vacuum state. To demonstrate the power of this framework, we address the paradigmatic problem of delayed coherent feedback, in which the system is driven by its own past state, and study its impact on the laser linewidth: we recover the narrowing observed well above threshold and predict an enhanced narrowing just above it. Crucially, the number of stochastic variables scales linearly with the system size, making the framework suitable for problems ranging from a few degrees of freedom to genuinely many-body systems. This opens the way to the systematic study of non-Markovian driven-dissipative quantum systems using the same analytical and numerical tools that have long made phase-space methods so successful in the Markovian regime.