Dynamics Of Cold Atoms Research Articles

Three-Dimensional Nonlinear Dynamics of Cold Atoms in an Optical Lattice and its Realizations

Three-Dimensional Nonlinear Dynamics of Cold Atoms in an Optical Lattice and its Realizations

Chaotic Walking of Cold Atoms in a 2D Optical Lattice

Coherent dynamics of cold atoms in a 2D optical lattice with interfering laser beams is studied with account for internal and external degrees of freedom of an atom. A system of differential equations for coupled degrees of freedom obtained in the semiclassical approximation has regular and chaotic solutions depending on the atomic-field detuning from resonance. The Hamilton chaos is manifested in the form of chaotic Rabi oscillations and random walks of cold atoms in the lattice for relatively small resonance detunings. It is shown that the deterministic chaos appears as a result of jumps in the value of the electric dipole moment of an atom approaching the nodes of a 2D standing wave. This in turn causes a pseudorandom behavior of momenta of atoms and, as a consequence, their random walks in the absolutely rigid 2D optical lattice without any external modulation of its parameters. It is shown in numerical experiments with 106 atoms that their distributions over the lattice for different resonance detunings differ significantly. This fact can be used for detecting the effect of random walks of cold atoms in a real experiment by the absorption image method.

Loading Dynamics of Cold Atoms into a Hollow-Core Photonic Crystal Fiber

Cold atoms trapped and guided in hollow-core photonic crystal fibers provide a scalable diffraction-free setting for atom–light interactions for quantum technologies. However, due to the mismatch of the depth and spatial extension of the trapping potential from free space to the fiber, the number of cold atoms in the fiber is mainly determined by the loading process from free space to waveguide confinement. Here, we provide a numerical study of the loading dynamics of cold atoms into a hollow-core photonic crystal fiber. We use the Monte Carlo method to simulate the trajectories of an ensemble of cold atoms from free space trapping potential to optical potential inside a hollow-core fiber and calculate the temperature, loading efficiency, and geometry of the ensemble. We also study the noise sources that cause heating and a loss of atoms during the process. Our result could be used to design and optimize the loading process of cold atoms into a hollow-core fiber for cold atom experiments.

Patterns with Cold Atoms in a Square Optical Lattice

We consider coherent dynamics of cold atoms in a square optical lattice without interference between counter-propagating laser beams. The dynamics is treated within the framework of semi-classical approximation, taking into account a coupling between the atom internal and external degrees of freedom. The corresponding set of equations of motion has been found before to be regular or chaotic in dependence on the values of the control parameters, the detuning between the atomic transition and laser frequencies, and the atom recoil frequency. In this paper, we carry out numerical experiments on spreading of cold atomic clouds in the lattice under different values of the detuning, keeping the recoil frequency to be fixed. The distributions of atoms differ strongly providing a way to control atomic transport by tuning just a single control parameter called the detuning. It is possible to drive cold atoms through different regimes of translational motion, from regular ballistic flights to chaotic walking. A possibility to observe the effect of chaotic walking in real experiments is discussed.

Dissipative dynamics of cold atoms in an optical lattice

We numerically investigate the quantum effects of cold atoms in a one-dimensional driven optical lattice in the presence of distance-selective dissipation and external driving. The combination of distance-selective dissipation, external driving, on-site interaction and tunneling dominates the system dynamics. The mean-field theory is used to approximate the system. In order to analyze the system dynamics, we calculate the relative density of atoms on each site and the standard deviation of relative density. Furthermore, the influence laws of environmental factors on the system dynamics are found out by the numerical simulation. Especially, we study the dissipative dynamics of the system under a time varying external driving. The results of the study are effectively applied to manipulate the distribution of cold atoms in an optical lattice and drive the system to the desired quantum state.

Weak Chaos with Cold Atoms in a 2D Optical Lattice with Orthogonal Polarizations of Laser Beams

We study theoretically coherent dynamics of cold atoms in the near-resonant 2D optical lattice with orthogonal polarizations, taking into account a coupling between the atomic internal (electronic) and external (translational) degrees of freedom. We show that in the semiclassical approximation this dynamics may be regular or chaotic in dependence on the values of the detuning between the electric-dipole transition and the laser field frequencies. Chaos manifests itself both in the Rabi oscillations and in the translational motion at comparatively small absolute values of the detuning. The center-of-mass motion in the chaotic regime resembles the random walk of atoms in a 2D lattice which is an absolutely rigid one. Chaos is quantified by the values of the maximal Lyapunov exponent and is shown to be weaker as compared with the case of cold atoms in a 1D lattice. In fact, chaos appears at the time moments when the atom crosses 1D or 2D nodes of the lattice potential when its induced electric dipole moment changes suddenly in a random-like manner.

Fluorescence dynamics of an ensemble of cold atoms

We have calculated the fluorescence dynamics of cold atoms excited by pulsed radiation. We have considered both Radon-Nikodym spectral method and multi-stage relaxation model describing collective effects in cold atomic gases. Relaxation times and amplitudes both at short times (superradiance) and long times (subradiance) have seen obtained.

Carrier thermometry of cold ytterbium atoms in an optical lattice clock

The ultracold atomic gas serving as the quantum reference is a key part of an optical lattice clock, and the temperature of atoms in the optical lattice affects the uncertainty and instability of the optical lattice clocks. Since the carrier spectrum of the clock transition in the lattices reflects the thermal dynamics of cold atoms, the temperature of atoms can be extracted from the carrier spectrum in a non-magic wavelength lattice of ytterbium optical clocks. Furthermore, the temperatures obtained from the carrier spectra are in good agreement with the results obtained by the time-of-flight method and thermometry based on the sideband spectrum. In addition, the heating effects caused by the lattice laser are studied on the basis of the sample temperatures.

Theory of a Quantum Scanning Microscope for Cold Atoms.

We propose and analyze a scanning microscope to monitor "live" the quantum dynamics of cold atoms in a cavity QED setup. The microscope measures the atomic density with subwavelength resolution via dispersive couplings to a cavity and homodyne detection within the framework of continuous measurement theory. We analyze two modes of operation. First, for a fixed focal point the microscope records the wave packet dynamics of atoms with time resolution set by the cavity lifetime. Second, a spatial scan of the microscope acts to map out the spatial density of stationary quantum states. Remarkably, in the latter case, for a good cavity limit, the microscope becomes an effective quantum nondemolition device, such that the spatial distribution of motional eigenstates can be measured backaction free in single scans, as an emergent quantum nondemolition measurement.

Symmetry Protected Dynamical Symmetry in the Generalized Hubbard Models

In this Letter we present a theorem on the dynamics of the generalized Hubbard models. This theorem shows that the symmetry of the single-particle Hamiltonian can protect a kind of dynamical symmetry driven by the interactions. Here the dynamical symmetry refers to the phenomenon that time evolution of certain observables are symmetric between the repulsive and attractive Hubbard models. We demonstrate our theorem with three different examples in which the symmetry involves bipartite lattice symmetry, reflection symmetry, and translation symmetry, respectively. Each of these examples relates to one recent cold atom experiment on the dynamics in the optical lattices where such a dynamical symmetry is manifested. These experiments include expansion dynamics of cold atoms, chirality of atomic motion within a synthetic magnetic field, and melting of charge-density-wave order. Therefore, our theorem provides a unified view of these seemingly disparate phenomena.

Quantum–classical correspondence in chaotic dynamics of laser-driven atoms

This paper is a review article on some aspects of quantum–classical correspondence in chaotic dynamics of cold atoms interacting with a standing-wave laser field forming an optical lattice. The problem is treated from both (semi)classical and quantum points of view. In both approaches, the interaction of an atomic electic dipole with the laser field is treated quantum mechanically. Translational motion is described, at first, classically (atoms are considered to be point-like objects) and then quantum mechanically as a propagation of matter waves. Semiclassical equations of motion are shown to be chaotic in the sense of classical dynamical chaos. Point-like atoms in an absolutely deterministic and rigid optical lattice can move in a random-like manner demonstrating a chaotic walking with typical features of classical chaos. This behavior is explained by random-like ‘jumps’ of one of the atomic internal variable when atoms cross nodes of the standing wave and occurs in a specific range of the atom-field detuning. When treating atoms as matter waves, we show that they can make nonadiabatic transitions when crossing the standing-wave nodes. The point is that atomic wave packets split at each node in the same range of the atom-field detuning where the classical chaos occurs. The key point is that the squared amplitude of those semiclassical ‘jumps’ equal to the quantum Landau–Zener parameter which defines the probability of nonadiabatic transitions at the nodes. Nonadiabatic atomic wave packets are much more complicated compared to adiabatic ones and may be called chaotic in this sense. A few possible experiments to observe some manifestations of classical and quantum chaos with cold atoms in horizontal and vertical optical lattices are proposed and discussed.

Infrared dynamics of cold atoms on hot graphene membranes

We study the infrared dynamics of low-energy atoms interacting with a sample of suspended graphene at finite temperature. The dynamics exhibits severe infrared divergences order by order in perturbation theory as a result of the singular nature of low-energy flexural phonon emission. Our model can be viewed as a two-channel generalization of the independent boson model with asymmetric atom-phonon coupling. This allows us to take advantage of the exact non-perturbative solution of the independent boson model in the stronger channel while treating the weaker one perturbatively. In the low-energy limit, the exact solution can be viewed as a resummation (exponentiation) of the most divergent diagrams in the perturbative expansion. As a result of this procedure, we obtain the atom's Green function which we use to calculate the atom damping rate, a quantity equal to the quantum sticking rate. A characteristic feature of our results is that the Green's function retains a weak, infrared cutoff dependence that reflects the reduced dimensionality of the problem. As a consequence, we predict a measurable dependence of the sticking rate on graphene sample size. We provide detailed predictions for the sticking rate of atomic hydrogen as a function of temperature and sample size. The resummation yields an enhanced sticking rate relative to the conventional Fermi golden rule result (equivalent to the one-loop atom self-energy), as higher-order processes increase damping at finite temperature.

Lévy walks

L\'evy walks are random walks in which the distribution of step length does not decay exponentially and the velocity of the moving particle is finite. Building on earlier concepts, they reconcile anomalously fast diffusion with a finite propagation speed and have applications that range from basic statistical mechanics and transport theory to optics, cold atom dynamics, and biophysics. This review gives an introduction to this important class of models and discusses applications in both physics and biology.

Publisher's Note: Phase space tomography of cold-atom dynamics in a weakly corrugated potential [Phys. Rev. A90, 033620 (2014)

Publisher's Note: Phase space tomography of cold-atom dynamics in a weakly corrugated potential [Phys. Rev. A<b>90</b>, 033620 (2014)

Phase space tomography of cold-atom dynamics in a weakly corrugated potential

We demonstrate tomographic reconstruction of the phase space distribution of atoms oscillating in a harmonic trap with weak potential corrugation caused by nanoscale imperfections in an atom chip. We find that deformations in these distributions are highly sensitive to anharmonic components of the potential. They are explained in terms of angular velocity dispersion of isoenergetic phase space trajectories. We show that the method is applicable for probing classical and quantum dynamics of cold atoms, and we note its importance for future technological applications.

Landauer, Kubo, and microcanonical approaches to quantum transport and noise: A comparison and implications for cold-atom dynamics

We compare the Landauer, Kubo, and microcanonical [J. Phys.: Condens. Matter 16, 8025 (2005)] approaches to quantum transport for the average current, the entanglement entropy, and the semiclassical full-counting statistics (FCS). Our focus is on the applicability of these approaches to isolated quantum systems such as ultracold atoms in engineered optical potentials. For two lattices connected by a junction, we find that the current and particle number fluctuations from the microcanonical approach compare well with the values predicted by the Landauer formalism and FCS assuming a binomial distribution. However, we demonstrate that well-defined reservoirs (i.e., particles in Fermi-Dirac distributions) are not present for a substantial duration of the quasi-steady state. Thus, on the one hand, the Landauer assumption of reservoirs and/or inelastic effects is not necessary for establishing a quasi-steady state. Maintaining such a state indefinitely requires an infinite system, and in this limit well-defined Fermi-Dirac distributions can occur. On the other hand, as we show, the existence of a finite speed of particle propagation preserves the quasi-steady state irrespective of the existence of well-defined reservoirs. This indicates that global observables in finite systems may be substantially different from those predicted by an uncritical application of the Landauer formalism, with its underlying thermodynamic limit. Therefore, the microcanonical formalism which is designed for closed, finite-size quantum systems seems more suitable for studying particle dynamics in ultracold atoms. Our results highlight both the connection and differences with more traditional approaches to calculating transport properties in condensed matter systems, and will help guide the way to their simulations in cold-atom systems.

Controlling mobility via rapidly oscillating time-periodic stimulus

To address the dynamics of a Brownian particle on a periodic symmetric substrate under high-frequency periodic forcing with a vanishing time average, we construct an effective Langevin dynamics by invoking Kapitza–Landau time window. Our result is then exploited to simulate the mobility both for original and effective dynamics which are in good agreement with theoretical predictions. This close agreement and the enhancement of mobility are very robust against the tailoring of amplitude-to-frequency ratio which substantiates the correctness of our calculation. Present results may be illuminating for understanding the dynamics of cold atoms in electromagnetic fields.

Effective dynamics of cold atoms flowing in two ring-shaped optical potentials with tunable tunneling

We study the current dynamics of coupled atomic condensates flowing in two ring-shaped optical potentials. We provide a specific setup where the ring-ring coupling can be tuned in experimentally feasible way. It is demonstrated that the imaginary time effective action of the system in a weak coupling regime provides a two-level-system-dynamics for the phase slip across the two rings. Through two-mode Gross- Pitaevskii mean field equations, the real time dynamics of the population imbalance and the phase difference between of the two condensates is thoroughly analyzed analytically, as function of the relevant physical parameters of the system. In particular, we find that the macroscopic quantum self trapping phenomenon is induced in the system if the flowing currents assume a non vanishing difference.

Shaking-induced dynamics of cold atoms in magnetic traps

We describe an experiment in which cold rubidium atoms, confined in an elongated magnetic trap, are excited by transverse oscillation of the trap centre. The temperature after excitation exhibits resonance as a function of the driving frequency. We measure these resonances at several different trap frequencies. In order to interpret the experiments, we develop a simple model that incorporates both collisions between atoms and the anharmonicity of the real three-dimensional trapping potential. As well as providing a precise connection between the transverse harmonic oscillation frequency and the temperature resonance frequency, this model gives insight into the heating and loss mechanisms, and into the dynamics of driven clouds of cold trapped atoms.

Fast closed-loop optimal control of ultracold atoms in an optical lattice

We present experimental evidence of the successful closed-loop optimization of the dynamics of cold atoms in an optical lattice. We optimize the loading of an ultracold atomic gas minimizing the excitations in an array of one-dimensional tubes (3D-1D crossover) and we perform an optimal crossing of the quantum phase-transition from a Superfluid to a Mott-Insulator in a three-dimensional lattice. In both cases we enhance the experiment performances with respect to those obtained via adiabatic dynamics, effectively speeding up the process by more than a factor three while improving the quality of the desired transformation.