Nonlinear coherent dynamics of an atom in an optical lattice

We consider a simple model of the lossless interaction between a two-level single atom and a standing-wave single-mode laser field which creates a one-dimensional optical lattice. The internal dynamics of the atom is governed by the laser field, which is treated as classical with a large number of photons. The center-of-mass classical atomic motion is governed by the optical potential and the internal atomic degrees of freedom. The resulting Hamilton-Schrö dinger equations of motion are a five-dimensional nonlinear dynamical system with two integrals of motion, and the total atomic energy and the Bloch vector length are conserved during the interaction. In our previous papers, the motion of the atom has been shown to be regular or chaotic (in the sense of exponential sensitivity to small variations of the initial conditions and/or the system’s control parameters) depending on the values of the control parameters, atom-field detuning, and recoil frequency. At the exact atom-field resonance, the exact solutions for both the external and internal atomic degrees of freedom can be derived. The center-of-mass motion does not depend in this case on the internal variables, whereas the Rabi oscillations of the atomic inversion is a frequency-modulated signal with the frequency defined by the atomic position in the optical lattice. We study analytically the correlations between the Rabi oscillations and the center-of-mass motion in two limiting cases of a regular motion out of the resonance: (1) far-detuned atoms and (2) rapidly moving atoms. This paper is concentrated on chaotic atomic motion that may be quantified strictly by positive values of the maximal Lyapunov exponent. It is shown that an atom, depending on the value of its total energy, can either oscillate chaotically in a well of the optical potential, or fly ballistically with weak chaotic oscillations of its momentum, or wander in the optical lattice, changing the direction of motion in a chaotic way. In the regime of chaotic wandering, the atomic motion is shown to have fractal properties. We find a useful tool to visualize complicated atomic motion-Poincaré mapping of atomic trajectories in an effective three-dimensional phase space onto planes of atomic internal variables and momentum. The Poincaré mappings are constructed using the translational invariance of the standing laser wave. We find common features with typical nonhyperbolic Hamiltonian systems-chains of resonant islands of different sizes imbedded in a stochastic sea, stochastic layers, bifurcations, and so on. The phenomenon of the atomic trajectories sticking to boundaries of regular islands, which should have a great influence on atomic transport in optical lattices, is found and demonstrated numerically.     

Dissipative quantum dynamics of bosonic atoms in a shallow 1D optical lattice

We theoretically study the dipolar motion of bosonic atoms in a very shallow, strongly confined 1D optical lattice using the parameters of the recent experiment [C. D. Fertig, Phys. Rev. Lett. 94, 120403 (2005)]. We find that, due to momentum uncertainty, a small, but non-negligible, atom population occupies the unstable velocity region of the corresponding classical dynamics, resulting in the observed dissipative atom transport. This population is generated even in a static vapor, due to quantum fluctuations which are enhanced by the lattice and the confinement, and is not notably affected by the motion of atoms or finite temperature.     

Single atom transistor in a 1D optical lattice

We propose a scheme utilizing a quantum interference phenomenon to switch the transport of atoms in a 1D optical lattice through a site containing an impurity atom. The impurity represents a qubit which in one spin state is transparent to the probe atoms, but in the other acts as a single atom mirror. This allows a single-shot quantum nondemolition measurement of the qubit spin.     

Anomalous properties of optical lattice vibrations in HgTe: A double-well model of the lattice potential for a Hg atom

A double-well potential model has been proposed for a Hg atom in the HgTe crystal lattice in which the Hg atom either occupies the center of the anion tetrahedron or is located at the off-center position. The fundamental TO mode of the Hg-Te vibrations at a frequency of ∼120 cm⁻¹ corresponds to the vibrations of the off-center Hg atom, and the additional mode is associated with the vibrations of the Hg atom located at the center of the anion tetrahedron. The model has made it possible to explain both the strong increase in the intensity of the additional mode with increasing temperature, which, at T = 300 K, is comparable to the intensity of the fundamental mode, and the anomalous change (decrease) in the damping parameter of the fundamental TO mode with increasing pressure, which corresponds to a more ordered crystal structure.     

光晶格中的冷原子

光晶格是一种人造光晶体,它是由反向传播激光束干涉形成的周期性势阱构成的。光晶格的周期、势深等参量可以通过调节激光的强度和频率等来准确控制。作为一个纯净可控的实验平台,光晶格已经逐渐成长为模拟多体系统的最便利的工具之一。文章对光晶格中冷原子进行了简单的介绍,重点阐述了玻色—爱因斯坦凝聚、激光冷却、光晶格和量子相变等内容。     

Cold atom dynamics in non-Abelian gauge fields

The dynamics of ultracold neutral atoms subject to a non-Abelian gauge field is investigated. In particular we analyze in detail a simple experimental scheme to achieve a constant, but non-Abelian gauge field, and discuss in the frame of this gauge field the non-Abelian Aharanov–Bohm effect. In the last part of this paper, we discuss intrinsic non-Abelian effects in the dynamics of cold atomic wavepackets. PACS 03.75.Hh     

Controllable electron dynamics in a finite-size quantum well lattice

The nonstationary electron dynamics in a quantum well lattice is considered. We investigate the influence of quasi-constant electric field applied to the system in addition to variable electric field periodic in time. It is shown that various types of controllable motion of an electron density in the lattice can be realized.     

Mesoscopic quantum coherence in an optical lattice

We observe the quantum coherent dynamics of atomic spinor wave packets in the double-well potentials of a far-off-resonance optical lattice. With appropriate initial conditions the system Rabi oscillates between the left and right localized states of the ground doublet, and at certain times the wave packet corresponds to a coherent superposition of these mesoscopically distinct quantum states. The atom/optical double-well potential is a flexible and powerful system for further study of quantum coherence, quantum control, and the quantum/classical transition.     

Expansion of a quantum gas released from an optical lattice

We analyze the interference pattern produced by ultracold atoms released from an optical lattice, commonly interpreted as the momentum distributions of the trapped quantum gas. We show that for finite times of flight the resulting density distribution can, however, be significantly altered, similar to a near-field diffraction regime in optics. We illustrate our findings with a simple model and realistic quantum Monte Carlo simulations for bosonic atoms and compare the latter to experiments.     

Cold atom simulation of interacting relativistic quantum field theories

We demonstrate that Dirac fermions self-interacting or coupled to dynamic scalar fields can emerge in the low energy sector of designed bosonic and fermionic cold atom systems. We illustrate this with two examples defined in two spacetime dimensions. The first one is the self-interacting Thirring model. The second one is a model of Dirac fermions coupled to a dynamic scalar field that gives rise to the Gross-Neveu model. The proposed cold atom experiments can be used to probe spectral or correlation properties of interacting quantum field theories thereby presenting an alternative to lattice gauge theory simulations.     

Strong laser–atom interaction as a quantum kicked dynamics

It is proved that an atom is periodically kicked under the effect of a strong laser field, obtaining in this way a connection with quantum chaos. Applicability hints of the theory to Rydberg atoms in a strong microwave field are also given.     

Bright soliton dynamics in Fourier synthesized optical lattice

We consider the dynamics of bright solitons in one dimensional Bose Einstein condensate with spin orbit coupling and trapped by an optical lattice potential. We mainly focus on the effects of the spin orbit coupling, Rabi coupling and detuning parameter on the soliton dynamics. The solution of the coupled Gross Pitaevskii equation is performed with the help of the variational and numerical methods for various parameters. The population imbalance and the center of mass motion show different dynamic behaviors depending on the parameters. We also obtain traveling bright solitons related with a given finite initial momentum.     

Phase controllable dynamical localization of a quantum particle in a driven optical lattice

The Dunlap–Kenkre (DK) result states that dynamical localization of a driven quantum particle in a periodic lattice happens when the ratio of the field magnitude to the field frequency of the diagonal drive is a root of the ordinary Bessel function of order 0. This has been experimentally verified. A generalization of the DK result is presented here. The hitherto considered DK model contains only the diagonal forcing. In the present extended version of the DK model we consider both off-diagonal and diagonal driving fields with different frequencies and a definite relative phase between them. We analytically show that new dynamical localizations conditions exist where an important role is played by the relative phase. In appropriate limits our results reduce to DK result.     

Oscillatory stability of quantum droplets in PT-symmetric optical lattice

We study stability and collisions of quantum droplets(QDs) forming in a binary bosonic condensate trapped in parity-time (PT)-symmetric optical lattices. It is found that the stability of QDs in the PT-symmetric system depends strongly on the values of the imaginary part W_0 of the PT-symmetric optical lattices, self-repulsion strength g, and the condensate norm N. As expected,the PT-symmetric QDs are entirely unstable in the broken PT-symmetric phase. However, the PT-symmetric QDs exhibit oscillatory stability with the increase of N and g in the unbroken PT-symmetric phase. Finally, collisions between PT-symmetric QDs are considered. The collisions of droplets with unequal norms are completely different from that in free space. Besides, a stable PT-symmetric QDs collides with an unstable ones tend to merge into breathers after the collision.     

Coherent optical spectroscopy due to lattice vibrations in a single quantum dot

We theoretically investigate a coherent optical spectroscopy of a strongly driven quantum dot without and with the coupling between exciton and phonons. In the absence of this coupling, we achieve the experimental results obtained by Xu et al. [Science 317, 929 (2007)]. However, while taking this coupling into account, we observe some new features in the probe absorption spectrum including two sharp phonon-induced sidebands. Our results also demonstrate that the lifetime of phonons will play an important role in this coherent spectroscopy.     

Anistropic Born-Mayer potential in lattice dynamics of vanadium

Summary A microscopic theory of the lattice dynamics of the transition metal vanadium is developed based on the Animalu's transition metal model potential (TMMP). The Born-Mayer potential associated with the distribution of the transition metald-electrons is treated as anisotropic. Good agreement with experimental phonon dispersion curves is obtained particularly with regards to symmetry and crossover of longitudinal branches in the [111] direction.

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Riassunto Si sviluppa una teoria microscoopica della dinamica reticolare del metallo di transizione vanadio basato sul modello di potenziale di transizione metallico (TMMP) di Animalu. Il potenziale di Born-Mayer associato con la distribuzione degli elettronid dei metalli di transizione è trattato come anisotropico. Si ottiene un buon accordo con le curve sperimentali di dispersione dei fononi particolarmente riguardo alla simmetria e l'incrocio delle ramificazioni longitudinali nella direzione [111].

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Резюме Развивается микроскопическая теория динамики решетки переходного металла ванадия, которая основана на модельном потенциале Анималу для переходного металла. Потенциал Борна-Майера, связанный с распределениемd-электронов в переходном металле, является анизотропным. Что касается симметрии и кроссовера продолных ветвей в направлении [111], получается хорошее согласие с экспериментальными дисперсионными кривыми фононов.

     

Phase control of nonadiabaticity-induced quantum chaos in an optical lattice

The qualitative nature (i.e., integrable vs chaotic) of the translational dynamics of a three-level atom in an optical lattice is shown to be controllable by varying the relative laser phase of two standing-wave lasers. Control is explained in terms of the nonadiabatic transition between optical potentials and the corresponding regular-to-chaotic transition in mixed classical-quantum dynamics. The results are of interest to both areas of coherent control and quantum chaos.     

Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm

We present an algorithm to study mixed-state dynamics in one-dimensional quantum lattice systems. The algorithm can be used, e.g., to construct thermal states or to simulate real time evolution given by a generic master equation. Its two main ingredients are (i) a superoperator renormalization scheme to efficiently describe the state of the system and (ii) the time evolving block decimation technique to efficiently update the state during a time evolution. The computational cost of a simulation increases significantly with the amount of correlations between subsystems, but it otherwise depends only linearly on the system size. We present simulations involving quantum spins and fermions in one spatial dimension.     

Controlling chaos in a Bose-Einstein condensate loaded into a moving optical lattice potential

The spatial structure of a Bose-Einstein condensate loaded into an optical lattice potential is investigated, and spatially chaotic distributions of the condensates are revealed. By means of changing of the s-wave scattering length with a Feshbach resonance, the chaotic behavior can be well controlled to enter into periodicity. Numerical simulation shows that there are different periodic orbits according to different s-wave scattering lengths only if the maximal Lyapunov exponent of the system is negative. The text was submitted by the authors in English.