Dynamical tunneling of a Bose-Einstein condensate in periodically driven systems

Coherent destruction of tunnelling in a symmetrical double well driven by a series of time dependent δ functions

It is analytically and numerically shown that the coherent tunnelling between the individual wells of a symmetrical double well potential can be totally suppressed when it is driven by a periodic series of δ function in time, depending on the time period and strength of the δ function. We have applied time dependent perturbation theory to have an understanding over the process. In absence of any kind of perturbation, the average position of the particle makes a sinusoidal oscillation between two wells. With the application of a periodic δ function, the amplitude and the frequency of the oscillation both get modified. In this article we have explored how the frequency and strength of the applied perturbation controls the quantum dynamics of tunnelling and finally, how these parameters drive the system towards a complete stand still situation, which is described as coherent destruction of tunnelling.

Many Body Quantum Chaos

This editorial remembers Shmuel Fishman, one of the founding fathers of the research field “quantum chaos”, and puts into context his contributions to the scientific community with respect to the twelve papers that form the special issue.

Revival and death of oscillation under mean-field coupling: Interplay of intrinsic and extrinsic filtering

Mean-field diffusive coupling was known to induce the phenomenon of quenching of oscillations even in identical systems, where the standard diffusive coupling (without mean-field) fails to do so [Phys. Rev. E 89, 052912 (2014)PLEEE81539-375510.1103/PhysRevE.89.052912]. In particular, the mean-field diffusive coupling facilitates the transition from amplitude to oscillation death states and the onset of a nontrivial amplitude death state via a subcritical pitchfork bifurcation. In this paper, we show that an adaptive coupling using a low-pass filter in both the intrinsic and extrinsic variables in the coupling is capable of inducing the counterintuitive phenomenon of reviving of oscillations from the death states induced by the mean-field coupling. In particular, even a weak filtering of the extrinsic (intrinsic) variable in the mean-field coupling facilitates the onset of revival (quenching) of oscillations, whereas a strong filtering of the extrinsic (intrinsic) variable results in quenching (revival) of oscillations. Our results reveal that the degree of filtering plays a predominant role in determining the effect of filtering in the extrinsic or intrinsic variables, thereby engineering the dynamics as desired. We also extend the analysis to networks of mean-field coupled limit-cycle and chaotic oscillators along with the low-pass filters to illustrate the generic nature of our results. Finally, we demonstrate the observed dynamical transition experimentally to elucidate the robustness of our results despite the presence of inherent parameter fluctuations and noise.

Impact of Lattice Vibrations on the Dynamics of a Spinor Atom-Optics Kicked Rotor

We investigate the effect of amplitude and phase noise on the dynamics of a discrete-time quantum walk and its related evolution. Our findings underline the robustness of the motion with respect to these noise sources, and can explain the stability of quantum walks that has recently been observed experimentally. This opens the road to measure topological properties of an atom-optics double kicked rotor with an additional internal spin degree of freedom.

Quantum Walk in Momentum Space with a Bose-Einstein Condensate

We present a discrete-time, one-dimensional quantum walk based on the entanglement between the momentum of ultracold rubidium atoms (the walk space) and two internal atomic states (the "coin" degree of freedom). Our scheme is highly flexible and can provide a platform for a wide range of applications such as quantum search algorithms, the observation of topological phases, and the realization of walks with higher dimensionality. Along with the investigation of the quantum-to-classical transition, we demonstrate the distinctive features of a quantum walk and contrast them to those of its classical counterpart. Also, by manipulating either the walk or coin operator, we show how the walk dynamics can be steered or even reversed.

Applications of fidelity measures to complex quantum systems

We revisit fidelity as a measure for the stability and the complexity of the quantum motion of single-and many-body systems. Within the context of cold atoms, we present an overview of applications of two fidelities, which we call static and dynamical fidelity, respectively. The static fidelity applies to quantum problems which can be diagonalized since it is defined via the eigenfunctions. In particular, we show that the static fidelity is a highly effective practical detector of avoided crossings characterizing the complexity of the systems and their evolutions. The dynamical fidelity is defined via the time-dependent wave functions. Focusing on the quantum kicked rotor system, we highlight a few practical applications of fidelity measurements in order to better understand the large variety of dynamical regimes of this paradigm of a low-dimensional system with mixed regular-chaotic phase space.

Experimental Observation of Resonance-Assisted Tunneling

We present the first experimental observation of resonance-assisted tunneling, a wave phenomenon, where regular-to-chaotic tunneling is strongly enhanced by the presence of a classical nonlinear resonance chain. For this we use a microwave cavity made of oxygen free copper with the shape of a desymmetrized cosine billiard designed with a large nonlinear resonance chain in the regular region. It is opened in a region, where only chaotic dynamics takes place, such that the tunneling rate of a regular mode to the chaotic region increases the line width of the mode. Resonance-assisted tunneling is demonstrated by (i) a parametric variation and (ii) the characteristic plateau and peak structure towards the semiclassical limit.

Nonlinear resonance-assisted tunneling induced by microcavity deformation

Noncircular two-dimensional microcavities support directional output and strong confinement of light, making them suitable for various photonics applications. It is now of primary interest to control the interactions among the cavity modes since novel functionality and enhanced light-matter coupling can be realized through intermode interactions. However, the interaction Hamiltonian induced by cavity deformation is basically unknown, limiting practical utilization of intermode interactions. Here we present the first experimental observation of resonance-assisted tunneling in a deformed two-dimensional microcavity. It is this tunneling mechanism that induces strong inter-mode interactions in mixed phase space as their strength can be directly obtained from a separatrix area in the phase space of intracavity ray dynamics. A selection rule for strong interactions is also found in terms of angular quantum numbers. Our findings, applicable to other physical systems in mixed phase space, make the interaction control more accessible.