Localization In Momentum Space Research Articles

Dynamical Stability in a Non-Hermitian Kicked Rotor Model

We investigate the quantum irreversibility and quantum diffusion in a non-Hermitian kicked rotor model for which the kicking strength is complex. Our results show that the exponential decay of Loschmidt echo gradually disappears with increasing the strength of the imaginary part of non-Hermitian driven potential, demonstrating the suppress of the exponential instability by non-Hermiticity. The quantum diffusion exhibits the dynamical localization in momentum space, namely, the mean square of momentum increases to saturation with time evolution, which decreases with the increase of the strength of the imaginary part of the kicking. This clearly reveals the enhancement of dynamical localization by non-Hermiticity. We find, both analytically and numerically, that the quantum state are mainly populated on a very few quasieigenstates with significantly large value of the imaginary part of quasienergies. Interestingly, the average value of the inverse participation ratio of quasieigenstates decreases with the increase of the strength of the imaginary part of the kicking potential, which implies that the feature of quasieigenstates determines the stability of wavepacket’s dynamics and the dynamical localization of energy diffusion.

Effective thermalization of a many-body dynamically localized Bose gas

Dynamical localization is the analog of Anderson localization in momentum space, where the system's energy saturates and the single-particle wave-functions are exponentially localized in momentum space. In the presence of interactions, in the context of a periodically kicked Bose gas, it has been argued that dynamical localization persists. Focusing on the Tonks (strongly interacting) regime, we show that the many-body dynamically localized phase is effectively thermal, a clear deviation from the breaking of ergodicity observed in standard many-body localized systems. We relate the effective temperature to the driving parameters, and thus quantitatively describe the loss of coherence at large distances in this phase. Contrary to the non-interacting case, the momentum distribution decays as a power-law at large momenta, characterized by an effectively thermal Tan's contact. This is a rare example where driving and many-body (dynamical) localization lead to an effectively ergodic state.

Universal principles of moiré band structures

Moiré materials provide a highly tunable environment for the realization of band structures with engineered physical properties. Specifically, moiré structures with Fermi surface flat bands—a synthetic environment for the realization of correlated phases—have moiré unit cells containing thousands of atoms and tantalizingly complex band structures. In this paper we show that statistical principles go a long way in explaining universal physical properties of these systems. Our approach builds on three conceptual elements: the presence of quantum chaos caused by the effective irregularity of the atomic configurations on short length scales, Anderson localization in momentum space, and the presence of approximate crystalline symmetries. Which of these principles dominates depends on material parameters such as the extension of the Fermi surface or the strength of the moiré lattice potential. The phenomenological consequences of this competition are predictions for the characteristic group velocity of moiré bands, a primary indicator for their average flatness. In addition to these generic features, we identify structures outside the statistical context, notably almost flat bands close to the extrema of the unperturbed spectra, and the celebrated zero energy ‘magic angle’ flat bands, where the latter require exceptionally fine tuned material parameters.

Gamma and neutron radiation effect on Compton profile of the multi-walled carbon nanotubes

In this study it has been investigated the effect of gamma and neutron radiation on the electron momentum distribution (Compton profile) of the Multiwall Carbon Nanotube (MWCNT) using a Compton spectrometer with an annular 241Am radioactive source. The samples were irradiated with 10 kGy (kGy) gamma rays, thermal and fast neutrons. The photons emitted from the 241Am source were incident on the irradiated samples and the scattered photons from the samples were recorded using HPGe detector. Scanning Electron Microscopy (SEM) and Transmission Electron Microscopy (TEM) results are also given to show the changes at the atomic structure of the MWCNT. The results clearly show that the Compton profile of multi-walled carbon nanotubes has changed with gamma and neutron irradiation. These changes are attributed to the delocalization of the electrons in the sample (in real space) which is clearly seen in the increased height of Compton profile of MWCNT at low momentum range (localization in momentum space) during sample’s irradiation.

Coherent backscattering and forward-scattering peaks in the quantum kicked rotor

We propose and analyze an experimental scheme using the quantum kicked rotor to observe the newly-predicted coherent forward scattering peak together with its long-known twin brother, the coherent backscattering peak. Contrary to coherent backscattering, which arises already under weak-localization conditions, coherent forward scattering is only triggered by Anderson or strong localization. So far, coherent forward scattering has not been observed in conservative systems with elastic scattering by spatial disorder. We propose to turn to the quantum kicked rotor, which has a long and succesful history as an accurate experimental platform to observe dynamical localization, i.e., Anderson localization in momentum space. We analyze the coherent forward scattering effect for the quantum kicked rotor by extensive numerical simulations, both in the orthogonal and unitary class of disordered quantum systems, and show that an experimental realization involving phase-space rotation techniques is within reach of state-of-the-art cold-atom experiments.

A non-Markovian Dissipative Maryland Model

The so-called Maryland model is a linear version of the quantum kicked rotor; it exhibits Anderson localization in momentum space. By turning the kicks into a Markovian stochastic process, the dynamics becomes a dissipative quantum process described by a discrete family of completely positive maps that allows to explicitly study the relation between divisibility of the maps and the degree of memory of the process.

A multi-state interferometer on an atom chip

Matter–wave interferometry is a powerful tool for high-precision measurements of the quantum properties of atoms, many-body phenomena and gravity. The most precise matter–wave interferometers exploit the excellent localization in momentum space and coherence of the degenerate gases. Further enhancement of the sensitivity and reduction of complexity are crucial conditions for the success and widening of their applications. Here we introduce a multi-state interferometric scheme that offers advances in both these aspects. The coherent coupling between Bose–Einstein condensates in different Zeeman states is used to generate high-harmonic output signals with an enhanced resolution and the maximum possible interferometric visibility. We demonstrate the realization of such an interferometer as a compact, easy to use, atom-chip device. This provides an alternative method for the measurement of the light–atom and surface–atom interactions and enables the application of multi-parameter sensing schemes in cold-atom interferometry.

Localization in momentum space of ultracold atoms in incommensurate lattices

We characterize the disorder induced localization in momentum space for ultracold atoms in one-dimensional incommensurate lattices, according to the dual Aubry-Andr\'e model. For low disorder the system is localized in momentum space, and the momentum distribution exhibits time-periodic oscillations of the relative intensity of its components. The behavior of these oscillations is explained by means of a simple three-mode approximation. We predict their frequency and visibility by using typical parameters of feasible experiments. Above the transition the system diffuses in momentum space, and the oscillations vanish when averaged over different realizations, offering a clear signature of the transition.

The dynamics of one-dimensional Bloch electrons in constant electric fields

We study the dynamics of a one-dimensional Bloch electron subjected to a constant electric field. The periodic potential is supposed to be less singular than the δ-like potential (Dirac comb). We give a rigorous proof of Ao’s result that for a large class of initial conditions (high momentum regime) there is no localization in momentum space. The proof is based on the mathematical substantiation of the two simplifying assumptions made in physical literature: the transitions between far away bands can be neglected and the transitions at the quasicrossing can be described by Landau–Zener-type formulas. Using the connection between the above model and the driven quantum ring (DQR) shown by Avron and Nemirovski, our results imply the increase of energy for weakly singular such DQR and appropiate initial conditions.

Classical and quantum scaling for localization of half-cycle pulse-driven Rydberg wave packets

Rydberg wave packets generated by a single half-cycle pulse (HCP) interacting with a stationary Rydberg state periodically localize within a narrow region in both momentum and coordinate space (i.e., phase space). This property is the key to shaping and manipulating wave packets. We investigate the dependence of this transient localization and focusing on the principal quantum number n and on the strength of the ultrashort HCP (``kick strength,'' $\ensuremath{\Delta}p).$ It is shown that the localization in momentum space of the wave packet, quantified by the momentum width, obeys a universal scaling rule which is controlled by an effective Planck constant ${\ensuremath{\Elzxh}}_{\mathrm{eff}}.$ Maximum focusing is reached in the classical limit $({\ensuremath{\Elzxh}}_{\mathrm{eff}}\ensuremath{\rightarrow}0).$

Electronic localization in momentum space during charge density wave phase transitions in 1 T-TaS 2

An investigation of the temperature dependence of the photoelectron angular distribution of the layered transition metal dichalcogenide 1 T-TaS 2 around the Fermi level reveals the strong influence of the charge density wave (CDW) phase transitions on the electronic states. Measurements of the k-resolved photoemission intensity distributions in the different phases allow an identification of photoemission intensity redistributions upon phase transitions in the entire k-space. Upon transition from the nearly commensurate to the commensurate CDW phase, the localization of lower Hubbard band electrons is directly illustrated.

Quantum chaos in channeling

The quantum eigen states of transverse motion in axial channel are studied. The wave functions have been founded using a proposed numerical relaxation procedure. The evolution of particle wave function with depth is calculated and compared with the evolution of classical particle flux. The quantum state localization in momentum space results in a difference of the two results. The correspondence with experiment is discussed.

Photoemission study of the surface states that pin the Fermi level at Si(100)2 x 1 surfaces.

Clean Si(100) surfaces of a heavily $n$-doped crystal have been studied with angle-resolved photoemission. A new surface state is observed at the Fermi level, only appearing close to the $\overline{\ensuremath{\Gamma}}$ and ${\overline{J}}^{\ensuremath{'}}$ points in the 2 \ifmmode\times\else\texttimes\fi{} 1 surface Brillouin zone. Because of the localization in momentum space it is concluded that the observed states are spatially extended and not related to localized defects. The emission at the Fermi level is assigned to the dispersion minima of an unoccupied surface-state band responsible for the pinning of the Fermi level at Si(100)2 \ifmmode\times\else\texttimes\fi{} 1 surfaces.