Atom Waves in Crystals of Light

Localization Properties of a Quasiperiodic Ladder under Physical Gain and Loss: Tuning of Critical Points, Mixed-Phase Zone and Mobility Edge

We explore the localization properties of a double-stranded ladder within a tight-binding framework where the site energies of different lattice sites are distributed in the cosine form following the Aubry-André-Harper (AAH) model. An imaginary site energy, which can be positive or negative, referred to as physical gain or loss, is included in each of these lattice sites which makes the system a non-Hermitian (NH) one. Depending on the distribution of imaginary site energies, we obtain balanced and imbalanced NH ladders of different types, and for all these cases, we critically investigate localization phenomena. Each ladder can be decoupled into two effective one-dimensional (1D) chains which exhibit two distinct critical points of transition from metallic to insulating (MI) phase. Because of the existence of two distinct critical points, a mixed-phase (MP) zone emerges which yields the possibility of getting a mobility edge (ME). The conducting behaviors of different energy eigenstates are investigated in terms of inverse participation ratio (IPR). The critical points and thus the MP window can be selectively controlled by tuning the strength of the imaginary site energies which brings a new insight into the localization aspect. A brief discussion on phase transition considering a multi-stranded ladder was also given as a general case, to make the present communication a self-contained one. Our theoretical analysis can be utilized to investigate the localization phenomena in different kinds of simple and complex quasicrystals in the presence of physical gain and/or loss.

Perfectly asymmetric Raman-Nath diffraction in disordered atomic gratings

We investigate the effects of geometrical and structural disorders on perfectly asymmetric diffraction (PAD) in Raman-Nath regime. The two types of disorders are realized by introducing random fluctuations in the position and width of one-dimensional (1D) driven atomic lattices. Raman-Nath diffraction is modified differently with respect to the geometrical and structural disorders. It is shown that the PAD is observed with a certain strength range of geometrical disorder, exceeding which it can be destroyed, while the PAD is rather robust against structural disorder. The different behaviors originate from the disorder-induced random variations of the spatial phase shifts of the standing-wave (SW) coupling field and atomic lattices with Gaussian profile. Furthermore, we find that, in the presence of geometrical disorder, the PAD is more susceptible to correlated disorder than to uncorrelated disorder. Our scheme may be useful for understanding the effects of disorder on the diffraction of light and matter waves in disordered potentials..

Transparent lattices and their solitary waves

We provide a family of transparent tight-binding models with nontrivial potentials and site-dependent hopping parameters. Their feasibility is discussed in electromagnetic resonators, dielectric slabs, and quantum-mechanical traps. In the second part of the paper, the arrays are obtained through a generalization of supersymmetric quantum mechanics in discrete variables. The formalism includes a finite-difference Darboux transformation applied to the scattering matrix of a periodic array. A procedure for constructing a hierarchy of discrete Hamiltonians is indicated and a particular biparametric family is given. The corresponding potentials and hopping functions are identified as solitary waves, pointing to a discrete spinorial generalization of the Korteweg-deVries family.

Reconfigurable directional lasing modes in cavities with generalized PT symmetry

We introduce a new family of generalized PT-symmetric cavities that involve gyrotropic elements and support reconfigurable unidirectional lasing modes. We derive conditions for which these modes exist and investigate a simple electronic circuit that experimentally demonstrates their feasibility in the radio-frequency domain.

Holographic Gratings for Slow-Neutron Optics

Recent progress in the development of holographic gratings for neutron-optics applications is reviewed. We summarize the properties of gratings recorded in deuterated (poly)methylmethacrylate, holographic polymer-dispersed liquid crystals and nanoparticle-polymer composites revealed by diffraction experiments with slow neutrons. Existing and anticipated neutron-optical instrumentations based on holographic gratings are discussed.

Exceptional points and non-Hermitian degeneracy of resonances in a two-channel model

We study the mixing and degeneracy of two unbound energy eigenstates (resonances) in a two coupled channel model of scattering and reactions. We derive the necessary and sufficient conditions for existence of an exceptional point in the extended spectrum of bound and resonance energy eigenvalues in this model and show that these are not the same as in the single channel case. When these conditions are satisfied, in the complex energy plane, the two simple resonance poles of the scattering matrix merge into one double pole at the exceptional point. In parameter space, the surface of the eigenenergies has a branch point of square root type and branch cuts in its real and imaginary parts that start at the exceptional point and extend in opposite directions. The rich phenomenology of crossings and anticrossings of energies and widths of the doublet of unbound states, as well as the changes of identity of the poles of the scattering matrix observed when one control parameter is varied while the other is kept constant, is fully explained in terms of sections of the eigenenergy surfaces.

PT-symmetric wave Chaos

We study a new class of chaotic systems with dynamical localization, where gain or loss mechanisms break the Hermiticity, while allowing for parity-time (PT) symmetry. For a value gamma{PT} of the gain or loss parameter the spectrum undergoes a spontaneous phase transition from real (exact phase) to complex values (broken phase). We develop a one parameter scaling theory for gamma{PT}, and show that chaos assists the exact PT phase. Our results have applications to the design of optical elements with PT symmetry.

Observation of an exceptional point in a chaotic optical microcavity

We present spectroscopic observation of an exceptional point or the transition point between mode crossing and avoided mode crossing of neighboring quasieigenmodes in a chaotic optical microcavity of a large size parameter. The transition to the avoided mode crossing was impeded until the degree of deformation exceeded a threshold deformation owing to the system's openness also enhanced by the shape deformation. As a result, a singular topology was observed around the exceptional point on the eigenfrequency surfaces, resulting in fundamental inconsistency in mode labeling.

Observation of PT-symmetry breaking in complex optical potentials

In 1998, Bender and Boettcher found that a wide class of Hamiltonians, even though non-Hermitian, can still exhibit entirely real spectra provided that they obey parity-time requirements or PT symmetry. Here we demonstrate experimentally passive PT-symmetry breaking within the realm of optics. This phase transition leads to a loss induced optical transparency in specially designed pseudo-Hermitian guiding potentials.

Beam dynamics in PT symmetric optical lattices

The possibility of parity-time (PT) symmetric periodic potentials is investigated within the context of optics. Beam dynamics in this new type of optical structures is examined in detail for both one- and two-dimensional lattice geometries. It is shown that PT periodic structures can exhibit unique characteristics stemming from the nonorthogonality of the associated Floquet-Bloch modes. Some of these features include double refraction, power oscillations, and eigenfunction unfolding as well as nonreciprocal diffraction patterns.

Exceptional points in atomic spectra

We report the existence of exceptional points for the hydrogen atom in crossed magnetic and electric fields in numerical calculations. The resonances of the system are investigated and it is shown how exceptional points can be found by exploiting characteristic properties of the degeneracies, which are branch point singularities. A possibility for the observation of exceptional points in an experiment with atoms is proposed.

Rabi oscillations at exceptional points in microwave billiards

We experimentally investigated the decay behavior with time t of resonances near and at exceptional points, where two complex eigenvalues and also the associated eigenfunctions coalesce. The measurements were performed with a dissipative microwave billiard, whose shape depends on two parameters. The t2 dependence predicted at the exceptional point on the basis of a two-state matrix model could be verified. Outside the exceptional point the predicted Rabi oscillations, also called quantum echoes in this context, were detected.

Non-Hermitian polarizers: a biorthogonal analysis

The non-Hermitian operators of the ideal nonorthogonal multilayer optical polarizers are spectrally analyzed in the framework of skew-angular biorthonormal vector bases. It is shown that these polarizers correspond to skew projectors and their operators are generated by skew projectors, exactly as the canonical ideal polarizers correspond to Hermitian projectors. Thus the common feature of all the polarizers (Hermitian and non-Hermitian) is that their "nuclei" are (orthogonal or skew) projectors--the generating projectors. It is shown that if these nonorthogonal polarizers are looked upon as variable devices, two kinds of degeneracy may occur for suitable values of the inner parameter of the device: The corresponding operators may become normal (more precisely, Hermitian) or, on the contrary, very pathological--defective and singular. In the first case their eigenvectors and biorthogonal conjugate eigenvectors collapse into a unique pair of eigenvectors; in the second case their eigenvectors (as well as their biorthogonal conjugates) collapse into a single vector.

Observation of nonspreading wave packets in an imaginary potential

We propose and experimentally demonstrate a method to prepare a nonspreading atomic wave packet. Our technique relies on a spatially modulated absorption constantly chiseling away from an initially broad de Broglie wave. The resulting contraction is balanced by dispersion due to Heisenberg's uncertainty principle. This quantum evolution results in the formation of a nonspreading wave packet of Gaussian form with a spatially quadratic phase. Experimentally, we confirm these predictions by observing the evolution of the momentum distribution. Moreover, by employing interferometric techniques, we measure the predicted quadratic phase across the wave packet. Nonspreading wave packets of this kind also exist in two space dimensions and we can control their amplitude and phase using optical elements.

Quantum kinetic energy densities: An operational approach

We propose and investigate a procedure to measure, at least in principle, a positive quantum version of the local kinetic energy density. This procedure is based, under certain idealized limits, on the detection rate of photons emitted by moving atoms which are excited by a localized laser beam. The same type of experiment, but in different limits, can also provide other non-positive-definite versions of the kinetic energy density. A connection with quantum arrival time distributions is discussed.

Atomic interferometer with amplitude gratings of light and its applications to atom based tests of the equivalence principle

We have developed a matter wave interferometer based on the diffraction of atoms from effective absorption gratings of light. In a setup with cold rubidium atoms in an atomic fountain the interferometer has been used to carry out tests of the equivalence principle on an atomic basis. The gravitational acceleration of the two isotopes 85Rb and 87Rb was compared, yielding a difference Deltag/g=(1.2+/-1.7)x10(-7). We also perform a differential free fall measurement of atoms in two different hyperfine states, and obtained a result of Deltag/g=(0.4+/-1.2)x10(-7).

Observation of a chiral state in a microwave cavity

A microwave experiment has been realized to measure the phase difference of the oscillating electric field at two points inside the cavity. The technique has been applied to a dissipative resonator which exhibits a singularity-called exceptional point-in its eigenvalue and eigenvector spectrum. At the singularity, two modes coalesce with a phase difference of pi/2. We conclude that the state excited at the singularity has a definitive chirality.

Localization transition in incommensurate non-Hermitian systems

A class of one-dimensional lattice models with an incommensurate complex potential V(theta)=2[lambda(r) cos(theta)+i(lambda)(i) sin(theta)] is found to exhibit a localization transition at /lambda(r)/+/lambda(i)/=1. This transition from extended to localized states manifests itself in the behavior of the complex eigenspectum. In the extended phase, states with real eigenenergies have a finite measure, and this measure goes to zero in the localized phase. Furthermore, all extended states exhibit real spectra provided /lambda(r)/>or=/lambda(i)/. Another interesting feature of the system is the fact that the imaginary part of the spectrum is sensitive to the boundary conditions only at the onset to localization.

Cold atom beam splitter realized with two crossing dipole guides

Cold rubidium atoms, coupled and guided in a vertical laser beam by the dipole force, have been split into two atomic beams, by using a second time-dependent laser beam crossing the vertical one at a 0.12 rad angle. Transfer efficiency as large as 40% has been obtained. At 10 mm below the cold atom source, the two atomic beams have a few hundred micron size and are more than one millimeter apart from each other.