Dario Jukić

Anderson localization of a Tonks-Girardeau gas in potentials with controlled disorder

We theoretically demonstrate features of Anderson localization in a Tonks-Girardeau gas confined in one-dimensional potentials with controlled disorder. That is, we investigate the evolution of the single-particle density and correlations of a Tonks-Girardeau wave packet in such disordered potentials. The wave packet is initially trapped, the trap is suddenly turned off, and after some time the system evolves into a localized steady state due to Anderson localization. The density tails of the steady state decay exponentially, while the coherence in these tails increases. The latter phenomenon corresponds to the same effect found in incoherent optical solitons.

Four-dimensional photonic lattices and discrete tesseract solitons

We theoretically study discrete photonic lattices in more than three dimensions and point out that such systems can exist in continuous three-dimensional space. We study discrete diffraction in the linear regime and demonstrate the existence of four-dimensional (4D) tesseract solitons in nonlinear 4D periodic photonic lattices. Finally, we propose a design towards a potential realization of such periodic 4D lattices in experiments.

Synthetic Lorentz force in classical atomic gases via Doppler effect and radiation pressure

We theoretically predict synthetic Lorentz force for classical (cold) atomic gases, which is based on the Doppler effect and radiation pressure. A fai

Flat photonic surface bands pinned between Dirac points

We point out that 2D photonic crystals (PhCs) can support surface bands that are pinned to Dirac points. These bands can be made very flat by optimizing the parameters of the system. Surface modes are found at the interface of two different cladding materials: one is a PhC with Dirac linear dispersion for the TE mode, and the other is a PhC that has a broad TE gap at the Dirac frequency.

Free expansion of a Lieb-Liniger gas: Asymptotic form of the wave functions

The asymptotic form of the wave functions describing a freely expanding Lieb-Liniger gas is derived by using a Fermi-Bose transformation for time-dependent states, and the stationary phase approximation. We find that asymptotically the wave functions approach the Tonks-Girardeau (TG) structure as they vanish when any two of the particle coordinates coincide. We point out that the properties of these asymptotic states can significantly differ from the properties of a TG gas in a ground state of an external potential. The dependence of the asymptotic wave function on the initial state is discussed. The analysis encompasses a large class of initial conditions, including the ground states of a Lieb-Liniger gas in physically realistic external potentials. It is also demonstrated that the interaction energy asymptotically decays as a universal power law with time, Eint ∝ t 3 .

Momentum distribution of a freely expanding Lieb-Liniger gas

We numerically study free expansion of a few Lieb-Liniger bosons, which are initially in the ground state of an infinitely deep hard-wall trap. Numerical calculation is carried out by employing a standard Fourier transform, as follows from the Fermi-Bose transformation for a time-dependent Lieb-Liniger gas. We study the evolution of the momentum distribution, the real-space single-particle density, and the occupancies of natural orbitals. Our numerical calculation allows us to explore the behavior of these observables in the transient regime of the expansion, where they are nontrivially affected by the particle interactions. We derive analytically (by using the stationary phase approximation) the formula which connects the asymptotic shape of the momentum distribution and the initial state. For sufficiently large times, the momentum distribution coincides (up to a simple scaling transformation) with the shape of the real-space single-particle density (the expansion is asymptotically ballistic). Our analytical and numerical results are in good agreement.

Evanescent fields of laser written waveguides

We investigate the evanescent field at the surface of laser written waveguides. The waveguides are written by a direct femtosecond laser writing process into fused silica, which is then sanded down to expose the guiding layer. These waveguides support eigenmodes which have an evanescent field reaching into the vacuum above the waveguide. We study the governing wave equations and present solution for the fundamental eigenmodes of the modified waveguides.

Lieb-Liniger gas in a constant-force potential

We use Gaudin’s Fermi-Bose mapping operator to calculate exact solutions for the Lieb-Liniger model in a linear (constant-force) potential (the constructed exact stationary solutions are referred to as the Lieb-Liniger-Airy wave functions). The ground-state properties of the gas in the wedgelike trapping potential are calculated in the strongly interacting regime by using Girardeau’s FermiBose mapping and the pseudopotential approach in the 1/c approximation (c denotes the strength of the interaction). We point out that quantum dynamics of Lieb-Liniger wave packets in the linear potential can be calculated by employing an N-dimensional Fourier transform as in the case of free expansion.

Reflection of a Lieb-Liniger wave packet from the hard-wall potential

Non-equilibrium dynamics of a Lieb?Liniger system in the presence of the hard-wall potential is studied. We demonstrate that a time-dependent wave function, which describes quantum dynamics of a Lieb?Liniger wave packet consisting of N particles, can be found by solving an N-dimensional Fourier transform; this follows from the symmetry properties of the many-body eigenstates in the presence of the hard-wall potential. The presented formalism is employed to numerically calculate reflection of a few-body wave packet from the hard wall for various interaction strengths and incident momenta.

Laser assisted tunneling in a Tonks–Girardeau gas

We investigate the applicability of laser assisted tunneling in a strongly interacting one-dimensional (1D) Bose gas (the Tonks– Girardeau gas) in optical lattices. We find that the stroboscopic dynamics of the Tonks–Girardeau gas in a continuous Wannier–Stark- ladder potential, supplemented with laser assisted tunneling, effectively realizes the ground state of 1D hard-core bosons in a discrete lattice with nontrivial hopping phases. We compare observables that are affected by the interactions, such as the momentum distribution, natural orbitals and their occupancies, in the time-dependent continuous system, to those of the ground state of the discrete system. Stroboscopically, we find an excellent agreement, indicating that laser assisted tunneling is a viable technique for realizing novel ground states and phases with hard- core 1D Bose gases.