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 (3D) space. We study discrete diffraction in the linear regime, and predict 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.Comment: Submitted to PRL on 14 May 201

Ground state properties of a one-dimensional strongly-interacting Bose-Fermi mixture in a double-well potential

We calculate the reduced single-particle density matrix (RSPDM), momentum distributions, natural orbitals and their occupancies, for a strongly interacting one-dimensional Bose-Fermi mixture in a double-well potential with a large central barrier. For mesoscopic systems, we find that the ground state properties qualitatively differ for mixtures with even number of particles (both odd-odd and even-even mixtures) in comparison to mixtures with odd particle numbers (odd-even and even-odd mixtures). For even mixtures the momentum distribution is smooth, whereas the momentum distribution of odd mixtures possesses distinct modulations; the differences are observed also in the off-diagonal correlations of the RSPDM, and in the occupancies of natural orbitals. The calculation is based on a derived formula which enables efficient calculation of the RSPDM for mesoscopic mixtures in various potentials.Comment: 10 figure

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 wedge-like trapping potential are calculated in the strongly interacting regime by using Girardeau's Fermi-Bose 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

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

We theoretically predict a novel type of synthetic Lorentz force for classical (cold) atomic gases, which is based on the Doppler effect and radiation pressure. A fairly uniform and strong force can be constructed for gases in macroscopic volumes of several cubic millimeters and more. This opens the possibility to mimic classical charged gases in magnetic fields, such as those in a tokamak, in cold atom experiments.Comment: are welcom

Experimental Demonstration of a Synthetic Lorentz Force by Using Radiation Pressure

Synthetic magnetism in cold atomic gases opened the doors to many exciting novel physical systems and phenomena. Ubiquitous are the methods used for the creation of synthetic magnetic fields. They include rapidly rotating Bose-Einstein condensates employing the analogy between the Coriolis and the Lorentz force, and laser-atom interactions employing the analogy between the Berry phase and the Aharonov-Bohm phase. Interestingly, radiation pressure - being one of the most common forces induced by light - has not yet been used for synthetic magnetism. We experimentally demonstrate a synthetic Lorentz force, based on the radiation pressure and the Doppler effect, by observing the centre-of-mass motion of a cold atomic cloud. The force is perpendicular to the velocity of the cold atomic cloud, and zero for the cloud at rest. Our novel concept is straightforward to implement in a large volume, for a broad range of velocities, and can be extended to different geometries.Comment: are welcom

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 non-trivially 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.Comment: small changes; references correcte

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, $E_\mathrm{int}\propto t^{-3}$.Comment: Section VI added to v2; published versio

Laser assisted tunneling in a Tonks-Girardeau gas

We investigate the applicability of laser assisted tunneling in a strongly interacting one-dimensional 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 one-dimensional 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 one-dimensional Bose gases.Comment: 17 pages, 5 figure

Solitary Waves Bifurcated from Bloch Band Edges in Two-dimensional Periodic Media

Solitary waves bifurcated from edges of Bloch bands in two-dimensional periodic media are determined both analytically and numerically in the context of a two-dimensional nonlinear Schr\"odinger equation with a periodic potential. Using multi-scale perturbation methods, envelope equations of solitary waves near Bloch bands are analytically derived. These envelope equations reveal that solitary waves can bifurcate from edges of Bloch bands under either focusing or defocusing nonlinearity, depending on the signs of second-order dispersion coefficients at the edge points. Interestingly, at edge points with two linearly independent Bloch modes, the envelope equations lead to a host of solitary wave structures including reduced-symmetry solitons, dipole-array solitons, vortex-cell solitons, and so on -- many of which have never been reported before. It is also shown analytically that the centers of envelope solutions can only be positioned at four possible locations at or between potential peaks. Numerically, families of these solitary waves are directly computed both near and far away from band edges. Near the band edges, the numerical solutions spread over many lattice sites, and they fully agree with the analytical solutions obtained from envelope equations. Far away from the band edges, solitary waves are strongly localized with intensity and phase profiles characteristic of individual families.Comment: 23 pages, 15 figures. To appear in Phys. Rev.

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

We theoretically demonstrate features of Anderson localization in the Tonks-Girardeau gas confined in one-dimensional (1D) 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