Momentum distribution dynamics of a Tonks-Girardeau gas: Bragg reflections of a quantum many-body wavepacket

The dynamics of the momentum distribution and the reduced single-particle density matrix (RSPDM) of a Tonks-Girardeau (TG) gas is studied in the context of Bragg-reflections of a many-body wavepacket. We find strong suppression of a Bragg-reflection peak for a dense TG wavepacket; our observation illustrates dependence of the momentum distribution on the interactions/wavefunction symmetry. The momentum distribution is calculated with a fast algorithm based on a formula expressing the RSPDM via a dynamically evolving single-particle basis

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

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

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

The pinning quantum phase transition in a Tonks Girardeau gas: diagnostics by ground state fidelity and the Loschmidt echo

We study the pinning quantum phase transition in a Tonks-Girardeau gas, both in equilibrium and out-of-equilibrium, using the ground state fidelity and the Loschmidt echo as diagnostic tools. The ground state fidelity (GSF) will have a dramatic decrease when the atomic density approaches the commensurate density of one particle per lattice well. This decrease is a signature of the pinning transition from the Tonks to the Mott insulating phase. We study the applicability of the fidelity for diagnosing the pinning transition in experimentally realistic scenarios. Our results are in excellent agreement with recent experimental work. In addition, we explore the out of equilibrium dynamics of the gas following a sudden quench with a lattice potential. We find all properties of the ground state fidelity are reflected in the Loschmidt echo dynamics i.e., in the non equilibrium dynamics of the Tonks-Girardeau gas initiated by a sudden quench of the lattice potential

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

Fermi-Bose transformation for the time-dependent Lieb-Liniger gas

Exact solutions of the Schrodinger equation describing a freely expanding Lieb-Liniger (LL) gas of delta-interacting bosons in one spatial dimension are constructed. The many-body wave function is obtained by transforming a fully antisymmetric (fermionic) time-dependent wave function which obeys the Schrodinger equation for a free gas. This transformation employs a differential Fermi-Bose mapping operator which depends on the strength of the interaction and the number of particles.Comment: 4+ pages, 1 figure; added reference

Loschmidt echo in one-dimensional interacting Bose gases

We explore Loschmidt echo in two regimes of one-dimensional (1D) interacting Bose gases: the strongly interacting Tonks-Girardeau (TG) regime, and the weakly-interacting mean-field regime. We find that the Loschmidt echo of a TG gas decays as a Gaussian when small perturbations are added to the Hamiltonian (the exponent is proportional to the number of particles and the magnitude of a small perturbation squared). In the mean-field regime the Loschmidt echo decays faster for larger interparticle interactions (nonlinearity), and it shows richer behavior than the TG Loschmidt echo dynamics, with oscillations superimposed on the overall decay.Comment: Comparison between Tonks-Girardeau and mean-field fidelities corrected; see new Figure 4 and the "Note added". New references are include