247 research outputs found
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, .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
-approximation ( 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 -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
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
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