97 research outputs found
Nonlinear Tight-Binding Approximation for Bose-Einstein Condensates in a Lattice
The dynamics of Bose-Einstein condensates trapped in a deep optical lattice
is governed by a discrete nonlinear equation (DNL). Its degree of nonlinearity
and the intersite hopping rates are retrieved from a nonlinear tight-binding
approximation taking into account the effective dimensionality of each
condensate. We derive analytically the Bloch and the Bogoliubov excitation
spectra, and the velocity of sound waves emitted by a traveling condensate.
Within a Lagrangian formalism, we obtain Newtonian-like equations of motion of
localized wavepackets. We calculate the ground-state atomic distribution in the
presence of an harmonic confining potential, and the frequencies of small
amplitude dipole and quadrupole oscillations. We finally quantize the DNL,
recovering an extended Bose-Hubbard model
Inverse Ising problem for one-dimensional chains with arbitrary finite-range couplings
We study Ising chains with arbitrary multispin finite-range couplings,
providing an explicit solution of the associated inverse Ising problem, i.e.
the problem of inferring the values of the coupling constants from the
correlation functions. As an application, we reconstruct the couplings of chain
Ising Hamiltonians having exponential or power-law two-spin plus three- or
four-spin couplings. The generalization of the method to ladders and to Ising
systems where a mean-field interaction is added to general finite-range
couplings is as well as discussed.Comment: Published version, typos correcte
Non-abelian anyons from degenerate Landau levels of ultracold atoms in artificial gauge potentials
We show that non-abelian potentials acting on ultracold gases with two
hyperfine levels can give rise to ground states with non-abelian excitations.
We consider a realistic gauge potential for which the Landau levels can be
exactly determined: the non-abelian part of the vector potential makes the
Landau levels non-degenerate. In the presence of strong repulsive interactions,
deformed Laughlin ground states occur in general. However, at the degeneracy
points of the Landau levels, non-abelian quantum Hall states appear: these
ground states, including deformed Moore-Read states (characterized by Ising
anyons as quasi-holes), are studied for both fermionic and bosonic gases.Comment: Published versio
Dipole Oscillations in Fermionic Mixtures
We study dipole oscillations in a general fermionic mixture: starting from
the Boltzmann equation, we classify the different solutions in the parameter
space through the number of real eigenvalues of the small oscillations matrix.
We discuss how this number can be computed using the Sturm algorithm and its
relation with the properties of the Laplace transform of the experimental
quantities. After considering two components in harmonic potentials having
different trapping frequencies, we study dipole oscillations in three-component
mixtures. Explicit computations are done for realistic experimental setups
using the classical Boltzmann equation without intra-species interactions. A
brief discussion of the application of this classification to general
collective oscillations is also presented.Comment: Published versio
Statistical Mechanics of an Ideal Gas of Non-Abelian Anyons
We study the thermodynamical properties of an ideal gas of non-Abelian
Chern-Simons particles and we compute the second virial coefficient,
considering the effect of general soft-core boundary conditions for the
two-body wavefunction at zero distance. The behaviour of the second virial
coefficient is studied as a function of the Chern-Simons coupling, the isospin
quantum number and the hard-coreness parameters. Expressions for the main
thermodynamical quantities at the lower order of the virial expansion are also
obtained: we find that at this order the relation between the internal energy
and the pressure is the same found (exactly) for 2D Bose and Fermi ideal gases.
A discussion of the comparison of obtained findings with available results in
literature for systems of hard-core non-Abelian Chern-Simons particles is also
supplied.Comment: Submitted versio
Characterization of the Bose-glass phase in low-dimensional lattices
We study by numerical simulation a disordered Bose-Hubbard model in
low-dimensional lattices. We show that a proper characterization of the phase
diagram on finite disordered clusters requires the knowledge of probability
distributions of physical quantities rather than their averages. This holds in
particular for determining the stability region of the Bose-glass phase, the
compressible but not superfluid phase that exists whenever disorder is present.
This result suggests that a similar statistical analysis should be performed
also to interpret experiments on cold gases trapped in disordered lattices,
limited as they are to finite sizes.Comment: 4+ epsilon pages and 4 figure
Integer Factorization by Quantum Measurements
Quantum algorithms are at the heart of the ongoing efforts to use quantum
mechanics to solve computational problems unsolvable on ordinary classical
computers. Their common feature is the use of genuine quantum properties such
as entanglement and superposition of states. Among the known quantum
algorithms, a special role is played by the Shor algorithm, i.e. a
polynomial-time quantum algorithm for integer factorization, with far reaching
potential applications in several fields, such as cryptography. Here we present
a different algorithm for integer factorization based on another genuine
quantum property: quantum measurement. In this new scheme, the factorization of
the integer is achieved in a number of steps equal to the number of its
prime factors, -- e.g., if is the product of two primes, two quantum
measurements are enough, regardless of the number of digits of the number
. Since is the lower bound to the number of operations one can do to
factorize a general integer, one sees that a quantum mechanical setup can
saturate such a bound.Comment: 7 pages, 3 Supplementary Materials, 3 figure
Deviations from Off-Diagonal Long-Range Order in One-Dimensional Quantum Systems
A quantum system exhibits off-diagonal long-range order (ODLRO) when the
largest eigenvalue of the one-body-density matrix scales as
, where is the total number of particles. Putting
to define the scaling exponent , then
corresponds to ODLRO and to the single-particle
occupation of the density matrix orbitals. When , can
be used to quantify deviations from ODLRO. In this paper we study the exponent
in a variety of one-dimensional bosonic and anyonic quantum systems.
For the Lieb-Liniger Bose gas we find that for small interactions is close to , implying a mesoscopic condensation, i.e. a value of the
"condensate" fraction appreciable at finite values of (as the
ones in experiments with ultracold atoms). anyons provide the
possibility to fully interpolate between and . The behaviour of
for these systems is found to be non-monotonic both with respect to
the coupling constant and the statistical parameter.Comment: 8 pages, 4 figure
Quantum dynamics of few dipolar bosons in a double-well potential
We study the few-body dynamics of dipolar bosons in one-dimensional
double-wells. Increasing the interaction strength, by investigating one-body
observables, we study in the considered few-body systems tunneling
oscillations, self-trapping and the regime exhibting an equilibrating
behaviour. The corresponding two-body correlation dynamics exhibits a strong
interplay between the interatomic correlation due to non-local nature of the
repulsion and the inter-well coherence. We also study the link between the
correlation dynamics and the occupation of natural orbitals of the one-body
density matrix.Comment: 8 pages, 7 figures. Corrections on abstract and the main text,
submitted versio
Holographic realization of the prime number quantum potential
We report the experimental realization of the prime number quantum potential VN(x), defined as the potential entering the single-particle Schrödinger Hamiltonian with eigenvalues given by the first N prime numbers. Using computer-generated holography, we create light intensity profiles suitable to optically trap ultracold atoms in these potentials for different N values. As a further application, we also implement a potential whose spectrum is given by the lucky numbers, a sequence of integers generated by a different sieve than the familiar Eratosthenes’s sieve used for the primes. Our results pave the way towards the realization of quantum potentials with arbitrary sequences of integers as energy levels and show, in perspective, the possibility to set up quantum systems for arithmetic manipulations or mathematical tests involving prime numbers.Publisher PDFPeer reviewe
- …