Quantum Effects in trapped cold atomic and ionic systems
In the last few years the great experimental advances in loading trapped gases of ultracold atoms into lattices built by sets of counter-propagating lasers has raised a huge amount of interest [1]. Indeed, these systems can represent an ideal implementation of several important models in condensed matter. While the Mott insulating behavior induced by an on-site interaction has already been observed, the possibility of mimicking the long-range part of interaction has finally been reached by trapping dipolar molecules/atoms. In particular, it has been speculated that ultracold fermionic atoms in optical lattices can provide a much purer realization of extended Hubbard Hamiltonians, with respect to real materials. Thus, some of the basic questions about this model, such as the possibility of superconducting order in two spatial dimension, may become experimentally addressable.
Another appealing aspect of ultracold atomic gases is the possibility to realize fractional quantum Hall effect (FQHE) states at arbitrary filling factor. The two dimensional geometry has been achieved by freezing one or two degrees of freedom of the particle wave-functions. It is possible to impose an effective magnetic field (trapped atoms are neutral-charged) by rapid rotation [2] or by engineered laser schemes. The high control of atomic systems, especially the possibility of slowly modifying the trap and interaction parameters, is a great opportunity to tune the many-body wave-functions with the aim to reproduce emblematic quantum states.
[1] I. Bloch, J. Dalibard and W. Zwerger, Rev. Mod. Phys. 80, 885 (2008).
[2] N. R. Cooper, Adv. Phys. 57, 539 (2008)
References
A. Anfossi, C. Degli Esposti Boschi, and A. Montorsi, Fulde-Ferrell-Larkin-Ovchinnikov oscillations and magnetic domains in the Hubbard model with off-diagonal Coulomb repulsion, J. Stat. Mech. P12014 (2011).
M. Roncaglia, C. Degli Esposti Boschi, and A. Montorsi, Hidden XY structure of the bond-charge Hubbard model, Phys. Rev. B 82, 233105 (2010).
A. Anfossi, L. Barbiero, and A. Montorsi, Detecting the tunneling rates for strongly interacting fermions on optical lattices, Phys. Rev. A 81, 043630 (2010).
A. Anfossi, L. Barbiero, and A. Montorsi, Phase diagram of imbalanced strongly interacting fermions on a one-dimensional optical lattice, Phys. Rev. A 80, 043602 (2009).
A.A. Aligia, A. Anfossi, L. Arrachea, C. Degli Esposti Boschi, A.O. Dobry, C. Gazza, A. Montorsi, F. Ortolani, M.E. Torio, Incommensurability and unconventional superconductor to insulator transition in the Hubbard model with bond-charge interaction, Phys. Rev. Lett. 99, 296401 (2007)
➤ Nonlinear Coherent States of Trapped Ions
Nonlinear coherent states are a tool of the utmost importance in quantum optics also with respect to their prospective applications in the field of quantum information and quantum computing. We have focused on the nonlinear coherent states which are realized by means of a trapped ion interacting with driving electromagnetic fields, showing that the very structure of the original states is strongly modified resulting into new states, for and close to certain values of the Lamb–Dicke parameter η = kL (h/4 π M ν)1/2 (M = ion mass, kL = lasers wavevectors, ν = trap frequency). We have analyzed the irregularities of the coherence and minimum-uncertainty properties of these new states.
References
F. A. Raffa, M. Rasetti, M. Genovese, Singularities in ion trap nonlinear coherent states, Phys. Lett. A 376, 330 (2012).
➤ Quantum simulators for strongly correlated lattice models
Very recently, experimental groups in Harvard and MPQ [W. Bakr et al., Nature 462, 74 (2009)] have implemented cold atom setups where the tunneling amplitudes between sites of an optical lattice can be tuned depending on the local particle occupation. Differently from conventional solid state implementations, where such terms are negligibly small and not included in the standard Hubbard model, in these systems the correlation effects induced by density-dependent tunneling yield the emergence of novel phases. These effects spur the interest in extending the Hubbard Hamiltonian to a wider class containing correlated tunneling terms, which is known to exhibit a peculiar ground state phase diagram, including non standard pairing mechanisms [Aligia]. The group have studied the ground state properties of several extensions of the Hubbard model especially those involving hopping terms that depend on the local occupation number.
References
M. Roncaglia, M. Rizzi, and J. Dalibard, From rotating atomic rings to quantum Hall states, Scientific Rep. 1, 43 (2011).
M. Roncaglia, M. Rizzi, J.I. Cirac, Pfaffian State Generation by Strong Three-Body Dissipation, Phys. Rev. Lett. 104, 096803 (2010).
➤ Fractional quantum Hall effect in rotating traps
We have recently proposed a scheme for preparing and stabilizing the Pfaffian state (known for its nontrivial topological properties) with high fidelity in rapidly rotating 2D traps containing a small number of bosons [MMI]. The goal is achieved by strongly increasing three-body loss processes, which suppress superpositions of three particles while permitting pairing. This filtering mechanism gives rise to reasonably small losses if the system is initialized with the right angular momentum. Two- and three-body interaction terms can be tuned independently
Considerable efforts are currently devoted to the preparation of ultracold neutral atoms in the strongly correlated quantum Hall regime. However, the necessary angular momentum is very large and in experiments with rotating traps this means spinning frequencies extremely near to the deconfinement limit; consequently, the required control on parameters turns out to be too stringent. Our group have proposed [MMJ] instead to follow a dynamic path starting from the gas initially confined in a rotating ring. The large moment of inertia of the ring-shaped fluid facilitates the access to large angular momenta, corresponding to giant vortex states. The trapping potential is then adiabatically transformed into a harmonic confinement, which brings the interacting atomic gas in the desired quantum-Hall regime. We have provided evidence that for a broad range of initial angular frequencies, the giant-vortex state is adiabatically connected to the bosonic ν = 1/2 Laughlin state.
➤ Anyons in one-dimensional optical lattices
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Using an exact mapping it is possible to convert abelian anyons into bosons with conditional hopping amplitudes in a 1D optical lattice. Our group have proposed a realistic experimental implementation of the resulting bosonic Hamiltonian to demonstrate the physics of a gas of interacting anyons in 1D [TSIM]. The phase diagram, examined in 1D by means of mean field and DMRG, shows extended Mott lobes with respect to the simple bosonic case, even at zero on-site interaction U. In particular, by varying the statistical angle θ it is possible to induce a superfluid-Mott insulator transition, while the other parameters J and U stay fixed.
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References
T. Keilmann, S. Lanzmich, I. McCulloch, and M. Roncaglia, Statistically induced phase transitions and anyons in 1D optical lattices, Nature Comm. 2, 361 (2011).
Increase of the first Mott lobe under variation of the statistical angle θ
Appearance of fractional plateaus moving continuously from Bose to Fermi statistics.
For strong three-body dissipation the Pfaffian state is rapidly attained, while the population remains finite thanks to a freezing mechanism similar to the quantum Zeno effect.
The Mexican-hat potential
Adiabatic deformation of the trap
Evolution of the density profile in the trap during deformation
Density-density correlation functions in the Hubbard model with correlated hopping are well described by spin-spin correlations in the XY model.
Phase diagram of imbalanced strongly interacting fermions on a one-dimensional optical lattice
Different tunneling processes considered in extended versions of the Hubbard model
Nanophysics and Quantum Systems
