[Show abstract][Hide abstract] ABSTRACT: We study the equilibrium and non-equilibrium properties of strongly
interacting bosons on a lattice in presence of a random bounded disorder
potential. Using a Gutzwiller projected variational technique, we study the
equilibrium phase diagram of the disordered Bose Hubbard model and obtain the
Mott insulator, Bose glass and superfluid phases. We also study the non
equilibrium response of the system under a periodic temporal drive where,
starting from the superfluid phase, the hopping parameter is ramped down
linearly in time, and back to its initial value. We study the density of
excitations created, the change in the superfluid order parameter and the
energy pumped into the system in this process as a function of the inverse ramp
rate $\tau$. For the clean case the density of excitations goes to a constant,
while the order parameter and energy relaxes as $1/\tau$ and $1/\tau^2$
respectively. With disorder, the excitation density decays exponentially with
$\tau$, with the decay rate increasing with the disorder, to an asymptotic
value independent of the disorder. The energy and change in order parameter
also decrease as $\tau$ is increased.
[Show abstract][Hide abstract] ABSTRACT: Motivated by a recent experimental report[1] claiming the likely observation
of the Majorana mode in a semiconductor-superconductor hybrid
structure[2,3,4,5], we study theoretically the dependence of the zero bias
conductance peak associated with the zero-energy Majorana mode in the
topological superconducting phase as a function of temperature, tunnel barrier
potential, and a magnetic field tilted from the direction of the wire for
realistic wires of finite lengths. We find that higher temperatures and tunnel
barriers as well as a large magnetic field in the direction transverse to the
wire length could very strongly suppress the zero-bias conductance peak as
observed in Ref.[1]. We also show that a strong magnetic field along the wire
could eventually lead to the splitting of the zero bias peak into a doublet
with the doublet energy splitting oscillating as a function of increasing
magnetic field. Our results based on the standard theory of topological
superconductivity in a semiconductor hybrid structure in the presence of
proximity-induced superconductivity, spin-orbit coupling, and Zeeman splitting
show that the recently reported experimental data are generally consistent with
the existing theory that led to the predictions for the existence of the
Majorana modes in the semiconductor hybrid structures in spite of some apparent
anomalies in the experimental observations at first sight. We also make several
concrete new predictions for future observations regarding Majorana splitting
in finite wires used in the experiments.
[Show abstract][Hide abstract] ABSTRACT: We use a strong coupling canonical transformation to study the phase
diagram of strongly interacting bosons in an optical lattice in the
presence of one-body disorder potential. Our strong coupling approach
treats the disorder potential non-perturbatively and can be applied to
moderately high disorder potentials as long as the on site repulsion
energy scale for the bosons (U) is larger than the scale of the disorder
potential (V). Within the strong coupling approach, we systematically
derive the low energy effective Hamiltonian, and, using variational
Gutzwiller type wavefunctions, study the phase diagram of the disordered
Hubbard model, identifying the Mott insulator, superfluid and Bose glass
phases.
[Show abstract][Hide abstract] ABSTRACT: Majorana fermions have been proposed to be realizable at the end of the semiconductor nanowire on top of an s-wave superconductor [1,2]. These proposals require gating the nanowire directly in contact with a superconductor which may be difficult in experiments. We analyze [1,2] in configurations where the wire is only gated away from the superconductor. We show that some signatures of the Majorana mode remain but the Majorana mode is not localized and hence not suitable for quantum computation. Therefore we propose an 1D periodic heterostructure which can support localized Majorana modes at the end of the wire without gating on the superconductor. [4pt] [1] Jay D. Sau et al., arXiv:1006.2829, Phys Rev B (in press)[0pt] [2] Roman M. Lutchyn et al., Phys. Rev. Lett. 105, 077001 (2010)
[Show abstract][Hide abstract] ABSTRACT: In this work, we theoretically construct exact mappings of many-particle
bosonic systems onto quantum rotor models. In particular, we analyze the rotor
representation of spinor Bose-Einstein condensates. In a previous work it was
shown that there is an exact mapping of a spin-one condensate of fixed particle
number with quadratic Zeeman interaction onto a quantum rotor model. Since the
rotor model has an unbounded spectrum from above, it has many more eigenstates
than the original bosonic model. Here we show that for each subset of states
with fixed spin F_z, the physical rotor eigenstates are always those with
lowest energy. We classify three distinct physical limits of the rotor model:
the Rabi, Josephson, and Fock regimes. The last regime corresponds to a
fragmented condensate and is thus not captured by the Bogoliubov theory. We
next consider the semiclassical limit of the rotor problem and make connections
with the quantum wave functions through use of the Husimi distribution
function. Finally, we describe how to extend the analysis to higher-spin
systems and derive a rotor model for the spin-two condensate. Theoretical
details of the rotor mapping are also provided here.
Physical Review A 11/2010; 83(2). DOI:10.1103/PhysRevA.83.023613 · 2.81 Impact Factor