5 research outputs found
Structural defects in ion crystals by quenching the external potential: the inhomogeneous Kibble-Zurek mechanism
The non-equilibrium dynamics of an ion chain in a highly anisotropic trap is
studied when the transverse trap frequency is quenched across the value at
which the chain undergoes a continuous phase transition from a linear to a
zigzag structure. Within Landau theory, an equation for the order parameter,
corresponding to the transverse size of the zigzag structure, is determined
when the vibrational motion is damped via laser cooling. The number of
structural defects produced during a linear quench of the transverse trapping
frequency is predicted and verified numerically. It is shown to obey the
scaling predicted by the Kibble-Zurek mechanism, when extended to take into
account the spatial inhomogeneities of the ion chain in a linear Paul trap.Comment: 5 pages, 3 figure
Formation of helical ion chains
We study the nonequilibrium dynamics of the linear to zigzag structural phase
transition exhibited by an ion chain confined in a trap with periodic boundary
conditions. The transition is driven by reducing the transverse confinement at
a finite quench rate, which can be accurately controlled. This results in the
formation of zigzag domains oriented along different transverse planes. The
twists between different domains can be stabilized by the topology of the trap
and under laser cooling the system has a chance to relax to a helical chain
with nonzero winding number. Molecular dynamics simulations are used to obtain
a large sample of possible trajectories for different quench rates. The scaling
of the average winding number with different quench rates is compared to the
prediction of the Kibble-Zurek theory, and a good quantitative agreement is
found
System size scaling of topological defect creation in a second-order dynamical quantum phase transition
We investigate the system size scaling of the net defect number created by a
rapid quench in a second-order quantum phase transition from an O(N) symmetric
state to a phase of broken symmetry. Using a controlled mean-field expansion
for large N, we find that the net defect number variance in convex volumina
scales like the surface area of the sample for short-range correlations. This
behaviour follows generally from spatial and internal symmetries. Conversely,
if spatial isotropy is broken, e.g., by a lattice, and in addition long-range
periodic correlations develop in the broken-symmetry phase, we get the rather
counterintuitive result that the scaling strongly depends on the dimension
being even or odd: For even dimensions, the net defect number variance scales
like the surface area squared, with a prefactor oscillating with the system
size, while for odd dimensions, it essentially vanishes.Comment: 20 pages of IOP style, 6 figures; as published in New Journal of
Physic
Adiabatic dynamics of an inhomogeneous quantum phase transition: the case of z > 1 dynamical exponent
We consider an inhomogeneous quantum phase transition across a multicritical
point of the XY quantum spin chain. This is an example of a Lifshitz transition
with a dynamical exponent z = 2. Just like in the case z = 1 considered in New
J. Phys. 12, 055007 (2010) when a critical front propagates much faster than
the maximal group velocity of quasiparticles vq, then the transition is
effectively homogeneous: density of excitations obeys a generalized
Kibble-Zurek mechanism and scales with the sixth root of the transition rate.
However, unlike for z = 1, the inhomogeneous transition becomes adiabatic not
below vq but a lower threshold velocity v', proportional to inhomogeneity of
the transition, where the excitations are suppressed exponentially.
Interestingly, the adiabatic threshold v' is nonzero despite vanishing minimal
group velocity of low energy quasiparticles. In the adiabatic regime below v'
the inhomogeneous transition can be used for efficient adiabatic quantum state
preparation in a quantum simulator: the time required for the critical front to
sweep across a chain of N spins adiabatically is merely linear in N, while the
corresponding time for a homogeneous transition across the multicritical point
scales with the sixth power of N. What is more, excitations after the adiabatic
inhomogeneous transition, if any, are brushed away by the critical front to the
end of the spin chain.Comment: 10 pages, 6 figures, improved version accepted in NJ