14 research outputs found
Testing quantum adiabaticity with quench echo
Adiabaticity of quantum evolution is important in many settings. One example
is the adiabatic quantum computation. Nevertheless, up to now, there is no
effective method to test the adiabaticity of the evolution when the
eigenenergies of the driven Hamiltonian are not known. We propose a simple
method to check adiabaticity of a quantum process for an arbitrary quantum
system. We further propose a operational method for finding a uniformly
adiabatic quench scheme based on Kibble-Zurek mechanism for the case when the
initial and the final Hamiltonians are given. This method should help in
implementing adiabatic quantum computation.Comment: This is a new version. Some typos in the New Journal of Physics
version have been correcte
Dynamics of an inhomogeneous quantum phase transition
We argue that in a second order quantum phase transition driven by an
inhomogeneous quench density of quasiparticle excitations is suppressed when
velocity at which a critical point propagates across a system falls below a
threshold velocity equal to the Kibble-Zurek correlation length times the
energy gap at freeze-out divided by . This general prediction is
supported by an analytic solution in the quantum Ising chain. Our results
suggest, in particular, that adiabatic quantum computers can be made more
adiabatic when operated in an "inhomogeneous" way.Comment: 7 pages; version to appear in a special issue of New J. Phy
How to fix a broken symmetry: Quantum dynamics of symmetry restoration in a ferromagnetic Bose-Einstein condensate
We discuss the dynamics of a quantum phase transition in a spin-1
Bose-Einstein condensate when it is driven from the magnetized
broken-symmetry phase to the unmagnetized ``symmetric'' polar phase. We
determine where the condensate goes out of equilibrium as it approaches the
critical point, and compute the condensate magnetization at the critical point.
This is done within a quantum Kibble-Zurek scheme traditionally employed in the
context of symmetry-breaking quantum phase transitions. Then we study the
influence of the nonequilibrium dynamics near a critical point on the
condensate magnetization. In particular, when the quench stops at the critical
point, nonlinear oscillations of magnetization occur. They are characterized by
a period and an amplitude that are inversely proportional. If we keep driving
the condensate far away from the critical point through the unmagnetized
``symmetric'' polar phase, the amplitude of magnetization oscillations slowly
decreases reaching a non-zero asymptotic value. That process is described by
the equation that can be mapped onto the classical mechanical problem of a
particle moving under the influence of harmonic and ``anti-friction'' forces
whose interplay leads to surprisingly simple fixed-amplitude oscillations. We
obtain several scaling results relating the condensate magnetization to the
quench rate, and verify numerically all analytical predictions.Comment: 15 pages, 11 figures, final version accepted in NJP (slight changes
with respect to the former submission
Causality and defect formation in the dynamics of an engineered quantum phase transition in a coupled binary Bose-Einstein condensate
Continuous phase transitions occur in a wide range of physical systems, and
provide a context for the study of non-equilibrium dynamics and the formation
of topological defects. The Kibble-Zurek (KZ) mechanism predicts the scaling of
the resulting density of defects as a function of the quench rate through a
critical point, and this can provide an estimate of the critical exponents of a
phase transition. In this work we extend our previous study of the
miscible-immiscible phase transition of a binary Bose-Einstein condensate (BEC)
composed of two hyperfine states in which the spin dynamics are confined to one
dimension [J. Sabbatini et al., Phys. Rev. Lett. 107, 230402 (2011)]. The
transition is engineered by controlling a Hamiltonian quench of the coupling
amplitude of the two hyperfine states, and results in the formation of a random
pattern of spatial domains. Using the numerical truncated Wigner phase space
method, we show that in a ring BEC the number of domains formed in the phase
transitions scales as predicted by the KZ theory. We also consider the same
experiment performed with a harmonically trapped BEC, and investigate how the
density inhomogeneity modifies the dynamics of the phase transition and the KZ
scaling law for the number of domains. We then make use of the symmetry between
inhomogeneous phase transitions in anisotropic systems, and an inhomogeneous
quench in a homogeneous system, to engineer coupling quenches that allow us to
quantify several aspects of inhomogeneous phase transitions. In particular, we
quantify the effect of causality in the propagation of the phase transition
front on the resulting formation of domain walls, and find indications that the
density of defects is determined during the impulse to adiabatic transition
after the crossing of the critical point.Comment: 23 pages, 10 figures. Minor corrections, typos, additional referenc
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
Spontaneous creation of Kibble-Zurek solitons in a Bose-Einstein condensate
When a system crosses a second-order phase transition on a finite timescale,
spontaneous symmetry breaking can cause the development of domains with
independent order parameters, which then grow and approach each other creating
boundary defects. This is known as Kibble-Zurek mechanism. Originally
introduced in cosmology, it applies both to classical and quantum phase
transitions, in a wide variety of physical systems. Here we report on the
spontaneous creation of solitons in Bose-Einstein condensates via the
Kibble-Zurek mechanism. We measure the power-law dependence of defects number
with the quench time, and provide a check of the Kibble-Zurek scaling with the
sonic horizon. These results provide a promising test bed for the determination
of critical exponents in Bose-Einstein condensates.Comment: 7 pages, 4 figure
Decoherence by engineered quantum baths
We introduce, and determine decoherence for, a wide class of non-trivial
quantum spin baths which embrace Ising, XY and Heisenberg universality classes
coupled to a two-level system. For the XY and Ising universality classes we
provide an exact expression for the decay of the loss of coherence beyond the
case of a central spin coupled uniformly to all the spins of the baths which
has been discussed so far in the literature. In the case of the Heisenberg spin
bath we study the decoherence by means of the time-dependent density matrix
renormalization group. We show how these baths can be engineered, by using
atoms in optical lattices.Comment: 4 pages, 4 figure