22 research outputs found
Photon molecules in atomic gases trapped near photonic crystal waveguides
Realizing systems that support robust, controlled interactions between
individual photons is an exciting frontier of nonlinear optics. To this end,
one approach that has emerged recently is to leverage atomic interactions to
create strong and spatially non-local interactions between photons. In
particular, effective interactions have been successfully created via
interactions between atoms excited to Rydberg levels. Here, we investigate an
alternative approach, in which atomic interactions arise via their common
coupling to photonic crystal waveguides. This technique takes advantage of the
ability to separately tailor the strength and range of interactions via the
dispersion engineering of the structure itself, which can lead to qualitatively
new types of phenomena. As an example, we discuss the formation of correlated
transparency windows, in which photonic states of a certain number and shape
selectively propagate through the system. Through this technique, we show in
particular that one can create molecular-like potentials that lead to molecular
bound states of photon pairs
Speeding up and slowing down the relaxation of a qubit by optimal control
We consider a two-level quantum system prepared in an arbitrary initial state
and relaxing to a steady state due to the action of a Markovian dissipative
channel. We study how optimal control can be used for speeding up or slowing
down the relaxation towards the fixed point of the dynamics. We analytically
derive the optimal relaxation times for different quantum channels in the ideal
ansatz of unconstrained quantum control (a magnetic field of infinite
strength). We also analyze the situation in which the control Hamiltonian is
bounded by a finite threshold. As byproducts of our analysis we find that: (i)
if the qubit is initially in a thermal state hotter than the environmental
bath, quantum control cannot speed up its natural cooling rate; (ii) if the
qubit is initially in a thermal state colder than the bath, it can reach the
fixed point of the dynamics in finite time if a strong control field is
applied; (iii) in the presence of unconstrained quantum control it is possible
to keep the evolved state indefinitely and arbitrarily close to special initial
states which are far away from the fixed points of the dynamics.Comment: 11 pages, 6 figure
Quantum Speed Limit and Optimal Control of Many-Boson Dynamics
We extend the concept of quantum speed limit -- the minimal time needed to
perform a driven evolution -- to complex interacting many-body systems. We
investigate a prototypical many-body system, a bosonic Josephson junction, at
increasing levels of complexity: (a) within the two-mode approximation
{corresponding to} a nonlinear two-level system, (b) at the mean-field level by
solving the nonlinear Gross-Pitaevskii equation in a double well potential, and
(c) at an exact many-body level by solving the time-dependent many-body
Schr\"odinger equation. We propose a control protocol to transfer atoms from
the ground state of a well to the ground state of the neighbouring well.
Furthermore, we show that the detrimental effects of the inter-particle
repulsion can be eliminated by means of a compensating control pulse, yielding,
quite surprisingly, an enhancement of the transfer speed because of the
particle interaction -- in contrast to the self-trapping scenario. Finally, we
perform numerical optimisations of both the nonlinear and the (exact) many-body
quantum dynamics in order to further enhance the transfer efficiency close to
the quantum speed limit.Comment: 5 pages, 3 figures, and supplemental material (4 pages 1 figure
Speeding up critical system dynamics through optimized evolution
The number of defects which are generated on crossing a quantum phase
transition can be minimized by choosing properly designed time-dependent
pulses. In this work we determine what are the ultimate limits of this
optimization. We discuss under which conditions the production of defects
across the phase transition is vanishing small. Furthermore we show that the
minimum time required to enter this regime is , where
is the minimum spectral gap, unveiling an intimate connection between
an optimized unitary dynamics and the intrinsic measure of the Hilbert space
for pure states. Surprisingly, the dynamics is non-adiabatic, this result can
be understood by assuming a simple two-level dynamics for the many-body system.
Finally we classify the possible dynamical regimes in terms of the action
.Comment: 6 pages, 6 figure
Adiabatic quantum dynamics of the Lipkin-Meshkov-Glick model
The adiabatic quantum evolution of the Lipkin-Meshkov-Glick (LMG) model
across its quantum critical point is studied. The dynamics is realized by
linearly switching the transverse field from an initial large value towards
zero and considering different transition rates. We concentrate our attention
on the residual energy after the quench in order to estimate the level of
diabaticity of the evolution. We discuss a Landau-Zener approximation of the
finite size LMG model, that is successful in reproducing the behavior of the
residual energy as function of the transition rate in the most part of the
regimes considered. We also support our description through the analysis of the
entanglement entropy of the evolved state. The system proposed is a paradigm of
infinite-range interaction or high-dimensional models.Comment: 8 pages, 7 figures. (v2) minor revisions, published versio
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Noise-Resistant Optimal Spin Squeezing via Quantum Control
Entangled atomic states, such as spin squeezed states, represent a promising resource for a new generation of quantum sensors and atomic clocks. We demonstrate that optimal control techniques can be used to substantially enhance the degree of spin squeezing in strongly interacting many-body systems, even in the presence of noise and imperfections. Specifically, we present a time-optimal protocol that yields more than two orders of magnitude improvement with respect to conventional adiabatic preparation. Potential experimental implementations are discussed.Physic
Chopped random-basis quantum optimization
In this work we describe in detail the "Chopped RAndom Basis" (CRAB) optimal
control technique recently introduced to optimize t-DMRG simulations
[arXiv:1003.3750]. Here we study the efficiency of this control technique in
optimizing different quantum processes and we show that in the considered cases
we obtain results equivalent to those obtained via different optimal control
methods while using less resources. We propose the CRAB optimization as a
general and versatile optimal control technique.Comment: 9 pages, 10 figure
Adiabatic quantum dynamics of a random Ising chain across its quantum critical point
We present here our study of the adiabatic quantum dynamics of a random Ising
chain across its quantum critical point. The model investigated is an Ising
chain in a transverse field with disorder present both in the exchange coupling
and in the transverse field. The transverse field term is proportional to a
function which, as in the Kibble-Zurek mechanism, is linearly
reduced to zero in time with a rate , , starting
at from the quantum disordered phase () and ending
at in the classical ferromagnetic phase (). We first analyze
the distribution of the gaps -- occurring at the critical point --
which are relevant for breaking the adiabaticity of the dynamics. We then
present extensive numerical simulations for the residual energy
and density of defects at the end of the annealing, as a function of
the annealing inverse rate . %for different lenghts of the chain. Both
the average and are found to behave
logarithmically for large , but with different exponents, with , and
. We propose a mechanism for
-behavior of based on the Landau-Zener
tunneling theory and on a Fisher's type real-space renormalization group
analysis of the relevant gaps. The model proposed shows therefore a
paradigmatic example of how an adiabatic quantum computation can become very
slow when disorder is at play, even in absence of any source of frustration.Comment: 10 pages, 11 figures; v2: added references, published versio
Quantum dynamics of propagating photons with strong interactions: a generalized input-output formalism
There has been rapid development of systems that yield strong interactions
between freely propagating photons in one dimension via controlled coupling to
quantum emitters. This raises interesting possibilities such as quantum
information processing with photons or quantum many-body states of light, but
treating such systems generally remains a difficult task theoretically. Here,
we describe a novel technique in which the dynamics and correlations of a few
photons can be exactly calculated, based upon knowledge of the initial photonic
state and the solution of the reduced effective dynamics of the quantum
emitters alone. We show that this generalized "input-output" formalism allows
for a straightforward numerical implementation regardless of system details,
such as emitter positions, external driving, and level structure. As a specific
example, we apply our technique to show how atomic systems with infinite-range
interactions and under conditions of electromagnetically induced transparency
enable the selective transmission of correlated multi-photon states