221 research outputs found
Time-Optimal Frictionless Atom Cooling in Harmonic Traps
Frictionless atom cooling in harmonic traps is formulated as a time-optimal
control problem and a synthesis of optimal controlled trajectories is obtained.
This work has already been used to determine the minimum time for transition
between two thermal states and to show the emergence of the third law of
classical thermodynamics from quantum thermodynamics. It can also find
application in the fast adiabatic-like expansion of Bose-Einstein condensates,
with possible applications in atom interferometry. This paper is based on our
recently published article in SIAM J. Control Optim.Comment: Submitted to 51st IEEE Conference on Decision and Control as a SIAM
regular paper, it is a shorter version of our recently published article in
SIAM J. Control Optim., vol. 49, pp. 2440-2462, 2011. It contains an elegant
proof of the main technical point using the symmetries of the system, and a
discussion of the implications of the results on finite time thermodynamic
processe
Time-Optimal Adiabatic-Like Expansion of Bose-Einstein Condensates
In this paper we study the fast adiabatic-like expansion of a one-dimensional
Bose-Einstein condensate (BEC) confined in a harmonic potential, using the
theory of time-optimal control. We find that under reasonable assumptions
suggested by the experimental setup, the minimum-time expansion occurs when the
frequency of the potential changes in a bang-bang form between the permitted
values. We calculate the necessary expansion time and show that it scales
logarithmically with large values of the expansion factor. This work is
expected to find applications in areas where the efficient manipulations of BEC
is of utmost importance. As an example we present the field of atom
interferometry with BEC, where the wavelike properties of atoms are used to
perform interference experiments that measure with unprecedented precision
small shifts induced by phenomena like rotation, acceleration, and gravity
gradients.Comment: Submitted to 51st IEEE Conference on Decision and Contro
Squeezing and robustness of frictionless cooling strategies
Quantum control strategies that provide shortcuts to adiabaticity are
increasingly considered in various contexts including atomic cooling. Recent
studies have emphasized practical issues in order to reduce the gap between the
idealized models and actual ongoing implementations. We rephrase here the
cooling features in terms of a peculiar squeezing effect, and use it to
parametrize the robustness of frictionless cooling techniques with respect to
noise-induced deviations from the ideal time-dependent trajectory for the
trapping frequency. We finally discuss qualitative issues for the experimental
implementation of this scheme using bichromatic optical traps and lattices,
which seem especially suitable for cooling Fermi-Bose mixtures and for
investigating equilibration of negative temperature states, respectively.Comment: 9 pages, 7 figures; To appear in Physical Review
Shortcuts to adiabaticity in a time-dependent box
A method is proposed to drive an ultrafast non-adiabatic dynamics of an
ultracold gas trapped in a box potential. The resulting state is free from
spurious excitations associated with the breakdown of adiabaticity, and
preserves the quantum correlations of the initial state up to a scaling factor.
The process relies on the existence of an adiabatic invariant and the inversion
of the dynamical self-similar scaling law dictated by it. Its physical
implementation generally requires the use of an auxiliary expulsive potential
analogous to those used in soliton control. The method is extended to a broad
family of many-body systems. As illustrative examples we consider the ultrafast
expansion of a Tonks-Girardeau gas and of Bose-Einstein condensates in
different dimensions, where the method exhibits an excellent robustness against
different regimes of interactions and the features of an experimentally
realizable box potential.Comment: 6 pp, 4 figures, typo in Eq. (6) fixe
Cooling and thermometry of atomic Fermi gases
We review the status of cooling techniques aimed at achieving the deepest
quantum degeneracy for atomic Fermi gases. We first discuss some physical
motivations, providing a quantitative assessment of the need for deep quantum
degeneracy in relevant physics cases, such as the search for unconventional
superfluid states. Attention is then focused on the most widespread technique
to reach deep quantum degeneracy for Fermi systems, sympathetic cooling of
Bose-Fermi mixtures, organizing the discussion according to the specific
species involved. Various proposals to circumvent some of the limitations on
achieving the deepest Fermi degeneracy, and their experimental realizations,
are then reviewed. Finally, we discuss the extension of these techniques to
optical lattices and the implementation of precision thermometry crucial to the
understanding of the phase diagram of classical and quantum phase transitions
in Fermi gases.Comment: 33 pages, 15 figures, contribution to the 100th anniversary of the
birth of Vitaly L. Ginzbur
Ehrenfest Dynamics and Frictionless Cooling Methods
Recently introduced methods which result in shortcuts to adiabaticity,
particularly in the context of frictionless cooling, are rederived and
discussed in the framework of an approach based on Ehrenfest dynamics. This
construction provides physical insights into the emergence of the Ermakov
equation, the choice of its boundary conditions, and the use of minimum
uncertainty states as indicators of the efficiency of the procedure.
Additionally, it facilitates the extension of frictionless cooling to more
general situations of physical relevance, such as optical dipole trapping
schemes. In this context, we discuss frictionless cooling in the short-time
limit, a complementary case to the one considered in the literature, making
explicit the limitations intrinsic to the technique when the full
three-dimensional case is analyzed.Comment: 9 pages, 4 figures, v2: To appear in Physical Review A. (some minor
typos corrected and some references added
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