46 research outputs found
Rosen-Zener model in cold molecule formation
The Rosen-Zener model for association of atoms in a Bose-Einstein condensate
is studied. Using a nonlinear Volterra integral equation, we obtain an analytic
formula for final probability of the transition to the molecular state for weak
interaction limit. Considering the strong coupling limit of high field
intensities, we show that the system reveals two different time-evolution
pictures depending on the detuning of the frequency of the associating field.
For both limit cases we derive highly accurate formulas for the molecular state
probability valid for the whole range of variation of time. Using these
formulas, we show that at large detuning regime the molecule formation process
occurs almost non-oscillatory in time and a Rosen-Zener pulse is not able to
associate more than one third of atoms at any time point. The system returns to
its initial all-atomic state at the end of the process and the maximal
transition probability is achieved when the field intensity reaches its peak.
In contrast, at small detuning the evolution of the system displays
large-amplitude oscillations between atomic and molecular populations. We find
that the shape of the oscillations in the first approximation is defined by the
field detuning only. Finally, a hidden singularity of the Rosen-Zener model due
to the specific time-variation of the field amplitude at the beginning of the
interaction is indicated. It is this singularity that stands for many of the
qualitative and quantitative properties of the model. The singularity may be
viewed as an effective resonance-touching
Two strong nonlinearity regimes in cold molecule formation
Two distinct strongly non-linear scenarios of molecule formation in an atomic
Bose-Einstein condensate (either by photoassociation or Feshbach resonance)
corresponding to large and small field detuning are revealed. By examining
arbitrary external field configurations, we show that the association process
in the first case is almost non-oscillatory in time while in the second case
the evolution of the system displays strongly pronounced Rabi-type
oscillations. We construct highly accurate approximate solutions for both limit
cases. We show that at strong coupling limit the non-crossing models are able
to provide conversion of no more than one third of the initial atomic
population. Finally, we show that for constant-amplitude models involving a
finite final detuning the strong interaction limit is not optimal for molecule
formation
Variational ansatz for the nonlinear Landau-Zener problem for cold atom association
We present a rigorous analysis of the Landau-Zener linear-in-time term
crossing problem for quadratic-nonlinear systems relevant to the coherent
association of ultracold atoms in degenerate quantum gases. Our treatment is
based on an exact third-order nonlinear differential equation for the molecular
state probability. Applying a variational two-term ansatz, we construct a
simple approximation that accurately describes the whole-time dynamics of
coupled atom-molecular system for any set of involved parameters. Ensuring an
absolute error less than for the final transition probability, the resultant
solution improves by several orders of magnitude the accuracy of the previous
approximations by A. Ishkhanyan et al. developed separately for the weak
coupling [J. Phys. A 38, 3505 (2005)] and strong interaction [J. Phys. A 39,
14887 (2006)] limits. In addition, the constructed approximation covers the
whole moderate-coupling regime, providing for this intermediate regime the same
accuracy as for the two mentioned limits. The obtained results reveal the
remarkable observation that for the strong-coupling limit the resonance
crossing is mostly governed by the nonlinearity, while the coherent
atom-molecular oscillations arising soon after the resonance has been crossed
are basically of linear nature. This observation is supposed to be of a general
character due to the basic attributes of the resonance crossing processes in
the nonlinear quantum systems of the discussed type of involved quadratic
nonlinearity
Landau-Zener Problem for Trilinear Hamiltonians
We consider a nonlinear version of the Landau-Zener problem, focusing on
photoassociation of a Bose-Einstein condensate as a specific example. Contrary
to the exponential rate dependence obtained for the linear problem, a series
expansion technique indicates that, when the resonance is crossed slowly, the
probability for failure of adiabaticity is directly proportional to the rate at
which the resonance is crossed.Comment: 4.5 pages, 1 figure, transferred to PRA; v2 adds discussion,
clarification, and explicit numbers for Na and 87R
Coherent Control of Atomic Beam Diffraction by Standing Light
Quantum interference is shown to deliver a means of regulating the
diffraction pattern of a thermal atomic beam interacting with two standing wave
electric fields. Parameters have been identified to enhance the diffraction
probability of one momentum component over the others, with specific
application to Rb atoms.Comment: 5 figure
Strong-coupling limit in cold-molecule formation via photoassociation or Feshbach resonance through Nikitin exponential resonance crossing
The strong-coupling limit of molecule formation in an atomic Bose-Einstein
condensate via two-mode one-color photoassociation or sweep across a Feshbach
resonance is examined using a basic nonlinear time-dependent two-state model.
For the general class of term-crossing models with constant coupling, a common
strategy for attacking the problem is developed based on the reduction of the
initial system of semiclassical equations for atom-molecule amplitudes to a
third order nonlinear differential equation for the molecular state
probability. This equation provides deriving exact solution for a class of
periodic level-crossing models. These models reveal much in common with the
Rabi problem. Discussing the strong-coupling limit for the general case of
variable detuning, the equation is further truncated to a limit first-order
nonlinear equation. Using this equation, the strong nonlinearity regime for the
first Nikitin exponential-crossing model is analyzed and accurate asymptotic
expressions for the nonlinear transition probability to the molecular state are
derived. It is shown that, because of a finite final detuning involved, this
model displays essential deviations from the Landau-Zener behavior. In
particular, it is shown that in the limit of strong coupling the final
conversion probability tends to 1/6. Thus, in this case the strong interaction
limit is not optimal for molecule formation. We have found that if optimal
field intensity is applied the molecular probability is increased up to 1/4
(i.e., the half of the initial atomic population)
A global experiment on motivating social distancing during the COVID-19 pandemic
Finding communication strategies that effectively motivate social distancing continues to be a global public health priority during the COVID-19 pandemic. This cross-country, preregistered experiment (n = 25,718 from 89 countries) tested hypotheses concerning generalizable positive and negative outcomes of social distancing messages that promoted personal agency and reflective choices (i.e., an autonomy-supportive message) or were restrictive and shaming (i.e., a controlling message) compared with no message at all. Results partially supported experimental hypotheses in that the controlling message increased controlled motivation (a poorly internalized form of motivation relying on shame, guilt, and fear of social consequences) relative to no message. On the other hand, the autonomy-supportive message lowered feelings of defiance compared with the controlling message, but the controlling message did not differ from receiving no message at all. Unexpectedly, messages did not influence autonomous motivation (a highly internalized form of motivation relying on one’s core values) or behavioral intentions. Results supported hypothesized associations between people’s existing autonomous and controlled motivations and self-reported behavioral intentions to engage in social distancing. Controlled motivation was associated with more defiance and less long-term behavioral intention to engage in social distancing, whereas autonomous motivation was associated with less defiance and more short- and long-term intentions to social distance. Overall, this work highlights the potential harm of using shaming and pressuring language in public health communication, with implications for the current and future global health challenges
A global experiment on motivating social distancing during the COVID-19 pandemic
Finding communication strategies that effectively motivate social distancing continues to be a global public health priority during the COVID-19 pandemic. This cross-country, preregistered experiment (n = 25,718 from 89 countries) tested hypotheses concerning generalizable positive and negative outcomes of social distancing messages that promoted personal agency and reflective choices (i.e., an autonomy-supportive message) or were restrictive and shaming (i.e. a controlling message) compared to no message at all. Results partially supported experimental hypotheses in that the controlling message increased controlled motivation (a poorly-internalized form of motivation relying on shame, guilt, and fear of social consequences) relative to no message. On the other hand, the autonomy-supportive message lowered feelings of defiance compared to the controlling message, but the controlling message did not differ from receiving no message at all. Unexpectedly, messages did not influence autonomous motivation (a highly-internalized form of motivation relying on one’s core values) or behavioral intentions. Results supported hypothesized associations between people’s existing autonomous and controlled motivations and self-reported behavioral intentions to engage in social distancing: Controlled motivation was associated with more defiance and less long-term behavioral intentions to engage in social distancing, whereas autonomous motivation was associated with less defiance and more short- and long-term intentions to social distance. Overall, this work highlights the potential harm of using shaming and pressuring language in public health communication, with implications for the current and future global health challenges
A global experiment on motivating social distancing during the COVID-19 pandemic
Significance
Communicating in ways that motivate engagement in social distancing remains a critical global public health priority during the COVID-19 pandemic. This study tested motivational qualities of messages about social distancing (those that promoted choice and agency vs. those that were forceful and shaming) in 25,718 people in 89 countries. The autonomy-supportive message decreased feelings of defying social distancing recommendations relative to the controlling message, and the controlling message increased controlled motivation, a less effective form of motivation, relative to no message. Message type did not impact intentions to socially distance, but people’s existing motivations were related to intentions. Findings were generalizable across a geographically diverse sample and may inform public health communication strategies in this and future global health emergencies.
Abstract
Finding communication strategies that effectively motivate social distancing continues to be a global public health priority during the COVID-19 pandemic. This cross-country, preregistered experiment (n = 25,718 from 89 countries) tested hypotheses concerning generalizable positive and negative outcomes of social distancing messages that promoted personal agency and reflective choices (i.e., an autonomy-supportive message) or were restrictive and shaming (i.e., a controlling message) compared with no message at all. Results partially supported experimental hypotheses in that the controlling message increased controlled motivation (a poorly internalized form of motivation relying on shame, guilt, and fear of social consequences) relative to no message. On the other hand, the autonomy-supportive message lowered feelings of defiance compared with the controlling message, but the controlling message did not differ from receiving no message at all. Unexpectedly, messages did not influence autonomous motivation (a highly internalized form of motivation relying on one’s core values) or behavioral intentions. Results supported hypothesized associations between people’s existing autonomous and controlled motivations and self-reported behavioral intentions to engage in social distancing. Controlled motivation was associated with more defiance and less long-term behavioral intention to engage in social distancing, whereas autonomous motivation was associated with less defiance and more short- and long-term intentions to social distance. Overall, this work highlights the potential harm of using shaming and pressuring language in public health communication, with implications for the current and future global health challenges