640 research outputs found
Phase Estimation from Atom Position Measurements
We study the measurement of the position of atoms as a means to estimate the
relative phase between two Bose-Einstein condensates. First, we consider
atoms released from a double-well trap, forming an interference pattern, and
show that a simple least-squares fit to the density gives a shot-noise limited
sensitivity. The shot-noise limit can instead be overcome by using correlation
functions of order or larger. The measurement of the
-order correlation function allows to estimate the relative phase
at the Heisenberg limit. Phase estimation through the measurement of the
center-of-mass of the interference pattern can also provide sub-shot-noise
sensitivity. Finally, we study the effect of the overlap between the two clouds
on the phase estimation, when Mach-Zehnder interferometry is performed in a
double-well.Comment: 20 pages, 6 figure
Mach-Zehnder interferometry with interacting trapped Bose-Einstein condensates
We theoretically analyze a Mach-Zehnder interferometer with trapped
condensates, and find that it is surprisingly stable against the nonlinearity
induced by inter-particle interactions. The phase sensitivity, which we study
for number squeezed input states, can overcome the shot noise limit and be
increased up to the Heisenberg limit provided that a Bayesian or
Maximum-Likelihood phase estimation strategy is used. We finally demonstrate
robustness of the Mach-Zehnder interferometer in presence of interactions
against condensate oscillations and a realistic atom counting error.Comment: 4 pages, 5 figures, minor revision
Atom interferometry with trapped Bose-Einstein condensates: Impact of atom-atom interactions
Interferometry with ultracold atoms promises the possibility of ultraprecise
and ultrasensitive measurements in many fields of physics, and is the basis of
our most precise atomic clocks. Key to a high sensitivity is the possibility to
achieve long measurement times and precise readout. Ultra cold atoms can be
precisely manipulated at the quantum level, held for very long times in traps,
and would therefore be an ideal setting for interferometry. In this paper we
discuss how the non-linearities from atom-atom interactions on one hand allow
to efficiently produce squeezed states for enhanced readout, but on the other
hand result in phase diffusion which limits the phase accumulation time. We
find that low dimensional geometries are favorable, with two-dimensional (2D)
settings giving the smallest contribution of phase diffusion caused by
atom-atom interactions. Even for time sequences generated by optimal control
the achievable minimal detectable interaction energy is on
the order of 0.001 times the chemical potential of the BEC in the trap. From
there we have to conclude that for more precise measurements with atom
interferometers more sophisticated strategies, or turning off the interaction
induced dephasing during the phase accumulation stage, will be necessary.Comment: 28 pages, 13 figures, extended and correcte
Spin squeezing, entanglement and quantum metrology with Bose-Einstein condensates
Squeezed states, a special kind of entangled states, are known as a useful
resource for quantum metrology. In interferometric sensors they allow to
overcome the "classical" projection noise limit stemming from the independent
nature of the individual photons or atoms within the interferometer. Motivated
by the potential impact on metrology as wells as by fundamental questions in
the context of entanglement, a lot of theoretical and experimental effort has
been made to study squeezed states. The first squeezed states useful for
quantum enhanced metrology have been proposed and generated in quantum optics,
where the squeezed variables are the coherences of the light field. In this
tutorial we focus on spin squeezing in atomic systems. We give an introduction
to its concepts and discuss its generation in Bose-Einstein condensates. We
discuss in detail the experimental requirements necessary for the generation
and direct detection of coherent spin squeezing. Two exemplary experiments
demonstrating adiabatically prepared spin squeezing based on motional degrees
of freedom and diabatically realized spin squeezing based on internal hyperfine
degrees of freedom are discussed.Comment: Phd tutorial, 23 pages, 17 figure
Shapiro effect in atomchip-based bosonic Josephson junctions
We analyze the emergence of Shapiro resonances in tunnel-coupled
Bose-Einstein condensates, realizing a bosonic Josephson junction. Our analysis
is based on an experimentally relevant implementation using magnetic double
well potentials on an atomchip. In this configuration the potential bias
(implementing the junction voltage) and the potential barrier (realizing the
Josephson link) are intrinsically coupled. We show that the dynamically driven
system exhibits significantly enhanced Shapiro resonances which will facilitate
experimental observation. To describe the systems response to the dynamic drive
we compare a single-mode Gross-Pitaevskii (GP) description, an improved
two-mode (TM) model and the self-consistent multi-configurational time
dependent Hartree for Bosons (MCTDHB) method. We show that in the case of
significant atom-atom interactions or strong driving, the spatial dynamics of
the involved modes have to be taken into account, and only the MCTDHB method
allows reliable predictions.Comment: 16 pages, 4 figure
Sub shot-noise interferometry from measurements of the one-body density
We derive the asymptotic maximum-likelihood phase estimation uncertainty for
any interferometric protocol where the positions of the probe particles are
measured to infer the phase, but where correlations between the particles are
not accessible. First, we apply our formula to the estimation of the phase
acquired in the Mach-Zehnder interferometer and recover the well-know momentum
formula for the phase sensitivity. Then, we apply our results to
interferometers with two spatially separated modes, which could be implemented
with a Bose-Einstein condensate trapped in a double-well potential. We show
that in a simple protocol which estimates the phase from an interference
pattern a sub shot-noise phase uncertainty of up to can be achieved. One important property of this estimation protocol
is that its sensitivity does not depend on the value of the phase ,
contrary to the sensitivity given by the momentum formula for the Mach-Zehnder
transformation. Finally, we study the experimental implementation of the above
protocol in detail, by numerically simulating the full statistics as well as by
considering the main sources of detection noise, and argue that the shot-noise
limit could be surpassed with current technology.Comment: 19 pages. 4 figure
Recurrent versus first cervical artery dissection - a retrospective study of clinical and vascular characteristics
Background and purpose Most recurrent cervical artery dissection (CeAD) events occur shortly after the acute first CeAD. This study compared the characteristics of recurrent and first CeAD events and searched for associations between subsequent events of an individual person. Methods Cervical artery dissection patients with a new CeAD event occurring during a 3-6 month follow-up were retrospectively selected in seven specialized stroke centers. Clinical and vascular characteristics of the initial and the recurrent CeADs were compared. Results The study sample included 76 patients. Recurrent CeADs were occlusive in one (1.3%) patient, caused cerebral ischaemia in 13 (17.1%) and were asymptomatic in 39 (51.3%) patients, compared to 29 (38.2%) occlusive, 42 (55.3%) ischaemic and no asymptomatic first CeAD events. In 52 (68.4%) patients, recurrent dissections affected both internal carotid arteries or both vertebral arteries, whilst 24 (31.6%) patients had subsequent dissections in both types of artery. Twelve (28.6%) of 42 patients with an ischaemic first dissection had ischaemic symptoms due to the recurrent CeADs, too. However, only one (1.3%) of 34 patients with a non-ischaemic first CeAD suffered ischaemia upon recurrence. Conclusion Recurrent CeAD typically affects the same site of artery. It causes ischaemic events less often than the first CeAD. The risk that patients who presented with solely non-ischaemic symptoms of a first CeAD will have ischaemic symptoms in the case of a recurrent CeAD seems very small.Peer reviewe
Recursive formulation of the multiconfigurational time-dependent Hartree method for fermions, bosons and mixtures thereof in terms of one-body density operators
The multiconfigurational time-dependent Hartree method (MCTDH) [Chem. Phys.
Lett. {\bf 165}, 73 (1990); J. Chem. Phys. {\bf 97}, 3199 (1992)] is
celebrating nowadays entering its third decade of tackling numerically-exactly
a broad range of correlated multi-dimensional non-equilibrium quantum dynamical
systems. Taking in recent years particles' statistics explicitly into account,
within the MCTDH for fermions (MCTDHF) and for bosons (MCTDHB), has opened up
further opportunities to treat larger systems of interacting identical
particles, primarily in laser-atom and cold-atom physics. With the increase of
experimental capabilities to simultaneously trap mixtures of two, three, and
possibly even multiple kinds of interacting composite identical particles
together, we set up the stage in the present work and specify the MCTDH method
for such cases. Explicitly, the MCTDH method for systems with three kinds of
identical particles interacting via all combinations of two- and three-body
forces is presented, and the resulting equations-of-motion are briefly
discussed. All four possible mixtures of fermions and bosons are presented in a
unified manner. Particular attention is paid to represent the coefficients'
part of the equations-of-motion in a compact recursive form in terms of
one-body density operators only. The recursion utilizes the recently proposed
Combinadic-based mapping for fermionic and bosonic operators in Fock space
[Phys. Rev. A {\bf 81}, 022124 (2010)] and successfully applied and implemented
within MCTDHB. Our work sheds new light on the representation of the
coefficients' part in MCTDHF and MCTDHB without resorting to the matrix
elements of the many-body Hamiltonian with respect to the time-dependent
configurations. It suggests a recipe for efficient implementation of the
schemes derived here for mixtures which is suitable for parallelization.Comment: 43 page
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