91 research outputs found
Entanglement and sensitivity in precision measurements with states of a fluctuating number of particles
The concepts of separability, entanglement, spin-squeezing and Heisenberg
limit are central in the theory of quantum enhanced metrology. In the current
literature, these are well established only in the case of linear
interferometers operating with input quantum states of a known fixed number of
particles. This manuscript generalizes these concepts and extends the quantum
phase estimation theory by taking into account classical and quantum
fluctuations of the particle number. Our analysis concerns most of the current
experiments on precision measurements where the number of particles is known
only in average.Comment: Published versio
Non-Linear Beam Splitter in Bose-Einstein Condensate Interferometers
A beam splitter is an important component of an atomic/optical Mach-Zehnder
interferometer. Here we study a Bose Einstein Condensate beam splitter,
realized with a double well potential of tunable height. We analyze how the
sensitivity of a Mach Zehnder interferometer is degraded by the non-linear
particle-particle interaction during the splitting dynamics. We distinguish
three regimes, Rabi, Josephson and Fock, and associate to them a different
scaling of the phase sensitivity with the total number of particles.Comment: draft, 19 pages, 10 figure
Localized and extended states in a disordered trap
We study Anderson localization in a disordered potential combined with an
inhomogeneous trap. We show that the spectrum displays both localized and
extended states, which coexist at intermediate energies. In the region of
coexistence, we find that the extended states result from confinement by the
trap and are weakly affected by the disorder. Conversely, the localized states
correspond to eigenstates of the disordered potential, which are only affected
by the trap via an inhomogeneous energy shift. These results are relevant to
disordered quantum gases and we propose a realistic scheme to observe the
coexistence of localized and extended states in these systems.Comment: Published versio
Quantum metrology at the Heisenberg limit with ion traps
Sub-Planck phase-space structures in the Wigner function of the motional
degree of freedom of a trapped ion can be used to perform weak force
measurements with Heisenberg-limited sensitivity. We propose methods to
engineer the Hamiltonian of the trapped ion to generate states with such small
scale structures, and we show how to use them in quantum metrology
applications.Comment: 10 pages, 6 figure
Sub Shot-Noise Phase Sensitivity with a Bose-Einstein Condensate Mach-Zehnder Interferometer
Bose Einstein Condensates, with their coherence properties, have attracted
wide interest for their possible application to ultra precise interferometry
and ultra weak force sensors. Since condensates, unlike photons, are
interacting, they may permit the realization of specific quantum states needed
as input of an interferometer to approach the Heisenberg limit, the supposed
lower bound to precision phase measurements. To this end, we study the
sensitivity to external weak perturbations of a representative matter-wave
Mach-Zehnder interferometer whose input are two Bose-Einstein condensates
created by splitting a single condensate in two parts. The interferometric
phase sensitivity depends on the specific quantum state created with the two
condensates, and, therefore, on the time scale of the splitting process. We
identify three different regimes, characterized by a phase sensitivity scaling with the total number of condensate particles as i) the
standard quantum limit , ii) the sub shot-noise
and the iii) the Heisenberg limit . However, in a realistic dynamical BEC splitting, the 1/N limit
requires a long adiabaticity time scale, which is hardly reachable
experimentally. On the other hand, the sub shot-noise sensitivity can be reached in a realistic experimental setting. We
also show that the scaling is a rigorous upper bound in the limit
, while keeping constant all different parameters of the bosonic
Mach-Zehnder interferometer.Comment: 4 figure
Phase detection at the quantum limit with multi-photon Mach-Zehnder interferometry
We study a Mach-Zehnder interferometer fed by a coherent state in one input
port and vacuum in the other. We explore a Bayesian phase estimation strategy
to demonstrate that it is possible to achieve the standard quantum limit
independently from the true value of the phase shift and specific assumptions
on the noise of the interferometer. We have been able to implement the protocol
using parallel operation of two photon-number-resolving detectors and
multiphoton coincidence logic electronics at the output ports of a
weakly-illuminated Mach-Zehnder interferometer. This protocol is unbiased and
saturates the Cramer-Rao phase uncertainty bound and, therefore, is an optimal
phase estimation strategy.Comment: 4 pages, 5 figures replaced fig. 1 to correct graphics bu
Mach-Zehnder Interferometry at the Heisenberg Limit with coherent and squeezed-vacuum light
We show that the phase sensitivity of a Mach-Zehnder
interferometer fed by a coherent state in one input port and squeezed-vacuum in
the other one is i) independent from the true value of the phase shift and ii)
can reach the Heisenberg limit , where is the
average number of particles of the input states. We also show that the
Cramer-Rao lower bound, , can be saturated for arbitrary values of the squeezing parameter
and the amplitude of the coherent mode by a Bayesian phase
inference protocol.Comment: 4 pages, 4 figure
Anisotropic 2D diffusive expansion of ultra-cold atoms in a disordered potential
We study the horizontal expansion of vertically confined ultra-cold atoms in
the presence of disorder. Vertical confinement allows us to realize a situation
with a few coupled harmonic oscillator quantum states. The disordered potential
is created by an optical speckle at an angle of 30{\deg} with respect to the
horizontal plane, resulting in an effective anisotropy of the correlation
lengths of a factor of 2 in that plane. We observe diffusion leading to
non-Gaussian density profiles. Diffusion coefficients, extracted from the
experimental results, show anisotropy and strong energy dependence, in
agreement with numerical calculations
Double-Slit Interferometry with a Bose-Einstein Condensate
A Bose-Einstein "double-slit" interferometer has been recently realized
experimentally by (Y. Shin et. al., Phys. Rev. Lett. 92 50405 (2004)). We
analyze the interferometric steps by solving numerically the time-dependent
Gross-Pitaevski equation in three-dimensional space. We focus on the
adiabaticity time scales of the problem and on the creation of spurious
collective excitations as a possible source of the strong dephasing observed
experimentally. The role of quantum fluctuations is discussed.Comment: 4 pages, 3 figure
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