12 research outputs found
Reduced dimensionality and spatial entanglement in highly anisotropic Bose-Einstein condensates
We investigate the reduced dimensionality of highly anisotropic Bose-Einstein
condensates (BECs) in connection to the entanglement between its spatial
degrees of freedom. We argue that the reduced-dimensionality of the BEC is
physically meaningful in a regime where spatial correlations are negligible. We
handle the problem analytically within the mean-field approximation for general
quasi-one-dimensional and -two-dimensional geometries, and obtain the optimal
reduced-dimension, pure-state description of the condensate mean field. We give
explicit solutions to the case of harmonic potentials, which we compare against
exact numerical integration of the three-dimensional Gross-Pitaevskii equation.Comment: 15 pages, 3 figures. Minor changes in text to be in agreement with
published versio
Entanglement-based perturbation theory for highly anisotropic Bose-Einstein condensates
We investigate the emergence of three-dimensional behavior in a
reduced-dimension Bose-Einstein condensate trapped by a highly anisotropic
potential. We handle the problem analytically by performing a perturbative
Schmidt decomposition of the condensate wave function between the tightly
confined (transverse) direction(s) and the loosely confined (longitudinal)
direction(s). The perturbation theory is valid when the nonlinear scattering
energy is small compared to the transverse energy scales. Our approach provides
a straightforward way, first, to derive corrections to the transverse and
longitudinal wave functions of the reduced-dimension approximation and, second,
to calculate the amount of entanglement that arises between the transverse and
longitudinal spatial directions. Numerical integration of the three-dimensional
Gross-Pitaevskii equation for different cigar-shaped potentials and
experimentally accessible parameters reveals good agreement with our analytical
model even for relatively high nonlinearities. In particular, we show that even
for such stronger nonlinearities the entanglement remains remarkably small,
which allows the condensate to be well described by a product wave function
that corresponds to a single Schmidt term.Comment: 12 pages, 7 figure
Mean-field dynamics of two-mode Bose-Einstein condensates in highly anisotropic potentials: Interference, dimensionality, and entanglement
We study the mean-field dynamics and the reduced-dimension character of
two-mode Bose-Einstein condensates (BECs) in highly anisotropic traps. By means
of perturbative techniques, we show that the tightly confined (transverse)
degrees of freedom can be decoupled from the dynamical equations at the expense
of introducing additional effective three-body, attractive, intra- and
inter-mode interactions into the dynamics of the loosely confined
(longitudinal) degrees of freedom. These effective interactions are mediated by
changes in the transverse wave function. The perturbation theory is valid as
long as the nonlinear scattering energy is small compared to the transverse
energy scales. This approach leads to reduced-dimension mean-field equations
that optimally describe the evolution of a two-mode condensate in general
quasi-1D and quasi-2D geometries. We use this model to investigate the relative
phase and density dynamics of a two-mode, cigar-shaped Rb BEC. We study
the relative-phase dynamics in the context of a nonlinear Ramsey interferometry
scheme, which has recently been proposed as a novel platform for high-precision
interferometry. Numerical integration of the coupled, time-dependent,
three-dimensional, two-mode Gross-Pitaevskii equations for various atom numbers
shows that this model gives a considerably more refined analytical account of
the mean-field evolution than an idealized quasi-1D description.Comment: 35 pages, 10 figures. Current version is as publishe
Nonlinear interferometry with Bose-Einstein condensates
We analyze a proposed experiment [Boixo et al., Phys. Rev. Lett. 101, 040403 (2008)] for achieving sensitivity scaling better than 1/N in a nonlinear Ramsey interferometer that uses a two-mode Bose-Einstein condensate (BEC) of N atoms. We present numerical simulations that confirm the analytical predictions for the effect of the spreading of the BEC ground-state wave function on the ideal 1/N^(3/2) scaling. Numerical integration of the coupled, time-dependent, two-mode Gross-Pitaevskii equations allows us to study the several simplifying assumptions made in the initial analytic study of the proposal and to explore when they can be justified. In particular, we find that the two modes share the same spatial wave function for a length of time that is sufficient to run the metrology scheme
Quantum metrology with Bose-Einstein condensates
We show how a generalized quantum metrology protocol can be implemented in a two-mode Bose-Einstein condensate of n atoms, achieving a sensitivity that scales better than 1/n and approaches 1/n^(3/2) for appropriate design of the condensate
Majorization-based benchmark of the complexity of quantum processors
Here we investigate the use of the majorization-based indicator introduced in
[R. O. Vallejos, F. de Melo, and G. G. Carlo, Phys. Rev. A 104, 012602 (2021)]
as a way to benchmark the complexity within reach of quantum processors. By
considering specific architectures and native gate sets of currently available
technologies, we numerically simulate and characterize the operation of various
quantum processors. We characterize their complexity for different native gate
sets, qubit connectivity and increasing number of gates. We identify and assess
quantum complexity by comparing the performance of each device against
benchmark lines provided by randomized Clifford circuits and Haar-random pure
states. In this way, we are able to specify, for each specific processor, the
number of native quantum gates which are necessary, on average, for achieving
those levels of complexity. Lastly, we study the performance of the
majorization-based characterization in the presence of distinct types of noise.
We find that the majorization-based benchmark holds as long as the circuits'
output states have, on average, high purity (). In such cases, the
indicator showed no significant differences from the noiseless case.Comment: 12 pages, 15 figure
Quantum-limited metrology and Bose-Einstein condensates
We discuss a quantum-metrology protocol designed to estimate a physical
parameter in a Bose-Einstein condensate of N atoms, and we show that the
measurement uncertainty can decrease faster than 1/N. The 1/N scaling is
usually thought to be the best possible in any measurement scheme. From the
perspective of quantum information theory, we outline the main idea that leads
to a measurement uncertainty that scales better than 1/N. We examine in detail
some potential problems and challenges that arise in implementing such a
measurement protocol using a Bose-Einstein condensate. We discuss how some of
these issues can be dealt with by using lower-dimensional condensates trapped
in nonharmonic potentials.Comment: 32 pages, 1 figure, updated reference
Tunable electron-electron interactions in LaAlO3/SrTiO3 nanostructures
The interface between the two complex oxides LaAlO3 and SrTiO3 has remarkable
properties that can be locally reconfigured between conducting and insulating
states using a conductive atomic force microscope. Prior investigations of
sketched quantum dot devices revealed a phase in which electrons form pairs,
implying a strongly attractive electron-electron interaction. Here, we show
that these devices with strong electron-electron interactions can exhibit a
gate-tunable transition from a pair-tunneling regime to a single-electron
(Andreev bound state) tunneling regime where the interactions become repulsive.
The electron-electron interaction sign change is associated with a Lifshitz
transition where the dxz and dyz bands start to become occupied. This
electronically tunable electron-electron interaction, combined with the
nanoscale reconfigurability of this system, provides an interesting starting
point towards solid-state quantum simulation.Comment: 25 pages, 7 figure
Quantum metrology from an information theory perspective
Questions about quantum limits on measurement precision were once viewed from the perspective of how to reduce or avoid the effects of quantum noise. With the advent of quantum information science came a paradigm shift to proving rigorous bounds on measurement precision. These bounds have been interpreted as saying, first, that the best achievable sensitivity scales as 1/n, where n is the number of particles one has available for a measurement and, second, that the only way to achieve this Heisenberg-Umited sensitivity is to use quantum entanglement. We review these residts and show that using quadratic couplings of n particles to a parameter to be estimated, one can achieve sensitivities that scale as 1/n if one uses entanglement, but even in the absence of any entanglement at any time during the measurement protocol, one can achieve a super-Heisenberg scaUng of 1/n'