764 research outputs found
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
Quantum annealing for systems of polynomial equations
Numerous scientific and engineering applications require numerically solving
systems of equations. Classically solving a general set of polynomial equations
requires iterative solvers, while linear equations may be solved either by
direct matrix inversion or iteratively with judicious preconditioning. However,
the convergence of iterative algorithms is highly variable and depends, in
part, on the condition number. We present a direct method for solving general
systems of polynomial equations based on quantum annealing, and we validate
this method using a system of second-order polynomial equations solved on a
commercially available quantum annealer. We then demonstrate applications for
linear regression, and discuss in more detail the scaling behavior for general
systems of linear equations with respect to problem size, condition number, and
search precision. Finally, we define an iterative annealing process and
demonstrate its efficacy in solving a linear system to a tolerance of
.Comment: 11 pages, 4 figures. Added example for a system of quadratic
equations. Supporting code is available at
https://github.com/cchang5/quantum_poly_solver . This is a post-peer-review,
pre-copyedit version of an article published in Scientific Reports. The final
authenticated version is available online at:
https://www.nature.com/articles/s41598-019-46729-
Floquet-engineered quantum state manipulation in a noisy qubit
Adiabatic evolution is a common strategy for manipulating quantum states and
has been employed in diverse fields such as quantum simulation, computation and
annealing. However, adiabatic evolution is inherently slow and therefore
susceptible to decoherence. Existing methods for speeding up adiabatic
evolution require complex many-body operators or are difficult to construct for
multi-level systems. Using the tools of Floquet engineering, we design a scheme
for high-fidelity quantum state manipulation, utilizing only the interactions
available in the original Hamiltonian. We apply this approach to a qubit and
experimentally demonstrate its performance with the electronic spin of a
Nitrogen-vacancy center in diamond. Our Floquet-engineered protocol achieves
state preparation fidelity of , on the same level as the
conventional fast-forward protocol, but is more robust to external noise acting
on the qubit. Floquet engineering provides a powerful platform for
high-fidelity quantum state manipulation in complex and noisy quantum systems
Landau-Zener problem with waiting at the minimum gap and related quench dynamics of a many-body system
We discuss a technique for solving the Landau-Zener (LZ) problem of finding
the probability of excitation in a two-level system. The idea of time reversal
for the Schrodinger equation is employed to obtain the state reached at the
final time and hence the excitation probability. Using this method, which can
reproduce the well-known expression for the LZ transition probability, we solve
a variant of the LZ problem which involves waiting at the minimum gap for a
time t_w; we find an exact expression for the excitation probability as a
function of t_w. We provide numerical results to support our analytical
expressions. We then discuss the problem of waiting at the quantum critical
point of a many-body system and calculate the residual energy generated by the
time-dependent Hamiltonian. Finally we discuss possible experimental
realizations of this work.Comment: 6 pages including 3 figures; significantly expanded -- this is the
published versio
Recommended from our members
Finding Low-Energy Conformations of Lattice Protein Models by Quantum Annealing
Lattice protein folding models are a cornerstone of computational biophysics. Although these models are a coarse grained representation, they provide useful insight into the energy landscape of natural proteins. Finding low-energy threedimensional structures is an intractable problem even in the simplest model, the Hydrophobic-Polar (HP) model. Description of protein-like properties are more accurately described by generalized models, such as the one proposed by Miyazawa and Jernigan (MJ), which explicitly take into account the unique interactions among all 20 amino acids. There is theoretical and experimental evidence of the advantage of solving classical optimization problems using quantum annealing over its classical analogue (simulated annealing). In this report, we present a benchmark implementation of quantum annealing for lattice protein folding problems (six different experiments up to 81 superconducting quantum bits). This first implementation of a biophysical problem paves the way towards studying optimization problems in biophysics and statistical mechanics using quantum devices.Chemistry and Chemical Biolog
Quantum metrology with nonclassical states of atomic ensembles
Quantum technologies exploit entanglement to revolutionize computing,
measurements, and communications. This has stimulated the research in different
areas of physics to engineer and manipulate fragile many-particle entangled
states. Progress has been particularly rapid for atoms. Thanks to the large and
tunable nonlinearities and the well developed techniques for trapping,
controlling and counting, many groundbreaking experiments have demonstrated the
generation of entangled states of trapped ions, cold and ultracold gases of
neutral atoms. Moreover, atoms can couple strongly to external forces and light
fields, which makes them ideal for ultra-precise sensing and time keeping. All
these factors call for generating non-classical atomic states designed for
phase estimation in atomic clocks and atom interferometers, exploiting
many-body entanglement to increase the sensitivity of precision measurements.
The goal of this article is to review and illustrate the theory and the
experiments with atomic ensembles that have demonstrated many-particle
entanglement and quantum-enhanced metrology.Comment: 76 pages, 40 figures, 1 table, 603 references. Some figures bitmapped
at 300 dpi to reduce file siz
- …