22 research outputs found
A dynamic scheme for generating number squeezing in Bose-Einstein condensates through nonlinear interactions
We develop a scheme to generate number squeezing in a Bose-Einstein
condensate by utilizing interference between two hyperfine levels and nonlinear
atomic interactions. We describe the scheme using a multimode quantum field
model and find agreement with a simple analytic model in certain regimes. We
demonstrate that the scheme gives strong squeezing for realistic choices of
parameters and atomic species. The number squeezing can result in noise well
below the quantum limit, even if the initial noise on the system is classical
and much greater than that of a poisson distribution.Comment: 4 pages, 3 figure
XMDS2: Fast, scalable simulation of coupled stochastic partial differential equations
XMDS2 is a cross-platform, GPL-licensed, open source package for numerically
integrating initial value problems that range from a single ordinary
differential equation up to systems of coupled stochastic partial differential
equations. The equations are described in a high-level XML-based script, and
the package generates low-level optionally parallelised C++ code for the
efficient solution of those equations. It combines the advantages of high-level
simulations, namely fast and low-error development, with the speed, portability
and scalability of hand-written code. XMDS2 is a complete redesign of the XMDS
package, and features support for a much wider problem space while also
producing faster code.Comment: 9 pages, 5 figure
Exact and lower bounds for the quantum speed limit in finite dimensional systems
A fundamental problem in quantum engineering is determining the lowest time
required to ensure that all possible unitaries can be generated with the tools
available, which is one of a number of possible quantum speed limits. We
examine this problem from the perspective of quantum control, where the system
of interest is described by a drift Hamiltonian and set of control
Hamiltonians. Our approach uses a combination of Lie algebra theory, Lie groups
and differential geometry, and formulates the problem in terms of geodesics on
a differentiable manifold. We provide explicit lower bounds on the quantum
speed limit for the case of an arbitrary drift, requiring only that the control
Hamiltonians generate a topologically closed subgroup of the full unitary
group, and formulate criteria as to when our expression for the speed limit is
exact and not merely a lower bound. These analytic results are then tested and
confirmed using a numerical optimization scheme. Finally we extend the analysis
to find a lower bound on the quantum speed limit in the common case where the
system is described by a drift Hamiltonian and a single control Hamiltonian.Comment: 13 page
Multimode quantum limits to the linewidth of an atom laser
The linewidth of an atom laser can be limited by excitation of higher energy
modes in the source Bose-Einstein condensate, energy shifts in that condensate
due to the atomic interactions, or phase diffusion of the lasing mode due to
those interactions. The first two are effects that can be described with a
semiclassical model, and have been studied in detail for both pumped and
unpumped atom lasers. The third is a purely quantum statistical effect, and has
been studied only in zero dimensional models. We examine an unpumped atom laser
in one dimension using a quantum field theory using stochastic methods based on
the truncated Wigner approach. This allows spatial and statistical effects to
be examined simultaneously, and the linewidth limit for unpumped atom lasers is
quantified in various limits.Comment: 8 Figure
Generating quadrature squeezing in an atom laser through self-interaction
We describe a scheme for creating quadrature- and intensity-squeezed atom lasers that do not require squeezed light as an input. The beam becomes squeezed due to nonlinear interactions between the atoms in the beam in an analogue to optical Kerr squeezing. We develop an analytic model of the process which we compare to a detailed stochastic simulation of the system using phase space methods. Finally we show that significant squeezing can be obtained in an experimentally realistic system and suggest ways of increasing the tunability of the squeezing
Generation of directional, coherent matter beams through dynamical instabilities in Bose-Einstein condensates
We present a theoretical analysis of a coupled, two-state Bose-Einstein
condensate with non-equal scattering lengths, and show that dynamical
instabilities can be excited. We demonstrate that these instabilities are
exponentially amplified resulting in highly-directional,
oppositely-propagating, coherent matter beams at specific momenta. To
accomplish this we prove that the mean field of our system is periodic, and
extend the standard Bogoliubov approach to consider a time-dependent, but
cyclic, background. This allows us to use Floquet's theorem to gain analytic
insight into such systems, rather than employing the usual Bogoliubov-de Gennes
approach, which is usually limited to numerical solutions. We apply our theory
to the metastable Helium atom laser experiment of Dall et al. [Phys. Rev. A 79,
011601(R) (2009)] and show it explains the anomalous beam profiles they
observed. Finally we demonstrate the paired particle beams will be
EPR-entangled on formation.Comment: Corrected reference
Generating nonlinearities from conditional linear operations, squeezing, and measurement for quantum computation and super-Heisenberg sensing
Large bosonic or continuous variable nonlinearities can have numerous applications, ranging from the generation of cat states for quantum computation, through to quantum sensing where the sensitivity exceeds Heisenberg scaling in the resources. However, the generation of ultra-large nonlinearities has proved immensely challenging experimentally. We describe a novel protocol where one can effectively generate large Kerr-type nonlinearities via the conditional application of a linear operation on an optical mode by an ancilla mode, followed by a measurement of the ancilla and corrective operation on the probe mode. Our protocol can generate high-quality Schrödinger cat states useful for quantum computing and can be used to perform sensing of an unknown rotation or displacement in phase space, with super-Heisenberg scaling in the resources. We finally describe a potential experimental implementation using atomic ensembles interacting with optical modes via the Faraday effect