1,546 research outputs found
Synthetic clock transitions via continuous dynamical decoupling
Decoherence of quantum systems due to uncontrolled fluctuations of the
environment presents fundamental obstacles in quantum science. `Clock'
transitions which are insensitive to such fluctuations are used to improve
coherence, however, they are not present in all systems or for arbitrary system
parameters. Here, we create a trio of synthetic clock transitions using
continuous dynamical decoupling in a spin-1 Bose-Einstein condensate in which
we observe a reduction of sensitivity to magnetic field noise of up to four
orders of magnitude; this work complements the parallel work by Anderson et al.
(submitted, 2017). In addition, using a concatenated scheme, we demonstrate
suppression of sensitivity to fluctuations in our control fields. These
field-insensitive states represent an ideal foundation for the next generation
of cold atom experiments focused on fragile many-body phases relevant to
quantum magnetism, artificial gauge fields, and topological matter.Comment: 8 pages, 4 figures, Supplemental material
Perpetual emulation threshold of PT-symmetric Hamiltonians
We describe a technique to emulate a two-level \PT-symmetric spin
Hamiltonian, replete with gain and loss, using only the unitary dynamics of a
larger quantum system. This we achieve by embedding the two-level system in
question in a subspace of a four-level Hamiltonian. Using an \textit{amplitude
recycling} scheme that couples the levels exterior to the \PT-symmetric
subspace, we show that it is possible to emulate the desired behaviour of the
\PT-symmetric Hamiltonian without depleting the exterior, reservoir levels. We
are thus able to extend the emulation time indefinitely, despite the
non-unitary \PT dynamics. We propose a realistic experimental implementation
using dynamically decoupled magnetic sublevels of ultracold atoms.Comment: 15 pages, 8 figure
Fourier transform spectroscopy of a spin-orbit coupled Bose gas
We describe a Fourier transform spectroscopy technique for directly measuring
band structures, and apply it to a spin-1 spin-orbit coupled Bose-Einstein
condensate. In our technique, we suddenly change the Hamiltonian of the system
by adding a spin-orbit coupling interaction and measure populations in
different spin states during the subsequent unitary evolution. We then
reconstruct the spin and momentum resolved spectrum from the peak frequencies
of the Fourier transformed populations. In addition, by periodically modulating
the Hamiltonian, we tune the spin-orbit coupling strength and use our
spectroscopy technique to probe the resulting dispersion relation. The
frequency resolution of our method is limited only by the coherent evolution
timescale of the Hamiltonian and can otherwise be applied to any system, for
example, to measure the band structure of atoms in optical lattice potentials
A Bose-Einstein Condensate in a Uniform Light-induced Vector Potential
We use a two-photon dressing field to create an effective vector gauge
potential for Bose-condensed Rb atoms in the F=1 hyperfine ground state. The
dressed states in this Raman field are spin and momentum superpositions, and we
adiabatically load the atoms into the lowest energy dressed state. The
effective Hamiltonian of these neutral atoms is like that of charged particles
in a uniform magnetic vector potential, whose magnitude is set by the strength
and detuning of Raman coupling. The spin and momentum decomposition of the
dressed states reveals the strength of the effective vector potential, and our
measurements agree quantitatively with a simple single-particle model. While
the uniform effective vector potential described here corresponds to zero
magnetic field, our technique can be extended to non-uniform vector potentials,
giving non-zero effective magnetic fields.Comment: 5 pages, submitted to Physical Review Letter
Smooth analysis of the condition number and the least singular value
Let \a be a complex random variable with mean zero and bounded variance.
Let be the random matrix of size whose entries are iid copies of
\a and be a fixed matrix of the same size. The goal of this paper is to
give a general estimate for the condition number and least singular value of
the matrix , generalizing an earlier result of Spielman and Teng for
the case when \a is gaussian.
Our investigation reveals an interesting fact that the "core" matrix does
play a role on tail bounds for the least singular value of . This
does not occur in Spielman-Teng studies when \a is gaussian.
Consequently, our general estimate involves the norm .
In the special case when is relatively small, this estimate is nearly
optimal and extends or refines existing results.Comment: 20 pages. An erratum to the published version has been adde
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