



@article {2004,
	title = {Entanglement and spin-squeezing without infinite-range interactions},
	year = {2016},
	month = {2016/12/22},
	abstract = {<p>Infinite-range interactions are known to facilitate the production of highly entangled states with applications in quantum information and metrology. However, many experimental systems have interactions that decay with distance, and the achievable benefits in this context are much less clear. Combining recent exact solutions with a controlled expansion in the system size, we analyze quench dynamics in Ising models with power-law (1/r α ) interactions in D dimensions, thereby expanding the understanding of spin squeezing into a broad and experimentally relevant context. In spatially homogeneous systems, we show that for small α the scaling of squeezing with system size is identical to the infinite-range (α = 0) case. This indifference to the interaction range persists up to a critical value α = 2D/3, above which squeezing degrades continuously. Boundaryinduced inhomogeneities present in most experimental systems modify this picture, but it nevertheless remains qualitatively correct for finite-sized systems.</p>},
	url = {https://arxiv.org/abs/1612.07805},
	author = {Michael Foss-Feig and Zhe-Xuan Gong and Alexey V. Gorshkov and Charles W. Clark}
}
@article {1178,
	title = {Nearly-linear light cones in long-range interacting quantum systems},
	journal = {Physical Review Letters},
	volume = {114},
	year = {2015},
	month = {2015/04/13},
	pages = {157201},
	abstract = {  In non-relativistic quantum theories with short-range Hamiltonians, a
velocity $v$ can be chosen such that the influence of any local perturbation is
approximately confined to within a distance $r$ until a time $t \sim r/v$,
thereby defining a linear light cone and giving rise to an emergent notion of
locality. In systems with power-law ($1/r^{\alpha}$) interactions, when
$\alpha$ exceeds the dimension $D$, an analogous bound confines influences to
within a distance $r$ only until a time $t\sim(\alpha/v)\log r$, suggesting
that the velocity, as calculated from the slope of the light cone, may grow
exponentially in time. We rule out this possibility; light cones of power-law
interacting systems are algebraic for $\alpha>2D$, becoming linear as
$\alpha\rightarrow\infty$. Our results impose strong new constraints on the
growth of correlations and the production of entangled states in a variety of
rapidly emerging, long-range interacting atomic, molecular, and optical
systems.
},
	doi = {10.1103/PhysRevLett.114.157201},
	url = {http://arxiv.org/abs/1410.3466v1},
	author = {Michael Foss-Feig and Zhe-Xuan Gong and Charles W. Clark and Alexey V. Gorshkov}
}
@article {1303,
	title = {Detecting paired and counterflow superfluidity via dipole oscillations},
	journal = {Physical Review A},
	volume = {84},
	year = {2011},
	month = {2011/10/27},
	abstract = {  We suggest an experimentally feasible procedure to observe paired and
counterflow superfluidity in ultra-cold atom systems. We study the time
evolution of one-dimensional mixtures of bosonic atoms in an optical lattice
following an abrupt displacement of an additional weak confining potential. We
find that the dynamic responses of the paired superfluid phase for attractive
inter-species interactions and the counterflow superfluid phase for repulsive
interactions are qualitatively distinct and reflect the quasi long-range order
that characterizes these states. These findings suggest a clear experimental
procedure to detect these phases, and give an intuitive insight into their
dynamics.
},
	doi = {10.1103/PhysRevA.84.041609},
	url = {http://arxiv.org/abs/1103.3513v3},
	author = {Anzi Hu and L. Mathey and Eite Tiesinga and Ippei Danshita and Carl J. Williams and Charles W. Clark}
}
@article {1413,
	title = {Noise correlations of one-dimensional Bose mixtures in optical lattices},
	journal = {Physical Review A},
	volume = {81},
	year = {2010},
	month = {2010/6/2},
	abstract = {  We study the noise correlations of one-dimensional binary Bose mixtures, as a
probe of their quantum phases. In previous work, we found a rich structure of
many-body phases in such mixtures, such as paired and counterflow
superfluidity. Here we investigate the signature of these phases in the noise
correlations of the atomic cloud after time-of-flight expansion, using both
Luttinger liquid theory and the time-evolving block decimation (TEBD) method.
We find that paired and counterflow superfluidity exhibit distinctive features
in the noise spectra. We treat both extended and inhomogeneous systems, and our
numerical work shows that the essential physics of the extended systems is
present in the trapped-atom systems of current experimental interest. For
paired and counterflow superfluid phases, we suggest methods for extracting
Luttinger parameters from noise correlation spectroscopy.
},
	doi = {10.1103/PhysRevA.81.063602},
	url = {http://arxiv.org/abs/1002.4918v2},
	author = {Anzi Hu and L. Mathey and Carl J. Williams and Charles W. Clark}
}
@article {1293,
	title = {Collisional cooling of ultra-cold atom ensembles using Feshbach  resonances
},
	journal = {Physical Review A},
	volume = {80},
	year = {2009},
	month = {2009/9/8},
	abstract = {  We propose a new type of cooling mechanism for ultra-cold fermionic atom
ensembles, which capitalizes on the energy dependence of inelastic collisions
in the presence of a Feshbach resonance. We first discuss the case of a single
magnetic resonance, and find that the final temperature and the cooling rate is
limited by the width of the resonance. A concrete example, based on a p-wave
resonance of $^{40}$K, is given. We then improve upon this setup by using both
a very sharp optical or radio-frequency induced resonance and a very broad
magnetic resonance and show that one can improve upon temperatures reached with
current technologies.
},
	doi = {10.1103/PhysRevA.80.030702},
	url = {http://arxiv.org/abs/0903.2568v1},
	author = {L. Mathey and Eite Tiesinga and Paul S. Julienne and Charles W. Clark}
}
@article {1299,
	title = {Counterflow and paired superfluidity in one-dimensional Bose mixtures in  optical lattices
},
	journal = {Physical Review A},
	volume = {80},
	year = {2009},
	month = {2009/8/24},
	abstract = {  We study the quantum phases of mixtures of ultra-cold bosonic atoms held in
an optical lattice that confines motion or hopping to one spatial dimension.
The phases are found by using Tomonaga-Luttinger liquid theory as well as the
numerical method of time evolving block decimation (TEBD). We consider a binary
mixture with repulsive intra-species interactions, and either repulsive or
attractive inter-species interaction. For a homogeneous system, we find paired-
and counterflow-superfluid phases at different filling and hopping energies. We
also predict parameter regions in which these types of superfluid order coexist
with charge density wave order. We show that the Tomonaga-Luttinger liquid
theory and TEBD qualitatively agree on the location of the phase boundary to
superfluidity. We then describe how these phases are modified and can be
detected when an additional harmonic trap is present. In particular, we show
how experimentally measurable quantities, such as time-of-flight images and the
structure factor, can be used to distinguish the quantum phases. Finally, we
suggest applying a Feshbach ramp to detect the paired superfluid state, and a
$\pi/2$ pulse followed by Bragg spectroscopy to detect the counterflow
superfluid phase.
},
	doi = {10.1103/PhysRevA.80.023619},
	url = {http://arxiv.org/abs/0906.2150v1},
	author = {Anzi Hu and L. Mathey and Ippei Danshita and Eite Tiesinga and Carl J. Williams and Charles W. Clark}
}
@article {1292,
	title = {Tunneling phase gate for neutral atoms in a double-well lattice},
	journal = {Physical Review A},
	volume = {77},
	year = {2008},
	month = {2008/5/12},
	abstract = {  We propose a new two--qubit phase gate for ultra--cold atoms confined in an
experimentally realized tilted double--well optical lattice [Sebby--Strabley et
al., Phys. Rev. A {\bf 73} 033605 (2006)]. Such a lattice is capable of
confining pairs of atoms in a two--dimensional array of double--well potentials
where control can be exercised over the barrier height and the energy
difference of the minima of the two wells (known as the {\textquoteleft}{\textquoteleft}tilt{\textquoteright}{\textquoteright}). The four
lowest single--particle motional states consist of two pairs of motional states
in which each pair is localized on one side of the central barrier, allowing
for two atoms confined in such a lattice to be spatially separated qubits. We
present a time--dependent scheme to manipulate the tilt to induce tunneling
oscillations which produce a collisional phase gate. Numerical simulations
demonstrate that this gate can be performed with high fidelity.
},
	doi = {10.1103/PhysRevA.77.050304},
	url = {http://arxiv.org/abs/0712.1856v1},
	author = {Frederick W. Strauch and Mark Edwards and Eite Tiesinga and Carl J. Williams and Charles W. Clark}
}
@article {1416,
	title = {Mean-field treatment of the damping of the oscillations of a 1D Bose gas  in an optical lattice
},
	journal = {Physical Review A},
	volume = {73},
	year = {2006},
	month = {2006/1/9},
	abstract = {  We present a theoretical treatment of the surprisingly large damping observed
recently in one-dimensional Bose-Einstein atomic condensates in optical
lattices. We show that time-dependent Hartree-Fock-Bogoliubov (HFB)
calculations can describe qualitatively the main features of the damping
observed over a range of lattice depths. We also derive a formula of the
fluctuation-dissipation type for the damping, based on a picture in which the
coherent motion of the condensate atoms is disrupted as they try to flow
through the random local potential created by the irregular motion of
noncondensate atoms. We expect this irregular motion to result from the
well-known dynamical instability exhibited by the mean-field theory for these
systems. When parameters for the characteristic strength and correlation times
of the fluctuations, obtained from the HFB calculations, are substituted in the
damping formula, we find very good agreement with the experimentally-observed
damping, as long as the lattice is shallow enough for the fraction of atoms in
the Mott insulator phase to be negligible. We also include, for completeness,
the results of other calculations based on the Gutzwiller ansatz, which appear
to work better for the deeper lattices.
},
	doi = {10.1103/PhysRevA.73.013605},
	url = {http://arxiv.org/abs/cond-mat/0410677v4},
	author = {Julio Gea-Banacloche and Ana Maria Rey and Guido Pupillo and Carl J. Williams and Charles W. Clark}
}
@article {1410,
	title = {Pseudo-fermionization of 1-D bosons in optical lattices},
	journal = {New Journal of Physics},
	volume = {8},
	year = {2006},
	month = {2006/08/30},
	pages = {161 - 161},
	abstract = {  We present a model that generalizes the Bose-Fermi mapping for strongly
correlated 1D bosons in an optical lattice, to cases in which the average
number of atoms per site is larger than one. This model gives an accurate
account of equilibrium properties of such systems, in parameter regimes
relevant to current experiments. The application of this model to
non-equilibrium phenomena is explored by a study of the dynamics of an atom
cloud subject to a sudden displacement of the confining potential. Good
agreement is found with results of recent experiments. The simplicity and
intuitive appeal of this model make it attractive as a general tool for
understanding bosonic systems in the strongly correlated regime.
},
	doi = {10.1088/1367-2630/8/8/161},
	url = {http://arxiv.org/abs/cond-mat/0505325v2},
	author = {Guido Pupillo and Ana Maria Rey and Carl J. Williams and Charles W. Clark}
}
@article {1415,
	title = {Bragg Spectroscopy of ultracold atoms loaded in an optical lattice},
	journal = {Physical Review A},
	volume = {72},
	year = {2005},
	month = {2005/8/12},
	abstract = {  We study Bragg spectroscopy of ultra-cold atoms in one-dimensional optical
lattices as a method for probing the excitation spectrum in the Mott insulator
phase, in particular the one particle-hole excitation band. Within the
framework of perturbation theory we obtain an analytical expression for the
dynamic structure factor $S(q,\omega)$ and use it to calculate the imparted
energy which has shown to be a relevant observable in recent experiments. We
test the accuracy of our approximations by comparing them with numerically
exact solutions of the Bose-Hubbard model in restricted cases and establish the
limits of validity of our linear response analysis. Finally we show that when
the system is deep in the Mott insulator regime, its response to the Bragg
perturbation is temperature dependent. We suggest that this dependence might be
used as a tool to probe temperatures of order of the Mott gap.
},
	doi = {10.1103/PhysRevA.72.023407},
	url = {http://arxiv.org/abs/cond-mat/0406552v2},
	author = {Ana Maria Rey and P. Blair Blakie and Guido Pupillo and Carl J. Williams and Charles W. Clark}
}
@article {1418,
	title = {Scalable register initialization for quantum computing in an optical  lattice
},
	journal = {Journal of Physics B: Atomic, Molecular and Optical Physics},
	volume = {38},
	year = {2005},
	month = {2005/06/14},
	pages = {1687 - 1694},
	abstract = {  The Mott insulator state created by loading an atomic Bose-Einstein
condensate (BEC) into an optical lattice may be used as a means to prepare a
register of atomic qubits in a quantum computer. Such architecture requires a
lattice commensurately filled with atoms, which corresponds to the insulator
state only in the limit of zero inter-well tunneling. We show that a lattice
with spatial inhomogeneity created by a quadratic magnetic trapping potential
can be used to isolate a subspace in the center which is impervious to
hole-hoping. Components of the wavefunction with more than one atom in any well
can be projected out by selective measurement on a molecular photo-associative
transition. Maintaining the molecular coupling induces a quantum Zeno effect
that can sustain a commensurately filled register for the duration of a quantum
computation.
},
	doi = {10.1088/0953-4075/38/11/010},
	url = {http://arxiv.org/abs/quant-ph/0312069v1},
	author = {Gavin K. Brennen and Guido Pupillo and Ana Maria Rey and Charles W. Clark and Carl J. Williams}
}
@article {1409,
	title = {Ultracold atoms confined in an optical lattice plus parabolic potential:  a closed-form approach
},
	journal = {Physical Review A},
	volume = {72},
	year = {2005},
	month = {2005/9/22},
	abstract = {  We discuss interacting and non-interacting one dimensional atomic systems
trapped in an optical lattice plus a parabolic potential. We show that, in the
tight-binding approximation, the non-interacting problem is exactly solvable in
terms of Mathieu functions. We use the analytic solutions to study the
collective oscillations of ideal bosonic and fermionic ensembles induced by
small displacements of the parabolic potential. We treat the interacting boson
problem by numerical diagonalization of the Bose-Hubbard Hamiltonian. From
analysis of the dependence upon lattice depth of the low-energy excitation
spectrum of the interacting system, we consider the problems of
"fermionization" of a Bose gas, and the superfluid-Mott insulator transition.
The spectrum of the noninteracting system turns out to provide a useful guide
to understanding the collective oscillations of the interacting system,
throughout a large and experimentally relevant parameter regime.
},
	doi = {10.1103/PhysRevA.72.033616},
	url = {http://arxiv.org/abs/cond-mat/0503477v2},
	author = {Ana Maria Rey and Guido Pupillo and Charles W. Clark and Carl J. Williams}
}
@article {1411,
	title = {Advantages of high-speed technique for quantum key distribution; reply  to quant-ph/0407050
},
	year = {2004},
	month = {2004/07/18},
	abstract = {  We respond to a comment on our high-speed technique for the implementation of
free-space quantum key distribution (QKD). The model used in the comment
assigns inappropriately high link losses to the technique in question. We show
that the use of reasonable loss parameters in the model invalidates the
comment{\textquoteright}s main conclusion and highlights the benefits of increased transmission
rates.
},
	url = {http://arxiv.org/abs/quant-ph/0407139v1},
	author = {J. C. Bienfang and Charles W. Clark and Carl J. Williams and E. W. Hagley and Jesse Wen}
}
@article {1406,
	title = {Relativistic many-body calculations of electric-dipole matrix elements,  lifetimes and polarizabilities in rubidium
},
	journal = {Physical Review A},
	volume = {69},
	year = {2004},
	month = {2004/2/27},
	abstract = {  Electric-dipole matrix elements for ns-n{\textquoteright}p, nd-n{\textquoteright}p, and 6d-4f transitions in
Rb are calculated using a relativistic all-order method. A third-order
calculation is also carried out for these matrix elements to evaluate the
importance of the high-order many-body perturbation theory contributions. The
all-order matrix elements are used to evaluate lifetimes of ns and np levels
with n=6, 7, 8 and nd levels with n=4, 5, 6 for comparison with experiment and
to provide benchmark values for these lifetimes. The dynamic polarizabilities
are calculated for ns states of rubidium. The resulting lifetime and
polarizability values are compared with available theory and experiment.
},
	doi = {10.1103/PhysRevA.69.022509},
	url = {http://arxiv.org/abs/physics/0307057v1},
	author = {M. S. Safronova and Carl J. Williams and Charles W. Clark}
}
@article {1419,
	title = {Scalable quantum computation in systems with Bose-Hubbard dynamics},
	journal = {Journal of Modern Optics},
	volume = {51},
	year = {2004},
	month = {2004/02/15},
	pages = {2395 - 2404},
	abstract = {  Several proposals for quantum computation utilize a lattice type architecture
with qubits trapped by a periodic potential. For systems undergoing many body
interactions described by the Bose-Hubbard Hamiltonian, the ground state of the
system carries number fluctuations that scale with the number of qubits. This
process degrades the initialization of the quantum computer register and can
introduce errors during error correction. In an earlier manuscript we proposed
a solution to this problem tailored to the loading of cold atoms into an
optical lattice via the Mott Insulator phase transition. It was shown that by
adding an inhomogeneity to the lattice and performing a continuous measurement,
the unit filled state suitable for a quantum computer register can be
maintained. Here, we give a more rigorous derivation of the register fidelity
in homogeneous and inhomogeneous lattices and provide evidence that the
protocol is effective in the finite temperature regime.
},
	doi = {10.1080/09500340408231798},
	url = {http://arxiv.org/abs/quant-ph/0403052v2},
	author = {Guido Pupillo and Ana Maria Rey and Gavin Brennen and Carl J. Williams and Charles W. Clark}
}
@article {1414,
	title = {Bogoliubov approach to superfluidity of atoms in an optical lattice},
	journal = {Journal of Physics B: Atomic, Molecular and Optical Physics},
	volume = {36},
	year = {2003},
	month = {2003/03/14},
	pages = {825 - 841},
	abstract = {  We use the Bogoliubov theory of atoms in an optical lattice to study the
approach to the Mott-insulator transition. We derive an explicit expression for
the superfluid density based on the rigidity of the system under phase
variations. This enables us to explore the connection between the quantum
depletion of the condensate and the quasi-momentum distribution on the one hand
and the superfluid fraction on the other. The approach to the insulator phase
may be characterized through the filling of the band by quantum depletion,
which should be directly observable via the matter wave interference patterns.
We complement these findings by self-consistent Hartree-Fock-Bogoliubov-Popov
calculations for one-dimensional lattices including the effects of a parabolic
trapping potential.
},
	doi = {10.1088/0953-4075/36/5/304},
	url = {http://arxiv.org/abs/cond-mat/0210550v2},
	author = {Ana Maria Rey and Keith Burnett and Robert Roth and Mark Edwards and Carl J. Williams and Charles W. Clark}
}
@article {1407,
	title = {Optimizing the fast Rydberg quantum gate},
	journal = {Physical Review A},
	volume = {67},
	year = {2003},
	month = {2003/4/17},
	abstract = {  The fast phase gate scheme, in which the qubits are atoms confined in sites
of an optical lattice, and gate operations are mediated by excitation of
Rydberg states, was proposed by Jaksch et al. Phys. Rev. Lett. 85, 2208 (2000).
A potential source of decoherence in this system derives from motional heating,
which occurs if the ground and Rydberg states of the atom move in different
optical lattice potentials. We propose to minimize this effect by choosing the
lattice photon frequency \omega so that the ground and Rydberg states have the
same frequency-dependent polarizability \alpha(omega). The results are
presented for the case of Rb.
},
	doi = {10.1103/PhysRevA.67.040303},
	url = {http://arxiv.org/abs/quant-ph/0212081v1},
	author = {M. S. Safronova and Carl J. Williams and Charles W. Clark}
}
