[Show abstract][Hide abstract] ABSTRACT: Can high energy physics can be simulated by low-energy, nonrelativistic,
many-body systems, such as ultracold atoms? Such ultracold atomic systems lack
the type of symmetries and dynamical properties of high energy physics models:
in particular, they manifest neither local gauge invariance nor Lorentz
invariance, which are crucial properties of the quantum field theories which
are the building blocks of the standard model of elementary particles.
However, it turns out, surprisingly, that there are ways to configure atomic
system to manifest both local gauge invariance and Lorentz invariance. In
particular, local gauge invariance can arise either as an effective, low
energy, symmetry, or as an "exact" symmetry, following from the conservation
laws in atomic interactions. Hence, one could hope that such quantum simulators
may lead to new type of (table-top) experiments, that shall be used to study
various QCD phenomena, as the con?nement of dynamical quarks, phase
transitions, and other effects, which are inaccessible using the currently
known computational methods.
In this report, we review the Hamiltonian formulation of lattice gauge
theories, and then describe our recent progress in constructing quantum
simulation of Abelian and non-Abelian lattice gauge theories in 1 + 1 and 2 + 1
dimensions using ultracold atoms in optical lattices.
Preview · Article · Mar 2015 · Reports on Progress in Physics
[Show abstract][Hide abstract] ABSTRACT: We present a physical (gedanken) implementation of a generalized remote state
preparation of relativistic quantum field states for an arbitrary set of
observers. The prepared states are created in regions which are outside the
future light-cone of the generating region. The mechanism, which is based on
utilizing the vacuum state of a relativistic quantum field as a resource, sheds
new light on the well known Reeh-Schlieder theorem, indicating its strong
connection with the mathematical phenomenon of superoscillations.
[Show abstract][Hide abstract] ABSTRACT: We suggest a natural mapping between bipartite states and quantum evolutions of local states, which is a Jamiolkowski map. It is shown that spatial correlations of weak measurements in bi-partite systems precisely coincide with temporal correlations of local systems. This mapping has several practical and conceptual implications on the correspondence between Bell and Leggett-Garg inequalities, the statistical properties of evolutions in large systems, temporal decoherence and computational gain, in evaluation of spatial correlations of large systems.
[Show abstract][Hide abstract] ABSTRACT: Laser cooled and trapped ions can crystallize and feature discrete solitons,
that are nonlinear, topologically-protected configurations of the so called
Coulomb crystal. Such solitons, as their continuum counterparts, can move
within the crystal, while their discreteness leads to the existence of a
gap-separated, spatially-localized motional mode of oscillation above the
spectrum. We suggest that such unique properties of discrete solitons (kinks),
can be used for the purpose of generating entanglement between different sites
of the crystal. We study a detailed proposal in the context of state-of-the-art
methods and experiments with trapped ions, and find that a discrete soliton can
be used to produce EPR and GHZ-type states with high fidelity. The realization
of our method requires Doppler cooling of the whole crystal, and sideband
cooling of the soliton's localized modes. Since the gap separation of the
latter is nearly independent of the crystal's size, the proposed approach could
be particularly helpful for producing entanglement and studying
system-environment interactions in large, quasi two-dimensional systems.
Preview · Article · Aug 2013 · Physical Review Letters
[Show abstract][Hide abstract] ABSTRACT: We study discrete solitons (kinks) accessible in state-of-the-art trapped ion
experiments, considering zigzag crystals and quasi-3D configurations, both
theoretically and experimentally. We first extend the theoretical understanding
of different phenomena predicted and recently experimentally observed in the
structure and dynamics of these topological excitations. Employing tools from
topological degree theory, we analyze bifurcations of crystal configurations in
dependence on the trapping parameters, and investigate the formation of kink
configurations and the transformations of kinks between different structures.
This allows us to accurately define and calculate the effective potential
experienced by solitons within the Wigner crystal, and study how this
(so-called Peierls-Nabarro) potential gets modified to a nonperiodic globally
trapping potential in certain parameter regimes. The kinks' rest mass (energy)
and spectrum of modes are computed and the dynamics of linear and nonlinear
kink oscillations are analyzed. We also present novel, experimentally observed,
configurations of kinks incorporating a large-mass defect realized by an
embedded molecular ion, and of pairs of interacting kinks stable for long
times, offering the perspective for exploring and exploiting complex collective
nonlinear excitations, controllable on the quantum level.
Preview · Article · May 2013 · New Journal of Physics
[Show abstract][Hide abstract] ABSTRACT: We study experimentally and theoretically structural defects which are formed during the transition from a laser cooled cloud to a Coulomb crystal, consisting of tens of ions in a linear radio frequency trap. We demonstrate the creation of predicted topological defects ("kinks") in purely two-dimensional crystals and also find kinks which show novel dynamical features in a regime of parameters not considered before. The kinks are always observed at the center of the trap, showing a large nonlinear localized excitation, and the probability of their occurrence saturates at ∼0.5. Simulations reveal a strong anharmonicity of the kink's internal mode of vibration, due to the kink's extension into three dimensions. As a consequence, the periodic Peierls-Nabarro potential experienced by a discrete kink becomes a globally confining potential, capable of trapping one cooled defect at the center of the crystal.
Preview · Article · Mar 2013 · Physical Review Letters
[Show abstract][Hide abstract] ABSTRACT: Quantum simulations of High Energy Physics, and especially of gauge theories,
is an emerging and exciting direction in quantum simulations. However,
simulations of such theories, compared to simulations of condensed matter
physics, must satisfy extra restrictions, such as local gauge and Lorentz
invariance. In this paper we discuss these special requirements, and present a
new method for quantum simulation of lattice gauge theories using ultracold
atoms. This method allows to include local gauge invariance as a fundamental
symmetry of the atomic Hamiltonian, arising from natural atomic interactions
and conservation laws (and not as a property of a low energy sector). This
allows us to implement elementary gauge invariant interactions for three
lattice gauge theories: compact QED (U(1)), SU(N) and Z_N, which can be used to
build quantum simulators in 1+1 dimensions. We also present a new loop method,
which uses the elementary interactions as building blocks in the effective
construction of quantum simulations for d+1 dimensional lattice gauge theories
(d>1), without having to use Gauss's law as a constraint, as in previous
proposals. We discuss in detail the quantum simulation of 2+1 dimensional
compact QED and provide a numerical proof of principle. The simplicity of the
already gauge invariant elementary interactions of this model suggests it may
be useful for future experimental realizations.
[Show abstract][Hide abstract] ABSTRACT: We suggest a method to simulate compact quantum electrodynamics using ultracold atoms in optical lattices, which includes dynamical Dirac fermions in 2+1 dimensions. This allows us to test the dynamical effects of confinement as well as the deformations and breaking of two-dimensional flux loops, and to observe the Wilson-loop area law.
Preview · Article · Feb 2013 · Physical Review Letters
[Show abstract][Hide abstract] ABSTRACT: Non-abelian gauge theories play an important role in the standard model of
particle physics, and unfold a partially unexplored world of exciting physical
phenomena. In this letter, we suggest a realization of a non-abelian lattice
gauge theory - SU(2) Yang-Mills in 1+1 dimensions, using ultracold atoms.
Remarkably, and in contrast to previous proposals, in our model gauge
invariance is a direct consequence of angular momentum conservation and thus is
fundamental and robust. Our proposal may serve as well as a starting point for
higher dimensional realizations.
Preview · Article · Nov 2012 · Physical Review Letters
[Show abstract][Hide abstract] ABSTRACT: We introduce a new topological effect involving interference of two meson
loops, manifesting a path-independent topological area dependence. The effect
also draws a connection between quark confinement, Wilson-loops and topological
interference effects. Although this is only a gedanken experiment in the
context of particle physics, such an experiment may be realized and used as a
tool to test confinement effects and phase transitions in quantum simulation of
dynamic gauge theories.
Preview · Article · Aug 2012 · New Journal of Physics
[Show abstract][Hide abstract] ABSTRACT: We propose a new method for implementing process tomography that is based on
the information extracted from temporal correlations between observables,
rather than on state preparation and state tomography. As such, the approach is
applicable to systems that are in a mixed state, and in particular to thermal
states. We illustrate the method for an arbitrary evolution described by Kraus
operators, as well as for simpler cases such as a general Gaussian channels,
and qubit dynamics.
Preview · Article · Jul 2012 · New Journal of Physics
[Show abstract][Hide abstract] ABSTRACT: We examine the time-dependent dynamics of ion crystals in radiofrequency
traps. The problem of stable trapping of general three-dimensional crystals is
considered and the validity of the pseudopotential approximation is discussed.
We derive analytically the micromotion amplitude of the ions, rigorously
proving well-known experimental observations. We use a method of infinite
determinants to find the modes which diagonalize the linearized time-dependent
dynamical problem. This allows obtaining explicitly the ('Floquet-Lyapunov')
transformation to coordinates of decoupled linear oscillators. We demonstrate
the utility of the method by analyzing the modes of a small `peculiar' crystal
in a linear Paul trap. The calculations can be readily generalized to
multispecies ion crystals in general multipole traps, and time-dependent
quantum wavefunctions of ion oscillations in such traps can be obtained.
Preview · Article · Jun 2012 · New Journal of Physics
[Show abstract][Hide abstract] ABSTRACT: We propose a method for measuring the string tension in gauge theories, by
considering an interference effect of mesons, which is governed by a space-time
area law, due to confinement. Although it is only a gedanken experiment for
real elementary particles, in the context of quantum simulations of confining
gauge theories such an experiment can be realized.
[Show abstract][Hide abstract] ABSTRACT: We expand the solutions of linearly coupled Mathieu equations in terms of
infinite-continued matrix inversions, and use it to find the modes which
diagonalize the dynamical problem. This allows obtaining explicitly the
('Floquet-Lyapunov') transformation to coordinates in which the motion is that
of decoupled linear oscillators. We use this transformation to solve the
Heisenberg equations of the corresponding quantum-mechanical problem, and find
the quantum wavefunctions for stable oscillations, expressed in
configuration-space. The obtained transformation and quantum solutions can be
applied to more general linear systems with periodic coefficients (coupled Hill
equations, periodically driven parametric oscillators), and to nonlinear
systems as a starting point for convenient perturbative treatment of the
Preview · Article · Jun 2012 · Journal of Physics A Mathematical and Theoretical
[Show abstract][Hide abstract] ABSTRACT: Recently, there has been much interest in simulating quantum field theory
effects of matter and gauge fields. In a recent work [Phys. Rev. Lett. 107,
275301 (2011)] a method for simulating compact Quantum Electrodynamics (cQED)
using Bose-Einstein condensates has been suggested. We suggest an alternative
approach, which relies on single atoms in an optical lattice, carrying 2l+1
internal levels, which converges rapidly to cQED as l increases. That enables
the simulation of cQED in 2+1 dimensions in both the weak and the strong
coupling regimes, hence allowing to probe confinement as well as other
nonperturbative effects of the theory. We provide an explicit construction for
the case l=1 which is sufficient for simulating the effect of confinement
between two external static charges.
[Show abstract][Hide abstract] ABSTRACT: We propose a method for simulating (2+1)D compact lattice quantum-electrodynamics, using ultracold atoms in optical lattices. In our model local Bose-Einstein condensates' (BECs) phases correspond to the electromagnetic vector potential, and the local number operators represent the conjugate electric field. The well-known gauge-invariant Kogut-Susskind Hamiltonian is obtained as an effective low-energy theory. The field is then coupled to external static charges. We show that in the strong coupling limit this gives rise to "electric flux tubes" and to confinement. This can be observed by measuring the local density deviations of the BECs, and is expected to hold even, to some extent, outside the perturbative calculable regime.
No preview · Article · Dec 2011 · Physical Review Letters
[Show abstract][Hide abstract] ABSTRACT: We propose a method for implementing remotely a generalized measurement (POVM). We show that remote generalized measurements consume less entanglement compared with remote projective measurements, and can be optimally performed using non-maximally entangled states. We derive the entanglement cost of such measurements.
No preview · Article · Nov 2011 · International Journal of Quantum Information
[Show abstract][Hide abstract] ABSTRACT: We propose a method for simulating 2+1-d compact lattice
quantum-electrodynamics (QED), using ultracold atoms in optical lattices. In
our model local Bose-Einstein condensates' phases correspond to the
electromagnetic vector-potential, and the fluctuations of the local number
operators represent the conjugate electric field. The gauge invariant
Kogut-Susskind Hamiltonian is obtained as an effective low energy theory. The
field is then coupled to external static charges. We show that in the strong
coupling limit this gives rise to 'electric flux-tubes' and to confinement. The
effect can be observed by measuring the local density fluctuations of the BECs.
[Show abstract][Hide abstract] ABSTRACT: The Hilbert space formalism of quantum theory manifests a map between
bipartite states and time evolutions, known as Jamiolkowski isomorphism. We
extend this map in a physical setting to prove the equality of spatial
correlations in bipartite systems and temporal correlations in local systems.
We show that these correlations can be observed using weak measurements. This
result has several practical and conceptual implications such as manifestation
of state independent decoherence, the correspondence between Bell and
Leggett-Garg inequalities, multipartite systems, the statistical properties of
evolutions in large systems, and computational gain, in evaluation of spatial
correlations in large systems.