arXiv subjects

Benni Reznik

Publications and source records attributed to Benni Reznik.

At least 19 recordsLinked to original sources

arXiv2021

Entanglement on curved hypersurfaces: A field-discretizer approach

We propose a covariant scheme for measuring entanglement on general hypersurfaces in relativistic quantum field theory. For that, we introduce an auxiliary relativistic field, 'the discretizer', that by locally interacting with the field along a hypersurface, fully swaps the field's and discretizer's states. It is shown, that the discretizer can be used to effectively cut-off the field's infinities, in a covariant fashion, and without having to introduce a spatial lattice. This, in turn, provides us an efficient way to evaluate entanglement between arbitrary regions on any hypersurface. As examples, we study the entanglement between complementary and separated regions in 1+1 dimensions, for flat hypersurfaces in Minkowski space, for curved hypersurfaces in Milne space, and for regions on hypersurfaces approaching null-surfaces. Our results show that the entanglement between regions on arbitrary hypersurfaces in 1+1 dimensions depends only on the space-time endpoints of the regions, and not on the shape of the interior. Our results corroborate and extend previous results for flat hypersurfaces.

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arXiv2017

Kaluza-Klein tower of masses in compactified Bose-Einstein condensates

We propose a method for using ultracold atomic Bose-Einstein condensates, to form an analog model of a scalar field in five dimensional space-time, where one of the spatial dimensions is compact. In the analog system the extra dimension is discrete, and realized using the internal degrees of freedom of the system. In the low energy regime, the Kaluza-Klein tower of masses is recovered, and the effective radius of the compact dimension is identified.

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arXiv2017

Digital lattice gauge theories

We propose a general scheme for a digital construction of lattice gauge theories with dynamical fermions. In this method, the four-body interactions arising in models with $2+1$ dimensions and higher, are obtained stroboscopically, through a sequence of two-body interactions with ancillary degrees of freedom. This yields stronger interactions than the ones obtained through pertubative methods, as typically done in previous proposals, and removes an important bottleneck in the road towards experimental realizations. The scheme applies to generic gauge theories with Lie or finite symmetry groups, both Abelian and non-Abelian. As a concrete example, we present the construction of a digital quantum simulator for a $\mathbb{Z}_{3}$ lattice gauge theory with dynamical fermionic matter in $2+1$ dimensions, using ultracold atoms in optical lattices, involving three atomic species, representing the matter, gauge and auxiliary degrees of freedom, that are separated in three different layers. By moving the ancilla atoms with a proper sequence of steps, we show how we can obtain the desired evolution in a clean, controlled way.

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arXiv2017

Digital quantum simulation of $\mathbb{Z}_2$ lattice gauge theories with dynamical fermionic matter

We propose a scheme for digital quantum simulation of lattice gauge theories with dynamical fermions. Using a layered optical lattice with ancilla atoms that can move and interact with the other atoms (simulating the physical degrees of freedom), we obtain a stroboscopic dynamics which yields the four-body plaquette interactions, arising in models with $2+1$ and higher dimensions, without the use of perturbation theory. As an example we show how to simulate a $\mathbb{Z}_2$ model in $2+1$ dimensions.

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arXiv2017

"Charged" phonons in an external field: a QED analog with Bose-Einstein condensates

We propose a method for using ultracold atomic Bose-Einstein condensates, to form an analog model of a relativistic massive field that carries "charge" and interacts with an external nondynamical gauge field. Such a "scalar QED" analog model, may be useful for simulating various effects of QFT involving charged particles, such as the Schwinger pair-creation of charged phonons in a constant external field, and vacuum instability.

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arXiv2015

Quantum Simulations of Lattice Gauge Theories using Ultracold Atoms in Optical Lattices

Can high energy physics be simulated by low-energy, non-relativistic, 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 confinement 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.

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arXiv2015

Superoscillations underlying remote state preparation for relativistic fields

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 that 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 light on the well known Reeh-Schlieder theorem, indicating its strong connection with the mathematical phenomenon of superoscillations.

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arXiv2013

Quantum simulations of gauge theories with ultracold atoms: local gauge invariance from angular momentum conservation

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.

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arXiv2013

Topological Wilson-loop area law manifested using a superposition of loops

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.

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arXiv2013

Process Tomography for Systems in a Thermal State

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.

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arXiv2012

A cold-atom quantum simulator for SU(2) Yang-Mills lattice gauge theory

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.

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arXiv2012

Simulating Compact Quantum Electrodynamics with ultracold atoms: Probing confinement and nonperturbative effects

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.

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arXiv2012

Simulating 2+1d Lattice QED with dynamical matter using ultracold atoms

We suggest a method to simulate lattice compact Quantum Electrodynamics (cQED) using ultracold atoms in optical lattices, which includes dynamical Dirac fermions in 2+1 dimensions. This allows to test dynamical effects of confinement as well as 2d flux loops deformations and breaking, and to observe Wilson-loop area-law.

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arXiv2012

String tension and area-law probed using quantum superposition

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.

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arXiv2011

Confinement and lattice QED electric flux-tubes simulated with ultracold atoms

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.

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arXiv2011

Correlation preserving map between bipartite states and temporal evolutions

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.

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arXiv2011

The Fermi Problem in Discrete Systems

The Fermi two-atom problem illustrates an apparent causality violation in Quantum Field Theory which has to do with the nature of the built in correlations in the vacuum. It has been a constant subject of theoretical debate and discussions during the last few decades. Nevertheless, although the issues at hand could in principle be tested experimentally, the smallness of such apparent violations of causality in Quantum Electrodynamics prevented the observation of the predicted effect. In the present paper we show that the problem can be simulated within the framework of discrete systems that can be manifested, for instance, by trapped atoms in optical lattices or trapped ions. Unlike the original continuum case, the causal structure is no longer sharp. Nevertheless, as we show, it is possible to distinguish between "trivial" effects due to "direct" causality violations, and the effects associated with Fermi's problem, even in such discrete settings. The ability to control externally the strength of the atom-field interactions, enables us also to study both the original Fermi problem with "bare atoms", as well as correction in the scenario that involves "dressed" atoms. Finally, we show that in principle, the Fermi effect can be detected using trapped ions.

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arXiv2011

Hawking Radiation on an Ion Ring in the Quantum Regime

This paper discusses a recent proposal for the simulation of acoustic black holes with ions. The ions are rotating on a ring with an inhomogeneous, but stationary velocity profile. Phonons cannot leave a region, in which the ion velocity exceeds the group velocity of the phonons, as light cannot escape from a black hole. The system is described by a discrete field theory with a nonlinear dispersion relation. Hawking radiation is emitted by this acoustic black hole, generating entanglement between the inside and the outside of the black hole. We study schemes to detect the Hawking effect in this setup.

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