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arXiv:quant-ph/0310039 · Physical Review A

Entanglement detection in optical lattices of bosonic atoms with collective measurements

Géza Tóth

Published May 24, 2004• 73 citations
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Abstract

The minimum requirements for entanglement detection are discussed for a spin chain in which the spins cannot be individually accessed. The methods presented detect entangled states close to a cluster state and a many-body singlet state, and seem to be viable for experimental realization in optical lattices of two-state bosonic atoms. The entanglement criteria are based on entanglement witnesses and on the uncertainty of collective observables.

DOI
10.1103/physreva.69.052327

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The minimum requirements for entanglement detection are discussed for a spin chain in which the spins cannot be individually accessed. The methods presented detect entangled states close to a cluster state and a many-body singlet state, and seem to be viable for experimental realization in optical lattices of two-state bosonic atoms. The entanglement criteria are based on entanglement witnesses and on the uncertainty of collective observables.
An optical lattice with cold trapped atoms represents a quantum system of fundamental importance as it enables the study of quantum many-body system in a controllable way. It is thus necessary to develop theoretical and experimental tools to explore quantum correlation in such systems to advance our understanding of many-body physics. While previous works have identified some profound aspects of quantum entanglement using e.g. entanglement entropy, there exists a critical demand to have an experimentally accessible tool to investigate many-body quantum entanglement in a broad context. We present an entanglement criterion characterizing collective entanglement in Boson lattice systems and enabling experimental observation readily. On applying our approach to the extended Bose-Hubbard model, we show that our criterion witnesses phase transitions such as Mott insulator--superfluid and Mott insulator--charge density wave transitions. Remarkably, it also makes it possible to detect multipartite entanglement among boson lattice sites in a rigorous sense. Our criterion can be experimentally tested via Raman scattering or time-of-flight methods, which are within the reach of current technology.
Entanglement between individual spins can be detected by using thermodynamics quantities as entanglement witnesses. This applies to collective spins also, provided that their internal degrees of freedom are frozen, as in the limit of weakly coupled nanomagnets. Here, we extend such approach to the detection of entanglement between subsystems of a spin cluster, beyond such weak-coupling limit. The resulting inequalities are violated in spin clusters with different geometries, thus allowing the detection of zero- and finite-temperature entanglement. Under relevant and experimentally verifiable conditions, all the required expectation values can be traced back to correlation functions of individual spins, which are now made selectively available by four-dimensional inelastic neutron scattering.
What is the relation between spin squeezing and entanglement? To clarify this, we derive the full set of generalized spin squeezing inequalities for the detection of entanglement. These are inequalities for the mean values and variances of the collective angular momentum components. They can be used for the experimental detection of entanglement in a system of spin‐12 particles in which the spins cannot be individually addressed. We also show how to obtain the complete set of entanglement conditions if the mean spin and the spin correlation matrix are known. Finally, we apply our criteria for entanglement detection in spin models, showing that they can be used to detect bound entanglement in the thermal state of these systems.
I present methods for detecting entanglement around symmetric Dicke states. In particular, I consider N-qubit symmetric Dicke states with N/2 excitations. I show that for large N these states have the smallest overlap possible with states without genuine multipartite entanglement. Thus these states are particularly well suited for the experimental examination of multipartite entanglement. I present fidelity-based entanglement witness operators for detecting multipartite entanglement around these states. I then consider entanglement criteria, somewhat similar to the spin squeezing criterion, based on the moments or variances of the collective spin operators. Surprisingly, these criteria are based on an upper bound for variances for separable states. I present criteria detecting entanglement in general and criteria detecting only genuine multipartite entanglement. The collective operator measured for this criteria is an important physical quantity: Its expectation value essentially gives the intensity of the radiation when a coherent atomic cloud emits light.
Entanglement generation between atomic ensembles is typically modeled using the framework of continuous variables (CV) which approximates discrete spin operators as canonical position and momentum operators. Although hugely successful with many applications, this approximation is valid only for small deviations in spin. Here we investigate entanglement generation between two atomic ensemble qubits using a measurement based scheme of a common light mode. Various methods of entanglement detection of the entangled state is discussed. We propose a entanglement witness for this state and discuss its further applications to optical states.