Measurement Protocol for the Entanglement Spectrum of Cold Atoms

Entanglement plays a major role in characterizing many-body quantum systems. In particular, the entanglement spectrum holds a great promise to characterize essential physics of quantum many-body systems. While there has been a surge of theoretical works on the subject, no experimental measurement has been performed to this date, due to the lack of an implementable measurement scheme. Here, we propose a measurement protocol to access the entanglement spectrum of many-body states in experiments with cold atoms in optical lattices. Our scheme effectively performs a Ramsey spectroscopy of the entanglement Hamiltonian, and is based on the ability to produce several copies of the state under investigation together with the possibility to perform a global swap gate between two copies conditioned on the state of an auxiliary qubit. We show how the required conditional swap gate can be implemented with cold atoms, either by using Rydberg interactions or coupling the atoms to a cavity mode. We illustrate these ideas on a simple (extended) Bose-Hubbard model where such a measurement protocol reveals topological features of the Haldane phase.

Scientific Reports, 2014

Optical manipulation of entanglement harnessing the frequency degree of freedom is important for encoding of quantum information. We here devise a phase-resonant excitation mechanism of an atomic interface where full control of a narrowband single-photon two-mode frequency entangled state can be efficiently achieved. We illustrate the working physical mechanism for an interface made of cold 87 Rb atoms where entanglement is well preserved from degradation over a typical 100 mm length scale of the interface and with fractional delays of the order of unity. The scheme provides a basis for efficient multi-frequency and multi-photon entanglement, which is not easily accessible to polarization and spatial encoding.

Physical Review A, 2009

The unequivocal detection of entanglement between two distinct matter-wave pulses is a significant challenge that has yet to be experimentally demonstrated. We describe a realistic scheme to generate and detect continuous-variable entanglement between two atomic matter-wave pulses produced via degenerate four-wave mixing from an initially trapped Bose-Einstein condensate loaded into a one-dimensional optical lattice. We perform a comprehensive numerical investigation for fixed condensate parameters to determine the maximum violation of separability and Einstein-Podolsky-Rosen inequalities for field quadrature entanglement, and describe and simulate an experimental scheme for measuring the necessary quadratures.

Journal of Physics B-atomic Molecular and Optical Physics, 2011

The Mermin inequality provides a criterion for experimentally ruling out local-realistic descriptions of multiparticle systems. A violation of this inequality means that the particles must be entangled, but does not, in general, indicate whether N -partite entanglement is present. For this, a stricter bound is required. Here we discuss this bound and use it to propose two different schemes for demonstrating N -partite entanglement with atoms. The first scheme involves Bose-Einstein condensates trapped in an optical lattice and the second uses Rydberg atoms in microwave cavities.

2011

We show how entanglement may be quantified in spin and cold atom many-body systems using standard experimental techniques only. The scheme requires no assumptions on the state in the laboratory and a lower bound to the entanglement can be read off directly from the scattering cross section of Neutrons deflected from solid state samples or the time-of-flight distribution of cold atoms in optical lattices, respectively. This removes a major obstacle which so far has prevented the direct and quantitative experimental study of genuine quantum correlations in many-body systems: The need for a full characterization of the state to quantify the entanglement contained in it. Instead, the scheme presented here relies solely on global measurements that are routinely performed and is versatile enough to accommodate systems and measurements different from the ones we exemplify in this work.

Physical Review Letters, 2003

We propose a method to prepare entangled states and implement quantum computation with atoms in optical cavities. The internal state of the atoms are entangled by a measurement of the phase of light transmitted through the cavity. By repeated measurements an entangled state is created with certainty, and this entanglement can be used to implement gates on qubits which are stored in different internal degrees of freedom of the atoms. This method, based on measurement induced dynamics, has a higher fidelity than schemes making use of controlled unitary dynamics.

Physical Review A, 2014

We present an efficient method for generating maximum entanglement in one-dimensional atomic lattices. The proposed method relies on adiabatic rapid transfer into two Rydberg states with strongly asymmetric interactions. The method is suitable for Rydberg S states in the absence of applied electrostatic fields. We show numerical simulations of entanglement generation in rubidium atoms using calculated van der Waals potentials under realistic experimental conditions. We study the effect of the chosen Rydberg states on the final entanglement.

New Journal of Physics, 2009

We discuss the possibility of preparing highly entangled states by simply cooling atoms into the ground state of an applied interaction Hamiltonian. As in laser sideband cooling, we take advantage of a relatively large detuning of the desired state, while all other qubit states experience resonant laser driving. Once spontaneous emission from excited atomic states prepares the system in its ground state, it remains there with a very high fidelity for a wide range of experimental parameters and all possible initial states. After presenting the general theory, we discuss concrete applications with one and two qubits.

Physical Review Letters, 2008

The mapping of photonic states to collective excitations of atomic ensembles is a powerful tool which finds a useful application in the realization of quantum memories and quantum repeaters. In this work we show that cold atoms in optical lattices can be used to perform an entangling unitary operation on the transferred atomic excitations. After the release of the quantum atomic state, our protocol results in a deterministic two qubit gate for photons. The proposed scheme is feasible with current experimental techniques and robust against the dominant sources of noise.

Physical Review Letters, 2004

We present an experimental demonstration of both quadrature and polarization entanglement generated via the interaction between a coherent linearly polarized field and cold atoms in a high finesse optical cavity. The non linear atom-field interaction produces two squeezed modes with orthogonal polarizations which are used to generate a pair of non separable beams, the entanglement of which is demonstrated by checking the inseparability criterion for continuous variables recently derived by Duan et al. [Phys. Rev. Lett. 84, 2722] and calculating the entanglement of formation [Giedke et al., Phys. Rev. Lett. 91, 107901 (2003)].