Visualising entanglement in atoms

Physical review letters, 2017

The frontier orbital sequence of individual dicyanovinyl-substituted oligothiophene molecules is studied by means of scanning tunneling microscopy. On NaCl/Cu(111), the molecules are neutral, and the two lowest unoccupied molecular states are observed in the expected order of increasing energy. On NaCl/Cu(311), where the molecules are negatively charged, the sequence of two observed molecular orbitals is reversed, such that the one with one more nodal plane appears lower in energy. These experimental results, in open contradiction with a single-particle interpretation, are explained by a many-body theory predicting a strongly entangled doubly charged ground state.

Physical Review Letters, 2008

Entangled many body systems have recently attracted significant attention in various contexts. Among them, spin squeezed atoms and ions have raised interest in the field of precision measurements, as they allow to overcome quantum noise of uncorrelated particles . Precise quantum state engineering is also required as a resource for quantum computation, and spin squeezing can be used to create multi-partite entangled states . Two-mode spin squeezed systems have been used for elementary quantum communication protocols . Until now spin squeezing has been always achieved via generation of entanglement between different atoms of the ensemble . In this Letter, we demonstrate for the first time ensemble spin squeezing generated by engineering the quantum state of each individual atom. More specifically, we entangle the nuclear and electronic spins of 10 12 Cesium atoms at room temperature. We verify entanglement and ensemble spin squeezing by performing quantum tomography on the atomic state.

2018

Visualisation of orbital angular momentum in a wavefunction may be accomplished by several methods: phase-colouring the wavefunction, plotting the current density (in the absence of magnetic field), or plotting the property density of the orbital angular momentum operator. Here, I present an additional method in which the orbital is animated by applying a time-dependent phase factor. This makes orbital angular momentum visible in a way that reflects the nature of the orbital angular momentum eigenfunction. This can be extended to examining the effects of spin-orbit coupling (SOC), which admixes higher orbital angular momentum states into the orbital; although the small extent of such admixture requires judicious scaling of one phase-component to properly visualise. The method is demonstrated using a model p-orbital and the singlyoccupied molecular orbitals (SOMOs) of small doublet radicals. This method may prove of interest to quantum chemists whose work involves analysing properties where SOC is important, such as magnetic resonance parameters.

Physical Review A, 2000

We propose an implementation for quantum logic and computing using trapped atomic spins of two different species, interacting via direct magnetic spin-spin interaction. In this scheme, the spins (electronic or nuclear) of distantly spaced trapped neutral atoms serve as the qubit arrays for quantum information processing and storage, and the controlled interaction between two spins, as required for universal quantum computing, is implemented in a three step process that involves state swapping with a movable auxiliary spin.

Physical Review B, 2011

Motivated by recent experiments on quasi-1D vanadium oxides, we study quantum phase transitions in a one-dimensional spin-orbital model describing a Haldane chain and a classical Ising chain locally coupled by the relativistic spin-orbit interaction. By employing a field-theoretical approach, we analyze the topology of the ground-state phase diagram and identify the nature of the phase transitions. In the strong coupling limit, a long-range N\'eel order of entangled spin and orbital angular momentum appears in the ground state. We find that, depending on the relative scales of the spin and orbital gaps, the linear chain follows two distinct routes to reach the N\'eel state. First, when the orbital exchange is the dominating energy scale, a two-stage ordering takes place in which the magnetic transition is followed by melting of the orbital Ising order; both transitions belong to the two-dimensional Ising universality class. In the opposite limit, the low-energy orbital modes undergo a continuous reordering transition which represents a line of Gaussian critical points. On this line the orbital degrees of freedom form a Tomonaga-Luttinger liquid. We argue that the emergence of the Gaussian criticality results from merging of the two Ising transitions in the strong hybridization region where the characteristic spin and orbital energy scales become comparable. Finally, we show that, due to the spin-orbit coupling, an external magnetic field acting on the spins can induce an orbital Ising transition.

International Journal of Computer Applications, 2012

In this paper, a method for computing entanglement of electrons in atoms and molecules is described. The importance of entanglement computation for Quantum Computers and for Biology is highlighted and the existing models' pros and cons are illustrated. A description of the algorithms follows, with some considerations about the execution times and how they scale increasing the system's Hilbert space dimension.

New Journal of Physics, 2009

We report a high fidelity tomographic reconstruction of the quantum state of photon pairs generated by parametric down-conversion with orbital angular momentum (OAM) entanglement. Our tomography method allows us to estimate an upper and lower bound for the entanglement between the downconverted photons. We investigate the two-dimensional state subspace defined by the OAM states ±`and superpositions thereof, with`= 1, 2, . . . , 30. We find that the reconstructed density matrix, even for OAMs up to around`= 20, is close to that of a maximally entangled Bell state with a fidelity in the range between F = 0.979 and F = 0.814. This demonstrates that, although the single count-rate diminishes with increasing`, entanglement persists in a large dimensional state space.

arXiv (Cornell University), 2018

In this work we explore the nature of quantum correlations between two-level atoms (or qubits) and a single mode of a quantum field in phase space. Similar to time-frequency plots, we introduce the notion of a quantum state spectrogram to allow for the visualisation of quantum correlations in coupled systems. By using our method, we are able to gain information on the quantum state in an accessible way that enables an appreciation of subtle quantum effects, without the need for sophisticated mathematics. We apply the method to the Jaynes-Cummings model and some of its extensions to demonstrate that quantum correlations of entanglement, microscopically distinct superposition, and a combination of the two can be readily identified.

Physics-Uspekhi, 2001

The current status of studies in the physics of entangled states of atomic systems Ð an interdisciplinary field involving quantum optics, quantum information, and the foundations of quantum mechanics Ð is reviewed. In the first part of the review, an introduction to the theory of entangled states is given, their properties and applications are described. In the second part, experiments on the creation and detection of entangled states in atomic systems are discussed along with associated experimental proposals for their refinement. Today's most advanced experimental technique for creating entangled ion states in an ion trap is considered, and promising methods focussed on the analogous states of neutral atoms are analyzed.

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.