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Physical Review A

Generation and characterization in a laboratory of C2⊗Cd states of flying electrons and ions with negative or positive partial transpose possessing free or bound entanglement

S. Parida, Naresh Chandra

Published Dec 4, 2012• 6 citations
Publisher

Abstract

In this paper, we show that bipartite states of an electronic qubit and ionic qudit, produced in a laboratory in as simple an experiment as photoionization in electric dipole approximation, can be separable or can possess either free or bound entanglement. The dimension of the Hilbert space of the qudit depends upon the electronic state $|{1}^{+}\ensuremath{\rangle}$ of the residual photoion ${A}^{1+}$: In the absence of spin-orbit interaction (SOI), when Russell-Saunders coupling is applicable, it is equal to the spin multiplicity of $|{1}^{+}\ensuremath{\rangle}$, but becomes (2$J$+1) in $j\ensuremath{-}j$ coupling, where $J$ is the total angular momentum of $|{1}^{+}\ensuremath{\rangle}$ when SOI is taken into account. In the case of $L\ensuremath{-}S$ coupling, all the properties (relevant to a study in quantum information) of a qubit-qudit state can readily be predicted merely with a knowledge of the spins of the atomic target and of the residual photoion which can experimentally be verified by measuring them using an entanglement witness, or any other such protocols, or by doing a full quantum-state tomography.

DOI
10.1103/physreva.86.062302

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In this paper, we show that bipartite states of an electronic qubit and ionic qudit, produced in a laboratory in as simple an experiment as photoionization in electric dipole approximation, can be separable or can possess either free or bound entanglement. The dimension of the Hilbert space of the qudit depends upon the electronic state ∣1+\ensuremath⟩|{1}^{+}\ensuremath{\rangle}∣1+\ensuremath⟩ of the residual photoion A1+{A}^{1+}A1+: In the absence of spin-orbit interaction (SOI), when Russell-Saunders coupling is applicable, it is equal to the spin multiplicity of ∣1+\ensuremath⟩|{1}^{+}\ensuremath{\rangle}∣1+\ensuremath⟩, but becomes (2JJJ+1) in j\ensuremath−jj\ensuremath{-}jj\ensuremath−j coupling, where JJJ is the total angular momentum of ∣1+\ensuremath⟩|{1}^{+}\ensuremath{\rangle}∣1+\ensuremath⟩ when SOI is taken into account. In the case of L\ensuremath−SL\ensuremath{-}SL\ensuremath−S coupling, all the properties (relevant to a study in quantum information) of a qubit-qudit state can readily be predicted merely with a knowledge of the spins of the atomic target and of the residual photoion which can experimentally be verified by measuring them using an entanglement witness, or any other such protocols, or by doing a full quantum-state tomography.
Quantum entanglement holds the key to an information processing revolution. In this article, we study the entanglement properties of tripartite states of two electronic qubits and ionic qudit,without observing spin orbit interaction (SOI), produced by single-step double photoionization from Xeon atom following the absorption of a single photon. The dimension of the Hilbert space of the qudit depends upon the electronic state of the residual photoion Xe2+. In absence of SOI, Russel-Salunders coupling (L-S coupling) is applicable. As the estimations of entanglement, we consider Peres-Horodecki condition and negativity. In case of L-S coupling, all the properties of a qubit-qudit system can be predicted merely with the knowledge of the spins of the target atom, the residual photoion, emitted electrons and state of polarization of the incident photons.
Objectives: To study of entanglement between two electronic qubits,without observing spin orbit interaction (SOI), produced by double photo ionization from Xeon atom following the absorption of a photon. Methods: In absence of SOI, Russel-Salunders coupling (L-S coupling) is applicable. As the estimations of entanglement we have considered PeresHorodecki condition and negativity. In case of L-Scoupling, all the properties of electronic qubits are predicted merely with the knowledge of the spins of the target atom, the residual photoion, emitted electrons and the state of polarization of the absorbed photon. Findings: We have found that the electronic qubits may be totally entangled, partially entangled or separable depending on spin states of target Xe, residualdication Xe2+,emitted electrons and the state of polarization of incident photon as well as of the direction sspin quantization and ejection of the photoelectrons. Applications/ Improvements: Studies of quantumen tanglement and its paradoxical properties hold the key to various Quantum information (QI) tasks such as quantum teleportation, quantum cryptography and quantum computer technology. Keywords: Density Operator PACS No. 32.30, L-S Coupling, Negativity, Peres-Horodecki Condition
Quantum entanglement holds the key to a revolution in information processing.This paper investigates the entanglement characteristics of tripartite states of two electronic qubits and an ionic qubit produced by single-step double photoionization (DPI) from a Xeon atom after absorption of a single photon, without observing spin orbit interaction (SOI). DPI is the most natural processes for simultaneously producing two electrons in continuum in a single step. The dimension of the Hilbert space of the qudit depends upon the electronic state of the residual photoion Xe2+. Russel-Salunders coupling (L-S coupling) is applicable in absence of SOI. We consider Peres-Horodecki condition and negativity as an estimation of entanglement. With L-S coupling, all of the properties of a qubit-qudit system can be predicted simply by knowing the spins of the target atom, the residual photoion, the emitted electrons, and the polarisation state of incident photons.
Multidimensional quantum systems (qudits), as a generalization of two-level quantum systems (qubits), can exhibit distinct quantum properties, provide higher capacity and noise robustness in quantum communications. Qudits also offer higher efficiency and flexibility in quantum computing. Present paper studies the bipartite entanglement betwixt a molecular photoion (qudit) and photoelectron (qubit) produced in the photoionization from rotationally state selected, oriented polyatomic molecule without observing spin-orbit interaction (SOI). In absence of SOI, Russell-Saunders (RS) coupling is applicable. The dimension of ionic qudit depends on its electronic state. The degree of entanglement is quantified by the concurrence obtained from the elements of density matrix (EDM) for photoionization. The theoretical formulation for entanglement has been developed for photoionization of rotationally state selected, oriented C3v molecules. It is applied, as an example, to photoionization in 2 13a1 orbital of a state selected oriented CH3I in a pure JKJMJ rotational state. We find that the entanglement depends significantly on the rotational states of the molecule as well as either or both on the directions of molecular orientation, of spin quantization, and of the incident beam along with its polarization. A significant effect on entanglement properties due to the circular dichroism (CD) has also been observed.
A scheme for generating states of three free electrons entangled with respect to their spins is suggested. It consists of sequential ejection of two Auger electrons (e2{e}_{2}e2​ and e3{e}_{3}e3​) in the nonradiative decay of an inner-shell vacancy created due to the emission of photoelectron e1{e}_{1}e1​ from an atom, say AAA. In the absence of spin-orbit interaction, the entanglement among the spin angular momenta of the flying (e1,e2,e3)({e}_{1},{e}_{2},{e}_{3})(e1​,e2​,e3​) is generated simply by the Coulomb interaction experienced by them inside AAA. Their states are classified according to the hierarchic structure suggested by D\"ur, Cirac, and Tarrach [Phys. Rev. Lett. 83, 3562 (1999); D\"ur and Cirac, Phys. Rev. A 61, 042314 (2000)]. The generation of fully separable, 1-electron biseparable, fully inseparable, or ``$1\ensuremath{\rightarrow}2$ entangled'' tripartite (in addition to various kinds of bipartite) states is shown to be completely determined only by the spin multiplicities of the electronic states of AAA and of its ionic species $({A}^{{+}^{\ensuremath{\ast}}},{A}^{2{+}^{\ensuremath{\ast}}},{A}^{3+})$ participating in the suggested scheme. The entanglement of three electrons is Greenberger-Horne-Zeilinger type. The experimental characterization of these states is fully achieved merely by the measurements of the energies of (e1,e2,e3)({e}_{1},{e}_{2},{e}_{3})(e1​,e2​,e3​), without requiring any entanglement witness or other similar protocols hitherto developed in quantum information.
Quantum entanglement is a unique phenomenon of quantum mechanics that explains how two subatomic particles are correlated even if they are separated by a vast distance. The phenomena of quantum entanglement are useful resources for quantum information. In this chapter, we will study the entanglement properties of bipartite states of two electronic qubits, without observing spin-orbit interaction (SOI), produced by single-step double photoionization in helium atom following the absorption of a single photon. In absence of SOI, Russell-Saunders coupling (L-S coupling) is applicable. We observe that the entanglement depends significantly on the direction of the ejection, as well as the spin quantization of photoelectrons.