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Open Systems & Information Dynamics

Quantum and Classical Correlations of Spatial and Spin Degrees of Freedom in Quantum Rings

Orsolya Kálmán, Péter Földi, M. G. Benedict

Published Nov 15, 2006• 4 citations
Publisher

Abstract

A one-dimensional mesoscopic ring with one input and two output leads acts as a spintronic beam splitter. The spatial degree of freedom, i.e., the presence of two different possible output channels, gets intertwined with the spin direction as a consequence of quantum interference and spin-orbit interaction. We investigate this kind of spatial-spin correlation, and show that the output density operator contains no quantum entanglement in the important special case when the device polarizes a perfectly random input spin state. However, the correlations are in general not purely classical, we also present specific input states with maximal spatial-spin entanglement after the ring.

DOI
10.1007/s11080-006-9015-1

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A one-dimensional mesoscopic ring with one input and two output leads acts as a spintronic beam splitter. The spatial degree of freedom, i.e., the presence of two different possible output channels, gets intertwined with the spin direction as a consequence of quantum interference and spin-orbit interaction. We investigate this kind of spatial-spin correlation, and show that the output density operator contains no quantum entanglement in the important special case when the device polarizes a perfectly random input spin state. However, the correlations are in general not purely classical, we also present specific input states with maximal spatial-spin entanglement after the ring.
We investigate the connection between biphoton states involving photons in product modes of their spin and orbital degrees of freedom and those involving photons in hybrid spin-orbit modes, as mediated by Hong-Ou-Mandel interference (HOMI) in an asymmetric Mach-Zehnder interferometer. We predict that two input photons in balanced superposition states of both their spin and orbital degrees of freedom will exhibit HOMI while undergoing a simultaneous mode conversion from product spin-orbit input modes to hybrid output modes bearing orbital angular momentum. These hybrid outputs contain a spatially varying polarization structure which may be controllably rotated about the photonic beam axis by varying the relative phase between the vertical and horizontal components of each input photon's polarization. Additionally, a type of coupling of the spin and orbital degrees of freedom is exhibited in this system: the transverse spatial profile of the output photons may be continuously manipulated by tuning the polarization parameters of the input photons, in such a way that the HOMI between the photons remains stable. An interesting corollary to this work is the possibility of demonstrating in a simple experimental system that HOMI may occur between distinguishable input modes.
Using a method of characterizing entanglement in the framework of quantum field theory, we investigate the optical generation and quantitative characterizations of quantum entanglement in an electron-hole system, in presence of spin-orbit coupling, and especially make a theoretical analysis of a recent experimental result. Basically, such entanglement should be considered as between occupation numbers of single-particle basis states, and is essentially generated by coupling between different single-particle basis states in the second-quantized Hamiltonian. Interaction with two resonant light modes of different circular polarizations generically leads to a superposition of ground state and two heavy-hole excitonic states. When and only when the state is a superposition of only the two excitonic eigenstates, the entanglement reduces to that between two distinguishable particles, each with two degrees of freedom, namely, band index, as characterized by angular momentum, and orbit, as characterized by position or momentum. The band-index state, obtained by tracing over the orbital degree of freedom, is found to be a pure state, hence the band index and orbital degrees of freedom are separated in this state. We propose some basic ideas on spatially separating the electron and the hole, so that the entanglement of band indices, or angular momenta, is between spatially separated electron and hole.
We identify universal spatial fluctuations in systems with nontrivial spin dynamics. To this end we calculate by exact numerical diagonalization a variety of experimentally relevant correlations between spinor amplitudes, spin polarizations, and spin currents, both in the bulk and near the boundary of a confined two-dimensional clean electron gas in the presence of spin-orbit interaction. We support our claim of universality with the excellent agreement between the numerical results and system-independent spatial correlations of a random field defined on both the spatial and spin degrees of freedom. A rigorous identity relating our universal predictions with response functions provides a direct physical interpretation of our results in the framework of linear response theory.
The generation of paired photons entangled in the spatial degree of freedom, i.e., in orbital angular momentum, offers a convenient physical resource to investigate the nature of entanglement in a multidimensional Hilbert space with controllable dimensionality. The two main physical processes that generate pairs of photons which show correlations in orbital angular momentum are (a) spontaneous parametric down-conversion (SPDC), and (b) Raman transitions induced in atomic ensembles. One question naturally arises: what kinds of correlations exist between the orbital angular momentum of the generated photons? The answer might be different if we consider the whole quantum state of the generated photons, i.e., all possible directions where the pairs of photons can be emitted, or if we consider only a small section of the full set of directions.
We demonstrate electromagnetic quantum states of single photons and of correlated photon pairs exhibiting ``hybrid'' entanglement between spin and orbital angular momentum. These states are obtained from entangled photon pairs emitted by spontaneous parametric down conversion by employing a qqq plate for coupling the spin and orbital degrees of freedom of a photon. Entanglement and contextual quantum behavior (that is also nonlocal, in the case of photon pairs) is demonstrated by the reported violation of the Clauser-Horne-Shimony-Holt inequality. In addition, a classical analog of the hybrid spin-orbit photonic entanglement is reported and discussed.
We propose a scheme to implement the one-dimensional coined quantum walk with electrons transported through a two-dimensional network of spintronic semiconductor quantum rings. The coin degree of freedom is represented by the spin of the electron while the discrete position of the walker corresponds to the label of the rings in one of the spatial directions in the network. We assume that Rashba-type spin-orbit interaction is present in the rings, the strength of which can be tuned by an external electric field. The geometry of the device, together with the appropriate spin-orbit interaction strengths, ensure the realization of the coin toss (i.e., spin flip) and the step operator.