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arXiv:1303.5257 · Physical Review Letters

Optical Spin Squeezing: Bright Beams as High-Flux Entangled Photon Sources

Federica A. Beduini, Morgan W. Mitchell

Published Sep 30, 2013• 12 citations
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Abstract

In analogy with the spin-squeezing inequality of Wang and Sanders [Phys. Rev. A 68, 012101 (2003)], we find inequalities describing macroscopic polarization correlations that are obeyed by all classical fields and whose violation implies entanglement of the photons that make up the optical beam. We consider a realistic and exactly solvable experimental scenario employing polarization-squeezed light from an optical parametric oscillator (OPO) and find polarization entanglement for postselected photon pairs separated by less than the OPO coherence time. The entanglement is robust against losses and extremely bright: efficiency can exceed that of existing "ultrabright" pair sources by at least an order of magnitude. This translation of spin-squeezing inequalities to the optical domain will enable direct tests of discrete-variable entanglement in a squeezed state.

DOI
10.1103/physrevlett.111.143601

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In analogy with the spin-squeezing inequality of Wang and Sanders [Phys. Rev. A 68, 012101 (2003)], we find inequalities describing macroscopic polarization correlations that are obeyed by all classical fields and whose violation implies entanglement of the photons that make up the optical beam. We consider a realistic and exactly solvable experimental scenario employing polarization-squeezed light from an optical parametric oscillator (OPO) and find polarization entanglement for postselected photon pairs separated by less than the OPO coherence time. The entanglement is robust against losses and extremely bright: efficiency can exceed that of existing "ultrabright" pair sources by at least an order of magnitude. This translation of spin-squeezing inequalities to the optical domain will enable direct tests of discrete-variable entanglement in a squeezed state.
We apply spin-squeezing techniques to identify and quantify highly multi-partite photonic entanglement in polarization-squeezed light. We consider a practical single-mode scenario, and find that Wineland-criterion polarization squeezing implies entanglement of a macroscopic fraction of the total photons. A Glauber-theory computation of the observable N -photon density matrix, with N up to 100, finds that N -partite entanglement is observable despite losses and without post-selection. Genuine multi-partite entanglement up to at least is similarly confirmed. The preparation method can be made intrinsically permutation-invariant, allowing highly efficient state reconstruction. In this scenario, generation plus detection requires experimental resources, in stark contrast to the typical exponential scaling. We estimate existing detectors could observe 1000-partite entanglement from a few dB of polarization squeezing.
A concept of polarization entanglement for continuous variables is introduced. For this purpose the Stokes-parameter operators and the associated Poincar\'e sphere, which describe the quantum-optical polarization properties of light, are defined and their basic properties are reviewed. The general features of the Stokes operators are illustrated by evaluation of their means and variances for a range of simple polarization states. Some of the examples show polarization squeezing, in which the variances of one or more Stokes parameters are smaller than the coherent-state value. The main object of the paper is the application of these concepts to bright squeezed light. It is shown that a light beam formed by interference of two orthogonally polarized quadrature-squeezed beams exhibits squeezing in some of the Stokes parameters. Passage of such a primary polarization-squeezed beam through suitable optical components generates a pair of polarization-entangled light beams with the nature of a two-mode squeezed state. Implementation of these schemes using the double-fiber Sagnac interferometer provides an efficient method for the generation of bright nonclassical polarization states. The important advantage of these nonclassical polarization states for quantum communication is the possibility of experimentally determining all of the relevant conjugate variables of both squeezed and entangled fields using only linear optical elements followed by direct detection.
We have generated bright squeezed light and quantum-correlated twin photon beams by using a cw semimonolithic KTP Optical Parametric Oscillator (OPO), which exhibits a low oscillation threshold and is capable of oscillating even in the free-running (no external-feedback) condition. The pump beam reflected by the OPO, after a cascading nonlinearity process in the crystal, appears as bright squeezed light. The squeezing observed on the reflected pump beam from the semimonolithic OPO was 30% (inferred squeezing: 48%). The signal and idler beams generated by the optical parametric oscillator are highly quantum-correlated twin photon beams. Since the squeezing property of the intensity difference between the twin photonbeams is robust in the condition where the two fields are balanced, the squeezing can be observed even in the freerunning condition of the OPO. This intensity-difference squeezing observed between the twin photon beams from the free-running semimonolithic OPO was 70% (inferred squeezing: 87%).
Optical parametric oscillators (OPO) have been extensively used in the continuous variable quantum optics community as a resource to produce non-classical states of light, including squeezed states or entangled beams. In this paper, general description of multimode OPOs is presented, show that they are able to produce a very wide variety of multimode quantum states of light, and give techniques to measure or separate them. The description applies equally to the spatial and temporal configurations, which are experimentally studied in lab.
Type II optical parametric oscillators are amongst the highest-quality sources of quantum-correlated light. In particular, when pumped above threshold, such devices generate a pair of bright orthogonally-polarized beams with strong continuous-variable entanglement. However, these sources are of limited practical use, because the entangled beams emerge with different frequencies and a diffusing phase difference. It has been proven that the use of an internal wave-plate coupling the modes with orthogonal polarization is capable of locking the frequencies of the emerging beams to half the pump frequency, as well as reducing the phase-difference diffusion, at the expense of reducing the entanglement levels. In this work we characterize theoretically an alternative locking mechanism: the injection of a laser at half the pump frequency. Apart from being less invasive, this method should allow for an easier real-time experimental control. We show that such an injection is capable of generating the desired phase locking between the emerging beams, while still allowing for large levels of entanglement. Moreover, we find an additional region of the parameter space (at relatively large injections) where a mode with well defined polarization is in a highly amplitude-squeezed state.