Colorful Quantum Entanglement

Paulo Nussenzveig (left) and Marcelo Martinelli in their lab, in Brazil.



[This is an invited article based on recently published works of the authors and their collaborators -- 2Physics.com]




Authors: Paulo Nussenzveig and Marcelo Martinelli

Affiliation: Experimental Physics Department, Instituto de Fisica -- USP,
Sao Paulo, Brazil
Link to the Laboratory of Coherent Manipulation of Atoms and Light (LMCAL) >>

Quantum entanglement has just become more colorful. In a recent experiment, three bright beams of light, all of different wavelengths, were entangled [1]. Physicists have been playing around with this mind-boggling concept since 1935, but recently they have acquired enormous control over quantum systems. Entanglement is now viewed as a valuable resource to enable sophisticated information tasks. Indeed, the field of quantum information science relies heavily on entanglement in order to perform quantum computing, teleportation, and communication. A quantum internet is envisaged as a dream to be pursued, with information being conveyed among its nodes via quantum teleportation [2].

Since quantum hardware is still composed of different physical systems, which do not always share common resonances for interaction with light, one faces challenges to exchange quantum information among them. By entangling light beams of different wavelengths, this is no longer a problem. This is what was achieved, with one beam in the visible portion of the spectrum (532.251 nm) and two in the near infrared (1062.102 nm and 1066.915 nm). Research was performed by a group at the University of São Paulo, in Brazil, with participation of two researchers (former students in Brazil) from the new Max Planck Institute for the Science of Light, in Germany.

Entanglement in continuous variable (CV) systems, such as bright beams of light, is generated by means of nonlinear optical processes [3]. The lowest nonlinear order is two, corresponding to processes in which three fields are coupled. Examples are second harmonic generation, sum- and difference-frequency generation, and parametric down-conversion. This latter process is used for the generation of twin photons, a well-known way of producing entangled qubits (e.g. polarization-entangled photons). A nonlinear crystal is pumped by a laser, generating spontaneously emitted pairs of photons. In each fundamental process, a pump photon is annihilated and a pair of lower-frequency photons is created. If the crystal is placed inside a cavity, resonant for all three fields involved, photons are emitted in occupied modes (stimulated emission). The resulting gain can overcome losses and the system oscillates, similarly to a laser. This optical parametric oscillator (OPO), as sketched in Fig. 1, was used by the researchers to generate the three-color entanglement.

Fig. 1 : Sketch of an OPO. A nonlinear optical crystal is placed within two mirrors, forming a cavity. Green incident light is down-converted into twin beams of infrared light.

In order to measure entanglement, researchers had to cool the crystal, to reduce thermal vibrations (phonons), which were responsible for generating unwelcome phase noise in the optical fields. In a tripartite Gaussian state, there is a necessary and sufficient criterion to check for entanglement, due to Simon [4] and extended by Werner and Wolf [5]. By measuring the full covariance matrix of the three-field system, researchers could check that the lowest symplectic eigenvalue under partial transposition with respect to each beam was smaller than one, demonstrating full inseparability (Fig. 2).

Fig. 2: Full tripartite inseparability. Symplectic eigenvalues corresponding to transposition by the pump (green), signal (red) and idler (blue) are lower than one for a broad range of values of the pump power relative to the threshold power (from ref. [1]).

Three-color entangled beams can be useful for communications. Since quantum resources are in general very fragile, the robustness of the entanglement against losses was studied. The researchers observed a subtle quantum property hitherto only witnessed in few-particle systems, called entanglement sudden death [6]. Entanglement was lost for partial attenuation, in certain situations. However, in others the researchers showed that entanglement can be kept alive. The states that were generated have different sensitivity to losses, warranting further investigations.

Entanglement implies a certain “familiarity” among the constituents of a system composed of different parts. The Brazilian experiment generates entanglement among the pump and the twins to which it gives birth: one can think of it as “quantum genealogy”, since it is shown that the twins are entangled to their “mother”.

References
[1] "Three-Color Entanglement", A. S. Coelho, F. A. S. Barbosa, K. N. Cassemiro, A. S. Villar, M. Martinelli, and P. Nussenzveig, Science Express, DOI: 10.1126/science.1178683 (September 17, 2009). Abstract.
[2] "The Quantum Internet", H. J. Kimble, Nature 453, 1023 (2008). Abstract.
[3] "Quantum information with continuous variables", S. L. Braunstein and P. van Loock, Rev. Mod. Phys. 77, 513 (2005). Abstract.
[4] "Peres-Horodecki Separability Criterion for Continuous Variable Systems", R. Simon, Phys. Rev. Lett. 84, 2726 (2000). Abstract.
[5] "Bound Entangled Gaussian States", R. F. Werner and M. M. Wolf, Phys. Rev. Lett. 86, 3658 (2001). Abstract.
[6] "Environment-Induced Sudden Death of Entanglement", M. P. Almeida, F. de Melo, M. Hor-Meyll, A. Salles, S. P. Walborn, P. H. Souto Ribeiro, and L. Davidovich, Science 316, 579 (2007). Abstract.