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# Macroscopic Entanglement

The last decade's experimental developments made it possible to test some of the most fascinating fundamental quantum physics predictions. Among those experiments we find gaseous Bose-Einstein condensation in a cloud of Rubidium atoms [1], quantum teleportation of the polarization state of a photon [2], deterministic quantum teleportation between a pair of trapped calcium ions [3], decoherence of (C70 fullerene) matter waves [4], and many others.

So far entanglement has been experimentally prepared and manipulated using microscopic quantum systems such as photons and ions and the answer to the question of at what extend should entanglement - "the most characteristic trait of quantum mechanics" (Schrodinger) - hold is yet unknown. On the other hand nothing in the principles of quantum mechanics prevents macroscopic systems to attain entanglement even though they may have to be cooled down to very small temperatures since the strong coupling that such systems maintain with their environment [7] may lead to fast decoherence [7]. Therefore it is of crucial importance to investigate the possibility of obtaining entangled states of mesoscopic and macroscopic systems at non zero temperature.

It is known that a cavity electromagnetic field interacting with a movable mirror through radiation pressure [8] is a good candidate for such a system, since as we have shown its quantum correlations are very robust against temperature [9]. The figure below (left) represents the entanglement as function of the effective coupling between light and mirror (k) and time (x axis - in units of the mirror's period). The red area is where entanglement is maximal.

The robustness of entanglement as function of the scaled temperature (y-axis) and scaled coupling strength (x-axis) is plotted in the other figure for the subspace of zero and one excitations of both fields (mirror/light). We see that only for very high temperature and very small coupling (region II) [*] entanglement vanishes in this subspace. However, we were able to prove that the area of region I decreases by moving into higher subspaces. This is the key feature of the radiation pressure mechanism that allows macrosocopic entanglement at non-zero temperature [9]. This has been our main motivation to study optomechanical entanglement under more realistic assumptions, i.e. by including thermal noise and leaking of the photons from the cavity. We aim to show that this specific bipartite system (mirror/cavity field) is able to support sizable entanglement at experimental accessible temperatures [10] and that its degree of entanglement can be extracted using an appropriate measuring scheme without significantly altering the dynamics of the system. Our results [10] are quite promising; using state-of-the-art experimental parameters we showed that entanglement survives up to 20K. On the other hand, recent experimental progress on the self-cooling of micromirrors [11] lead us to believe that mesoscopic and macroscopic entanglement between matter and light will be achieved in the near future.

[*] More precisely the function b (x-axis) depends also on time. Thus, the absence of entanglement in region I is due to the fact that entanglement cannot be present for all times.[1] M. H. Anderson

*et al*, Science

**269**, 198 (1995);

[2] D. Bouwmeester

*et al*, Nature

**390**, 575 (1997);

[3] M. Riebe

*et al*, Nature

**429**, 734 (2004);

[4] L. Hackermuller

*et al*, Nature

**427**, 711 (2004);

[5] M.B. Plenio and V. Vedral, Contemp. Phys.

**39**, 431 (1998);

[6] S. Sachdev, Quantum Phase Transitions, (Cambridge University Press, Cambridge, 2000);

[7] W. H. Zurek, Rev. Mod. Phys.

**75**, 715 (2003);

[8] C. K. Law, Phys. Rev. A

**51**, 2537 (1995);

[9] A. Ferreira

*et al*, Phys. Rev. Lett.

**96**, 060407 (2006);

[10] D. Vitali

*et al*, Phys. Rev. Lett.

**98**, 030405 (2007);

[11] S. Gigan

*et al*, Nature

**444**, 67-70(2 November 2006).

Stories about our work my be found at the web. (e.g. IOP Press).

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