Quantop > Quantum Optics Lab > Research > Cs Cell Experiment > Scientific Topics > Entanglement Generation

The first entanglement experiment was performed in 2001 and since then we have refined the experimental setup. Accordingly there are more generations of this experiment. Below we describe very shortly the principles which are common to all our entanglement experiments.

We are interested in the transverse components of two macroscopically oriented spin samples denoted J₁ and J₂. Each sample is oriented along the x-axis and contains of the order 10¹² atoms. We may regard J_x1 and J_x2 as classical c-numbers, and the transverse spin components must for each sample fulfil the Heisenberg uncertainty relation Var(J_y)Var(J_z) ≥ J_x²/4. This uncertainty is symbolized by the gray disks below. The transverse spin components are mathematically similar to ordinary position x and momentum p. The entanglement we create is similar to the state discussed by Einstein, Podolsky, and Rosen in Phys. Rev. 47, 777 (1935).

For entanglement generation we orient two spin samples along opposite directions with same macroscopic magnitude, i.e. J_x = J_x1 = -J_x2. This ensures that the sum of transverse components J_y1 + J_y2 and J_z1 + J_z2 commute. As a result, these sums can in principle be know to very high precision. If the spins "know each other better that they may ever know themselves", then they are in an entangled state. The sums of transverse spin components can be measured in a QND fashion by a pulse of laser light.

If a pulse of light with linear polarization is tuned off-resonantly to a dipole transition in cesium, one can show that the polarization will rotate when passing trough the atomic sample. This rotation is proportional to the spin component along the direction of light propagation. This is known as the Faraday effect. We employ this effect to measure the sum of the transverse spin components, and this inevitably drives the spins into an entangled state. We must prove that the reduction in uncertainty of J_y1 + J_y2 and J_z1 + J_z2 is such that the state is entangled. Mathematically we must satisfy the inequality below.

It can easily be shown that if two macroscopic spins are independent and in the coherent spin state (i.e. if each of all atomic spins are oriented along the x-axis) the above inequality holds with equality. The coherent spin state is the most quiet state we can make classically, and entanglement arises when this boundary is broken.

In the experiments we measure the spin operators J_y1 + J_y2 and J_z1 + J_z2 with outcomes A and B. These outcomes will also have a contribution from the initial light state - the shot noise of light. When the first pulse of light has been sent through resulting in measurement outcomes A₁ and B₁ it is our task to confirm that this created an entangled state of the spins. To this end we send a second measurement pulse of light which gives the results A₂ and B₂. In our first generation of experiments we considered the differences A₁-A₂ and B₁-B₂. In the case of sufficiently small values of these we prove entanglement generation. In our later experiments we perform a more intelligent analysis.

• The first entanglement experiment published in 2001.


• A newer entanglement experiment where the vapour cells are contained in completely separate environments.

• B. Julsgaard, A. Kozhekin, and E. S. Polzik,
  Experimental long-lived entanglement of two macroscopic objects,
  Nature 413, 400 (2001).
  
  
• J. I. Cirac,
  Quantum physics: Entangled atomic samples
  Nature (News and Views) 413, 375 (2001).
  
  
• E. S. Polzik, B. Julsgaard, J. Sherson, and J. L. Sørensen,
  Entanglement and quantum teleportation with multi-atom ensembles,
  Phil. Trans. Roy. Soc. A 361, 1391 (2003).
  
  
• E. S. Polzik, B. Julsgaard, C. Schori, and J. L. Sørensen,
  in The Expanding Frontier of Atomic Physics,
  Invited talks of the XVIII International Conference on Atomic Physics,
  eds. H. R. Sadeghpour, E. J. Heller, and D. Pritchard, World Scientific (2003).
  
  
• B. Julsgaard,
  Entanglement and Quantum Interactions with Macroscopic Gas Samples,
  PhD-thesis, University of Aarhus (2003).