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Here we discuss a few physical details of the experiment. This includes the introduction of the light and the atomic systems used in the memory protocol and some discussion of experimental results.

In the real experiment the atoms are polarized and placed in a constant, homogeneous magnetic field. This causes Larmor rotation and complicates the picture. Below we will assume that there is no Larmor precession and that the input light state is interacting with a single atomic spin sample. In real life the complications of the Larmor precession can be overcome by using two oppositely oriented atomic samples. For a discussion of this we refer to the published work (nature 432, 482 (2004)).

The light pulse which travels through the atomic sample consists of two parts. Each of these have the same duration and spatial profile. The two polarization degrees of freedom are used for different purposes. The interesting one is a weak, y-polarized part containing only a small number of photons (or it may be the vacuum state). This is the quantum field to be stored in the atomic memory. The x-polarized part is strong and is providing the interaction strength required for the light and atomic states to communicate.

It is convenient to express the light quantum variables in the language of position- and momentum-like operators X and P satisfying the usual commutation relation [X,P] = i:

The quantum variables X,P for light are defined below. T is the pulse duration and the creation- and annihilation operators in the integrals refer to the y-polarized mode of light.

In the atoms it is the spin degree of freedom that is relevant. We use cesium atoms in the F=4 ground state and define collective spin operators J_x, J_y, and J_z as sums over all individual spin components.

The atomic sample consists of roughly 10¹¹ atoms. By optical pumping it is possible to initially orient all atoms along the x-direction with an efficiency of 99%. Hence J_x has a very large mean value and its fluctuations are unimportant. The interesting quantum degrees of freedom are the transverse components J_y and J_z. Hence we define quantum variables X and P for atoms as below:

The quantum variables X,P for atoms. The atoms are spin polarized along the x-direction and J_x is effectively a classical c-number.

In the interaction process the light and atomic quantum variables will affect each other as described below. The interaction strength k depends on the strength and duration of the light in the x-polarized mode, on the number of atoms in the sample, and on laser and geometrical settings. For details we refer to the paper Quantum Information and Computation 3, Special issue, 518 (2003) or to Brian Julsgaard's PhD-thesis.

The equations of interaction for the light and atomic quantum variables. "in" and "out" refer to the state before and after the light and atoms have interacted. The interaction strength is parametrized by the dimensionless parameter k which is of the order of unity in the experiment.