Quantum State Reconstruction Using Atom Optics

The development of methods for completely determining the quantum state of an atom or cavity field @1# continues to be an important issue in atomic physics. For example, in the field of quantum optics, schemes have been recently proposed, based on the Stem-Gerlach effect, for completely determining the quantum state of an atom as a way of fully characterizing the quantized electromagnetic field of a cavity mode @2#. The reconstruction of an internal atomic state is important for goals as far reaching as reading the end state of a quantum gate operation @3# and teleportation of internal atomic states @4#. Walser et al. @2# describe a scheme whereby the field state of a cavity could be transferred to the magnetic sublevels of the internal state of an atom through the technique of adiabatic passage, thus converting the problem to one of determining a quantum state of an atom. Atom deflection has been suggested as a probe of the photon number in a cavity @5# and has also been used to measure the Mandel Q parameter of photon statistics for resonance fluorescence @6,7#. This technique provides a significant improvement over conventional photon counting schemes due to the poor efficiency of photon detection, which affects measurements of the Q parameter. In the field of electronatom collision physics, the measurement of the atomic collision density matrix using coincidence and superelastic scattering methods depends on the complete determination of the quantum state of the atom @8#. The internal quantum state of an atom can be described by the density matrix formalism, which contains all the information about the quantum system. In principle, if one can measure all elements of the density matrix, then complete reconstruction of the quantum state of a system is possible. Atomic states are relatively insensitive to decoherence and can maintain an initial quantum state for long time scales compared to the characteristic times for preparation and detection, and as such they are frequently used in quantum computing proposals where insensitivity to decoherence is a requirement @9#. In this Rapid Communication, a method is presented for completely determining the density matrix of an atomic state based on laser induced deflection of the atom. The experiment is a realization of a suggestion put forward by Summy and co-workers @10–12# and represents the direct measurement of atomic density matrix elements for a state that has