Spin Squeezing in Degenerate and Non-degenerate Atomic Vapors: Some Approaches to Atomic Entanglement

Entanglement is one of the most intrinsically quan­ tum aspects of the quantum theory; Entanglement is of importance to advanced quantum technologies such as quantum computers and teleportation devices. En­ tanglement of many atoms has developed into an im­ portant frontier of contemporary physics and quantum optics. In this paper we describe our recent work on the creation of entanglement via the creation of spinsqueezed states of a gas of neutral atoms. The specific problem of spin-squeezing is a particularly interesting aspect of entanglement because it can have important consequences for precision measurements and mea­ surements where quantum “noise” is important. Consider the case of a neutral atom atomic clock: many atom entanglement can, in principle, dramati­ cally improve the measurement sensitivity of a typ­ ical clock (or any atom interferometer) from \ l \ f N to UN, where N is the number of detected atoms. In turn, this improvement implies a much greater short­ term stability for the same number of detected atoms. Quite recently, a fundamental performance barrier for the cold-atom “fountain” clocks has been observed: the so-called “projection-noise” limit [1], The entan­ glement of the many atoms used in such a clock mea­ surement promises to provide an intriguing quantum means to break this limit. The extensive research activity devoted to the gen­ eration of the non-classical states of the electro­ magnetic field and to their applications to reduce the uncertainty of phase measurement is therefore now being paralleled by the quest for similar states in other physical systems, systems which could be used to improve measurements relevant to a broader range of physical effects. A notable example of the latter is represented by the spin squeezed state (SSS) of atomic particles [2, 3]. Just as squeezed states of light allow for a reduction in the measurement un­ certainty due to quantum fluctuations of light, SSS of atoms and ions hold the promise to reduce uncer­ tainties induced by quantum fluctuations in atomic measurement systems. As a starting point, we consider the measurement of atomic projection noise. In a variety of experiments, quantum spin-noise has already been investigated [4]. For this paper we focus on recent work carried out in our laboratories in which we have demonstrated the ability to detect atomic spin-noise at the shot-noise limit [5], We then describe how we used our apparatus to explore spin state measurement and control, and how we have used it to realize non-classical states of the collective atomic spin of the gas.