We propose a method for the detection of ground state quantum phases of spinor gases through a series of two quantum nondemolition measurements performed by sending off-resonant, polarized light pulses through the gas. Signatures of various mean-field as well as strongly correlated phases of F=1 and F=2 spinor gases obtained by detecting quantum fluctuations and mean values of polarization of transmitted light are identified.

We investigate magnetic properties of Mott-insulating phases of ultracold Bose and Fermi spinor gases in optical lattices. We consider in particular the F = 2 Bose gas, and the F = 3/2 and F = 5/2 Fermi gases. We derive effective spin Hamiltonians for one and two atoms per site and discuss the possibilities of manipulating the magnetic properties of the system using optical Feshbach resonances. We discuss low temperature quantum phases of a 87 Rb gas in the F = 2 hyperfine state, as well as possible realizations of high spin Fermi gases with either 6 Li or 132 Cs atoms in the F = 3/2 state, and with 173 Yb atoms in the F = 5/2 state.

Fluctuations of the number of condensed atoms in a finite-size, weakly interacting Bose gas confined in a box potential are investigated for temperatures up to the critical region. The canonical partition functions are evaluated using a recursive scheme for smaller systems, and a saddle-point approximation for larger samples, that allows to treat realistic size systems containing up to N ∼ 10 5 particles. We point out the importance of particle-number constrain and interactions between out of condensate atoms for the statistics near the critical region. For sufficiently large systems the crossover from the anomalous to normal scaling of the fluctuations is observed. The excitations are described in a self-consistent way within the Bogoliubov-Popov approximation, and the interactions between thermal atoms are described by means of the Hartree-Fock method. A breakdown of the standard, grand-canonical ensemble to describe fluctuations of an ideal Bose gas and a necessity for canonical or microcanonical description has been noticed already long time ago [1], but only in recent decade the problem of fluctuations has received renewed attention due to the experimental achievement of BoseEinstein condensate (BEC) in ultracold trapped gases. For ideal gases, the canonical and microcanonical fluctuations have been thoroughly investigated [2,3,4,5,6,7,8,9,10], and several powerful techniques, like the Maxwell Demon ensemble [4,6,7], have been developed. For interacting particles the fluctuations have been studied mainly within the Bogoliubov approximation [11] of weakly interacting gases [12,13,14,15,16,17], that proved to be extremely successful to describe many other properties of BEC. The exact treatments, so far applied only for one-dimensional systems [18], confirmed an excellent agreement with predictions of the Bogoliubov method. We note that some controversy exists about the applicability of the mean-field theory to this problem [19], on the other hand, other approaches, like the perturbation theory, lead to qualitatively different results for fluctuations of relatively small condensates [20,21]. The ultimate verification will be done in experiments. However, to date only the statistics of the total number of atoms has been measured [22], and a technique involving scattering of short laser pulses has been proposed [23] but not realized So far the studies of fluctuations in weakly interacting gases have been limited to the regime of low temperatures, and only recently the critical region (close to the critical temperature T c ) in a finite-size system has been explored [24]. In this case the Bogoliubov-Popov (B-P) approximation [25] has been applied to account for the condensate depletion at finite temperatures and to obtain a description that smoothly interpolates between the degenerate regime below T c and an ideal gas statistics above T c .In this Letter we reinvestigate the problem of fluctuations for weakly interacting gas, putting a special emphasis on the interactions of out of condensate atoms, that apart fr...