Conventional interferometers usually utilize beam splitters for wave splitting and recombination. These interferometers are widely used for precision measurement. Their sensitivity for phase measurement is limited by the shot noise, which can be suppressed with squeezed states of light. Here we study a new type of interferometer in which the beam splitting and recombination elements are parametric amplifiers. We observe an improvement of 4.1±0.3 dB in signal-to-noise ratio compared with a conventional interferometer under the same operating condition, which is a 1.6-fold enhancement in rms phase measurement sensitivity beyond the shot noise limit. The improvement is due to signal enhancement. Combined with the squeezed state technique for shot noise suppression, this interferometer promises further improvement in sensitivity. Furthermore, because nonlinear processes are involved in this interferometer, we can couple a variety of different waves and form new types of hybrid interferometers, opening a door for many applications in metrology.

We construct an interferometer with parametric amplifiers as beam splitters. Because of the gain in the parametric amplifiers, the maximum output intensity of the interferometer can be much bigger than the input intensity as well as the intensity inside the interferometer (the phase sensing intensity). We find that the fringe intensity depends quadratically on the intensity of the phase sensing field at high gain. This type of nonlinear interferometer has better sensitivity than the traditional linear interferometer made of beam splitters with the same phase sensing intensity.

We show that an ensemble of spinor Bose-Einstein condensates confined in a one dimensional optical lattice can undergo a ferromagnetic phase transition and spontaneous magnetization arises due to the magnetic dipole-dipole interaction. This phenomenon is analogous to ferromagnetism in solid state physics, but occurs with bosons instead of fermions.

We theoretically study the phase sensitivity of an SU(1,1) interferometer with a coherent state in one input port and a squeezed-vacuum state in the other input port using the method of homodyne detection. In this interferometer, beam splitting and recombination are generated by the parametric amplifiers instead of the beam splitters. Compared with the traditional Mach-Zehnder interferometer, the phase sensitivity of this interferometer can be improved due to the amplification process of the parametric amplifiers. Combined with the squeezed state input, the sensitivity can be improved further due to the noise reduction. The phase sensitivity of our scheme can approach the Heisenberg limit and the associated optimal condition is analyzed. The scheme can be implemented with current experimental technology.

We investigate theoretically the four-wave mixing of optical and matter waves resulting from the scattering of a short light pulse off an atomic Bose-Einstein condensate, as recently demonstrated by D. Schneble et al. [Science 300, 475 (2003)]]. We show that atomic "pair production" from the condensate results in the generation of both forward- and backward-propagating matter waves. These waves are characterized by different phase-matching conditions, resulting in different angular distributions and temporal evolutions.

We theoretically investigate the phase sensitivity with parity detection on an SU(1,1) interferometer with a coherent state combined with a squeezed vacuum state. This interferometer is formed with two parametric amplifiers for beam splitting and recombination instead of beam splitters. We show that the sensitivity of estimation phase approaches Heisenberg limit and give the corresponding optimal condition. Moreover, we derive the quantum Cramér-Rao bound of the SU(1,1) interferometer.

A new type of hybrid atom-light interferometer is demonstrated with atomic Raman amplification processes replacing the beam splitting elements in a traditional interferometer. This nonconventional interferometer involves correlated optical and atomic waves in the two arms. The correlation between atoms and light developed with the Raman process makes this interferometer different from conventional interferometers with linear beam splitters. It is observed that the high-contrast interference fringes are sensitive to the optical phase via a path change as well as the atomic phase via a magnetic field change. This new atom-light correlated hybrid interferometer is a sensitive probe of the atomic internal state and should find wide applications in precision measurement and quantum control with atoms and photons. [4]. They are widely used in precision measurement of a variety of physical quantities. Building on this foundation, nonconventional interferometers can be constructed with nonlinear processes such as wave splitting and recombination elements [5][6][7][8][9][10], as shown in the inset of Fig. 1.Different from the conventional interferometers with beam splitters, the involvement of nonlinear processes in the nonconventional interferometers allows the coupling between two waves of different types, and it can lead to interference fringes that are sensitive to different types of phase shifts. We thus use the word "hybrid" to label these interferometers involving different types of waves. In fact, hybrid interference also occurs via coherent interactions between atoms and light in phenomena such as quantum storage in electromagnetically induced transparency [11][12][13], gradient echo memory [14,15], and slow light [16][17][18][19][20]. However, the hybrid interference effects in these phenomena are in essence still of the same type as the conventional interference effect where the input wave is linearly split into a linear superposition of atom and light fields in the form of a polariton state [11,15]. On the other hand, a nonconventional SU(1,1) interferometer [5,9,10,21] utilizes parametric amplifiers as wave splitting and recombination elements and performs quite differently from the conventional linear interferometers. The name SU(1,1) comes from the nonlinear interaction Hamiltonian for the parametric process [5]:which amplifies an input signal field (â s ) and produces a correlated idler field (â i ) simultaneously. The idler field is coherent with the input field, thus realizing coherent wave splitting.One of the nonlinear processes described by Eq. (1) is the collective atomic Raman amplification process, which FIG. 1 (color online). Experimental sketch for the hybrid atomlight interferometer. A strong Raman write beam (W 1 , red) and a Stokes input field (S 0 , blue) in orthogonal polarization interact with a Λ-shaped atomic system to generate an amplified Stokes field (S 1 ) and a correlated atomic spin wave S a that stays in the atomic system. The amplified Stokes beam (S 1 ), after reflection (S 0 1...

We propose a scheme for the creation of skyrmions (coreless vortices) in a Bose-Einstein condensate with hyperfine spin F = 1. In this scheme, four traveling-wave laser beams, with Gaussian or Laguerre-Gaussian transverse profiles, induce Raman transitions with an anomalous dependence on the laser polarization, thereby generating the optical potential required for producing skyrmions. 03.75.Fi, The recent experimental success in all-optical trapping of an atomic Bose-Einstein condensate (BEC) [1] opens the prospect of studies into the internal structure of spinor BECs, including the possibility of creating vortex states without core, or skyrmions, in the BEC [2][3][4][5][6]. Skyrmions, which do not have an ordinary vortex core due to the spin degree of freedom, offer a myriad of new physical phenomena beyond those presented by other vortex states. One feature is the reduction of kinetic energy associated with the rotation by transferring this energy to the spin. Another interesting property of skyrmions is that they do not represent a topological excitation, although their flux is vortex-like far away from the line of symmetry [7]. In this paper, we propose an optical method to create skyrmions in a condensate of alkali atoms. This method, which employs laser beams and Raman transition to generate skyrmions in the BEC, is related to proposals for the creation of vortices in a single-component BEC [8,9].For a BEC with hyperfine spin F = 1, a skyrmion wave function, which is axially symmetric around the z-axis, has the form [2]with ρ(z, r ⊥ ) the total density of atoms, r ⊥ = (x, y) the transverse coordinate vector and r ⊥ = |r ⊥ | the radial distance from the z-axis. The angle φ corresponds to the orientation of r ⊥ in the x-y-plane. The function β(r ⊥ ), which characterizes the spin state of the condensed atoms, is related to the superfluid velocity v s of the system bywhere e φ ≡ (cos φ, − sin φ, 0) is the unit vector in the φ direction. Because a skyrmion has no vortex core, β(0) = 0 must hold in order to avoid a singularity. For β(r ⊥ ) = π/2, the superfluid velocity reduces to that of an ordinary vortex state.To create a skyrmion we consider a BEC which first is magnetically trapped in the m = −1 hyperfine state. We assume that the trap is then switched off and the optical potential is applied to the BEC. Thus, our initial state is given by ψ −1 = ρ(r ⊥ , z) and ψ 0 = ψ 1 = 0. Our objective is to design an optical potential which transfers this state into the state (1).Generally a coherent optical potential for atoms is created by applying several highly detuned laser beams which induce Raman transitions between different angular momentum states or internal states of the atomic BEC (cf Fig. 1). In order to preserve the cylindrical symmetry of the skyrmions along the z-axis, the laser beams must also propagate along this axis. This restriction raises the following challenge: the polarization orientation of laser beams propagating along the z-axis is generally presumed to be in a superposition of e x and e y ....