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Active interferometers are designed to enhance phase sensitivity beyond the standard quantum limit by generating entanglement inside the interferometer. An atomic version of such a device can be constructed by means of a spinor Bose-Einstein condensate with an $F=1$ groundstate manifold in which spin-changing collisions create entangled pairs of $m=pm1$ atoms. We use Bethe Ansatz techniques to find exact eigenstates and eigenvalues of the Hamiltonian that models such spin-changing collisions. Using these results, we express the interferometers phase sensitivity, Fisher information, and Hellinger distance in terms of the Bethe rapidities. By evaluating these expressions we study scaling properties and the interferometers performance under the full Hamiltonian that models the spin-changing collisions, i.e., without the idealising approximations of earlier works that force the model into the framework of SU(1,1) interferometry.
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Compared to light interferometers, the flux in cold-atom interferometers is low and the associated shot noise large. Sensitivities beyond these limitations require the preparation of entangled atoms in different momentum modes. Here, we demonstrate a source of entangled atoms that is compatible with state-of-the-art interferometers. Entanglement is transferred from the spin degree of freedom of a Bose-Einstein condensate to well-separated momentum modes, witnessed by a squeezing parameter of -3.1(8) dB. Entanglement-enhanced atom interferometers open up unprecedented sensitivities for quantum gradiometers or gravitational wave detectors.
We investigate the prospect of enhancing the phase sensitivity of atom interferometers in the Mach-Zehnder configuration with squeezed light. Ultimately, this enhancement is achieved by transferring the quantum state of squeezed light to one or more of the atomic input beams, thereby allowing operation below the standard quantum limit. We analyze in detail three specific schemes that utilize (1) single-mode squeezed optical vacuum (i.e. low frequency squeezing), (2) two-mode squeezed optical vacuum (i.e. high frequency squeezing) transferred to both atomic inputs, and (3) two-mode squeezed optical vacuum transferred to a single atomic input. Crucially, our analysis considers incomplete quantum state transfer (QST) between the optical and atomic modes, and the effects of depleting the initially-prepared atomic source. Unsurprisingly, incomplete QST degrades the sensitivity in all three schemes. We show that by measuring the transmitted photons and using information recycling [Phys. Rev. Lett. 110, 053002 (2013)], the degrading effects of incomplete QST on the sensitivity can be substantially reduced. In particular, information recycling allows scheme (2) to operate at the Heisenberg limit irrespective of the QST efficiency, even when depletion is significant. Although we concentrate on Bose-condensed atomic systems, our scheme is equally applicable to ultracold thermal vapors.
Optics and interferometry with matter waves is the art of coherently manipulating the translational motion of particles like neutrons, atoms and molecules. Coherent atom optics is an extension of techniques that were developed for manipulating emph{internal} quantum states. Applying these ideas to translational motion required the development of techniques to localize atoms and transfer population coherently between distant localities. In this view position and momentum are (continuouse) quantum mechanical degree of freedom analogous to discrete internal quantum states. In our contribution we start with an introduction into matter-wave optics in section 1, discuss coherent atom optics and atom interferometry techniques for molecular beams in section 2 and for trapped atoms in section 3. In section 4 we then describe tools and experiments that allow us to probe the evolution of quantum states of many-body systems by atom interference.
Active interferometers use amplifying elements for beam splitting and recombination. We experimentally implement such a device by using spin exchange in a Bose-Einstein condensate. The two interferometry modes are initially empty spin states that get spontaneously populated in the process of parametric amplification. This nonlinear mechanism scatters atoms into both modes in a pairwise fashion and generates a nonclassical state. Finally, a matched second period of spin exchange is performed that nonlinearly amplifies the output signal and maps the phase onto readily detectable first moments. Depending on the accumulated phase this nonlinear readout can reverse the initial dynamics and deamplify the entangled state back to empty spin states. This sequence is described in the framework of SU(1,1) mode transformations and compared to the SU(2) angular momentum description of passive interferometers.
We propose the use of photonic crystal structures to design subwavelength optical lattices in two dimensions for ultracold atoms by using both Guided Modes and Casimir-Polder forces. We further show how to use Guided Modes for photon-induced large and strongly long-range interactions between trapped atoms. Finally, we analyze the prospects of this scheme to implement spin models for quantum simulation
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