Session T6: Matter Wave Interferometry

Hong-Ou-Mandel atom interferometry in tunnel-coupled optical tweezers

We present recent work in which we demonstrate near-complete control over all the internal and external degrees of freedom of laser-cooled $^{87}$Rb atoms trapped in sub-micron optical tweezers. Utilizing this control for two atoms in two optical tweezers, we implement a massive-particle analog of the Hong-Ou-Mandel interferometer where atom tunneling plays the role of the photon beamsplitter. The interferometer is used to probe the effect of atomic indistinguishability on the two-atom dynamics for a variety of initial conditions. These experiments demonstrate the viability of the optical tweezer platform for bottom-up generation of low-entropy quantum systems and pave the way toward the direct observation of quantum dynamics in more complex finite-sized systems.   

Matter-wave quantum interference in the Hong-Ou-Mandel setup

We propose an experiment to realize a matter-wave analog of the optical Hong-Ou-Mandel (HOM) effect [1]. This is achieved by utilizing a pair of colliding Bose-Einstein condensates of ultracold atoms to generate a scattering halo of pair-correlated atoms via spontaneous four-wave mixing, analogous to optical parametric down-conversion used in the optical experiment to generate pairs of indistinguishable photons. Coupling the pair-correlated atoms by a $\pi$ and $\pi/2$ Bragg pulse realises the atom-optics analogs of mirror and beam-splitter elements of the optical HOM interferometer. We use a stochastic (positive-$P$ representation) Bogoliubov approach to simulate the full dynamics of the experiment and by proposing a measurement protocol appropriate for the multimode nature of the scattering halo we predict a HOM-dip visibility of $\sim69$\% [2], indicating strong quantum correlations between the scattered atoms and paves the way for a possible demonstration of a Bell inequality violation with matter-waves in a related Rarity-Tapster setup [3].\\[4pt] [1] C. K. Hong, Z. Y. Ou, and L. Mandel, Phys. Rev. Lett. \textbf{59}, 2044 (1987);\\[0pt] [2] R. J. Lewis-Swan and K. V. Kheruntsyan, arXiv:1312.3933;\\[0pt] [3] J. G. Rarity and P. R. Tapster, Phys. Rev. Lett. \textbf{64}, 2495 (1990).   

Atom interferometry in an optical cavity

We have demonstrated the first light pulse atom interferometer using an in-vacuum optical cavity to generate the matter wave beamsplitters. An optical cavity allows for a compact setup with several advantages over traditional atom interferometers. Even with modest laser power, large intracavity intensity should enable high order multiphoton beamsplitters which increase the sensitivity of an interferometer. Clean wavefronts from spatial mode filtering can reduce contrast loss for both light pulse interferometers as well as optical lattice based interferometers. In addition, well-defined spatial modes allow many useful properties such as the beam size, waist position, and divergence to be determined with high accuracy. Finally, the use of high order transverse spatial modes gives multiple self-aligned beams useful in applications such as Sagnac interferometry for rotation sensing. We discuss our recent investigations into novel beamsplitters and interferometer geometries in the optical cavity and the implications for a compact inertial sensor as well as measurements of the gravitational Aharanov-Bohm effect and Newton's gravitational constant.   

Interferometry of atoms in concentric ring traps

Recently, an interference experiment of a rotating and a stationary Bose-Einstein condensate was conducted in NIST, as a part of efforts to create the atomic analogue of a SQUID. Inspired by this experiment, we model the interference of two atoms after release from a ``double-ring'' trap. The trap consist of two concentric rings with tight radial and azimuthal confinement, which makes the system before release effectively one-dimensional. One of the rings has a rotating barrier potential, which we model as a $\delta$-function potential. Initially, the particles are in a coherent superposition of being present in either ring. After the trap is released or turned off, the atoms produce a spiral interference pattern. The number of arms of the spiral is determined by the rotation rate of the barrier potential. We investigate numerically and analytically the effect of atom-atom interactions between the atoms and the strength of the barrier on the interference pattern.   

Tunnelling and Reflection of Matter-waves by a Repulsive Barrier

Ultracold atomic systems provide us with a unique opportunity to study matter-waves and their interactions in a controlled environment. The broad Feshbach resonance of $^7$Li atoms in the $|1,1\rangle$ state allows us to tune the scattering length from positive to negative in order to produce quasi-$1$-D bright matter-wave solitons. In our work, we examine reflection and transmission of a degenerate gas at a repulsive barrier, derived from a near-resonant, cylindrically-focussed Gaussian beam, and the effect of interactions is explored by varying the scattering length.   

Diffraction Phases and Atomic Interactions in a Bose-Einstein Condensate Interferometer

We report on recent progress from our Yb Bose-Einstein condensate (BEC) matter-wave interferometer. We have studied, both theoretically and experimentally, large phase shifts due to diffraction of the matter waves from standing waves of light. These shifts constitute the largest systematic effect for a contrast interferometer. The second largest systematic effect comes from atomic interactions. Several different types of interaction effect have been studied, verifying our theoretical models. We also report long interrogation times (up to 22ms), showing no degradation of interferometer contrast, with which we are able to achieve the highest precision yet for a matter-wave interferometer using a BEC as a source. We will briefly discuss a new machine dedicated to precision interferometry and prospects for studying phase transitions with our BEC interferometer.   

Nonlinear interferometric scaling from spinor atom density measurements

Quantum effects can improve the measurement precision beyond the shot noise limit to reach the Heisenberg limit. The effects of nonlinearity due to multi-particle interactions can further boost the precision beyond the Heisenberg limit. We show that the spin-dependent atom-atom interactions for spin-1 atoms in an optical lattice can be measured with super-Heisenberg scaling $n^{-5/4}$, where $n$ is the mean number of atoms per lattice site. In our proposal, we start from a superfluid ground state in a shallow lattice and suddenly raise the lattice depth, thus creating a nonequilibrium state where the populations of different spin components oscillate. These oscillations have nonlinear characteristics arising from atom-atom spin-exchange collisions. We show that an in-situ measurement of the population density dynamics and its variance can reveal the nonlinear scaling. We further explore the improvement and degradation of the precision limit for different compositions of the initial state. Since spin-mixing density oscillations have already been observed with spin-1 atoms in a harmonic trap, we argue that the attainment of nonlinear precision scaling is within reach of current ultra-cold atom experiments.   

Effect of Interatomic Separation in Ensembles in Determining the Fidelity of Collective Excitation

An ensemble of $N$ independent non-interacting two-level atoms gets excited to $2N$ states on interaction with a classical laser. Of these, only $N+1$ are symmetric. In the regime where the interatomic separation, $\Delta{z}$, is much smaller than the wavelength of radiation, $\lambda_L$, and the atoms do not overlap, the asymmetric states disappear and the cluster is reduced to a manifold of symmetric states. However, when $\Delta{z}\gg\lambda_L$, the asymmetric states remain coupled to the ensemble. In this talk, we will describe a technique to determine the dependence of the symmetric and asymmetric states on $\Delta{z}$. We will show the algorithm for determining the asymmetric states corresponding to any $n$ of $N$ atoms in the excited state. The number of atoms in the excited state and the size of the cluster govern the dependence of the ensemble on $\Delta{z}$. An understanding of the evolution of these states is imperative for the realization of a collective state atom interferometer, where the Compton frequency is $N$ times higher than that of a single atom. The scale factor, defined as phase shift for a given rate of rotation, for such an interferometer increases linearly as $\sqrt{N}$ for a given area.   

Raman Spectroscopy Using a Tilted 2D MOT

We demonstrate Raman spectroscopy using a cold and continuous beam of Rubidium atoms from a vapor-loaded, tilted two-dimensional magneto optical trap (2D MOT). The atoms emerge through a pinhole into an ultra-high vacuum chamber, and form a cold and slow moving beam of atoms with flux $10^9$ atoms/sec with a most probable velocity of 10 m/s. The atoms travel across a set of laser beams which include an on-resonant state preparation beam, a beam tuned to drive a stimulated Raman transition, and another on-resonant readout beam. We observed Raman spectra which can include as many as 11 peaks. The width of the clock transition is consistent with the transit time of the atoms through the Raman fields. The width of the magnetic transitions is determined by laboratory magnetic noise. We have measured Rabi cycling on the clock transition using Raman beams in a co-propagating geometry by varying the laser power rather than pulse duration. Further developments will be made by introducing a momentum kick by using Raman beams in a counter-propagating geometry.   

Increasing the Coherence Time in a Magnetic Stimulated Raman Transition in $^{85}$Rb

We experimentally study, compare and contrast Ramsey and spin echo pulse sequence protocols in a cold $^{85}$Rb gas. Our measurements, performed in an {\em unshielded} metal vacuum canister, are dominated by laboratory noise. Both Ramsey and spin echo show a decay of the interference in about $100\, \mu $sec, while we have found that changing the axis of rotation of the echo pulse by $90^{\circ}$ can increase coherence time by nearly a factor of $10$. These results show that this new pulse sequence can be used in our system to reduce dephasing on magnetic transitions.