Optical lattices as waveguides and beam splitters for atom interferometry: An analytical treatment and proposal of applications

Tim Kovachy, Jason M. Hogan, David M. S. Johnson, and Mark A. Kasevich

Phys. Rev. A 82, 013638 – Published 27 July 2010

Abstract

We provide an analytical description of the dynamics of an atom in an optical lattice using the method of perturbative adiabatic expansion. A precise understanding of the lattice-atom interaction is essential to taking full advantage of the promising applications that optical lattices offer in the field of atom interferometry. One such application is the implementation of large momentum transfer (LMT) beam splitters that can potentially provide multiple order of magnitude increases in momentum space separations over current technology. We also propose interferometer geometries where optical lattices are used as waveguides for the atoms throughout the duration of the interferometer sequence. Such a technique could simultaneously provide a multiple order of magnitude increase in sensitivity and a multiple order of magnitude decrease in interferometer size for many applications as compared to current state-of-the-art atom interferometers.

Received 18 October 2009

DOI:https://doi.org/10.1103/PhysRevA.82.013638

Authors & Affiliations

Tim Kovachy^*, Jason M. Hogan^†, David M. S. Johnson^‡, and Mark A. Kasevich^§

Department of Physics, Stanford University, Stanford, California 94305, USA

^*tkovachy@stanford.edu
^†hogan@stanford.edu
^‡david.m.johnson@stanford.edu
^§kasevich@stanford.edu

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Vol. 82, Iss. 1 — July 2010

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Images

Figure 1
The physical setup for applying a periodic potential. We expose atoms to counterpropagating laser beams with respective single-photon Rabi frequencies $Ω_{up}$ and $Ω_{down}$ . The lasers are detuned from the transition between the atom’s internal ground state and excited state so that the atom’s external momentum states are coupled through two-photon transitions, creating an effective lattice potential.Reuse & Permissions
Figure 2
The left panel shows a numerical simulation of a lattice acceleration in momentum space that transfers $10 ℏ k$ of momentum. The lattice depth and velocity are shown as functions of time in the right panel, where in this particular case the relevant parameters are $T_{ramp} = 120 (4 ω_{r})^{- 1}$ , $T_{accel} = 16 (4 ω_{r})^{- 1}$ , ${Ω̃}_{\max} = 19.5 / 8$ , and $α_{\max} = 10$ (corresponding to a final lattice velocity of 10 $v_{r}$ ). First, we adiabatically ramp up the lattice to a depth of $19.5 E_{r}$ so that the lattice is loaded into the ground state of the dressed-state Hamiltonian. Subsequently, we accelerate and ramp down the lattice, leaving the atom in a single momentum eigenstate.Reuse & Permissions
Figure 3
Nonadiabatic correction to the phase difference between an arm that is accelerated by an experimentally plausible lattice beam splitter and an arm that is not accelerated [which is in our notation $δ ϕ (α̇)$ ], as calculated using a simplified adiabatic expansion method in which we keep only leading terms versus numerical simulations of the Schrodinger equation. The curve represents the prediction made by the adiabatic expansion method, while the points represent the numerical results.Reuse & Permissions
Figure 4
An array of lattice gravimeters can be used to achieve measurements of a local gravitational field with high spatial resolution. The trajectories shown hold in the laboratory frame. After separating the atoms in each gravimeter by a small amount, we can implement a hold sequence to greatly increase sensitivity. Bragg pulses are used at times $t_{0}$ , $t_{1}$ , $t_{2}$ , and $t_{3}$ . Such an array could be used to study general relativistic effects, search for extra dimensions, examine local mass distributions, or measure Newton’s constant. In addition, the ability of lattice interferometers with hold sequences to provide extremely precise measurements with a small interrogation region makes them ideal candidates for compact, mobile sensors.Reuse & Permissions
Figure 5
Conjugate interferometer geometry that could be used to measure $ℏ / m$ . The trajectories shown hold in the laboratory frame. Bragg pulses are used at times $t_{0}$ , $t_{1}$ , and $t_{2}$ (at $t_{0}$ , a sequence of multiple Bragg pulses is necessary to split the system into the two arms of the two conjugate interferometers). The phase shift of the lower interferometer is subtracted from the phase shift of the upper interferometer, which suppresses the effects of laser phase noise and eliminates the gravitational phase shift up to gradients [10]. With such a scheme, a measurement of $ℏ / m$ to a part in $10^{14}$ may be possible, which could lead to the most accurate determination of the fine structure constant to date.Reuse & Permissions

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