Representation-free description of atom interferometers in time-dependent linear potentials

Abstract

In this article we present a new representation-free formalism, which can significantly simplify the analysis of interferometers comprised of atoms moving in time-dependent linear potentials. We present a methodology for the construction of two pairs of time-dependent functions that, once determined, lead to two conditions for the closing of the interferometer, and determine the phase and the contrast of the resultant interference. Using this new formalism, we explore the dependency of the interferometer phase on the interferometer time T for different atom interferometers. By now, it is well established that light pulse atom interferometers of the type first demonstrated by Kasevich and Chu (1991 Phys. Rev. Lett. 67, 181-4; Appl. Phys. B 54, 321-32), henceforth referred to as Mach-Zehnder (MZ) atom interferometers, have a phase scaling as T 2 . A few years ago, McDonald et al (2014 Europhys. Lett. 105, 63001) have experimentally demonstrated a novel type of atom interferometer, referred to as the continuous-acceleration bloch (CAB) interferometer, where the phase reveals a mixed scaling which is governed by a combination of T 2 and T 3 . Moreover, we have recently proposed a different type of atom interferometer (Zimmermann et al 2017 Appl . Phys. B 123, 102), referred to as the T 3 -interferometer, which has a pure T 3 scaling, as demonstrated theoretically. Finally, we conclude that the CAB interferometer can be shown to be a hybrid of the standard MZ interferometer and the T 3 -interferometer. Enhancing the sensitivity of atom interferometersBecause of their extreme interferometric sensitivity, atom interferometers have been used to precisely measure physical quantities such as the polarizability of alkali atoms [6-9], the 'magic wavelength' for potassium, rubidium and calcium [10-12], Planck's constant to the cesium mass ratio h/m Cs [13], the fine structure OPEN ACCESS RECEIVED

T3 Stern-Gerlach Matter-Wave Interferometer

“…Since V i is linear in the coordinate z, we can obtain the explicit expression [34] forÛ i which consists of the product of (i) the time evolution operatorÛ 0 (t, 0) ≡ exp −itp 2 z /(2m ) of the centerof-mass motion of the free atom, (ii) the displacement…”

Limitations for field-enhanced atom interferometry

“…A simple case is when the initial wavepacket (|ψ 0 in the pure case), or the initial phase-space distribution (in the statistical ensemble case), is gaussian and the evolution is quadratic. In such case, as shown before, the positionmomentum mean and (co-)variance evolves in very simple an analytical manner given by the classical evolution (in the so-called ABCD ξ theorem) [58,76,77,[79][80][81]) directly giving the final contrast (using obvious notations) Ce iφ = ψ 0 |Û † uÛl |ψ 0 = ψ u |ψ l = ψ * u (z)ψ l (z)dz. However our case is more complex with non quadratic terms in the hamiltonian.…”

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