The superposition principle in quantum mechanics leads to intriguing and remarkable effects. Among its many applications is quantum interference and atom interferometers are nowadays used to measure gravitational acceleration and to test the equivalence principle up to high accuracy.

In this project we study a new type of atom interferometer based on the so-called \( T^3 \)-phase. This phase has already been noticed in 1927 by Earle H. Kennard and appears in the propagator of a particle in a linear potential. It is determined by the mass of the particle and the strength of the constant force, and scales with the third power of the time \( T \) the particle experiences the corresponding force. However, it has not been observed in an experiment so far.

Fig. 1: Space-time diagram of the \( T^3\)-interferometer using an three-level atom with state-dependent magnetic moments, which interacts with four short Raman laser pulses.

In order to observe the quantum mechanical \( T^3 \)-phase for atoms we propose an atom interferometer with four co-propagating Raman light pulses depicted in Fig. 1 and consisting of two distinct ''blocks'': (i) four Raman pulses forming a \(\frac{\pi}{2}-\pi-\pi-\frac{\pi}{2}\) sequence, and (ii) three regions of the atomic center-of-mass motion with constant accelerations \(a_1\) and \( a_2 \), induced by a uniform gravitational field and a time-independent magnetic field of constant gradient for a magnetic insensitive and sensitive internal atomic states \( |g_1\rangle \) and \( |g_2\rangle \), respectively. The resulting interferometer phase displays the cubic scaling in \( T \) and is also determined by the magnitudes of the gravitational acceleration and the magnetic field gradient. This interferometer is currently realized in the labs of Frank Narducci.

Due to the analogy between the two physical problems of a massive particle, which experiences a constant gravitational acceleration, and a charge in an ideal capacitor with the constant electric field, we also study a possible setup to observe the \(T^3\)-phase for a charged particle.


F. Ziesel, M. Zimmermann, A. Roura, M.A. Efremov, W.P. Schleich


J.P. Davis (AMPAC, North Wales, USA), S.A. DeSavage (Naval Air Systems Command, Patuxent River, USA), F.A. Narducci (Naval Air Systems Command, Patuxent River, USA), E.M. Rasel (Leibniz Universität Hannover), A. Srinivasan (St. Mary's College of Maryland, St. Mary's City, USA), S.A. Werner (Physics Laboratory, NIST, Gaithersburg, USA)


The German-Israeli Project Cooperation (DIP)
Deutsches Zentrum für Luft- und Raumfahrt (DLR)


[1] S.A. DeSavage, K.H. Gordon, E.M. Clifton, J.P. Davis, and F.A. Narducci, Raman resonances in arbitrary magnetic fields, J. Mod. Opt. 58, 2028 (2011)
[2] S.A. DeSavage, J.P. Davis, and F.A. Narducci, Controlling Raman resonances with magnetic fields, J. Mod. Opt. 60, 95 (2013)
[3] M. Zimmermann, M.A. Efremov, A. Roura, W.P. Schleich, S.A. DeSavage, J.P. Davis, A. Srinivasan, F.A. Narducci, S.A. Werner, and E.M. Rasel, T³-interferometer for atoms, Appl. Phys. B 123:102 (2017)
[4] M. Zimmermann, M.A. Efremov, W. Zeller, W.P. Schleich, J.P. Davis, and F.A. Narducci, Representation-free description of atom interferometers in time-dependent linear potentials, New J. Phys. 21(7):073031 (2019)
[5] O. Amit, Y. Margalit, O. Dobkowski, Z. Zhou, Y. Japha, M. Zimmermann, M. A. Efremov, F. A. Narducci, E. M. Rasel, W. P. Schleich, and R. Folman, T³ Stern-Gerlach Matter-Wave Interferometer, Phys. Rev. Lett. 123:083601 (2019)